Daily Papers

An accurate description of the scalar potential at finite temperature is crucial for studying cosmological first-order phase transitions (FOPT) in the early Universe. At finite temperatures, a precise treatment of thermal resummations is essential, as bosonic fields encounter significant infrared issues that can compromise standard perturbative approaches. The Partial Dressing (or the tadpole resummation) method provides a self consistent resummation of higher order corrections, allowing the computation of thermal masses and the effective potential including the proper Boltzmann suppression factors and without relying on any high-temperature approximation. We systematically compare the Partial dressing resummation scheme results with the Parwani and Arnold Espinosa (AE) ones to investigate the thermal phase transition dynamics in the Two-Higgs-Doublet Model (2HDM). Our findings reveal that different resummation prescriptions can significantly alter the nature of the phase transition within the same region of parameter space, confirming the differences that have already been noticed between the Parwani and AE schemes. Notably, the more refined resummation prescription, the Partial Dressing scheme, does not support symmetry non-restoration in 2HDM at high temperatures observed using the AE prescription. Furthermore, we quantify the uncertainties in the stochastic gravitational wave (GW) spectrum from an FOPT due to variations in resummation methods, illustrating their role in shaping theoretical predictions for upcoming GW experiments. Finally, we discuss the capability of the High-Luminosity LHC and proposed GW experiments to probe the FOEWPT-favored region of the parameter space.

We introduce Tadpole, a novel foundation model for three-dimensional partial differential equations (PDEs) that addresses key challenges in transferability, scalability to high dimensionality, and multi-functionality. Tadpole is pre-trained as an autoencoder on synthetic 3D PDE data generated by an efficient online data-generation framework. This enables large-scale, diverse training without storage or I/O overhead, demonstrated by scaling to an equivalent of hundreds of terabytes of training data. By autoencoding single-channel spatial crops, Tadpole learns rich and transferable representations across heterogeneous physical systems with varying numbers of state variables and spatial resolutions. Although pre-trained solely as an autoencoder, Tadpole can be efficiently applied for multiple downstream tasks beyond reconstruction, including dynamics learning and generative modeling. For dynamics learning, we propose a novel parameter-efficient fine-tuning strategy that integrates low-rank adaptation, latent-space transformations, and reintroduced skip connections, achieving accurate temporal modeling with a minimal number of trainable parameters. Tadpole demonstrates strong fine-tuning performance across various downstream tasks, highlighting its versatility and effectiveness as a foundation model for 3D PDE learning. Source code and pre-trained weights of Tadpole are available at https://github.com/tum-pbs/tadpole

Our aim is to contribute to quantum field theory (QFT) formalisms useful for descriptions of short time phenomena, dominant especially in heavy ion collisions. We formulate out-of-equilibrium QFT within the finite-time-path formalism (FTP) and renormalization theory (RT). The potential conflict of FTP and RT is investigated in g phi^3 QFT, by using the retarded/advanced (R/A) basis of Green functions and dimensional renormalization (DR). For example, vertices immediately after (in time) divergent self-energy loops do not conserve energy, as integrals diverge. We "repair" them, while keeping d<4, to obtain energy conservation at those vertices. Already in the S-matrix theory, the renormalized, finite part of Feynman self-energy Sigma_{F}(p_0) does not vanish when |p_0|rightarrowinfty and cannot be split to retarded and advanced parts. In the Glaser--Epstein approach, the causality is repaired in the composite object G_F(p_0)Sigma_{F}(p_0). In the FTP approach, after repairing the vertices, the corresponding composite objects are G_R(p_0)Sigma_{R}(p_0) and Sigma_{A}(p_0)G_A(p_0). In the limit drightarrow 4, one obtains causal QFT. The tadpole contribution splits into diverging and finite parts. The diverging, constant component is eliminated by the renormalization condition langle 0|phi|0rangle =0 of the S-matrix theory. The finite, oscillating energy-nonconserving tadpole contributions vanish in the limit trightarrow infty .

We compute the cross section for the inclusive photoproduction of a pair of jets at next-to-leading order accuracy in the Color Glass Condensate (CGC) effective theory. The aim is to study the back-to-back limit, to investigate whether transverse momentum dependent (TMD) factorization can be recovered at this order. In particular, we focus on the large Sudakov double logarithms, which are major ingredients of the TMD evolution. Interestingly, the kinematical improvement of the low-x resummation scheme turns out to be a key ingredient in the analysis.

