Daily Papers

Surface reconstruction with preservation of geometric features is a challenging computer vision task. Despite significant progress in implicit shape reconstruction, state-of-the-art mesh extraction methods often produce aliased, perceptually distorted surfaces and lack scalability to high-resolution 3D shapes. We present a data-driven approach for automatic feature detection and remeshing that requires only a coarse, aliased mesh as input and scales to arbitrary resolution reconstructions. We define and learn a collection of surface-based fields to (1) capture sharp geometric features in the shape with an implicit vertexwise model and (2) approximate improvements in normals alignment obtained by applying edge-flips with an edgewise model. To support scaling to arbitrary complexity shapes, we learn our fields using local triangulated patches, fusing estimates on complete surface meshes. Our feature remeshing algorithm integrates the learned fields as sharp feature priors and optimizes vertex placement and mesh connectivity for maximum expected surface improvement. On a challenging collection of high-resolution shape reconstructions in the ABC dataset, our algorithm improves over state-of-the-art by 26% normals F-score and 42% perceptual RMSE_{v}.

We introduce ReMatching, a novel shape correspondence solution based on the functional maps framework. Our method, by exploiting a new and appropriate re-meshing paradigm, can target shape-matching tasks even on meshes counting millions of vertices, where the original functional maps does not apply or requires a massive computational cost. The core of our procedure is a time-efficient remeshing algorithm which constructs a low-resolution geometry while acting conservatively on the original topology and metric. These properties allow translating the functional maps optimization problem on the resulting low-resolution representation, thus enabling efficient computation of correspondences with functional map approaches. Finally, we propose an efficient technique for extending the estimated correspondence to the original meshes. We show that our method is more efficient and effective through quantitative and qualitative comparisons, outperforming state-of-the-art pipelines in quality and computational cost.

Implicit Neural Spatial Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR. Classical PDE solvers introduce both temporal and spatial discretizations. Common spatial discretizations include meshes and meshless point clouds, where each degree-of-freedom corresponds to a location in space. While these explicit spatial correspondences are intuitive to model and understand, these representations are not necessarily optimal for accuracy, memory usage, or adaptivity. Keeping the classical temporal discretization unchanged (e.g., explicit/implicit Euler), we explore INSR as an alternative spatial discretization, where spatial information is implicitly stored in the neural network weights. The network weights then evolve over time via time integration. Our approach does not require any training data generated by existing solvers because our approach is the solver itself. We validate our approach on various PDEs with examples involving large elastic deformations, turbulent fluids, and multi-scale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy and lower memory consumption. Whereas classical solvers can dynamically adapt their spatial representation only by resorting to complex remeshing algorithms, our INSR approach is intrinsically adaptive. By tapping into the rich literature of classic time integrators, e.g., operator-splitting schemes, our method enables challenging simulations in contact mechanics and turbulent flows where previous neural-physics approaches struggle. Videos and codes are available on the project page: http://www.cs.columbia.edu/cg/INSR-PDE/

The dominant paradigm for high-fidelity 3D generation relies on a VAE-Diffusion pipeline, where the VAE's reconstruction capability sets a firm upper bound on generation quality. A fundamental challenge limiting existing VAEs is the representation mismatch between ground-truth meshes and network predictions: GT meshes have arbitrary, variable topology, while VAEs typically predict fixed-structure implicit fields (\eg, SDF on regular grids). This inherent misalignment prevents establishing explicit mesh-level correspondences, forcing prior work to rely on indirect supervision signals such as SDF or rendering losses. Consequently, fine geometric details, particularly sharp features, are poorly preserved during reconstruction. To address this, we introduce TopoMesh, a sparse voxel-based VAE that unifies both GT and predicted meshes under a shared Dual Marching Cubes (DMC) topological framework. Specifically, we convert arbitrary input meshes into DMC-compliant representations via a remeshing algorithm that preserves sharp edges using an Linfty distance metric. Our decoder outputs meshes in the same DMC format, ensuring that both predicted and target meshes share identical topological structures. This establishes explicit correspondences at the vertex and face level, allowing us to derive explicit mesh-level supervision signals for topology, vertex positions, and face orientations with clear gradients. Our sparse VAE architecture employs this unified framework and is trained with Teacher Forcing and progressive resolution training for stable and efficient convergence. Extensive experiments demonstrate that TopoMesh significantly outperforms existing VAEs in reconstruction fidelity, achieving superior preservation of sharp features and geometric details.

Realistic and efficient 3D garment generation remains a longstanding challenge in computer vision and digital fashion. Existing methods typically rely on large vision- language models to produce serialized representations of 2D sewing patterns, which are then transformed into simulation-ready 3D meshes using garment modeling framework such as GarmentCode. Although these approaches yield high-quality results, they often suffer from slow inference times, ranging from 30 seconds to a minute. In this work, we introduce SwiftTailor, a novel two-stage framework that unifies sewing-pattern reasoning and geometry-based mesh synthesis through a compact geometry image representation. SwiftTailor comprises two lightweight modules: PatternMaker, an efficient vision-language model that predicts sewing patterns from diverse input modalities, and GarmentSewer, an efficient dense prediction transformer that converts these patterns into a novel Garment Geometry Image, encoding the 3D surface of all garment panels in a unified UV space. The final 3D mesh is reconstructed through an efficient inverse mapping process that incorporates remeshing and dynamic stitching algorithms to directly assemble the garment, thereby amortizing the cost of physical simulation. Extensive experiments on the Multimodal GarmentCodeData demonstrate that SwiftTailor achieves state-of-the-art accuracy and visual fidelity while significantly reducing inference time. This work offers a scalable, interpretable, and high-performance solution for next-generation 3D garment generation.

In this work we develop a novel domain splitting strategy for the solution of partial differential equations. Focusing on a uniform discretization of the d-dimensional advection-diffusion equation, our proposal is a two-level algorithm that merges the solutions obtained from the discretization of the equation over highly anisotropic submeshes to compute an initial approximation of the fine solution. The algorithm then iteratively refines the initial guess by leveraging the structure of the residual. Performing costly calculations on anisotropic submeshes enable us to reduce the dimensionality of the problem by one, and the merging process, which involves the computation of solutions over disjoint domains, allows for parallel implementation.

We present a novel generative 3D modeling system, coined CraftsMan, which can generate high-fidelity 3D geometries with highly varied shapes, regular mesh topologies, and detailed surfaces, and, notably, allows for refining the geometry in an interactive manner. Despite the significant advancements in 3D generation, existing methods still struggle with lengthy optimization processes, irregular mesh topologies, noisy surfaces, and difficulties in accommodating user edits, consequently impeding their widespread adoption and implementation in 3D modeling software. Our work is inspired by the craftsman, who usually roughs out the holistic figure of the work first and elaborates the surface details subsequently. Specifically, we employ a 3D native diffusion model, which operates on latent space learned from latent set-based 3D representations, to generate coarse geometries with regular mesh topology in seconds. In particular, this process takes as input a text prompt or a reference image and leverages a powerful multi-view (MV) diffusion model to generate multiple views of the coarse geometry, which are fed into our MV-conditioned 3D diffusion model for generating the 3D geometry, significantly improving robustness and generalizability. Following that, a normal-based geometry refiner is used to significantly enhance the surface details. This refinement can be performed automatically, or interactively with user-supplied edits. Extensive experiments demonstrate that our method achieves high efficacy in producing superior-quality 3D assets compared to existing methods. HomePage: https://craftsman3d.github.io/, Code: https://github.com/wyysf-98/CraftsMan

Dynamic garment reconstruction from monocular video is an important yet challenging task due to the complex dynamics and unconstrained nature of the garments. Recent advancements in neural rendering have enabled high-quality geometric reconstruction with image/video supervision. However, implicit representation methods that use volume rendering often provide smooth geometry and fail to model high-frequency details. While template reconstruction methods model explicit geometry, they use vertex displacement for deformation, which results in artifacts. Addressing these limitations, we propose NGD, a Neural Gradient-based Deformation method to reconstruct dynamically evolving textured garments from monocular videos. Additionally, we propose a novel adaptive remeshing strategy for modelling dynamically evolving surfaces like wrinkles and pleats of the skirt, leading to high-quality reconstruction. Finally, we learn dynamic texture maps to capture per-frame lighting and shadow effects. We provide extensive qualitative and quantitative evaluations to demonstrate significant improvements over existing SOTA methods and provide high-quality garment reconstructions.

We present a topology-informed inverse rendering approach for reconstructing high-genus surface meshes from multi-view images. Compared to 3D representations like voxels and point clouds, mesh-based representations are preferred as they enable the application of differential geometry theory and are optimized for modern graphics pipelines. However, existing inverse rendering methods often fail catastrophically on high-genus surfaces, leading to the loss of key topological features, and tend to oversmooth low-genus surfaces, resulting in the loss of surface details. This failure stems from their overreliance on Adam-based optimizers, which can lead to vanishing and exploding gradients. To overcome these challenges, we introduce an adaptive V-cycle remeshing scheme in conjunction with a re-parametrized Adam optimizer to enhance topological and geometric awareness. By periodically coarsening and refining the deforming mesh, our method informs mesh vertices of their current topology and geometry before optimization, mitigating gradient issues while preserving essential topological features. Additionally, we enforce topological consistency by constructing topological primitives with genus numbers that match those of ground truth using Gauss-Bonnet theorem. Experimental results demonstrate that our inverse rendering approach outperforms the current state-of-the-art method, achieving significant improvements in Chamfer Distance and Volume IoU, particularly for high-genus surfaces, while also enhancing surface details for low-genus surfaces.

We introduce ReplaceMe, a generalized training-free depth pruning method that effectively replaces transformer blocks with a linear operation, while maintaining high performance for low compression ratios. In contrast to conventional pruning approaches that require additional training or fine-tuning, our approach requires only a small calibration dataset that is used to estimate a linear transformation to approximate the pruned blocks. This estimated linear mapping can be seamlessly merged with the remaining transformer blocks, eliminating the need for any additional network parameters. Our experiments show that ReplaceMe consistently outperforms other training-free approaches and remains highly competitive with state-of-the-art pruning methods that involve extensive retraining/fine-tuning and architectural modifications. Applied to several large language models (LLMs), ReplaceMe achieves up to 25% pruning while retaining approximately 90% of the original model's performance on open benchmarks - without any training or healing steps, resulting in minimal computational overhead (see Fig.1). We provide an open-source library implementing ReplaceMe alongside several state-of-the-art depth pruning techniques, available at this repository.

The performance of large language models (LLMs) in program synthesis and mathematical reasoning is fundamentally limited by the quality of their pre-training corpora. We introduce two openly licensed datasets, released under the Llama 3.3 Community License, that significantly enhance LLM performance by systematically rewriting public data. SwallowCode (approximately 16.1 billion tokens) refines Python snippets from The-Stack-v2 through a novel four-stage pipeline: syntax validation, pylint-based style filtering, and a two-stage LLM rewriting process that enforces style conformity and transforms snippets into self-contained, algorithmically efficient examples. Unlike prior methods that rely on exclusionary filtering or limited transformations, our transform-and-retain approach upgrades low-quality code, maximizing data utility. SwallowMath (approximately 2.3 billion tokens) enhances Finemath-4+ by removing boilerplate, restoring context, and reformatting solutions into concise, step-by-step explanations. Within a fixed 50 billion token training budget, continual pre-training of Llama-3.1-8B with SwallowCode boosts pass@1 by +17.0 on HumanEval and +17.7 on HumanEval+ compared to Stack-Edu, surpassing the baseline model's code generation capabilities. Similarly, substituting SwallowMath yields +12.4 accuracy on GSM8K and +7.6 on MATH. Ablation studies confirm that each pipeline stage contributes incrementally, with rewriting delivering the largest gains. All datasets, prompts, and checkpoints are publicly available, enabling reproducible research and advancing LLM pre-training for specialized domains.

Seam carving is an image editing method that enable content-aware resizing, including operations like removing objects. However, the seam-finding strategy based on dynamic programming or graph-cut limits its applications to broader visual data formats and degrees of freedom for editing. Our observation is that describing the editing and retargeting of images more generally by a displacement field yields a generalisation of content-aware deformations. We propose to learn a deformation with a neural network that keeps the output plausible while trying to deform it only in places with low information content. This technique applies to different kinds of visual data, including images, 3D scenes given as neural radiance fields, or even polygon meshes. Experiments conducted on different visual data show that our method achieves better content-aware retargeting compared to previous methods.

We introduce TreeMeshGPT, an autoregressive Transformer designed to generate high-quality artistic meshes aligned with input point clouds. Instead of the conventional next-token prediction in autoregressive Transformer, we propose a novel Autoregressive Tree Sequencing where the next input token is retrieved from a dynamically growing tree structure that is built upon the triangle adjacency of faces within the mesh. Our sequencing enables the mesh to extend locally from the last generated triangular face at each step, and therefore reduces training difficulty and improves mesh quality. Our approach represents each triangular face with two tokens, achieving a compression rate of approximately 22% compared to the naive face tokenization. This efficient tokenization enables our model to generate highly detailed artistic meshes with strong point cloud conditioning, surpassing previous methods in both capacity and fidelity. Furthermore, our method generates mesh with strong normal orientation constraints, minimizing flipped normals commonly encountered in previous methods. Our experiments show that TreeMeshGPT enhances the mesh generation quality with refined details and normal orientation consistency.

We tackle the task of geometric image editing, where an object within an image is repositioned, reoriented, or reshaped while preserving overall scene coherence. Previous diffusion-based editing methods often attempt to handle all relevant subtasks in a single step, proving difficult when transformations become large or structurally complex. We address this by proposing a decoupled pipeline that separates object transformation, source region inpainting, and target region refinement. Both inpainting and refinement are implemented using a training-free diffusion approach, FreeFine. In experiments on our new GeoBench benchmark, which contains both 2D and 3D editing scenarios, FreeFine outperforms state-of-the-art alternatives in image fidelity, and edit precision, especially under demanding transformations. Code and benchmark are available at: https://github.com/CIawevy/FreeFine

Recently, neural networks have been extensively employed to solve partial differential equations (PDEs) in physical system modeling. While major studies focus on learning system evolution on predefined static mesh discretizations, some methods utilize reinforcement learning or supervised learning techniques to create adaptive and dynamic meshes, due to the dynamic nature of these systems. However, these approaches face two primary challenges: (1) the need for expensive optimal mesh data, and (2) the change of the solution space's degree of freedom and topology during mesh refinement. To address these challenges, this paper proposes a neural PDE solver with a neural mesh adapter. To begin with, we introduce a novel data-free neural mesh adaptor, called Data-free Mesh Mover (DMM), with two main innovations. Firstly, it is an operator that maps the solution to adaptive meshes and is trained using the Monge-Amp\`ere equation without optimal mesh data. Secondly, it dynamically changes the mesh by moving existing nodes rather than adding or deleting nodes and edges. Theoretical analysis shows that meshes generated by DMM have the lowest interpolation error bound. Based on DMM, to efficiently and accurately model dynamic systems, we develop a moving mesh based neural PDE solver (MM-PDE) that embeds the moving mesh with a two-branch architecture and a learnable interpolation framework to preserve information within the data. Empirical experiments demonstrate that our method generates suitable meshes and considerably enhances accuracy when modeling widely considered PDE systems. The code can be found at: https://github.com/Peiyannn/MM-PDE.git.