We present the findings of "The Alzheimer's Disease Prediction Of Longitudinal Evolution" (TADPOLE) Challenge, which compared the performance of 92 algorithms from 33 international teams at predicting the future trajectory of 219 individuals at risk of Alzheimer's disease. Challenge participants were required to make a prediction, for each month of a 5-year future time period, of three key outcomes: clinical diagnosis, Alzheimer's Disease Assessment Scale Cognitive Subdomain (ADAS-Cog13), and total volume of the ventricles. The methods used by challenge participants included multivariate linear regression, machine learning methods such as support vector machines and deep neural networks, as well as disease progression models. No single submission was best at predicting all three outcomes. For clinical diagnosis and ventricle volume prediction, the best algorithms strongly outperform simple baselines in predictive ability. However, for ADAS-Cog13 no single submitted prediction method was significantly better than random guesswork. Two ensemble methods based on taking the mean and median over all predictions, obtained top scores on almost all tasks. Better than average performance at diagnosis prediction was generally associated with the additional inclusion of features from cerebrospinal fluid (CSF) samples and diffusion tensor imaging (DTI). On the other hand, better performance at ventricle volume prediction was associated with inclusion of summary statistics, such as the slope or maxima/minima of biomarkers. TADPOLE's unique results suggest that current prediction algorithms provide sufficient accuracy to exploit biomarkers related to clinical diagnosis and ventricle volume, for cohort refinement in clinical trials for Alzheimer's disease. However, results call into question the usage of cognitive test scores for patient selection and as a primary endpoint in clinical trials.

A fully differential calculation in perturbative quantum chromodynamics is presented for the production of massive photon pairs at hadron colliders. All next-to-leading order perturbative contributions from quark-antiquark, gluon-(anti)quark, and gluon-gluon subprocesses are included, as well as all-orders resummation of initial-state gluon radiation valid at next-to-next-to-leading logarithmic accuracy. The region of phase space is specified in which the calculation is most reliable. Good agreement is demonstrated with data from the Fermilab Tevatron, and predictions are made for more detailed tests with CDF and DO data. Predictions are shown for distributions of diphoton pairs produced at the energy of the Large Hadron Collider (LHC). Distributions of the diphoton pairs from the decay of a Higgs boson are contrasted with those produced from QCD processes at the LHC, showing that enhanced sensitivity to the signal can be obtained with judicious selection of events.

A persistent and fascinating problem at the high energy colliders are jets. Often trying to observe physics underlying the hard interactions at colliders requires experimental cuts in phase space, defining several jet or beam regions. QCD being a gauge theory that readily decays into infra-red modes, correlations between jet regions is almost inevitable, spoiling the predictivity of fixed order QCD calculations. One is faced with the task of calculating the evolution of a reduced density matrix, where successively less energetic (jet) regions are integrated out, to gain control of the calculation. I relate the decay rates governing the flow into the IR to an effective field theory expansion in soft jets, allowing a systematic and resummed calculation of these rates, while further relating them to physically observable features of the QCD cascade. To demonstrate the utility of the soft jet expansion, I present a factorization theorem for a soft subjet collinearly splitting in and out of a parent fat jet. Using the resummation properties of this factorization theorem, I elucidate the structure of the subleading non-global logs (encoding the jet correlations) in the hemisphere jet mass distribution, as well as give a collinear improvement of the leading order resummation equation, the BMS equation. I compare to other approaches to subleading resummation of NGLs, and find the collinear improvement of the leading order equation removes the need for kinematic-dependent corrections in the IR averaging procedure of the reduced density matrix, so that no further large logs can be generated in the IR. Finally I end with speculation about connections with collinear improvements of the NLO B-JIMWLK hierarchy for small-x resummation.

An observable in an Effective Field Theory (EFT) is an expansion in a set of small parameters, no different than any other perturbation series. Truncating such a series expansion leaves the leading dropped term as the dominant source of error, and that term itself contains a calculable portion. We explore the partial calculation of this next-order error, available at dim-6^2 in SMEFT with no additional tools needed to simulate it, and explore how to efficiently use that partial calculation to model the next-order uncertainty in full using a minimal number of nuisance parameters. This estimate of the uncertainty of the EFT signal rate naturally imposes EFT validity by ensuring that bounds are driven by kinematic regions where truncation uncertainties are parametrically smaller than the signal. We incorporate the calculable dim-6^2 piece into the signal and cover the remaining higher-dimension uncertainty with a small set of nuisance parameters derived from a scan over Wilson-coefficient values. Our algorithm to determine the relevant nuisance parameters and distributions is automation-friendly and applies to arbitrary truncation choices. We then provide multiple examples of its implementation in high-energy collider processes focused on SMEFT truncated at O(Λ^{-2}), where the dim-6^2 piece is used to estimate the full mathcal O(Λ^{-4}) dependence. In the examples considered here the reduction of nuisance parameters is appreciable, generically reducing the nuisance parameter count by an order of magnitude compared to naïve estimates.

We present compact analytic results for tree-level amplitudes containing a t t pair accompanied by up to four massless partons, t tgg, t tggg, t tgggg, t tqq, t tqqg, t tqqgg and ttqqq^prime q^prime. The results, obtained using BCFW on-shell recursion, are based both on previous published results and on the new calculations performed in this paper. These amplitudes are sufficient to calculate the production of a tt pair and zero, one, or two light parton jets, with the option to include the tree-level decays t to b νe^+ and t to b e^- barν efficiently. Our results are part of the NNLO corrections to t t production including the decay correlations for on-shell top quarks.