Recent advances in 4D content generation have attracted increasing attention, yet creating high-quality animated 3D models remains challenging due to the complexity of modeling spatio-temporal distributions and the scarcity of 4D training data. In this paper, we present AnimateAnyMesh, the first feed-forward framework that enables efficient text-driven animation of arbitrary 3D meshes. Our approach leverages a novel DyMeshVAE architecture that effectively compresses and reconstructs dynamic mesh sequences by disentangling spatial and temporal features while preserving local topological structures. To enable high-quality text-conditional generation, we employ a Rectified Flow-based training strategy in the compressed latent space. Additionally, we contribute the DyMesh Dataset, containing over 4M diverse dynamic mesh sequences with text annotations. Experimental results demonstrate that our method generates semantically accurate and temporally coherent mesh animations in a few seconds, significantly outperforming existing approaches in both quality and efficiency. Our work marks a substantial step forward in making 4D content creation more accessible and practical. All the data, code, and models will be open-released.

Solving an NP-hard optimization problem often requires reformulating it for a specific solver -- quantum hardware, a commercial optimizer, or a domain heuristic. A tool for polynomial-time reductions between hard problems would let practitioners route any supported problem to any supported solver through a single interface. Building such a library at scale, however, has remained out of reach. We show that harness engineering, the practice of designing constraints, verification systems, and feedback loops that channel AI coding agents, can overcome this barrier. Our harness combines a no-code contribution route for domain experts, a multilayer verification stack ranging from type-level checks to agentic feature tests (AI agents role-playing as end users), and a fully automated implementation-review-integration pipeline. In about three months, we built a command-line tool backed by a library of 100+ problem types and 200+~reduction rules in over 170k lines of Rust. The result suggests that a well-engineered harness lets agents build well-tested software at a scale and pace beyond prior reduction-library efforts. Because the reduction graph composes transitively, a new solver registered for any single problem type instantly becomes available to every problem connected by a reduction path. The source code is available at https://github.com/CodingThrust/problem-reductions.

We introduce RE-Adapt, an approach to fine-tuning large language models on new domains without degrading any pre-existing instruction-tuning. We reverse engineer an adapter which isolates what an instruction-tuned model has learned beyond its corresponding pretrained base model. Importantly, this requires no additional data or training. We can then fine-tune the base model on a new domain and readapt it to instruction following with the reverse engineered adapter. RE-Adapt and our low-rank variant LoRE-Adapt both outperform other methods of fine-tuning, across multiple popular LLMs and datasets, even when the models are used in conjunction with retrieval-augmented generation.

This paper introduces a method for simplifying textured surface triangle meshes in the wild while maintaining high visual quality. While previous methods achieve excellent results on manifold meshes by using the quadric error metric, they struggle to produce high-quality outputs for meshes in the wild, which typically contain non-manifold elements and multiple connected components. In this work, we propose a method for simplifying these wild textured triangle meshes. We formulate mesh simplification as a problem of decimating simplicial 2-complexes to handle multiple non-manifold mesh components collectively. Building on the success of quadric error simplification, we iteratively collapse 1-simplices (vertex pairs). Our approach employs a modified quadric error that converges to the original quadric error metric for watertight manifold meshes, while significantly improving the results on wild meshes. For textures, instead of following existing strategies to preserve UVs, we adopt a novel perspective which focuses on computing mesh correspondences throughout the decimation, independent of the UV layout. This combination yields a textured mesh simplification system that is capable of handling arbitrary triangle meshes, achieving to high-quality results on wild inputs without sacrificing the excellent performance on clean inputs. Our method guarantees to avoid common problems in textured mesh simplification, including the prevalent problem of texture bleeding. We extensively evaluate our method on multiple datasets, showing improvements over prior techniques through qualitative, quantitative, and user study evaluations.

Large Language Models (LLMs) present an intriguing avenue for exploration in the field of formal theorem proving. Nevertheless, their full potential, particularly concerning the mitigation of hallucinations and refinement through prover error messages, remains an area that has yet to be thoroughly investigated. To enhance the effectiveness of LLMs in the field, we introduce the Lyra, a new framework that employs two distinct correction mechanisms: Tool Correction (TC) and Conjecture Correction (CC). To implement Tool Correction in the post-processing of formal proofs, we leverage prior knowledge to utilize predefined prover tools (e.g., Sledgehammer) for guiding the replacement of incorrect tools. Tool Correction significantly contributes to mitigating hallucinations, thereby improving the overall accuracy of the proof. In addition, we introduce Conjecture Correction, an error feedback mechanism designed to interact with prover to refine formal proof conjectures with prover error messages. Compared to the previous refinement framework, the proposed Conjecture Correction refines generation with instruction but does not collect paired (generation, error & refinement) prompts. Our method has achieved state-of-the-art (SOTA) performance on both miniF2F validation (48.0% -> 55.3%) and test (45.5% -> 51.2%). We also present 3 IMO problems solved by Lyra. We believe Tool Correction (post-process for hallucination mitigation) and Conjecture Correction (subgoal adjustment from interaction with environment) could provide a promising avenue for future research in this field.

Diffusion models have greatly improved visual generation but are hindered by slow generation speed due to the computationally intensive nature of solving generative ODEs. Rectified flow, a widely recognized solution, improves generation speed by straightening the ODE path. Its key components include: 1) using the diffusion form of flow-matching, 2) employing boldsymbol v-prediction, and 3) performing rectification (a.k.a. reflow). In this paper, we argue that the success of rectification primarily lies in using a pretrained diffusion model to obtain matched pairs of noise and samples, followed by retraining with these matched noise-sample pairs. Based on this, components 1) and 2) are unnecessary. Furthermore, we highlight that straightness is not an essential training target for rectification; rather, it is a specific case of flow-matching models. The more critical training target is to achieve a first-order approximate ODE path, which is inherently curved for models like DDPM and Sub-VP. Building on this insight, we propose Rectified Diffusion, which generalizes the design space and application scope of rectification to encompass the broader category of diffusion models, rather than being restricted to flow-matching models. We validate our method on Stable Diffusion v1-5 and Stable Diffusion XL. Our method not only greatly simplifies the training procedure of rectified flow-based previous works (e.g., InstaFlow) but also achieves superior performance with even lower training cost. Our code is available at https://github.com/G-U-N/Rectified-Diffusion.

We introduce Mesh Silksong, a compact and efficient mesh representation tailored to generate the polygon mesh in an auto-regressive manner akin to silk weaving. Existing mesh tokenization methods always produce token sequences with repeated vertex tokens, wasting the network capability. Therefore, our approach tokenizes mesh vertices by accessing each mesh vertice only once, reduces the token sequence's redundancy by 50\%, and achieves a state-of-the-art compression rate of approximately 22\%. Furthermore, Mesh Silksong produces polygon meshes with superior geometric properties, including manifold topology, watertight detection, and consistent face normals, which are critical for practical applications. Experimental results demonstrate the effectiveness of our approach, showcasing not only intricate mesh generation but also significantly improved geometric integrity.

Tools for rewriting, refactoring and optimizing code should be fast and correct. Large language models (LLMs), by their nature, possess neither of these qualities. Yet, there remains tremendous opportunity in using LLMs to improve code. We explore the use of LLMs not to transform code, but to code transforms. We propose a chain-of-thought approach to synthesizing code transformations from a small number of input/output code examples that incorporates execution and feedback. Unlike the direct rewrite approach, LLM-generated transformations are easy to inspect, debug, and validate. The logic of the rewrite is explicitly coded and easy to adapt. The compute required to run code transformations is minute compared to that of LLM rewriting. We test our approach on 16 Python code transformations and find that LLM- generated transforms are perfectly precise for 7 of them and less imprecise than direct LLM rewriting on the others. We hope to encourage further research to improving the precision of LLM code rewriting.

UV unwrapping flattens 3D surfaces to 2D with minimal distortion, often requiring the complex surface to be decomposed into multiple charts. Although extensively studied, existing UV unwrapping methods frequently struggle with AI-generated meshes, which are typically noisy, bumpy, and poorly conditioned. These methods often produce highly fragmented charts and suboptimal boundaries, introducing artifacts and hindering downstream tasks. We introduce PartUV, a part-based UV unwrapping pipeline that generates significantly fewer, part-aligned charts while maintaining low distortion. Built on top of a recent learning-based part decomposition method PartField, PartUV combines high-level semantic part decomposition with novel geometric heuristics in a top-down recursive framework. It ensures each chart's distortion remains below a user-specified threshold while minimizing the total number of charts. The pipeline integrates and extends parameterization and packing algorithms, incorporates dedicated handling of non-manifold and degenerate meshes, and is extensively parallelized for efficiency. Evaluated across four diverse datasets, including man-made, CAD, AI-generated, and Common Shapes, PartUV outperforms existing tools and recent neural methods in chart count and seam length, achieves comparable distortion, exhibits high success rates on challenging meshes, and enables new applications like part-specific multi-tiles packing. Our project page is at https://www.zhaoningwang.com/PartUV.

Surface cutting is a fundamental task in computer graphics, with applications in UV parameterization, texture mapping, and mesh decomposition. However, existing methods often produce technically valid but overly fragmented atlases that lack semantic coherence. We introduce SeamGPT, an auto-regressive model that generates cutting seams by mimicking professional workflows. Our key technical innovation lies in formulating surface cutting as a next token prediction task: sample point clouds on mesh vertices and edges, encode them as shape conditions, and employ a GPT-style transformer to sequentially predict seam segments with quantized 3D coordinates. Our approach achieves exceptional performance on UV unwrapping benchmarks containing both manifold and non-manifold meshes, including artist-created, and 3D-scanned models. In addition, it enhances existing 3D segmentation tools by providing clean boundaries for part decomposition.

In this article, we study the parameterized complexity of the Set Cover problem restricted to semi-ladder-free hypergraphs, a class defined by Fabianski et al. [Proceedings of STACS 2019]. We observe that two algorithms introduced by Langerman and Morin [Discrete & Computational Geometry 2005] in the context of geometric covering problems can be adapted to this setting, yielding simple FPT and kernelization algorithms for Set Cover in semi-ladder-free hypergraphs. We complement our algorithmic results with a compression lower bound for the problem, which proves the tightness of our kernelization under standard complexity-theoretic assumptions.

Modern large language models (LLMs) such as GPT, Claude, and Gemini have transformed the way we learn, work, and communicate. Yet, their ability to produce highly human-like text raises serious concerns about misinformation and academic integrity, making it an urgent need for reliable algorithms to detect LLM-generated content. In this paper, we start by presenting a geometric approach to demystify rewrite-based detection algorithms, revealing their underlying rationale and demonstrating their generalization ability. Building on this insight, we introduce a novel rewrite-based detection algorithm that adaptively learns the distance between the original and rewritten text. Theoretically, we demonstrate that employing an adaptively learned distance function is more effective for detection than using a fixed distance. Empirically, we conduct extensive experiments with over 100 settings, and find that our approach demonstrates superior performance over baseline algorithms in the majority of scenarios. In particular, it achieves relative improvements from 57.8\% to 80.6\% over the strongest baseline across different target LLMs (e.g., GPT, Claude, and Gemini).

In this paper, we study the ideas of composition and decomposition in the context of vector spaces, graphs and matroids. For vector spaces V_{AB}, treated as collection of row vectors, with specified column set Auplus B, we define V_{SP}lrarv V_{PQ}, Scap Q= emptyset, to be the collection of all vectors (f_S,f_Q) such that (f_S,f_P)in V_{SP}, (f_P,f_Q)in V_{PQ}. An analogous operation G_{SP}lrarg G_{PQ}equivd G_{PQ} can be defined in relation to graphs G_{SP}, G_{PQ}, on edge sets Suplus P, Puplus Q, respectively in terms of an overlapping subgraph G_P which gets deleted in the right side graph (see for instance the notion of k-sum oxley). For matroids we define the `linking' M_{SP}lrarm M_{PQ} equivd (M_{SP}vee M_{PQ})times (Suplus Q), denoting the contraction operation by 'times'. In each case, we examine how to minimize the size of the `overlap' set P, without affecting the right side entity. In the case of vector spaces, there is a polynomial time algorithm for achieving the minimum, which we present. Similar ideas work for graphs and for matroids under appropriate conditions. Next we consider the problem of decomposition. Here, in the case of vector spaces, the problem is to decompose V_{SQ} as V_{SP}lrarv V_{PQ}, with minimum size P. We give a polynomial time algorithm for this purpose. In the case of graphs and matroids we give a solution to this problem under certain restrictions.

As mathematical computing becomes more democratized in high-level languages, high-performance symbolic-numeric systems are necessary for domain scientists and engineers to get the best performance out of their machine without deep knowledge of code optimization. Naturally, users need different term types either to have different algebraic properties for them, or to use efficient data structures. To this end, we developed Symbolics.jl, an extendable symbolic system which uses dynamic multiple dispatch to change behavior depending on the domain needs. In this work we detail an underlying abstract term interface which allows for speed without sacrificing generality. We show that by formalizing a generic API on actions independent of implementation, we can retroactively add optimized data structures to our system without changing the pre-existing term rewriters. We showcase how this can be used to optimize term construction and give a 113x acceleration on general symbolic transformations. Further, we show that such a generic API allows for complementary term-rewriting implementations. We demonstrate the ability to swap between classical term-rewriting simplifiers and e-graph-based term-rewriting simplifiers. We showcase an e-graph ruleset which minimizes the number of CPU cycles during expression evaluation, and demonstrate how it simplifies a real-world reaction-network simulation to halve the runtime. Additionally, we show a reaction-diffusion partial differential equation solver which is able to be automatically converted into symbolic expressions via multiple dispatch tracing, which is subsequently accelerated and parallelized to give a 157x simulation speedup. Together, this presents Symbolics.jl as a next-generation symbolic-numeric computing environment geared towards modeling and simulation.

Triangle meshes play a crucial role in 3D applications for efficient manipulation and rendering. While auto-regressive methods generate structured meshes by predicting discrete vertex tokens, they are often constrained by limited face counts and mesh incompleteness. To address these challenges, we propose DeepMesh, a framework that optimizes mesh generation through two key innovations: (1) an efficient pre-training strategy incorporating a novel tokenization algorithm, along with improvements in data curation and processing, and (2) the introduction of Reinforcement Learning (RL) into 3D mesh generation to achieve human preference alignment via Direct Preference Optimization (DPO). We design a scoring standard that combines human evaluation with 3D metrics to collect preference pairs for DPO, ensuring both visual appeal and geometric accuracy. Conditioned on point clouds and images, DeepMesh generates meshes with intricate details and precise topology, outperforming state-of-the-art methods in both precision and quality. Project page: https://zhaorw02.github.io/DeepMesh/

We present a new method for large language models to solve compositional tasks. Although they have shown strong performance on traditional language understanding tasks, large language models struggle to solve compositional tasks, where the solution depends on solving smaller instances of the same problem. We propose a natural approach to solve compositional tasks recursively. Our method, Re-Tuning, tunes models to break down a problem into subproblems, solve those subproblems, and combine the results. We show that our method significantly improves model performance on three representative compositional tasks: integer addition, dynamic programming, and parity. Compared to state-of-the-art methods that keep intermediate steps towards solving the problems, Re-Tuning achieves significantly higher accuracy and is more GPU memory efficient.

AlphaEvolve is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines algorithmic solutions to challenging scientific and practical problems. In this paper we showcase AlphaEvolve as a tool for autonomously discovering novel mathematical constructions and advancing our understanding of long-standing open problems. To demonstrate its breadth, we considered a list of 67 problems spanning mathematical analysis, combinatorics, geometry, and number theory. The system rediscovered the best known solutions in most of the cases and discovered improved solutions in several. In some instances, AlphaEvolve is also able to generalize results for a finite number of input values into a formula valid for all input values. Furthermore, we are able to combine this methodology with Deep Think and AlphaProof in a broader framework where the additional proof-assistants and reasoning systems provide automated proof generation and further mathematical insights. These results demonstrate that large language model-guided evolutionary search can autonomously discover mathematical constructions that complement human intuition, at times matching or even improving the best known results, highlighting the potential for significant new ways of interaction between mathematicians and AI systems. We present AlphaEvolve as a powerful new tool for mathematical discovery, capable of exploring vast search spaces to solve complex optimization problems at scale, often with significantly reduced requirements on preparation and computation time.

While reasoning models (e.g., DeepSeek R1) trained with reinforcement learning (RL), excel in textual reasoning, they struggle in scenarios requiring structured problem-solving, such as geometric reasoning, concise computation, or complex equation solving-areas where computational tools like code interpreters (CI) demonstrate distinct advantages. To bridge this gap, we propose ReTool, which enhances long-form reasoning with tool-integrated learning, including two key features: (1) dynamic interleaving of real-time code execution within natural language reasoning processes, and (2) an automated RL paradigm that allows policy rollouts with multi-turn real-time code execution and teaches the model in learning when and how to invoke tools based on outcome feedback. ReTool employs a systematic training framework, beginning with synthetic cold-start data generation to produce code-augmented long-form reasoning traces for fine-tuning base models. Subsequent RL training leverages task outcomes as rewards to iteratively refine the model's tool use strategy, enabling autonomous discovery of optimal tool invocation patterns without human priors. Experiments on the challenging MATH Olympiad benchmark AIME demonstrate ReTool's superiority: Our 32B model achieves 67% accuracy with 400 training steps, outperforming text-based RL baseline (40% accuracy, 1080 steps) in efficiency and performance. Remarkably, ReTool-32B attains 72.5% accuracy in extended settings, surpassing OpenAI's o1-preview by 27.9%. Further analysis reveals emergent behaviors such as code self-correction, signaling an ''aha moment'' in which the model autonomously masters adaptive tool use. These findings highlight the promise of outcome-driven tool integration for advancing complex mathematical reasoning and offer new insights into hybrid neuro-symbolic systems.

Neural Networks can be efficiently compressed through pruning, significantly reducing storage and computational demands while maintaining predictive performance. Simple yet effective methods like Iterative Magnitude Pruning (IMP, Han et al., 2015) remove less important parameters and require a costly retraining procedure to recover performance after pruning. However, with the rise of Large Language Models (LLMs), full retraining has become infeasible due to memory and compute constraints. In this study, we challenge the practice of retraining all parameters by demonstrating that updating only a small subset of highly expressive parameters is often sufficient to recover or even improve performance compared to full retraining. Surprisingly, retraining as little as 0.27%-0.35% of the parameters of GPT-architectures (OPT-2.7B/6.7B/13B/30B) achieves comparable performance to One Shot IMP across various sparsity levels. Our method, Parameter-Efficient Retraining after Pruning (PERP), drastically reduces compute and memory demands, enabling pruning and retraining of up to 30 billion parameter models on a single NVIDIA A100 GPU within minutes. Despite magnitude pruning being considered as unsuited for pruning LLMs, our findings show that PERP positions it as a strong contender against state-of-the-art retraining-free approaches such as Wanda (Sun et al., 2023) and SparseGPT (Frantar & Alistarh, 2023), opening up a promising alternative to avoiding retraining.

Sublinear time complexity is required by the massively parallel computation (MPC) model. Breaking dynamic programs into a set of sparse dynamic programs that can be divided, solved, and merged in sublinear time. The rectangle escape problem (REP) is defined as follows: For n axis-aligned rectangles inside an axis-aligned bounding box B, extend each rectangle in only one of the four directions: up, down, left, or right until it reaches B and the density k is minimized, where k is the maximum number of extensions of rectangles to the boundary that pass through a point inside bounding box B. REP is NP-hard for k>1. If the rectangles are points of a grid (or unit squares of a grid), the problem is called the square escape problem (SEP) and it is still NP-hard. We give a 2-approximation algorithm for SEP with kgeq2 with time complexity O(n^{3/2}k^2). This improves the time complexity of existing algorithms which are at least quadratic. Also, the approximation ratio of our algorithm for kgeq 3 is 3/2 which is tight. We also give a 8-approximation algorithm for REP with time complexity O(nlog n+nk) and give a MPC version of this algorithm for k=O(1) which is the first parallel algorithm for this problem.

We introduce MeshGPT, a new approach for generating triangle meshes that reflects the compactness typical of artist-created meshes, in contrast to dense triangle meshes extracted by iso-surfacing methods from neural fields. Inspired by recent advances in powerful large language models, we adopt a sequence-based approach to autoregressively generate triangle meshes as sequences of triangles. We first learn a vocabulary of latent quantized embeddings, using graph convolutions, which inform these embeddings of the local mesh geometry and topology. These embeddings are sequenced and decoded into triangles by a decoder, ensuring that they can effectively reconstruct the mesh. A transformer is then trained on this learned vocabulary to predict the index of the next embedding given previous embeddings. Once trained, our model can be autoregressively sampled to generate new triangle meshes, directly generating compact meshes with sharp edges, more closely imitating the efficient triangulation patterns of human-crafted meshes. MeshGPT demonstrates a notable improvement over state of the art mesh generation methods, with a 9% increase in shape coverage and a 30-point enhancement in FID scores across various categories.

We propose Gaussian Frosting, a novel mesh-based representation for high-quality rendering and editing of complex 3D effects in real-time. Our approach builds on the recent 3D Gaussian Splatting framework, which optimizes a set of 3D Gaussians to approximate a radiance field from images. We propose first extracting a base mesh from Gaussians during optimization, then building and refining an adaptive layer of Gaussians with a variable thickness around the mesh to better capture the fine details and volumetric effects near the surface, such as hair or grass. We call this layer Gaussian Frosting, as it resembles a coating of frosting on a cake. The fuzzier the material, the thicker the frosting. We also introduce a parameterization of the Gaussians to enforce them to stay inside the frosting layer and automatically adjust their parameters when deforming, rescaling, editing or animating the mesh. Our representation allows for efficient rendering using Gaussian splatting, as well as editing and animation by modifying the base mesh. We demonstrate the effectiveness of our method on various synthetic and real scenes, and show that it outperforms existing surface-based approaches. We will release our code and a web-based viewer as additional contributions. Our project page is the following: https://anttwo.github.io/frosting/

Extensive compute and memory requirements limit the deployment of large language models (LLMs) on any hardware. Compression methods, such as pruning, can reduce model size, which in turn reduces resource requirements. State-of-the-art pruning is based on coarse-grained methods. They are time-consuming and inherently remove critical model parameters, adversely impacting the quality of the pruned model. This paper introduces projection pruning, a novel fine-grained method for pruning LLMs. In addition, LLM projection pruning is enhanced by a new approach we refer to as composite projection pruning - the synergistic combination of unstructured pruning that retains accuracy and structured pruning that reduces model size. We develop Mosaic, a novel system to create and deploy pruned LLMs using composite projection pruning. Mosaic is evaluated using a range of performance and quality metrics on multiple hardware platforms, LLMs, and datasets. Mosaic is 7.19x faster in producing models than existing approaches. Mosaic models achieve up to 84.2% lower perplexity and 31.4% higher accuracy than models obtained from coarse-grained pruning. Up to 67% faster inference and 68% lower GPU memory use is noted for Mosaic models.

Recent mesh generation approaches typically tokenize triangle meshes into sequences of tokens and train autoregressive models to generate these tokens sequentially. Despite substantial progress, such token sequences inevitably reuse vertices multiple times to fully represent manifold meshes, as each vertex is shared by multiple faces. This redundancy leads to excessively long token sequences and inefficient generation processes. In this paper, we propose an efficient framework that generates artistic meshes by treating vertices and faces separately, significantly reducing redundancy. We employ an autoregressive model solely for vertex generation, decreasing the token count to approximately 23\% of that required by the most compact existing tokenizer. Next, we leverage a bidirectional transformer to complete the mesh in a single step by capturing inter-vertex relationships and constructing the adjacency matrix that defines the mesh faces. To further improve the generation quality, we introduce a fidelity enhancer to refine vertex positioning into more natural arrangements and propose a post-processing framework to remove undesirable edge connections. Experimental results show that our method achieves more than 8times faster speed on mesh generation compared to state-of-the-art approaches, while producing higher mesh quality.

We introduce VertexRegen, a novel mesh generation framework that enables generation at a continuous level of detail. Existing autoregressive methods generate meshes in a partial-to-complete manner and thus intermediate steps of generation represent incomplete structures. VertexRegen takes inspiration from progressive meshes and reformulates the process as the reversal of edge collapse, i.e. vertex split, learned through a generative model. Experimental results demonstrate that VertexRegen produces meshes of comparable quality to state-of-the-art methods while uniquely offering anytime generation with the flexibility to halt at any step to yield valid meshes with varying levels of detail.

We propose Segment Any Mesh, a novel zero-shot mesh part segmentation method that overcomes the limitations of shape analysis-based, learning-based, and contemporary approaches. Our approach operates in two phases: multimodal rendering and 2D-to-3D lifting. In the first phase, multiview renders of the mesh are individually processed through Segment Anything to generate 2D masks. These masks are then lifted into a mesh part segmentation by associating masks that refer to the same mesh part across the multiview renders. We find that applying Segment Anything to multimodal feature renders of normals and shape diameter scalars achieves better results than using only untextured renders of meshes. By building our method on top of Segment Anything, we seamlessly inherit any future improvements made to 2D segmentation. We compare our method with a robust, well-evaluated shape analysis method, Shape Diameter Function, and show that our method is comparable to or exceeds its performance. Since current benchmarks contain limited object diversity, we also curate and release a dataset of generated meshes and use it to demonstrate our method's improved generalization over Shape Diameter Function via human evaluation. We release the code and dataset at https://github.com/gtangg12/samesh

As first-order optimization methods become the method of choice for solving large-scale optimization problems, optimization solvers based on first-order algorithms are being built. Such general-purpose solvers must robustly detect infeasible or misspecified problem instances, but the computational complexity of first-order methods for doing so has yet to be formally studied. In this work, we characterize the optimal accelerated rate of infeasibility detection. We show that the standard fixed-point iteration achieves a O(1/k^2) and O(1/k) rates, respectively, on the normalized iterates and the fixed-point residual converging to the infimal displacement vector, while the accelerated fixed-point iteration achieves O(1/k^2) and mathcal{O}(1/k^2) rates. We then provide a matching complexity lower bound to establish that Theta(1/k^2) is indeed the optimal accelerated rate.

We propose a compressive yet effective mesh representation, Blocked and Patchified Tokenization (BPT), facilitating the generation of meshes exceeding 8k faces. BPT compresses mesh sequences by employing block-wise indexing and patch aggregation, reducing their length by approximately 75\% compared to the original sequences. This compression milestone unlocks the potential to utilize mesh data with significantly more faces, thereby enhancing detail richness and improving generation robustness. Empowered with the BPT, we have built a foundation mesh generative model training on scaled mesh data to support flexible control for point clouds and images. Our model demonstrates the capability to generate meshes with intricate details and accurate topology, achieving SoTA performance on mesh generation and reaching the level for direct product usage.

We present AlphaGeometry2, a significantly improved version of AlphaGeometry introduced in Trinh et al. (2024), which has now surpassed an average gold medalist in solving Olympiad geometry problems. To achieve this, we first extend the original AlphaGeometry language to tackle harder problems involving movements of objects, and problems containing linear equations of angles, ratios, and distances. This, together with other additions, has markedly improved the coverage rate of the AlphaGeometry language on International Math Olympiads (IMO) 2000-2024 geometry problems from 66% to 88%. The search process of AlphaGeometry2 has also been greatly improved through the use of Gemini architecture for better language modeling, and a novel knowledge-sharing mechanism that combines multiple search trees. Together with further enhancements to the symbolic engine and synthetic data generation, we have significantly boosted the overall solving rate of AlphaGeometry2 to 84% for all geometry problems over the last 25 years, compared to 54% previously. AlphaGeometry2 was also part of the system that achieved silver-medal standard at IMO 2024 https://dpmd.ai/imo-silver. Last but not least, we report progress towards using AlphaGeometry2 as a part of a fully automated system that reliably solves geometry problems directly from natural language input.