We construct an exact analytic solution of the revised small-x helicity evolution equations, where the contributions of the quark-to-gluon and gluon-to-quark transition operators were newly included. These evolution equations are written in the large-N_c&N_f limit and are double-logarithmic, resumming powers of alpha_sln^2(1/x). Here N_c and N_f are the numbers of quark colors and flavors, while alpha_s is the strong coupling constant and x is the Bjorken-x variable. Using our solution, we obtain analytic expressions for the flavor singlet quark and gluon helicity parton distribution functions (PDFs) and for the g_1 structure function as double-inverse Laplace transforms. We also extract analytic expressions for the four DGLAP polarized anomalous dimensions Delta gamma_{qq}, Delta gamma_{qG}, Delta gamma_{Gq}, and Delta gamma_{GG}: these expressions resum powers of alpha_s/omega^2 to all orders at large-N_c&N_f (with omega the Mellin moment variable). We extract the leading small-x growth of the helicity distributions, align \Delta\Sigma(x,Q^2) \sim \Delta G(x,Q^2)\sim g_1(x,Q^2) \sim \left(1{x}\right)^{\alpha_h}, align where the intercept alpha_h satisfies an algebraic equation. We determine alpha_h numerically for various values of N_c and N_f. We further obtain the explicit asymptotic expressions for the helicity distributions, which yield numerical values for the ratio of the gluon helicity PDF to the flavor singlet quark helicity PDF in the small-x asymptotic limit (for different N_f/N_c). We find that all our predictions for polarized DGLAP anomalous dimensions are fully consistent with the existing finite-order calculations. Similar to the large-N_c case, our intercept alpha_h exhibits a very slight disagreement with the predictions made within the infrared evolution equations framework.

We present a hardware-oriented description of GoldenFloat (GF), a static-split floating-point family generated by a single closed rule, and three concrete artefacts: (i) an open multi-width RTL generator covering GF4-GF256 with a continuous-integration differential sweep against a correctly-rounded reference; (ii) an integer-backed Lucas-exact accumulator path verified at 500-digit precision for n = 1, ..., 256; and (iii) a GF16 FPGA codec passing a 35-of-35 testbench at 323 MHz on Artix-7 (Xilinx XC7A35T). For each total width N >= 4, the exponent width is e = round((N-1)/phi^2) with fraction f = N-1-e and phi = (1+sqrt(5))/2. The rule reproduces the realised exponent widths of nine formats (9/9) and extends consistently to GF128, GF512, GF1024. The rule is positioned alongside posit, takum, OCP-MX, and the IEEE P3109 multi-width float draft. We make no per-rung accuracy or superiority claim against any of them. The breadth/toolchain-coherence framing is recorded as an open conjecture with a pre-registered falsification path. A falsification ledger (FL-002) records open questions and the experiments that would settle them. An RTL-correctness erratum dated 2026-05-31 is reported; the fabricated TTSKY26b dies carry the defective multiplier portfolio, and the corrected generator is the regeneration baseline.

Disassembly is a crucial yet challenging step in binary analysis. While emerging neural disassemblers show promise for efficiency and accuracy, they frequently generate outputs violating fundamental structural constraints, which significantly compromise their practical usability. To address this critical problem, we regularize the disassembly solution space by formalizing and applying key structural constraints based on post-dominance relations. This approach systematically detects widespread errors in existing neural disassemblers' outputs. These errors often originate from models' limited context modeling and instruction-level decoding that neglect global structural integrity. We introduce Tady, a novel neural disassembler featuring an improved model architecture and a dedicated post-processing algorithm, specifically engineered to address these deficiencies. Comprehensive evaluations on diverse binaries demonstrate that Tady effectively eliminates structural constraint violations and functions with high efficiency, while maintaining instruction-level accuracy.

We present egglog, a fixpoint reasoning system that unifies Datalog and equality saturation (EqSat). Like Datalog, it supports efficient incremental execution, cooperating analyses, and lattice-based reasoning. Like EqSat, it supports term rewriting, efficient congruence closure, and extraction of optimized terms. We identify two recent applications--a unification-based pointer analysis in Datalog and an EqSat-based floating-point term rewriter--that have been hampered by features missing from Datalog but found in EqSat or vice-versa. We evaluate egglog by reimplementing those projects in egglog. The resulting systems in egglog are faster, simpler, and fix bugs found in the original systems.