In astrophysical and cosmological analyses, the increasing quality and volume of astronomical data demand efficient and precise computational tools. This work introduces a novel adaptive algorithm for automatic knots (AutoKnots) allocation in spline interpolation, designed to meet user-defined precision requirements. Unlike traditional methods that rely on manually configured knot distributions with numerous parameters, the proposed technique automatically determines the optimal number and placement of knots based on interpolation error criteria. This simplifies configuration, often requiring only a single parameter. The algorithm progressively improves the interpolation by adaptively sampling the function-to-be-approximated, f(x), in regions where the interpolation error exceeds the desired threshold. All function evaluations contribute directly to the final approximation, ensuring efficiency. While each resampling step involves recomputing the interpolation table, this process is highly optimized and usually computationally negligible compared to the cost of evaluating f(x). We show the algorithm's efficacy through a series of precision tests on different functions. However, the study underscores the necessity for caution when dealing with certain function types, notably those featuring plateaus. To address this challenge, a heuristic enhancement is incorporated, improving accuracy in flat regions. This algorithm has been extensively used and tested over the years. NumCosmo includes a comprehensive set of unit tests that rigorously evaluate the algorithm both directly and indirectly, underscoring its robustness and reliability. As a practical application, we compute the surface mass density Sigma(R) and the average surface mass density Sigma(<R) for Navarro-Frenk-White and Hernquist halo density profiles, which provide analytical benchmarks. (abridged)

We present AI-SARAH, a practical variant of SARAH. As a variant of SARAH, this algorithm employs the stochastic recursive gradient yet adjusts step-size based on local geometry. AI-SARAH implicitly computes step-size and efficiently estimates local Lipschitz smoothness of stochastic functions. It is fully adaptive, tune-free, straightforward to implement, and computationally efficient. We provide technical insight and intuitive illustrations on its design and convergence. We conduct extensive empirical analysis and demonstrate its strong performance compared with its classical counterparts and other state-of-the-art first-order methods in solving convex machine learning problems.

Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of mathematics. Previous studies have employed techniques such as supervised fine-tuning (SFT), prompt engineering, and search-based methods to improve the mathematical problem-solving abilities of LLMs. Despite these efforts, their performance remains suboptimal and demands substantial computational resources. To address this issue, we propose a novel approach, BEATS, to enhance mathematical problem-solving abilities. Our method leverages newly designed prompts that guide the model to iteratively rewrite, advance by one step, and generate answers based on previous steps. Additionally, we introduce a new back-verification technique that uses LLMs to validate the correctness of the generated answers. Furthermore, we employ a pruning tree search to optimize search time while achieving strong performance. Notably, our method improves Qwen2-7b-Instruct's score from 36.94 to 61.52, outperforming GPT4's 42.5 on the MATH benchmark.

Query rewrite, which aims to generate more efficient queries by altering a SQL query's structure without changing the query result, has been an important research problem. In order to maintain equivalence between the rewritten query and the original one during rewriting, traditional query rewrite methods always rewrite the queries following certain rewrite rules. However, some problems still remain. Firstly, existing methods of finding the optimal choice or sequence of rewrite rules are still limited and the process always costs a lot of resources. Methods involving discovering new rewrite rules typically require complicated proofs of structural logic or extensive user interactions. Secondly, current query rewrite methods usually rely highly on DBMS cost estimators which are often not accurate. In this paper, we address these problems by proposing a novel method of query rewrite named LLM-R2, adopting a large language model (LLM) to propose possible rewrite rules for a database rewrite system. To further improve the inference ability of LLM in recommending rewrite rules, we train a contrastive model by curriculum to learn query representations and select effective query demonstrations for the LLM. Experimental results have shown that our method can significantly improve the query execution efficiency and outperform the baseline methods. In addition, our method enjoys high robustness across different datasets.

In this paper, we address the problem of degradation in inpainting quality of neural networks operating at high resolutions. Inpainting networks are often unable to generate globally coherent structures at resolutions higher than their training set. This is partially attributed to the receptive field remaining static, despite an increase in image resolution. Although downscaling the image prior to inpainting produces coherent structure, it inherently lacks detail present at higher resolutions. To get the best of both worlds, we optimize the intermediate featuremaps of a network by minimizing a multiscale consistency loss at inference. This runtime optimization improves the inpainting results and establishes a new state-of-the-art for high resolution inpainting. Code is available at: https://github.com/geomagical/lama-with-refiner/tree/refinement.

We introduce MeshAnything V2, an autoregressive transformer that generates Artist-Created Meshes (AM) aligned to given shapes. It can be integrated with various 3D asset production pipelines to achieve high-quality, highly controllable AM generation. MeshAnything V2 surpasses previous methods in both efficiency and performance using models of the same size. These improvements are due to our newly proposed mesh tokenization method: Adjacent Mesh Tokenization (AMT). Different from previous methods that represent each face with three vertices, AMT uses a single vertex whenever possible. Compared to previous methods, AMT requires about half the token sequence length to represent the same mesh in average. Furthermore, the token sequences from AMT are more compact and well-structured, fundamentally benefiting AM generation. Our extensive experiments show that AMT significantly improves the efficiency and performance of AM generation. Project Page: https://buaacyw.github.io/meshanything-v2/

The problem of designing NLP solvers for math word problems (MWP) has seen sustained research activity and steady gains in the test accuracy. Since existing solvers achieve high performance on the benchmark datasets for elementary level MWPs containing one-unknown arithmetic word problems, such problems are often considered "solved" with the bulk of research attention moving to more complex MWPs. In this paper, we restrict our attention to English MWPs taught in grades four and lower. We provide strong evidence that the existing MWP solvers rely on shallow heuristics to achieve high performance on the benchmark datasets. To this end, we show that MWP solvers that do not have access to the question asked in the MWP can still solve a large fraction of MWPs. Similarly, models that treat MWPs as bag-of-words can also achieve surprisingly high accuracy. Further, we introduce a challenge dataset, SVAMP, created by applying carefully chosen variations over examples sampled from existing datasets. The best accuracy achieved by state-of-the-art models is substantially lower on SVAMP, thus showing that much remains to be done even for the simplest of the MWPs.

Flow-based generative models have recently demonstrated strong performance, yet sampling typically relies on expensive numerical integration of ordinary differential equations (ODEs). Rectified Flow enables one-step sampling by learning nearly straight probability paths, but achieving such straightness requires multiple computationally intensive reflow iterations. MeanFlow achieves one-step generation by directly modeling the average velocity over time; however, when trained on highly curved flows, it suffers from slow convergence and noisy supervision. To address these limitations, we propose Rectified MeanFlow, a framework that models the mean velocity field along the rectified trajectory using only a single reflow step. This eliminates the need for perfectly straightened trajectories while enabling efficient training. Furthermore, we introduce a simple yet effective truncation heuristic that aims to reduce residual curvature and further improve performance. Extensive experiments on ImageNet at 64, 256, and 512 resolutions show that Re-MeanFlow consistently outperforms prior one-step flow distillation and Rectified Flow methods in both sample quality and training efficiency. Code is available at https://github.com/Xinxi-Zhang/Re-MeanFlow.

Recent studies suggest that with sufficiently wide models, most SGD solutions can, up to permutation, converge into the same basin. This phenomenon, known as the model re-basin regime, has significant implications for model averaging by ensuring the linear mode connectivity. However, current re-basin strategies are ineffective in many scenarios due to a lack of comprehensive understanding of underlying mechanisms. Addressing this gap, this paper provides novel insights into understanding and improving the standard practice. Firstly, we decompose re-normalization into rescaling and reshift, uncovering that rescaling plays a crucial role in re-normalization while re-basin performance is sensitive to shifts in model activation. The finding calls for a more nuanced handling of the activation shift. Secondly, we identify that the merged model suffers from the issue of activation collapse and magnitude collapse. Varying the learning rate, weight decay, and initialization method can mitigate the issues and improve model performance. Lastly, we propose a new perspective to unify the re-basin and pruning, under which a lightweight yet effective post-pruning technique is derived, which can significantly improve the model performance after pruning. Our implementation is available at https://github.com/XingyuQu/rethink-re-basin.

Generative Artificial Intelligence image models have achieved outstanding performance in text-to-image generation and other tasks, such as inpainting that completes images with missing fragments. The performance of inpainting can be accurately measured by taking an image, removing some fragments, performing the inpainting to restore them, and comparing the results with the original image. Interestingly, inpainting can also be applied recursively, starting from an image, removing some parts, applying inpainting to reconstruct the image, and then starting the inpainting process again on the reconstructed image, and so forth. This process of recursively applying inpainting can lead to an image that is similar or completely different from the original one, depending on the fragments that are removed and the ability of the model to reconstruct them. Intuitively, stability, understood as the capability to recover an image that is similar to the original one even after many recursive inpainting operations, is a desirable feature and can be used as an additional performance metric for inpainting. The concept of stability is also being studied in the context of recursive training of generative AI models with their own data. Recursive inpainting is an inference-only recursive process whose understanding may complement ongoing efforts to study the behavior of generative AI models under training recursion. In this paper, the impact of recursive inpainting is studied for one of the most widely used image models: Stable Diffusion. The results show that recursive inpainting can lead to image collapse, so ending with a nonmeaningful image, and that the outcome depends on several factors such as the type of image, the size of the inpainting masks, and the number of iterations.

Current auto-regressive models can generate high-quality, topologically precise meshes; however, they necessitate thousands-or even tens of thousands-of next-token predictions during inference, resulting in substantial latency. We introduce XSpecMesh, a quality-preserving acceleration method for auto-regressive mesh generation models. XSpecMesh employs a lightweight, multi-head speculative decoding scheme to predict multiple tokens in parallel within a single forward pass, thereby accelerating inference. We further propose a verification and resampling strategy: the backbone model verifies each predicted token and resamples any tokens that do not meet the quality criteria. In addition, we propose a distillation strategy that trains the lightweight decoding heads by distilling from the backbone model, encouraging their prediction distributions to align and improving the success rate of speculative predictions. Extensive experiments demonstrate that our method achieves a 1.7x speedup without sacrificing generation quality. Our code will be released.

We address the computational challenges of solving parametric PDEs with non parametrized geometric variations and non-reducible problems, such as those involving shocks and discontinuities of variable positions. Traditional dimensionality reduction methods like POD struggle with these scenarios due to slowly decaying Kolmogorov widths. To overcome this, we propose a novel non-linear dimensionality reduction technique to reduce the required modes for representation. The non-linear reduction is obtained through a POD after applying a transformation on the fields, which we call optimal mappings, and is a solution to an optimization problem in infinite dimension. The proposed learning framework combines morphing techniques, non-linear dimensionality reduction, and Gaussian Process Regression (GPR). The problem is reformulated on a reference geometry before applying the dimensionality reduction. Our method learns both the optimal mapping, and the solution fields, using a series of GPR models, enabling efficient and accurate modeling of complex parametric PDEs with geometrical variability. The results obtained concur with current state-of-the-art models. We mainly compare our method with the winning solution of the ML4CFD NeurIPS 2024 competition.

Byte-Pair Encoding (BPE) is a popular algorithm used for tokenizing data in NLP, despite being devised initially as a compression method. BPE appears to be a greedy algorithm at face value, but the underlying optimization problem that BPE seeks to solve has not yet been laid down. We formalize BPE as a combinatorial optimization problem. Via submodular functions, we prove that the iterative greedy version is a 1{{sigma(mu^star)}}(1-e^{-{sigma(mu^star)}})-approximation of an optimal merge sequence, where {sigma(mu^star)} is the total backward curvature with respect to the optimal merge sequence mu^star. Empirically the lower bound of the approximation is approx 0.37. We provide a faster implementation of BPE which improves the runtime complexity from Oleft(N Mright) to Oleft(N log Mright), where N is the sequence length and M is the merge count. Finally, we optimize the brute-force algorithm for optimal BPE using memoization.

Controllable, high-fidelity mesh editing remains a significant challenge in 3D content creation. Existing generative methods often struggle with complex geometries and fail to produce detailed results. We propose CraftMesh, a novel framework for high-fidelity generative mesh manipulation via Poisson Seamless Fusion. Our key insight is to decompose mesh editing into a pipeline that leverages the strengths of 2D and 3D generative models: we edit a 2D reference image, then generate a region-specific 3D mesh, and seamlessly fuse it into the original model. We introduce two core techniques: Poisson Geometric Fusion, which utilizes a hybrid SDF/Mesh representation with normal blending to achieve harmonious geometric integration, and Poisson Texture Harmonization for visually consistent texture blending. Experimental results demonstrate that CraftMesh outperforms state-of-the-art methods, delivering superior global consistency and local detail in complex editing tasks.

Mixture-of-experts (MoEs) have been adopted for reducing inference costs by sparsely activating experts in Large language models (LLMs). Despite this reduction, the massive number of experts in MoEs still makes them expensive to serve. In this paper, we study how to address this, by pruning MoEs. Among pruning methodologies, unstructured pruning has been known to achieve the highest performance for a given pruning ratio, compared to structured pruning, since the latter imposes constraints on the sparsification structure. This is intuitive, as the solution space of unstructured pruning subsumes that of structured pruning. However, our counterintuitive finding reveals that expert pruning, a form of structured pruning, can actually precede unstructured pruning to outperform unstructured-only pruning. As existing expert pruning, requiring O(k^n{n}) forward passes for n experts, cannot scale for recent MoEs, we propose a scalable alternative with O(1) complexity, yet outperforming the more expensive methods. The key idea is leveraging a latent structure between experts, based on behavior similarity, such that the greedy decision of whether to prune closely captures the joint pruning effect. Ours is highly effective -- for Snowflake Arctic, a 480B-sized MoE with 128 experts, our method needs only one H100 and two hours to achieve nearly no loss in performance with 40% sparsity, even in generative tasks such as GSM8K, where state-of-the-art unstructured pruning fails to. The code will be made publicly available.

Large language model (LLM) agents exhibit strong mathematical problem-solving abilities and can even solve International Mathematical Olympiad (IMO) level problems with the assistance of formal proof systems. However, due to weak heuristics for auxiliary constructions, AI for geometry problem solving remains dominated by expert models such as AlphaGeometry 2, which rely heavily on large-scale data synthesis and search for both training and evaluation. In this work, we make the first attempt to build a medalist-level LLM agent for geometry and present InternGeometry. InternGeometry overcomes the heuristic limitations in geometry by iteratively proposing propositions and auxiliary constructions, verifying them with a symbolic engine, and reflecting on the engine's feedback to guide subsequent proposals. A dynamic memory mechanism enables InternGeometry to conduct more than two hundred interactions with the symbolic engine per problem. To further accelerate learning, we introduce Complexity-Boosting Reinforcement Learning (CBRL), which gradually increases the complexity of synthesized problems across training stages. Built on InternThinker-32B, InternGeometry solves 44 of 50 IMO geometry problems (2000-2024), exceeding the average gold medalist score (40.9), using only 13K training examples, just 0.004% of the data used by AlphaGeometry 2, demonstrating the potential of LLM agents on expert-level geometry tasks. InternGeometry can also propose novel auxiliary constructions for IMO problems that do not appear in human solutions. We will release the model, data, and symbolic engine to support future research.

We present InstantMesh, a feed-forward framework for instant 3D mesh generation from a single image, featuring state-of-the-art generation quality and significant training scalability. By synergizing the strengths of an off-the-shelf multiview diffusion model and a sparse-view reconstruction model based on the LRM architecture, InstantMesh is able to create diverse 3D assets within 10 seconds. To enhance the training efficiency and exploit more geometric supervisions, e.g, depths and normals, we integrate a differentiable iso-surface extraction module into our framework and directly optimize on the mesh representation. Experimental results on public datasets demonstrate that InstantMesh significantly outperforms other latest image-to-3D baselines, both qualitatively and quantitatively. We release all the code, weights, and demo of InstantMesh, with the intention that it can make substantial contributions to the community of 3D generative AI and empower both researchers and content creators.

We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and information present from past problems to rapidly predict and solve new problems. Otherwise, standard methods ignore the knowledge of the past solutions and suboptimally re-solve each problem from scratch. We instantiate Meta OT models in discrete and continuous settings between grayscale images, spherical data, classification labels, and color palettes and use them to improve the computational time of standard OT solvers. Our source code is available at http://github.com/facebookresearch/meta-ot

Computationally intensive decoding procedures--including search, reranking, and self-critique--can improve the quality of language model (LM) outputs in problems spanning code generation, numerical reasoning, and dialog. Existing work typically applies the same decoding procedure for every input to an LM. But not all inputs require the same amount of computation to process. Can we allocate decoding computation adaptively, using more resources to answer questions whose answers will be harder to compute? We present an approach that predicts the distribution of rewards given an input and computation budget, then allocates additional computation to inputs for which it is predicted to be most useful. We apply this approach in two decoding procedures: first, an adaptive best-of-k procedure that dynamically selects the number of samples to generate as input to a reranker; second, a routing procedure that dynamically responds to a query using a decoding procedure that is expensive but accurate, or one that is cheaper but less capable. Across a suite of programming, mathematics, and dialog tasks, we show that accurate computation-allocation procedures can be learned, and reduce computation by up to 50% at no cost to response quality, or improve quality by up to 10% at a fixed computational budget.

Algorithm configuration (AC) is concerned with the automated search of the most suitable parameter configuration of a parametrized algorithm. There is currently a wide variety of AC problem variants and methods proposed in the literature. Existing reviews do not take into account all derivatives of the AC problem, nor do they offer a complete classification scheme. To this end, we introduce taxonomies to describe the AC problem and features of configuration methods, respectively. We review existing AC literature within the lens of our taxonomies, outline relevant design choices of configuration approaches, contrast methods and problem variants against each other, and describe the state of AC in industry. Finally, our review provides researchers and practitioners with a look at future research directions in the field of AC.

This paper aims to generate materials for 3D meshes from text descriptions. Unlike existing methods that synthesize texture maps, we propose to generate segment-wise procedural material graphs as the appearance representation, which supports high-quality rendering and provides substantial flexibility in editing. Instead of relying on extensive paired data, i.e., 3D meshes with material graphs and corresponding text descriptions, to train a material graph generative model, we propose to leverage the pre-trained 2D diffusion model as a bridge to connect the text and material graphs. Specifically, our approach decomposes a shape into a set of segments and designs a segment-controlled diffusion model to synthesize 2D images that are aligned with mesh parts. Based on generated images, we initialize parameters of material graphs and fine-tune them through the differentiable rendering module to produce materials in accordance with the textual description. Extensive experiments demonstrate the superior performance of our framework in photorealism, resolution, and editability over existing methods. Project page: https://zhanghe3z.github.io/MaPa/

We develop a fast, tractable technique called Net-Trim for simplifying a trained neural network. The method is a convex post-processing module, which prunes (sparsifies) a trained network layer by layer, while preserving the internal responses. We present a comprehensive analysis of Net-Trim from both the algorithmic and sample complexity standpoints, centered on a fast, scalable convex optimization program. Our analysis includes consistency results between the initial and retrained models before and after Net-Trim application and guarantees on the number of training samples needed to discover a network that can be expressed using a certain number of nonzero terms. Specifically, if there is a set of weights that uses at most s terms that can re-create the layer outputs from the layer inputs, we can find these weights from O(slog N/s) samples, where N is the input size. These theoretical results are similar to those for sparse regression using the Lasso, and our analysis uses some of the same recently-developed tools (namely recent results on the concentration of measure and convex analysis). Finally, we propose an algorithmic framework based on the alternating direction method of multipliers (ADMM), which allows a fast and simple implementation of Net-Trim for network pruning and compression.

Generating animated 3D objects is at the heart of many applications, yet most advanced works are typically difficult to apply in practice because of their limited setup, their long runtime, or their limited quality. We introduce ActionMesh, a generative model that predicts production-ready 3D meshes "in action" in a feed-forward manner. Drawing inspiration from early video models, our key insight is to modify existing 3D diffusion models to include a temporal axis, resulting in a framework we dubbed "temporal 3D diffusion". Specifically, we first adapt the 3D diffusion stage to generate a sequence of synchronized latents representing time-varying and independent 3D shapes. Second, we design a temporal 3D autoencoder that translates a sequence of independent shapes into the corresponding deformations of a pre-defined reference shape, allowing us to build an animation. Combining these two components, ActionMesh generates animated 3D meshes from different inputs like a monocular video, a text description, or even a 3D mesh with a text prompt describing its animation. Besides, compared to previous approaches, our method is fast and produces results that are rig-free and topology consistent, hence enabling rapid iteration and seamless applications like texturing and retargeting. We evaluate our model on standard video-to-4D benchmarks (Consistent4D, Objaverse) and report state-of-the-art performances on both geometric accuracy and temporal consistency, demonstrating that our model can deliver animated 3D meshes with unprecedented speed and quality.

Solving complex Partial Differential Equations (PDEs) accurately and efficiently is an essential and challenging problem in all scientific and engineering disciplines. Mesh movement methods provide the capability to improve the accuracy of the numerical solution without increasing the overall mesh degree of freedom count. Conventional sophisticated mesh movement methods are extremely expensive and struggle to handle scenarios with complex boundary geometries. However, existing learning-based methods require re-training from scratch given a different PDE type or boundary geometry, which limits their applicability, and also often suffer from robustness issues in the form of inverted elements. In this paper, we introduce the Universal Mesh Movement Network (UM2N), which -- once trained -- can be applied in a non-intrusive, zero-shot manner to move meshes with different size distributions and structures, for solvers applicable to different PDE types and boundary geometries. UM2N consists of a Graph Transformer (GT) encoder for extracting features and a Graph Attention Network (GAT) based decoder for moving the mesh. We evaluate our method on advection and Navier-Stokes based examples, as well as a real-world tsunami simulation case. Our method outperforms existing learning-based mesh movement methods in terms of the benchmarks described above. In comparison to the conventional sophisticated Monge-Amp\`ere PDE-solver based method, our approach not only significantly accelerates mesh movement, but also proves effective in scenarios where the conventional method fails. Our project page is at https://erizmr.github.io/UM2N/.

Several first order stochastic optimization methods commonly used in the Euclidean domain such as stochastic gradient descent (SGD), accelerated gradient descent or variance reduced methods have already been adapted to certain Riemannian settings. However, some of the most popular of these optimization tools - namely Adam , Adagrad and the more recent Amsgrad - remain to be generalized to Riemannian manifolds. We discuss the difficulty of generalizing such adaptive schemes to the most agnostic Riemannian setting, and then provide algorithms and convergence proofs for geodesically convex objectives in the particular case of a product of Riemannian manifolds, in which adaptivity is implemented across manifolds in the cartesian product. Our generalization is tight in the sense that choosing the Euclidean space as Riemannian manifold yields the same algorithms and regret bounds as those that were already known for the standard algorithms. Experimentally, we show faster convergence and to a lower train loss value for Riemannian adaptive methods over their corresponding baselines on the realistic task of embedding the WordNet taxonomy in the Poincare ball.

Code efficiency is a fundamental aspect of software quality, yet how to harness large language models (LLMs) to optimize programs remains challenging. Prior approaches have sought for one-shot rewriting, retrieved exemplars, or prompt-based search, but they do not explicitly distill reusable optimization knowledge, which limits generalization beyond individual instances. In this paper, we present EffiSkill, a framework for code-efficiency optimization that builds a portable optimization toolbox for LLM-based agents. The key idea is to model recurring slow-to-fast transformations as reusable agent skills that capture both concrete transformation mechanisms and higher-level optimization strategies. EffiSkill adopts a two-stage design: Stage I mines Operator and Meta Skills from large-scale slow/fast program pairs to build a skill library; Stage II applies this library to unseen programs through execution-free diagnosis, skill retrieval, plan composition, and candidate generation, without runtime feedback. Results on EffiBench-X show that EffiSkill achieves higher optimization success rates, improving over the strongest baseline by 3.69 to 12.52 percentage points across model and language settings. These findings suggest that mechanism-level skill reuse provides a useful foundation for execution-free code optimization, and that the resulting skill library can serve as a reusable resource for broader agent workflows.

In this paper, we introduce Point2Mesh, a technique for reconstructing a surface mesh from an input point cloud. Instead of explicitly specifying a prior that encodes the expected shape properties, the prior is defined automatically using the input point cloud, which we refer to as a self-prior. The self-prior encapsulates reoccurring geometric repetitions from a single shape within the weights of a deep neural network. We optimize the network weights to deform an initial mesh to shrink-wrap a single input point cloud. This explicitly considers the entire reconstructed shape, since shared local kernels are calculated to fit the overall object. The convolutional kernels are optimized globally across the entire shape, which inherently encourages local-scale geometric self-similarity across the shape surface. We show that shrink-wrapping a point cloud with a self-prior converges to a desirable solution; compared to a prescribed smoothness prior, which often becomes trapped in undesirable local minima. While the performance of traditional reconstruction approaches degrades in non-ideal conditions that are often present in real world scanning, i.e., unoriented normals, noise and missing (low density) parts, Point2Mesh is robust to non-ideal conditions. We demonstrate the performance of Point2Mesh on a large variety of shapes with varying complexity.

Large Language Models (LLMs) have demonstrated impressive zero-shot capabilities in long-form text generation tasks expressed through natural language instructions. However, user expectations for long-form text rewriting is high, and unintended rewrites (''hallucinations'') produced by the model can negatively impact its overall performance. Existing evaluation benchmarks primarily focus on limited rewriting styles and sentence-level rewriting rather than long-form open-ended rewriting.We introduce OpenRewriteEval, a novel benchmark that covers a wide variety of rewriting types expressed through natural language instructions. It is specifically designed to facilitate the evaluation of open-ended rewriting of long-form texts. In addition, we propose a strong baseline model, RewriteLM, an instruction-tuned large language model for long-form text rewriting. We develop new strategies that facilitate the generation of diverse instructions and preference data with minimal human intervention. We conduct empirical experiments and demonstrate that our model outperforms the current state-of-the-art LLMs in text rewriting. Specifically, it excels in preserving the essential content and meaning of the source text, minimizing the generation of ''hallucinated'' content, while showcasing the ability to generate rewrites with diverse wording and structures.

Animating various character drawings is an engaging visual content creation task. Given a single character drawing, existing animation methods are limited to flat 2D motions and thus lack 3D effects. An alternative solution is to reconstruct a 3D model from a character drawing as a proxy and then retarget 3D motion data onto it. However, the existing image-to-3D methods could not work well for amateur character drawings in terms of appearance and geometry. We observe the contour lines, commonly existing in character drawings, would introduce significant ambiguity in texture synthesis due to their view-dependence. Additionally, thin regions represented by single-line contours are difficult to reconstruct (e.g., slim limbs of a stick figure) due to their delicate structures. To address these issues, we propose a novel system, DrawingSpinUp, to produce plausible 3D animations and breathe life into character drawings, allowing them to freely spin up, leap, and even perform a hip-hop dance. For appearance improvement, we adopt a removal-then-restoration strategy to first remove the view-dependent contour lines and then render them back after retargeting the reconstructed character. For geometry refinement, we develop a skeleton-based thinning deformation algorithm to refine the slim structures represented by the single-line contours. The experimental evaluations and a perceptual user study show that our proposed method outperforms the existing 2D and 3D animation methods and generates high-quality 3D animations from a single character drawing. Please refer to our project page (https://lordliang.github.io/DrawingSpinUp) for the code and generated animations.

Let T be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in T is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high. We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes. We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in R^d. We use these partitions with slack for embedding ultrametrics into d-dimensional Euclidean space: we give a rm polylog(Delta)-approximation algorithm for embedding n-point ultrametrics into R^d with minimum distortion, where Delta denotes the spread of the metric, i.e., the ratio between the largest and the smallest distance between two points. The previously best-known approximation ratio for this problem was polynomial in n. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.

Reranking, the process of refining the output of a first-stage retriever, is often considered computationally expensive, especially with Large Language Models. Borrowing from recent advances in document compression for RAG, we reduce the input size by compressing documents into fixed-size embedding representations. We then teach a reranker to use compressed inputs by distillation. Although based on a billion-size model, our trained reranker using this compressed input can challenge smaller rerankers in terms of both effectiveness and efficiency, especially for long documents. Given that text compressors are still in their early development stages, we view this approach as promising.

We propose a method to allow precise and extremely fast mesh extraction from 3D Gaussian Splatting. Gaussian Splatting has recently become very popular as it yields realistic rendering while being significantly faster to train than NeRFs. It is however challenging to extract a mesh from the millions of tiny 3D gaussians as these gaussians tend to be unorganized after optimization and no method has been proposed so far. Our first key contribution is a regularization term that encourages the gaussians to align well with the surface of the scene. We then introduce a method that exploits this alignment to extract a mesh from the Gaussians using Poisson reconstruction, which is fast, scalable, and preserves details, in contrast to the Marching Cubes algorithm usually applied to extract meshes from Neural SDFs. Finally, we introduce an optional refinement strategy that binds gaussians to the surface of the mesh, and jointly optimizes these Gaussians and the mesh through Gaussian splatting rendering. This enables easy editing, sculpting, rigging, animating, compositing and relighting of the Gaussians using traditional softwares by manipulating the mesh instead of the gaussians themselves. Retrieving such an editable mesh for realistic rendering is done within minutes with our method, compared to hours with the state-of-the-art methods on neural SDFs, while providing a better rendering quality.

Pruning methods have recently grown in popularity as an effective way to reduce the size and computational complexity of deep neural networks. Large numbers of parameters can be removed from trained models with little discernible loss in accuracy after a small number of continued training epochs. However, pruning too many parameters at once often causes an initial steep drop in accuracy which can undermine convergence quality. Iterative pruning approaches mitigate this by gradually removing a small number of parameters over multiple epochs. However, this can still lead to subnetworks that overfit local regions of the loss landscape. We introduce a novel and effective approach to tuning subnetworks through a regularization technique we call Stochastic Subnetwork Annealing. Instead of removing parameters in a discrete manner, we instead represent subnetworks with stochastic masks where each parameter has a probabilistic chance of being included or excluded on any given forward pass. We anneal these probabilities over time such that subnetwork structure slowly evolves as mask values become more deterministic, allowing for a smoother and more robust optimization of subnetworks at high levels of sparsity.