Conformal prediction offers a powerful framework for building distribution-free prediction intervals for exchangeable data. Existing methods that extend conformal prediction to sequential data rely on fitting a relatively complex model to capture temporal dependencies. However, these methods can fail if the sample size is small and often require expensive retraining when the underlying data distribution changes. To overcome these limitations, we propose Reservoir Conformal Prediction (ResCP), a novel training-free conformal prediction method for time series. Our approach leverages the efficiency and representation learning capabilities of reservoir computing to dynamically reweight conformity scores. In particular, we compute similarity scores among reservoir states and use them to adaptively reweight the observed residuals at each step. With this approach, ResCP enables us to account for local temporal dynamics when modeling the error distribution without compromising computational scalability. We prove that, under reasonable assumptions, ResCP achieves asymptotic conditional coverage, and we empirically demonstrate its effectiveness across diverse forecasting tasks.

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.

Yes. Can it cure doom loops? Probably not. The Gemma 4 instruction-tuned models share a reproducible failure: on long factual enumeration prompts, such as listing every episode of a TV series, the 88 IAU constellations, or the 151 original Pokemon, they collapse into repetition, either a tight verbatim loop or a list whose entries decay onto a single answer. These loops occur at rates as high as 95% and survive prompt rewording, inference-engine changes, and most sampling adjustments. In this paper we explore whether this behavior is localized enough to remove by weight edits. To localize the cause, we use per-layer ablation and per-neuron attribution, then confirm the strongest candidates with full-generation sweeps. The loops trace to a small set of MLP neurons (or, in the 26B-A4B Mixture-of-Experts model, a few routed experts) which we suppress with static weight edits. These "surgeries" can be as small as a single sign-inverted neuron (in the E2B model). The size of the effective edits grows with model scale, but in all cases, the loop patterns can be addressed at normal generation budgets while preserving general-purpose benchmark scores. However, the edits do not solve everything: we also study longer thinking budgets, where the two larger models most visibly enter doom looping, i.e. a non-convergent regime in which the model self-corrects in circles over a fact it cannot recall, exhausting the budget without committing to a final answer. We show this residual failure is reduced but not eliminated by the same edits, and argue it is fundamentally a knowledge-precision problem rather than a removable circuit; weight surgery can delete a loop, but it cannot supply a missing fact. Our results are both a feasibility demonstration, that is, evidence that a concrete generation pathology can be localized to a few parameters and edited out, and a delineation of where that approach stops.

Precision beta decay experiments serve as powerful probes of physics beyond the Standard Model, enabling stringent tests of fundamental symmetries of nature. In particular, these experiments primarily focus on precise determinations of the Cabibbo-Kobayashi-Maskawa matrix element Vud and the search for exotic weak currents, both of which depend critically on theoretical calculations of radiative, recoil-order, and isospin-breaking corrections with quantified uncertainties. In recent years, ab initio nuclear many-body methods--grounded in realistic nucleon-nucleon interactions and systematically improvable approximations--have advanced considerably in their ability to compute these higher-order corrections for various nuclei. This review provides a comprehensive overview of state-of-the-art ab initio calculations of beta-decay corrections, encompassing both radiative corrections and recoil-order terms, and examines their significance for precision tests of the Standard Model. We discuss the theoretical formalisms employed, including the integration of effective field theory frameworks with many-body approaches. Particular attention is given to recent results for superallowed Fermi decays (e.g., 10C -> 10B and 14O -> 14C) and allowed Gamow-Teller transitions (e.g., 6He -> 6Li, 8Li -> 8Be, 8B -> 8Be), where ab initio calculations have achieved unprecedented precision. We also highlight emerging calculations for unique forbidden decays, which offer complementary sensitivity to BSM physics. Finally, we outline future directions aimed at extending the reach of ab initio calculations to heavier nuclei and additional decay modes, thereby strengthening the synergy between theory and experiment in the ongoing search for new physics.

Starting from the Mellin-Barnes integral representation of a Feynman integral depending on set of kinematic variables z_i, we derive a system of partial differential equations w.r.t.\ new variables x_j, which parameterize the differentiable constraints z_i=y_i(x_j). In our algorithm, the powers of propagators can be considered as arbitrary parameters. Our algorithm can also be used for the reduction of multiple hypergeometric sums to sums of lower dimension, finding special values and reduction equations of hypergeometric functions in a singular locus of continuous variables, or finding systems of partial differential equations for master integrals with arbitrary powers of propagators. As an illustration, we produce a differential equation of fourth order in one variable for the one-loop two-point Feynman diagram with two different masses and arbitrary propagator powers.

Large Language Models (LLMs) have made significant strides in mathematical reasoning, underscoring the need for a comprehensive and fair evaluation of their capabilities. However, existing benchmarks often fall short, either lacking extensive coverage of undergraduate-level mathematical problems or probably suffering from test-set contamination. To address these issues, we introduce UGMathBench, a diverse and dynamic benchmark specifically designed for evaluating undergraduate-level mathematical reasoning with LLMs. UGMathBench comprises 5,062 problems across 16 subjects and 111 topics, featuring 10 distinct answer types. Each problem includes three randomized versions, with additional versions planned for release as leading open-source LLMs become saturated in UGMathBench. Furthermore, we propose two key metrics: effective accuracy (EAcc), which measures the percentage of correctly solved problems across all three versions, and reasoning gap (Delta), which assesses reasoning robustness by calculating the difference between the average accuracy across all versions and EAcc. Our extensive evaluation of 23 leading LLMs reveals that the highest EAcc achieved is 56.3\% by OpenAI-o1-mini, with large Delta values observed across different models. This highlights the need for future research aimed at developing "large reasoning models" with high EAcc and Delta = 0. We anticipate that the release of UGMathBench, along with its detailed evaluation codes, will serve as a valuable resource to advance the development of LLMs in solving mathematical problems.