Query rewriting is a classical technique for transforming complex declarative SQL queries into ``lean'' equivalents that are conducive to (a) faster execution from a performance perspective, and (b) better understanding from a developer perspective. The rewriting is typically achieved via transformation rules, but these rules are limited in scope and difficult to update in a production system. In recent times, LLM-based techniques have also been mooted, but they are prone to both semantic and syntactic errors. We investigate here, how the remarkable cognitive capabilities of LLMs can be leveraged for performant query rewriting while incorporating safeguards and optimizations to ensure correctness and efficiency. Our study shows that these goals can be progressively achieved through incorporation of (a) an ensemble suite of basic prompts, (b) database-sensitive prompts via redundancy removal and selectivity-based rewriting rules, and (c) LLM token probability-guided rewrite paths. Further, a suite of statistical and logic-based tools can be used to guard against errors produced by the model. We have implemented the above LLM-infused techniques in the LITHE system, and evaluated complex analytic queries from multiple benchmarks on contemporary database platforms. The results show significant improvements over SOTA rewriting techniques -- for instance, on TPC-DS, LITHE constructed productive (>1.5x speedup) rewrites for two-thirds of the query suite, delivering four times more coverage than SOTA. Further, the geometric mean of its estimated execution speedups was an order-of-magnitude jump over SOTA performance. In essence, LITHE offers a potent and robust LLM-based intermediary between enterprise applications and database engines.

We consider learning in an adversarial Markov Decision Process (MDP) where the loss functions can change arbitrarily over K episodes and the state space can be arbitrarily large. We assume that the Q-function of any policy is linear in some known features, that is, a linear function approximation exists. The best existing regret upper bound for this setting (Luo et al., 2021) is of order mathcal O(K^{2/3}) (omitting all other dependencies), given access to a simulator. This paper provides two algorithms that improve the regret to mathcal O(sqrt K) in the same setting. Our first algorithm makes use of a refined analysis of the Follow-the-Regularized-Leader (FTRL) algorithm with the log-barrier regularizer. This analysis allows the loss estimators to be arbitrarily negative and might be of independent interest. Our second algorithm develops a magnitude-reduced loss estimator, further removing the polynomial dependency on the number of actions in the first algorithm and leading to the optimal regret bound (up to logarithmic terms and dependency on the horizon). Moreover, we also extend the first algorithm to simulator-free linear MDPs, which achieves mathcal O(K^{8/9}) regret and greatly improves over the best existing bound mathcal O(K^{14/15}). This algorithm relies on a better alternative to the Matrix Geometric Resampling procedure by Neu & Olkhovskaya (2020), which could again be of independent interest.

Constructing an adaptive hexahedral tessellation to fit an input triangle boundary is a key challenge in grid-based methods. The conventional method first removes outside elements (RO) and then projects the axis-aligned boundary onto the input triangle boundary, which has no guarantee on improving the initial Intersection over Union (IoU) and Hausdorff distance ratio (HR, w.r.t bounding box diagonal). The proposed MCHex approach replaces RO with a Marching Cubes method MCHex. Given the same computational budget (benchmarked using an identical precomputed Signed Distance Field, which dominates the runtime), MCHex provides better boundary approximation (higher IoU and lower HR) while guaranteeing a lower, yet still positive, minimum scaled Jacobian (>0 vs. RO's >0.48).

Mesh generation has become a critical topic in recent years, forming the foundation of all 3D objects used across various applications, such as virtual reality, gaming, and 3D printing. With advancements in computational resources and machine learning, neural networks have emerged as powerful tools for generating high-quality 3D object representations, enabling accurate scene and object reconstructions. Despite these advancements, many methods produce meshes that lack realism or exhibit geometric and textural flaws, necessitating additional processing to improve their quality. This research introduces a convex optimization programming called disciplined convex programming to enhance existing meshes by refining their texture and geometry with a conic solver. By focusing on a sparse set of point clouds from both the original and target meshes, this method demonstrates significant improvements in mesh quality with minimal data requirements. To evaluate the approach, the classical dolphin mesh dataset from Facebook AI was used as a case study, with optimization performed using the CVXPY library. The results reveal promising potential for streamlined and effective mesh refinement.

Autoformalization, which translates natural language mathematics into formal statements to enable machine reasoning, faces fundamental challenges in the wild due to the multimodal nature of the physical world, where physics requires inferring hidden constraints (e.g., mass or energy) from visual elements. To address this, we propose MMFormalizer, which extends autoformalization beyond text by integrating adaptive grounding with entities from real-world mathematical and physical domains. MMFormalizer recursively constructs formal propositions from perceptually grounded primitives through recursive grounding and axiom composition, with adaptive recursive termination ensuring that every abstraction is supported by visual evidence and anchored in dimensional or axiomatic grounding. We evaluate MMFormalizer on a new benchmark, PhyX-AF, comprising 115 curated samples from MathVerse, PhyX, Synthetic Geometry, and Analytic Geometry, covering diverse multimodal autoformalization tasks. Results show that frontier models such as GPT-5 and Gemini-3-Pro achieve the highest compile and semantic accuracy, with GPT-5 excelling in physical reasoning, while geometry remains the most challenging domain. Overall, MMFormalizer provides a scalable framework for unified multimodal autoformalization, bridging perception and formal reasoning. To the best of our knowledge, this is the first multimodal autoformalization method capable of handling classical mechanics (derived from the Hamiltonian), as well as relativity, quantum mechanics, and thermodynamics. More details are available on our project page: MMFormalizer.github.io

In the era of AIGC, the demand for low-budget or even on-device applications of diffusion models emerged. In terms of compressing the Stable Diffusion models (SDMs), several approaches have been proposed, and most of them leveraged the handcrafted layer removal methods to obtain smaller U-Nets, along with knowledge distillation to recover the network performance. However, such a handcrafting manner of layer removal is inefficient and lacks scalability and generalization, and the feature distillation employed in the retraining phase faces an imbalance issue that a few numerically significant feature loss terms dominate over others throughout the retraining process. To this end, we proposed the layer pruning and normalized distillation for compressing diffusion models (LAPTOP-Diff). We, 1) introduced the layer pruning method to compress SDM's U-Net automatically and proposed an effective one-shot pruning criterion whose one-shot performance is guaranteed by its good additivity property, surpassing other layer pruning and handcrafted layer removal methods, 2) proposed the normalized feature distillation for retraining, alleviated the imbalance issue. Using the proposed LAPTOP-Diff, we compressed the U-Nets of SDXL and SDM-v1.5 for the most advanced performance, achieving a minimal 4.0% decline in PickScore at a pruning ratio of 50% while the comparative methods' minimal PickScore decline is 8.2%. We will release our code.

Any optimization algorithm programming interface can be seen as a black-box function with additional free parameters. In this spirit, simulated annealing (SA) can be implemented in pseudo-code within the dimensions of a single slide with free parameters relating to the annealing schedule. Such an implementation, however, necessarily neglects much of the structure necessary to take advantage of advances in computing resources and algorithmic breakthroughs. Simulated annealing is often introduced in myriad disciplines, from discrete examples like the Traveling Salesman Problem (TSP) to molecular cluster potential energy exploration or even explorations of a protein's configurational space. Theoretical guarantees also demand a stricter structure in terms of statistical quantities, which cannot simply be left to the user. We will introduce several standard paradigms and demonstrate how these can be "lifted" into a unified framework using object-oriented programming in Python. We demonstrate how clean, interoperable, reproducible programming libraries can be used to access and rapidly iterate on variants of Simulated Annealing in a manner which can be extended to serve as a best practices blueprint or design pattern for a data-driven optimization library.

Large language models have made significant progress in complex but easy-to-verify problems, yet they still struggle with discovering the unknown. In this paper, we present AlphaResearch, an autonomous research agent designed to discover new algorithms on open-ended problems. To synergize the feasibility and innovation of the discovery process, we construct a novel dual research environment by combining the execution-based verify and simulated real-world peer review environment. AlphaResearch discovers new algorithm by iteratively running the following steps: (1) propose new ideas (2) verify the ideas in the dual research environment (3) optimize the research proposals for better performance. To promote a transparent evaluation process, we construct AlphaResearchComp, a new evaluation benchmark that includes an eight open-ended algorithmic problems competition, with each problem carefully curated and verified through executable pipelines, objective metrics, and reproducibility checks. AlphaResearch gets a 2/8 win rate in head-to-head comparison with human researchers, demonstrate the possibility of accelerating algorithm discovery with LLMs. Notably, the algorithm discovered by AlphaResearch on the ``packing circles'' problem achieves the best-of-known performance, surpassing the results of human researchers and strong baselines from recent work (e.g., AlphaEvolve). Additionally, we conduct a comprehensive analysis of the remaining challenges of the 6/8 failure cases, providing valuable insights for future research.

Structured adaptive mesh refinement (AMR), commonly implemented via quadtrees and octrees, underpins a wide range of applications including databases, computer graphics, physics simulations, and machine learning. However, octrees enforce isotropic refinement in regions of interest, which can be especially inefficient for problems that are intrinsically anisotropic--much resolution is spent where little information is gained. This paper presents omnitrees as an anisotropic generalization of octrees and related data structures. Omnitrees allow to refine only the locally most important dimensions, providing tree structures that are less deep than bintrees and less wide than octrees. As a result, the convergence of the AMR schemes can be increased by up to a factor of the dimensionality d for very anisotropic problems, quickly offsetting their modest increase in storage overhead. We validate this finding on the problem of binary shape representation across 4,166 three-dimensional objects: Omnitrees increase the mean convergence rate by 1.5x, require less storage to achieve equivalent error bounds, and maximize the information density of the stored function faster than octrees. These advantages are projected to be even stronger for higher-dimensional problems. We provide a first validation by introducing a time-dependent rotation to create four-dimensional representations, and discuss the properties of their 4-d octree and omnitree approximations. Overall, omnitree discretizations can make existing AMR approaches more efficient, and open up new possibilities for high-dimensional applications.

Artificial neural networks are a popular and effective machine learning technique. Great progress has been made parallelizing the expensive training phase of an individual network, leading to highly specialized pieces of hardware, many based on GPU-type architectures, and more concurrent algorithms such as synthetic gradients. However, the training phase continues to be a bottleneck, where the training data must be processed serially over thousands of individual training runs. This work considers a multigrid reduction in time (MGRIT) algorithm that is able to parallelize over the thousands of training runs and converge to the exact same solution as traditional training would provide. MGRIT was originally developed to provide parallelism for time evolution problems that serially step through a finite number of time-steps. This work recasts the training of a neural network similarly, treating neural network training as an evolution equation that evolves the network weights from one step to the next. Thus, this work concerns distributed computing approaches for neural networks, but is distinct from other approaches which seek to parallelize only over individual training runs. The work concludes with supporting numerical results for two model problems.

We present DreamPolisher, a novel Gaussian Splatting based method with geometric guidance, tailored to learn cross-view consistency and intricate detail from textual descriptions. While recent progress on text-to-3D generation methods have been promising, prevailing methods often fail to ensure view-consistency and textural richness. This problem becomes particularly noticeable for methods that work with text input alone. To address this, we propose a two-stage Gaussian Splatting based approach that enforces geometric consistency among views. Initially, a coarse 3D generation undergoes refinement via geometric optimization. Subsequently, we use a ControlNet driven refiner coupled with the geometric consistency term to improve both texture fidelity and overall consistency of the generated 3D asset. Empirical evaluations across diverse textual prompts spanning various object categories demonstrate the efficacy of DreamPolisher in generating consistent and realistic 3D objects, aligning closely with the semantics of the textual instructions.

The recursive Neville algorithm allows one to calculate interpolating functions recursively. Upon a judicious choice of the abscissas used for the interpolation (and extrapolation), this algorithm leads to a method for convergence acceleration. For example, one can use the Neville algorithm in order to successively eliminate inverse powers of the upper limit of the summation from the partial sums of a given, slowly convergent input series. Here, we show that, for a particular choice of the abscissas used for the extrapolation, one can replace the recursive Neville scheme by a simple one-step transformation, while also obtaining access to subleading terms for the transformed series after convergence acceleration. The matrix-based, unified formulas allow one to estimate the rate of convergence of the partial sums of the input series to their limit. In particular, Bethe logarithms for hydrogen are calculated to 100 decimal digits. Generalizations of the method to series whose remainder terms can be expanded in terms of inverse factorial series, or series with half-integer powers, are also discussed.

In this report, we introduce UltraShape 1.0, a scalable 3D diffusion framework for high-fidelity 3D geometry generation. The proposed approach adopts a two-stage generation pipeline: a coarse global structure is first synthesized and then refined to produce detailed, high-quality geometry. To support reliable 3D generation, we develop a comprehensive data processing pipeline that includes a novel watertight processing method and high-quality data filtering. This pipeline improves the geometric quality of publicly available 3D datasets by removing low-quality samples, filling holes, and thickening thin structures, while preserving fine-grained geometric details. To enable fine-grained geometry refinement, we decouple spatial localization from geometric detail synthesis in the diffusion process. We achieve this by performing voxel-based refinement at fixed spatial locations, where voxel queries derived from coarse geometry provide explicit positional anchors encoded via RoPE, allowing the diffusion model to focus on synthesizing local geometric details within a reduced, structured solution space. Our model is trained exclusively on publicly available 3D datasets, achieving strong geometric quality despite limited training resources. Extensive evaluations demonstrate that UltraShape 1.0 performs competitively with existing open-source methods in both data processing quality and geometry generation. All code and trained models will be released to support future research.

We study the problem of few-shot physically-aware articulated mesh generation. By observing an articulated object dataset containing only a few examples, we wish to learn a model that can generate diverse meshes with high visual fidelity and physical validity. Previous mesh generative models either have difficulties in depicting a diverse data space from only a few examples or fail to ensure physical validity of their samples. Regarding the above challenges, we propose two key innovations, including 1) a hierarchical mesh deformation-based generative model based upon the divide-and-conquer philosophy to alleviate the few-shot challenge by borrowing transferrable deformation patterns from large scale rigid meshes and 2) a physics-aware deformation correction scheme to encourage physically plausible generations. We conduct extensive experiments on 6 articulated categories to demonstrate the superiority of our method in generating articulated meshes with better diversity, higher visual fidelity, and better physical validity over previous methods in the few-shot setting. Further, we validate solid contributions of our two innovations in the ablation study. Project page with code is available at https://meowuu7.github.io/few-arti-obj-gen.