Large Language Model (LLM)-based web agents demonstrate strong performance on knowledge-intensive tasks but are hindered by context window limitations in paradigms like ReAct. Complex queries involving multiple entities, intertwined relationships, and high uncertainty demand extensive search cycles that rapidly exhaust context budgets before reaching complete solutions. To overcome this challenge, we introduce ReSum, a novel paradigm that enables indefinite exploration through periodic context summarization. ReSum converts growing interaction histories into compact reasoning states, maintaining awareness of prior discoveries while bypassing context constraints. For paradigm adaptation, we propose ReSum-GRPO, integrating GRPO with segmented trajectory training and advantage broadcasting to familiarize agents with summary-conditioned reasoning. Extensive experiments on web agents of varying scales across three benchmarks demonstrate that ReSum delivers an average absolute improvement of 4.5\% over ReAct, with further gains of up to 8.2\% following ReSum-GRPO training. Notably, with only 1K training samples, our WebResummer-30B (a ReSum-GRPO-trained version of WebSailor-30B) achieves 33.3\% Pass@1 on BrowseComp-zh and 18.3\% on BrowseComp-en, surpassing existing open-source web agents.

Diffusion large language models (dLLMs) have emerged as a promising alternative to autoregressive models, offering flexible generation orders and strong performance on complex reasoning tasks. However, instruction-tuned dLLMs exhibit a critical vulnerability we term <eos> overflow: as allocated sequence length increases, responses paradoxically become shorter, collapsing into early termination or degenerating into streams of <eos> tokens. Although noticed in practice, this issue has not been systematically analyzed. We trace its root cause to the dual role of <eos> as both termination and padding, which concentrates probability mass on <eos> at later positions and propagates backward to trigger early termination. To address this, we introduce Rainbow Padding, a simple remedy that replaces repeated <eos> placeholders with a repeating cycle of distinct padding tokens, distributing probability mass and breaking <eos> dominance. Experiments show that Rainbow Padding substantially improves length robustness and output quality, with as few as seven padding tokens sufficient to prevent early termination. Moreover, the method integrates efficiently into existing instruction-tuned models: LoRA fine-tuning for a single epoch on minimal data yields significant improvements, making this solution highly practical. The code is publicly available at https://github.com/quasar529/rainbow-padding.

The production of a top-quark pair, the heaviest known elementary particle, in association with a light jet is a key process for studying the properties of the Standard Model of Particle Physics. Due to its significance as a signal process with considerable sensitivity to the top-quark mass and as a background process for new physics searches, it is crucial to predict differential cross sections with high precision. In this article, we present, for the first time, predictions for various kinematical observables at next-to-next-to-leading order in Quantum Chromodynamics. The perturbative behavior is analyzed, and uncertainties arising from missing higher-order contributions are substantially reduced. The necessary two-loop amplitudes have been evaluated in the leading-color approximation, and we provide estimates for the impact of the missing contributions.

Pretraining large language models (LLMs) on high-quality, structured data such as mathematics and code substantially enhances reasoning capabilities. However, existing math-focused datasets built from Common Crawl suffer from degraded quality due to brittle extraction heuristics, lossy HTML-to-text conversion, and the failure to reliably preserve mathematical structure. In this work, we introduce Nemotron-CC-Math, a large-scale, high-quality mathematical corpus constructed from Common Crawl using a novel, domain-agnostic pipeline specifically designed for robust scientific text extraction. Unlike previous efforts, our pipeline recovers math across various formats (e.g., MathJax, KaTeX, MathML) by leveraging layout-aware rendering with lynx and a targeted LLM-based cleaning stage. This approach preserves the structural integrity of equations and code blocks while removing boilerplate, standardizing notation into LaTeX representation, and correcting inconsistencies. We collected a large, high-quality math corpus, namely Nemotron-CC-Math-3+ (133B tokens) and Nemotron-CC-Math-4+ (52B tokens). Notably, Nemotron-CC-Math-4+ not only surpasses all prior open math datasets-including MegaMath, FineMath, and OpenWebMath-but also contains 5.5 times more tokens than FineMath-4+, which was previously the highest-quality math pretraining dataset. When used to pretrain a Nemotron-T 8B model, our corpus yields +4.8 to +12.6 gains on MATH and +4.6 to +14.3 gains on MBPP+ over strong baselines, while also improving general-domain performance on MMLU and MMLU-Stem. We present the first pipeline to reliably extract scientific content--including math--from noisy web-scale data, yielding measurable gains in math, code, and general reasoning, and setting a new state of the art among open math pretraining corpora. To support open-source efforts, we release our code and datasets.