The deployment and training of neural networks on edge computing devices pose many challenges. The low memory nature of edge devices is often one of the biggest limiting factors encountered in the deployment of large neural network models. Tensor rematerialization or recompute is a way to address high memory requirements for neural network training and inference. In this paper we consider the problem of execution time minimization of compute graphs subject to a memory budget. In particular, we develop a new constraint programming formulation called Moccasin with only O(n) integer variables, where n is the number of nodes in the compute graph. This is a significant improvement over the works in the recent literature that propose formulations with O(n^2) Boolean variables. We present numerical studies that show that our approach is up to an order of magnitude faster than recent work especially for large-scale graphs.

We propose a novel and flexible roof modeling approach that can be used for constructing planar 3D polygon roof meshes. Our method uses a graph structure to encode roof topology and enforces the roof validity by optimizing a simple but effective planarity metric we propose. This approach is significantly more efficient than using general purpose 3D modeling tools such as 3ds Max or SketchUp, and more powerful and expressive than specialized tools such as the straight skeleton. Our optimization-based formulation is also flexible and can accommodate different styles and user preferences for roof modeling. We showcase two applications. The first application is an interactive roof editing framework that can be used for roof design or roof reconstruction from aerial images. We highlight the efficiency and generality of our approach by constructing a mesh-image paired dataset consisting of 2539 roofs. Our second application is a generative model to synthesize new roof meshes from scratch. We use our novel dataset to combine machine learning and our roof optimization techniques, by using transformers and graph convolutional networks to model roof topology, and our roof optimization methods to enforce the planarity constraint.

Recently, 3D assets created via reconstruction and generation have matched the quality of manually crafted assets, highlighting their potential for replacement. However, this potential is largely unrealized because these assets always need to be converted to meshes for 3D industry applications, and the meshes produced by current mesh extraction methods are significantly inferior to Artist-Created Meshes (AMs), i.e., meshes created by human artists. Specifically, current mesh extraction methods rely on dense faces and ignore geometric features, leading to inefficiencies, complicated post-processing, and lower representation quality. To address these issues, we introduce MeshAnything, a model that treats mesh extraction as a generation problem, producing AMs aligned with specified shapes. By converting 3D assets in any 3D representation into AMs, MeshAnything can be integrated with various 3D asset production methods, thereby enhancing their application across the 3D industry. The architecture of MeshAnything comprises a VQ-VAE and a shape-conditioned decoder-only transformer. We first learn a mesh vocabulary using the VQ-VAE, then train the shape-conditioned decoder-only transformer on this vocabulary for shape-conditioned autoregressive mesh generation. Our extensive experiments show that our method generates AMs with hundreds of times fewer faces, significantly improving storage, rendering, and simulation efficiencies, while achieving precision comparable to previous methods.

Pruning large language models (LLMs) is a challenging task due to their enormous size. The primary difficulty is fine-tuning the model after pruning, which is needed to recover the lost performance caused by dropping weights. Recent approaches have either ignored fine-tuning entirely, focusing on efficient pruning criteria, or attempted layer-wise weight updates, preserving the behavior of each layer. However, even layer-wise weight updates can be costly for LLMs, and previous works have resorted to various approximations. In our paper, we propose a fast and optimal weight update algorithm for pruned layers based on the Alternating Direction Method of Multipliers (ADMM). Coupled with a simple iterative pruning mask selection, our algorithm achieves state-of-the-art pruning performance across a wide range of LLMs. Code is available at https://github.com/fmfi-compbio/admm-pruning.

This note describes the development of an exact solver for Minimal Directed Feedback Vertex Set as part of the PACE 2022 competition. The solver is powered largely by aggressively trying to reduce the DFVS problem to a Minimal Cover problem, and applying reduction rules adapted from Vertex Cover literature. The resulting problem is solved as an Integer Linear Program (ILP) using SCIP. The resulting solver performed the second-best in the competition, although a bug at submission time disqualified it. As an additional note, we describe a new vertex cover reduction generalizing the Desk reduction rule.

Recently, several point-based image editing methods (e.g., DragDiffusion, FreeDrag, DragNoise) have emerged, yielding precise and high-quality results based on user instructions. However, these methods often make insufficient use of semantic information, leading to less desirable results. In this paper, we proposed a novel mask-free point-based image editing method, AdaptiveDrag, which provides a more flexible editing approach and generates images that better align with user intent. Specifically, we design an auto mask generation module using super-pixel division for user-friendliness. Next, we leverage a pre-trained diffusion model to optimize the latent, enabling the dragging of features from handle points to target points. To ensure a comprehensive connection between the input image and the drag process, we have developed a semantic-driven optimization. We design adaptive steps that are supervised by the positions of the points and the semantic regions derived from super-pixel segmentation. This refined optimization process also leads to more realistic and accurate drag results. Furthermore, to address the limitations in the generative consistency of the diffusion model, we introduce an innovative corresponding loss during the sampling process. Building on these effective designs, our method delivers superior generation results using only the single input image and the handle-target point pairs. Extensive experiments have been conducted and demonstrate that the proposed method outperforms others in handling various drag instructions (e.g., resize, movement, extension) across different domains (e.g., animals, human face, land space, clothing).

We formulate the predicted-updates dynamic model, one of the first beyond-worst-case models for dynamic algorithms, which generalizes a large set of well-studied dynamic models including the offline dynamic, incremental, and decremental models to the fully dynamic setting when given predictions about the update times of the elements. In the most basic form of our model, we receive a set of predicted update times for all of the updates that occur over the event horizon. We give a novel framework that "lifts" offline divide-and-conquer algorithms into the fully dynamic setting with little overhead. Using this, we are able to interpolate between the offline and fully dynamic settings; when the ell_1 error of the prediction is linear in the number of updates, we achieve the offline runtime of the algorithm (up to poly log n factors). Provided a fully dynamic backstop algorithm, our algorithm will never do worse than the backstop algorithm regardless of the prediction error. Furthermore, our framework achieves a smooth linear trade-off between ell_1 error in the predictions and runtime. These correspond to the desiderata of consistency, robustness, and graceful degradation of the algorithms-with-predictions literature. We further extend our techniques to incremental and decremental settings, transforming algorithms in these settings when given predictions of only the deletion and insertion times, respectively. Our framework is general, and we apply it to obtain improved efficiency bounds over the state-of-the-art dynamic algorithms for a variety of problems including triconnectivity, planar digraph all pairs shortest paths, k-edge connectivity, and others, for prediction error of reasonable magnitude.

In this white paper, we present AlphaEvolve, an evolutionary coding agent that substantially enhances capabilities of state-of-the-art LLMs on highly challenging tasks such as tackling open scientific problems or optimizing critical pieces of computational infrastructure. AlphaEvolve orchestrates an autonomous pipeline of LLMs, whose task is to improve an algorithm by making direct changes to the code. Using an evolutionary approach, continuously receiving feedback from one or more evaluators, AlphaEvolve iteratively improves the algorithm, potentially leading to new scientific and practical discoveries. We demonstrate the broad applicability of this approach by applying it to a number of important computational problems. When applied to optimizing critical components of large-scale computational stacks at Google, AlphaEvolve developed a more efficient scheduling algorithm for data centers, found a functionally equivalent simplification in the circuit design of hardware accelerators, and accelerated the training of the LLM underpinning AlphaEvolve itself. Furthermore, AlphaEvolve discovered novel, provably correct algorithms that surpass state-of-the-art solutions on a spectrum of problems in mathematics and computer science, significantly expanding the scope of prior automated discovery methods (Romera-Paredes et al., 2023). Notably, AlphaEvolve developed a search algorithm that found a procedure to multiply two 4 times 4 complex-valued matrices using 48 scalar multiplications; offering the first improvement, after 56 years, over Strassen's algorithm in this setting. We believe AlphaEvolve and coding agents like it can have a significant impact in improving solutions of problems across many areas of science and computation.

Pruning neural networks has become popular in the last decade when it was shown that a large number of weights can be safely removed from modern neural networks without compromising accuracy. Numerous pruning methods have been proposed since then, each claiming to be better than the previous. Many state-of-the-art (SOTA) techniques today rely on complex pruning methodologies utilizing importance scores, getting feedback through back-propagation or having heuristics-based pruning rules amongst others. In this work, we question whether this pattern of introducing complexity is really necessary to achieve better pruning results. We benchmark these SOTA techniques against a naive pruning baseline, namely, Global Magnitude Pruning (Global MP). Global MP ranks weights in order of their magnitudes and prunes the smallest ones. Hence, in its vanilla form, it is one of the simplest pruning techniques. Surprisingly, we find that vanilla Global MP outperforms all the other SOTA techniques and achieves a new SOTA result. It also achieves promising performance on FLOPs sparsification, which we find is enhanced, when pruning is conducted in a gradual fashion. We also find that Global MP is generalizable across tasks, datasets, and models with superior performance. Moreover, a common issue that many pruning algorithms run into at high sparsity rates, namely, layer-collapse, can be easily fixed in Global MP by setting a minimum threshold of weights to be retained in each layer. Lastly, unlike many other SOTA techniques, Global MP does not require any additional algorithm specific hyper-parameters and is very straightforward to tune and implement. We showcase our findings on various models (WRN-28-8, ResNet-32, ResNet-50, MobileNet-V1 and FastGRNN) and multiple datasets (CIFAR-10, ImageNet and HAR-2). Code is available at https://github.com/manasgupta-1/GlobalMP.

Oracle pruning, which selects unimportant weights by minimizing the pruned train loss, has been taken as the foundation for most neural network pruning methods for over 35 years, while few (if not none) have thought about how much the foundation really holds. This paper, for the first time, attempts to examine its validity on modern deep models through empirical correlation analyses and provide reflections on the field of neural network pruning. Specifically, for a typical pruning algorithm with three stages (pertaining, pruning, and retraining), we analyze the model performance correlation before and after retraining. Extensive experiments (37K models are trained) across a wide spectrum of models (LeNet5, VGG, ResNets, ViT, MLLM) and datasets (MNIST and its variants, CIFAR10/CIFAR100, ImageNet-1K, MLLM data) are conducted. The results lead to a surprising conclusion: on modern deep learning models, the performance before retraining is barely correlated with the performance after retraining. Namely, the weights selected by oracle pruning can hardly guarantee a good performance after retraining. This further implies that existing works using oracle pruning to derive pruning criteria may be groundless from the beginning. Further studies suggest the rising task complexity is one factor that makes oracle pruning invalid nowadays. Finally, given the evidence, we argue that the retraining stage in a pruning algorithm should be accounted for when developing any pruning criterion.

Retouching is an essential task in post-manipulation of raw photographs. Generative editing, guided by text or strokes, provides a new tool accessible to users but can easily change the identity of the original objects in unacceptable and unpredictable ways. In contrast, although traditional procedural edits, as commonly supported by photoediting tools (e.g., Gimp, Lightroom), are conservative, they are still preferred by professionals. Unfortunately, professional quality retouching involves many individual procedural editing operations that is challenging to plan for most novices. In this paper, we ask if a multimodal large language model (MLLM) can be taught to critique raw photographs, suggest suitable remedies, and finally realize them with a given set of pre-authored procedural image operations. We demonstrate that MLLMs can be first made aware of the underlying image processing operations, by training them to solve specially designed visual puzzles. Subsequently, such an operation-aware MLLM can both plan and propose edit sequences. To facilitate training, given a set of expert-edited photos, we synthesize a reasoning dataset by procedurally manipulating the expert edits and then grounding a pretrained LLM on the visual adjustments, to synthesize reasoning for finetuning. The proposed retouching operations are, by construction, understandable by the users, preserve object details and resolution, and can be optionally overridden. We evaluate our setup on a variety of test examples and show advantages, in terms of explainability and identity preservation, over existing generative and other procedural alternatives. Code, data, models, and supplementary results can be found via our project website at https://monetgpt.github.io.

We propose MeshLRM, a novel LRM-based approach that can reconstruct a high-quality mesh from merely four input images in less than one second. Different from previous large reconstruction models (LRMs) that focus on NeRF-based reconstruction, MeshLRM incorporates differentiable mesh extraction and rendering within the LRM framework. This allows for end-to-end mesh reconstruction by fine-tuning a pre-trained NeRF LRM with mesh rendering. Moreover, we improve the LRM architecture by simplifying several complex designs in previous LRMs. MeshLRM's NeRF initialization is sequentially trained with low- and high-resolution images; this new LRM training strategy enables significantly faster convergence and thereby leads to better quality with less compute. Our approach achieves state-of-the-art mesh reconstruction from sparse-view inputs and also allows for many downstream applications, including text-to-3D and single-image-to-3D generation. Project page: https://sarahweiii.github.io/meshlrm/

One of the major optimizations employed in deep learning frameworks is graph rewriting. Production frameworks rely on heuristics to decide if rewrite rules should be applied and in which order. Prior research has shown that one can discover more optimal tensor computation graphs if we search for a better sequence of substitutions instead of relying on heuristics. However, we observe that existing approaches for tensor graph superoptimization both in production and research frameworks apply substitutions in a sequential manner. Such sequential search methods are sensitive to the order in which the substitutions are applied and often only explore a small fragment of the exponential space of equivalent graphs. This paper presents a novel technique for tensor graph superoptimization that employs equality saturation to apply all possible substitutions at once. We show that our approach can find optimized graphs with up to 16% speedup over state-of-the-art, while spending on average 48x less time optimizing.

Scaling artist-designed meshes to high triangle numbers remains challenging for autoregressive generative models. Existing transformer-based methods suffer from long-sequence bottlenecks and limited quantization resolution, primarily due to the large number of tokens required and constrained quantization granularity. These issues prevent faithful reproduction of fine geometric details and structured density patterns. We introduce MeshMosaic, a novel local-to-global framework for artist mesh generation that scales to over 100K triangles--substantially surpassing prior methods, which typically handle only around 8K faces. MeshMosaic first segments shapes into patches, generating each patch autoregressively and leveraging shared boundary conditions to promote coherence, symmetry, and seamless connectivity between neighboring regions. This strategy enhances scalability to high-resolution meshes by quantizing patches individually, resulting in more symmetrical and organized mesh density and structure. Extensive experiments across multiple public datasets demonstrate that MeshMosaic significantly outperforms state-of-the-art methods in both geometric fidelity and user preference, supporting superior detail representation and practical mesh generation for real-world applications.