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.

Sparse Autoencoders (SAEs) extract interpretable features from Large Language Models, but standard variants enforce non-negativity, forcing separate latents for diametrically opposed concepts (e.g., "pressure too high" vs. "pressure too low") and wasting dictionary capacity when features are anticorrelated. We propose the Sign-Aware Gated SAE (SA-GSAE): two-sided gated sparsity with signed magnitude and auxiliary supervision. A polarity-sensitive gate selects support on either sign, a signed-magnitude path avoids L1 shrinkage, and an auxiliary reconstruction prevents gate collapse. Bipolar sharing - one latent encoding both signs along a shared direction - is realised via a new Bi-Jump-ReLU activation; parameter accounting shows sign-awareness stays parameter-efficient even when anticorrelated pairs are rare. On real LLM activations across three mid-depth hookpoints on Pythia-1B and SmolLM3-3B (6 cells, 3 seeds), a half-width SA-GSAE at width H strictly Pareto-dominates a full-width Gated SAE at 2H over the entire swept L0 overlap on 3 of 6 cells (both MLP-output hookpoints and resid-mid/Pythia-1B); on the remaining 3 it matches R^2 within 0.025 (max gap -0.008) while cutting dead fraction by 0.35-0.62 absolute. Sweep-geomean dead-fraction reductions are ~100x-500x on MLP-output cells and Pythia-1B resid, ~2x-4x on attention cells and SmolLM3-3B resid. Ablations show the two-sided gate and auxiliary loss are load-bearing (no auxiliary collapses LR to 0.27, 98% dead); tying r_i^+ = r_i^- is indistinguishable (|Delta R^2| = 0.0015), and we recommend this symmetric variant as default. MLP-output gains come from most latents carrying both polarities; on attention, bipolar structure concentrates in a small set of top latents. Full-width SA-GSAE exhibits a reproducible reconstruction collapse at SmolLM3-3B resid that the half-width entirely avoids.

We introduce MAmmoTH, a series of open-source large language models (LLMs) specifically tailored for general math problem-solving. The MAmmoTH models are trained on MathInstruct, our meticulously curated instruction tuning dataset. MathInstruct is compiled from 13 math datasets with intermediate rationales, six of which have rationales newly curated by us. It presents a unique hybrid of chain-of-thought (CoT) and program-of-thought (PoT) rationales, and also ensures extensive coverage of diverse fields in math. The hybrid of CoT and PoT not only unleashes the potential of tool use but also allows different thought processes for different math problems. As a result, the MAmmoTH series substantially outperform existing open-source models on nine mathematical reasoning datasets across all scales with an average accuracy gain between 13% and 29%. Remarkably, our MAmmoTH-7B model reaches 35% on MATH (a competition-level dataset), which exceeds the best open-source 7B model (WizardMath) by 25%, and the MAmmoTH-34B model achieves 46% accuracy on MATH, even surpassing GPT-4's CoT result. Our work underscores the importance of diverse problem coverage and the use of hybrid rationales in developing superior math generalist models.

The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic regression. However, existing approaches are dominated by heuristic algorithms or data-hungry black-box methods, which often demand low-noise settings and lack principled uncertainty quantification. Motivated by interpretable Statistical Artificial Intelligence, we develop a hierarchical Bayesian framework for symbolic regression that represents scientific laws as ensembles of tree-structured symbolic expressions endowed with a regularized tree prior. This coherent probabilistic formulation enables full posterior inference via an efficient Markov chain Monte Carlo algorithm, yielding a balance between predictive accuracy and structural parsimony. To guide symbolic model selection, we develop a marginal posterior-based criterion adhering to the Occam's window principle and further quantify structural fidelity to ground truth through a tailored expression-distance metric. On the theoretical front, we establish near-minimax rate of Bayesian posterior concentration, providing the first rigorous guarantee in context of symbolic regression. Empirical evaluation demonstrates robust performance of our proposed methodology against state-of-the-art competing modules on a simulated example, a suite of canonical Feynman equations, and single-atom catalysis dataset.

Recent advances in Reinforcement Learning with Verified Reward (RLVR) have driven the emergence of more sophisticated cognitive behaviors in large language models (LLMs), thereby enhancing their reasoning capabilities. However, in prior RLVR pipelines, the repeated use of static initial-state sampling drawn exactly from the dataset distribution during each sampling phase produced overly deterministic, low diversity model behavior, which manifested as rapid entropy collapse and hindered sustained performance gains during prolonged training. To address this issue, we introduce CURE (Critical-token-gUided Re concatenation for Entropy-collapse prevention), a two-stage framework that balances exploration and exploitation. Specifically, in the first stage, to deliberately steer the model toward novel yet coherent contexts, we re-generate at high-entropy critical tokens and jointly optimize the original and the branched trajectories. The further comparison with vanilla DAPO shows that the regeneration process achieves a better performance on math reasoning tasks while sustaining a high-level entropy degree for exploration. In the second stage, we continue training with static initial-state sampling by DAPO, intentionally placing the model in a familiar state to gradually strengthen exploitation. Extensive experiments on Qwen-2.5-Math-7B show that, compared to other RLVR methods, CURE achieves a 5% performance gain across six math benchmarks, establishing state-of-the-art performance in both entropy and accuracy. A series of experiments further validate the effectiveness of our approach. Code is available at https://github.com/bytedance/CURE.

Type inference for dynamically typed languages must reconcile four qualitatively different sources of information about a parameter: values assigned inside a definition, explicit declarations, contextual requirements, and structural operations. Existing systems often combine these sources into one constraint set, causing spurious conflicts and requiring redundant annotations. We present Generic Constraint Projection (GCP), a zero-annotation inference framework that stores the four sources in separate monotone slots on a stable definition-time template and checks each call in a fresh projection session. Ordinary calls verify concrete arguments and specialize returns without mutating the template, while partial calls produce residual projected functions. On the success fragment of a finite-height type preorder, we prove monotonicity, local and global convergence, conditional projection-obligation soundness, projection termination, multi-module convergence, and order-independence under fair iteration. For the pure recursion-free core Outline_0, we also prove evaluation definedness, type preservation, runtime receiver retention, and projection-evaluation coherence. GCP uses Outline Equational Matching as an extensible structural compatibility relation and future this to preserve concrete receiver shape across fluent method chains. We instantiate the framework in Outline for typed ontology worlds and in Python for recovery of PEP 484 annotations from unannotated source.

Zero-knowledge proof (ZKP) provers remain costly because multi-scalar multiplication (MSM) and number-theoretic transforms (NTTs) dominate runtime as they need significant computation. AI ASICs such as TPUs provide massive matrix throughput and SotA energy efficiency. We present MORPH, the first framework that reformulates ZKP kernels to match AI-ASIC execution. We introduce Big-T complexity, a hardware-aware complexity model that exposes heterogeneous bottlenecks and layout-transformation costs ignored by Big-O. Guided by this analysis, (1) at arithmetic level, MORPH develops an MXU-centric extended-RNS lazy reduction that converts high-precision modular arithmetic into dense low-precision GEMMs, eliminating all carry chains, and (2) at dataflow level, MORPH constructs a unified-sharding layout-stationary TPU Pippenger MSM and optimized 3/5-step NTT that avoid on-TPU shuffles to minimize costly memory reorganization. Implemented in JAX, MORPH enables TPUv6e8 to achieve up-to 10x higher throughput on NTT and comparable throughput on MSM than GZKP. Our code: https://github.com/EfficientPPML/MORPH.

Using two benchmark models containing extended scalar sectors beyond the Standard Model, we study deep learning techniques to enhance the sensitivity of resonant triple Higgs boson searches in the fully hadronic 6b channel, which suffers from the combinatorial challenge of reconstructing the Higgs bosons correctly from the multiple b-jets. More specifically, we employ the framework of Symmetry Preserving Attention Network (Spa-Net), which takes into account the permutational symmetry when a correct pairing of b-jets is achieved, to tackle both jet pairing and event classification. Significantly improved efficiency is achieved in signal and background discrimination. When comparing with the conventional Dense Neural Networks, Spa-Net results in up to 40\% more stringent limits on resonant production cross-sections. These results highlight the potential of using advanced machine learning techniques to significantly improve the sensitivity of triple Higgs boson searches in the fully hadronic channel.

Tau leptons serve as an important tool for studying the production of Higgs and electroweak bosons, both within and beyond the Standard Model of particle physics. Accurate reconstruction and identification of hadronically decaying tau leptons is a crucial task for current and future high energy physics experiments. Given the advances in jet tagging, we demonstrate how tau lepton reconstruction can be decomposed into tau identification, kinematic reconstruction, and decay mode classification in a multi-task machine learning setup. Based on an electron-positron collision dataset with full detector simulation and reconstruction, we show that common jet tagging architectures can be effectively used for these sub-tasks. We achieve comparable momentum resolutions of 2-3% with all the tested models, while the precision of reconstructing individual decay modes is between 80-95%. We find ParticleTransformer to be the best-performing approach, significantly outperforming the heuristic baseline. This paper also serves as an introduction to a new publicly available Fuτure dataset for the development of tau reconstruction algorithms. This allows to further study the resilience of ML models to domain shifts and the efficient use of foundation models for such tasks.

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.