The demand for Large Language Models (LLMs) capable of sophisticated mathematical reasoning is growing across industries. However, the development of performant mathematical LLMs is critically bottlenecked by the scarcity of difficult, novel training data. We introduce SAND-Math (Synthetic Augmented Novel and Difficult Mathematics problems and solutions), a pipeline that addresses this by first generating high-quality problems from scratch and then systematically elevating their complexity via a new Difficulty Hiking step. We demonstrate the effectiveness of our approach through two key findings. First, augmenting a strong baseline with SAND-Math data significantly boosts performance, outperforming the next-best synthetic dataset by uparrow 17.85 absolute points on the AIME25 benchmark. Second, in a dedicated ablation study, we show our Difficulty Hiking process is highly effective: by increasing average problem difficulty from 5.02 to 5.98, this step lifts AIME25 performance from 46.38\% to 49.23\%. The full generation pipeline, final dataset, and a fine-tuned model form a practical and scalable toolkit for building more capable and efficient mathematical reasoning LLMs. SAND-Math dataset is released here: https://huggingface.co/datasets/amd/SAND-MATH{https://huggingface.co/datasets/amd/SAND-MATH}

Recent advances in 3D vision have led to specialized models for either 3D understanding (e.g., shape classification, segmentation, reconstruction) or 3D generation (e.g., synthesis, completion, and editing). However, these tasks are often tackled in isolation, resulting in fragmented architectures and representations that hinder knowledge transfer and holistic scene modeling. To address these challenges, we propose UniMesh, a unified framework that jointly learns 3D generation and understanding within a single architecture. First, we introduce a novel Mesh Head that acts as a cross model interface, bridging diffusion based image generation with implicit shape decoders. Second, we develop Chain of Mesh (CoM), a geometric instantiation of iterative reasoning that enables user driven semantic mesh editing through a closed loop latent, prompting, and re generation cycle. Third, we incorporate a self reflection mechanism based on an Actor Evaluator Self reflection triad to diagnose and correct failures in high level tasks like 3D captioning. Experimental results demonstrate that UniMesh not only achieves competitive performance on standard benchmarks but also unlocks novel capabilities in iterative editing and mutual enhancement between generation and understanding. Code: https://github.com/AIGeeksGroup/UniMesh. Website: https://aigeeksgroup.github.io/UniMesh.

Recently, using diffusion models for zero-shot image restoration (IR) has become a new hot paradigm. This type of method only needs to use the pre-trained off-the-shelf diffusion models, without any finetuning, and can directly handle various IR tasks. The upper limit of the restoration performance depends on the pre-trained diffusion models, which are in rapid evolution. However, current methods only discuss how to deal with fixed-size images, but dealing with images of arbitrary sizes is very important for practical applications. This paper focuses on how to use those diffusion-based zero-shot IR methods to deal with any size while maintaining the excellent characteristics of zero-shot. A simple way to solve arbitrary size is to divide it into fixed-size patches and solve each patch independently. But this may yield significant artifacts since it neither considers the global semantics of all patches nor the local information of adjacent patches. Inspired by the Range-Null space Decomposition, we propose the Mask-Shift Restoration to address local incoherence and propose the Hierarchical Restoration to alleviate out-of-domain issues. Our simple, parameter-free approaches can be used not only for image restoration but also for image generation of unlimited sizes, with the potential to be a general tool for diffusion models. Code: https://github.com/wyhuai/DDNM/tree/main/hq_demo

We propose a novel approach to scaling LLM inference for code generation. We frame code generation as a black box optimization problem within the code space, and employ optimization-inspired techniques to enhance exploration. Specifically, we introduce Scattered Forest Search to enhance solution diversity while searching for solutions. Our theoretical analysis illustrates how these methods avoid local optima during optimization. Extensive experiments on HumanEval, MBPP, APPS, CodeContests, and Leetcode reveal significant performance improvements. For instance, our method achieves a pass@1 rate of 67.1% on HumanEval+ and 87.2% on HumanEval with GPT-3.5, marking improvements of 8.6% and 4.3% over the state-of-the-art, while also halving the iterations needed to find the correct solution. Furthermore, our method scales more efficiently than existing search techniques, including tree search, line search, and repeated sampling.

Flow matching is a powerful framework for generating high-quality samples in various applications, especially image synthesis. However, the intensive computational demands of these models, especially during the fine-tuning process and sampling processes, pose significant challenges for low-resource scenarios. This paper introduces Bellman Optimal Step-size Straightening (BOSS) technique for distilling flow-matching generative models: it aims specifically for a few-step efficient image sampling while adhering to a computational budget constraint. First, this technique involves a dynamic programming algorithm that optimizes the step sizes of the pretrained network. Then, it refines the velocity network to match the optimal step sizes, aiming to straighten the generation paths. Extensive experimental evaluations across image generation tasks demonstrate the efficacy of BOSS in terms of both resource utilization and image quality. Our results reveal that BOSS achieves substantial gains in efficiency while maintaining competitive sample quality, effectively bridging the gap between low-resource constraints and the demanding requirements of flow-matching generative models. Our paper also fortifies the responsible development of artificial intelligence, offering a more sustainable generative model that reduces computational costs and environmental footprints. Our code can be found at https://github.com/nguyenngocbaocmt02/BOSS.

We introduce MeshPad, a generative approach that creates 3D meshes from sketch inputs. Building on recent advances in artistic-designed triangle mesh generation, our approach addresses the need for interactive artistic mesh creation. To this end, we focus on enabling consistent edits by decomposing editing into 'deletion' of regions of a mesh, followed by 'addition' of new mesh geometry. Both operations are invoked by simple user edits of a sketch image, facilitating an iterative content creation process and enabling the construction of complex 3D meshes. Our approach is based on a triangle sequence-based mesh representation, exploiting a large Transformer model for mesh triangle addition and deletion. In order to perform edits interactively, we introduce a vertex-aligned speculative prediction strategy on top of our additive mesh generator. This speculator predicts multiple output tokens corresponding to a vertex, thus significantly reducing the computational cost of inference and accelerating the editing process, making it possible to execute each editing step in only a few seconds. Comprehensive experiments demonstrate that MeshPad outperforms state-of-the-art sketch-conditioned mesh generation methods, achieving more than 22% mesh quality improvement in Chamfer distance, and being preferred by 90% of participants in perceptual evaluations.

We present Piecewise Rectified Flow (PeRFlow), a flow-based method for accelerating diffusion models. PeRFlow divides the sampling process of generative flows into several time windows and straightens the trajectories in each interval via the reflow operation, thereby approaching piecewise linear flows. PeRFlow achieves superior performance in a few-step generation. Moreover, through dedicated parameterizations, the obtained PeRFlow models show advantageous transfer ability, serving as universal plug-and-play accelerators that are compatible with various workflows based on the pre-trained diffusion models. The implementations of training and inference are fully open-sourced. https://github.com/magic-research/piecewise-rectified-flow

This paper presents a parallel random-search method for reducing additive complexity in fast matrix multiplication. The approach replaces expensive exact evaluation with fast heuristic scoring, including the new Greedy-Intersections strategy. The method runs many independent common subexpression elimination processes in parallel, exploring the search space through random pair substitutions and diverse selection strategies while sharing promising partial solutions. Tested on 164 ternary-coefficient schemes, the method achieves lower addition counts than the state-of-the-art Greedy-Potential on 103 schemes, matches it on 59, and is outperformed on 2. For most schemes, it gives equal or better results while being much faster, making it practical for algorithm exploration. All software and results are open source.

In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional configuration spaces. This algorithm is proven to be asymptotically optimal and is shown to converge to an optimal solution faster than its state-of-the-art counterparts, chiefly PRM* and RRT*. The FMT* algorithm performs a "lazy" dynamic programming recursion on a predetermined number of probabilistically-drawn samples to grow a tree of paths, which moves steadily outward in cost-to-arrive space. As a departure from previous analysis approaches that are based on the notion of almost sure convergence, the FMT* algorithm is analyzed under the notion of convergence in probability: the extra mathematical flexibility of this approach allows for convergence rate bounds--the first in the field of optimal sampling-based motion planning. Specifically, for a certain selection of tuning parameters and configuration spaces, we obtain a convergence rate bound of order O(n^{-1/d+ρ}), where n is the number of sampled points, d is the dimension of the configuration space, and ρ is an arbitrarily small constant. We go on to demonstrate asymptotic optimality for a number of variations on FMT*, namely when the configuration space is sampled non-uniformly, when the cost is not arc length, and when connections are made based on the number of nearest neighbors instead of a fixed connection radius. Numerical experiments over a range of dimensions and obstacle configurations confirm our theoretical and heuristic arguments by showing that FMT*, for a given execution time, returns substantially better solutions than either PRM* or RRT*, especially in high-dimensional configuration spaces and in scenarios where collision-checking is expensive.

We present a pipeline for generating defurnished replicas of indoor spaces represented as textured meshes and corresponding multi-view panoramic images. To achieve this, we first segment and remove furniture from the mesh representation, extend planes, and fill holes, obtaining a simplified defurnished mesh (SDM). This SDM acts as an ``X-ray'' of the scene's underlying structure, guiding the defurnishing process. We extract Canny edges from depth and normal images rendered from the SDM. We then use these as a guide to remove the furniture from panorama images via ControlNet inpainting. This control signal ensures the availability of global geometric information that may be hidden from a particular panoramic view by the furniture being removed. The inpainted panoramas are used to texture the mesh. We show that our approach produces higher quality assets than methods that rely on neural radiance fields, which tend to produce blurry low-resolution images, or RGB-D inpainting, which is highly susceptible to hallucinations.

Conventional production workflow of high-precision mesh assets necessitates a cumbersome and laborious process of manual sculpting by specialized 3D artists/modelers. The recent years have witnessed remarkable advances in AI-empowered 3D content creation for generating plausible structures and intricate appearances from images or text prompts. However, synthesizing realistic surface details still poses great challenges, and enhancing the geometry fidelity of existing lower-quality 3D meshes (instead of image/text-to-3D generation) remains an open problem. In this paper, we introduce SuperCarver, a 3D geometry super-resolution pipeline for supplementing texture-consistent surface details onto a given coarse mesh. We start by rendering the original textured mesh into the image domain from multiple viewpoints. To achieve detail boosting, we construct a deterministic prior-guided normal diffusion model, which is fine-tuned on a carefully curated dataset of paired detail-lacking and detail-rich normal map renderings. To update mesh surfaces from potentially imperfect normal map predictions, we design a noise-resistant inverse rendering scheme through deformable distance field. Experiments demonstrate that our SuperCarver is capable of generating realistic and expressive surface details depicted by the actual texture appearance, making it a powerful tool to both upgrade historical low-quality 3D assets and reduce the workload of sculpting high-poly meshes.

Using parts of existing models to rebuild new models, commonly termed as example-based modeling, is a classical methodology in the realm of computer graphics. Previous works mostly focus on shape composition, making them very hard to use for realistic composition of 3D objects captured from real-world scenes. This leads to combining multiple NeRFs into a single 3D scene to achieve seamless appearance blending. However, the current SeamlessNeRF method struggles to achieve interactive editing and harmonious stitching for real-world scenes due to its gradient-based strategy and grid-based representation. To this end, we present an example-based modeling method that combines multiple Gaussian fields in a point-based representation using sample-guided synthesis. Specifically, as for composition, we create a GUI to segment and transform multiple fields in real time, easily obtaining a semantically meaningful composition of models represented by 3D Gaussian Splatting (3DGS). For texture blending, due to the discrete and irregular nature of 3DGS, straightforwardly applying gradient propagation as SeamlssNeRF is not supported. Thus, a novel sampling-based cloning method is proposed to harmonize the blending while preserving the original rich texture and content. Our workflow consists of three steps: 1) real-time segmentation and transformation of a Gaussian model using a well-tailored GUI, 2) KNN analysis to identify boundary points in the intersecting area between the source and target models, and 3) two-phase optimization of the target model using sampling-based cloning and gradient constraints. Extensive experimental results validate that our approach significantly outperforms previous works in terms of realistic synthesis, demonstrating its practicality. More demos are available at https://ingra14m.github.io/gs_stitching_website.

Current auto-regressive mesh generation methods suffer from issues such as incompleteness, insufficient detail, and poor generalization. In this paper, we propose an Auto-regressive Auto-encoder (ArAE) model capable of generating high-quality 3D meshes with up to 4,000 faces at a spatial resolution of 512^3. We introduce a novel mesh tokenization algorithm that efficiently compresses triangular meshes into 1D token sequences, significantly enhancing training efficiency. Furthermore, our model compresses variable-length triangular meshes into a fixed-length latent space, enabling training latent diffusion models for better generalization. Extensive experiments demonstrate the superior quality, diversity, and generalization capabilities of our model in both point cloud and image-conditioned mesh generation tasks.

Learning radiance fields (NeRF) with powerful 2D diffusion models has garnered popularity for text-to-3D generation. Nevertheless, the implicit 3D representations of NeRF lack explicit modeling of meshes and textures over surfaces, and such surface-undefined way may suffer from the issues, e.g., noisy surfaces with ambiguous texture details or cross-view inconsistency. To alleviate this, we present DreamMesh, a novel text-to-3D architecture that pivots on well-defined surfaces (triangle meshes) to generate high-fidelity explicit 3D model. Technically, DreamMesh capitalizes on a distinctive coarse-to-fine scheme. In the coarse stage, the mesh is first deformed by text-guided Jacobians and then DreamMesh textures the mesh with an interlaced use of 2D diffusion models in a tuning free manner from multiple viewpoints. In the fine stage, DreamMesh jointly manipulates the mesh and refines the texture map, leading to high-quality triangle meshes with high-fidelity textured materials. Extensive experiments demonstrate that DreamMesh significantly outperforms state-of-the-art text-to-3D methods in faithfully generating 3D content with richer textual details and enhanced geometry. Our project page is available at https://dreammesh.github.io.

In recent years, deep network pruning has attracted significant attention in order to enable the rapid deployment of AI into small devices with computation and memory constraints. Pruning is often achieved by dropping redundant weights, neurons, or layers of a deep network while attempting to retain a comparable test performance. Many deep pruning algorithms have been proposed with impressive empirical success. However, existing approaches lack a quantifiable measure to estimate the compressibility of a sub-network during each pruning iteration and thus may under-prune or over-prune the model. In this work, we propose PQ Index (PQI) to measure the potential compressibility of deep neural networks and use this to develop a Sparsity-informed Adaptive Pruning (SAP) algorithm. Our extensive experiments corroborate the hypothesis that for a generic pruning procedure, PQI decreases first when a large model is being effectively regularized and then increases when its compressibility reaches a limit that appears to correspond to the beginning of underfitting. Subsequently, PQI decreases again when the model collapse and significant deterioration in the performance of the model start to occur. Additionally, our experiments demonstrate that the proposed adaptive pruning algorithm with proper choice of hyper-parameters is superior to the iterative pruning algorithms such as the lottery ticket-based pruning methods, in terms of both compression efficiency and robustness.