Mathematical reasoning is an increasingly important indicator of large language model (LLM) capabilities, yet we lack understanding of how LLMs process even simple mathematical tasks. To address this, we reverse engineer how three mid-sized LLMs compute addition. We first discover that numbers are represented in these LLMs as a generalized helix, which is strongly causally implicated for the tasks of addition and subtraction, and is also causally relevant for integer division, multiplication, and modular arithmetic. We then propose that LLMs compute addition by manipulating this generalized helix using the "Clock" algorithm: to solve a+b, the helices for a and b are manipulated to produce the a+b answer helix which is then read out to model logits. We model influential MLP outputs, attention head outputs, and even individual neuron preactivations with these helices and verify our understanding with causal interventions. By demonstrating that LLMs represent numbers on a helix and manipulate this helix to perform addition, we present the first representation-level explanation of an LLM's mathematical capability.

Single-minus tree-level n-gluon scattering amplitudes are reconsidered. Often presumed to vanish, they are shown here to be nonvanishing for certain "half-collinear" configurations existing in Klein space or for complexified momenta. We derive a piecewise-constant closed-form expression for the decay of a single minus-helicity gluon into n-1 plus-helicity gluons as a function of their momenta. This formula nontrivially satisfies multiple consistency conditions including Weinberg's soft theorem.

Automatic program repair seeks to generate correct code from buggy programs, with most approaches searching the correct program in a discrete, symbolic space of source code tokens. This symbolic search is fundamentally limited by its inability to directly reason about program behavior. We introduce Gradient-Based Program Repair (GBPR), a new paradigm that reframes program repair as continuous optimization in a differentiable numerical program space. Our core insight is to compile symbolic programs into differentiable numerical representations, enabling search in the numerical program space directly guided by program behavior. To evaluate GBPR, we present RaspBugs, a new benchmark of 1,466 buggy symbolic RASP programs and their respective numerical representations. Our experiments demonstrate that GBPR can effectively repair buggy symbolic programs by gradient-based optimization in the numerical program space, with convincing repair trajectories. To our knowledge, we are the first to state program repair as continuous optimization in a numerical program space. Our work establishes a new direction for program repair research, bridging two rich worlds: continuous optimization and program behavior.

Recent advancements in Chain-of-Thoughts (CoT) and Program-of-Thoughts (PoT) methods have greatly enhanced language models' mathematical reasoning capabilities, facilitating their integration into instruction tuning datasets with LLMs. However, existing methods for large-scale dataset creation require substantial seed data and high computational costs for data synthesis, posing significant challenges for scalability. We introduce InfinityMATH, a scalable instruction tuning dataset for programmatic mathematical reasoning. The construction pipeline emphasizes decoupling numbers from mathematical problems to synthesize number-independent programs, enabling efficient and flexible scaling while minimizing dependency on specific numerical values. Fine-tuning experiments with open-source language and code models, such as Llama2 and CodeLlama, demonstrate the practical benefits of InfinityMATH. These fine-tuned models, showed significant relative improvements on both in-domain and out-of-domain benchmarks, ranging from 184.7% to 514.3% on average. Additionally, these models exhibited high robustness on the GSM8K+ and MATH+ benchmarks, which are enhanced version of test sets with simply the number variations. InfinityMATH ensures that models are more versatile and effective across a broader range of mathematical problems. The data is available at https://huggingface.co/datasets/flagopen/InfinityMATH.

We propose a mass-dependent MOM scheme to renormalize UV divergence of unpolarized PDFs at one-loop order. This approach which is based on a once subtracted dispersion relation does not need any regulator. The overall counterterms are obtained from the imaginary part of large transverse momentum region in loop integrals. The mass-dependent characteristic of the scheme yields to mass-dependent splitting functions for the DGLAP evolution equations. While the flavor number is fixed at any renormalization scale, the decoupling theorem is automatically imposed by the mass-dependent splitting functions. The required symmetries are also automatically respected by our prescription.

This paper presents the Relational Machine Calculus (RMC): a simple, foundational model of first-order relational programming. The RMC originates from the Functional Machine Calculus (FMC), which generalizes the lambda-calculus and its standard call-by-name stack machine in two directions. One, "locations", introduces multiple stacks, which enable effect operators to be encoded into the abstraction and application constructs. The second, "sequencing", introduces the imperative notions of "skip" and "sequence", similar to kappa-calculus and concatenative programming languages. The key observation of the RMC is that the first-order fragment of the FMC exhibits a latent duality which, given a simple decomposition of the relevant constructors, can be concretely expressed as an involution on syntax. Semantically, this gives rise to a sound and complete calculus for string diagrams of Frobenius monoids. We consider unification as the corresponding symmetric generalization of beta-reduction. By further including standard operators of Kleene algebra, the RMC embeds a range of computational models: the kappa-calculus, logic programming, automata, Interaction Nets, and Petri Nets, among others. These embeddings preserve operational semantics, which for the RMC is again given by a generalization of the standard stack machine for the lambda-calculus. The equational theory of the RMC (which supports reasoning about its operational semantics) is conservative over both the first-order lambda-calculus and Kleene algebra, and can be oriented to give a confluent reduction relation.