Daily Papers

Low-resource speech recognition has been long-suffering from insufficient training data. In this paper, we propose an approach that leverages neighboring languages to improve low-resource scenario performance, founded on the hypothesis that similar linguistic units in neighboring languages exhibit comparable term frequency distributions, which enables us to construct a Huffman tree for performing multilingual hierarchical Softmax decoding. This hierarchical structure enables cross-lingual knowledge sharing among similar tokens, thereby enhancing low-resource training outcomes. Empirical analyses demonstrate that our method is effective in improving the accuracy and efficiency of low-resource speech recognition.

Term frequency is a common method for identifying the importance of a term in a query or document. But it is a weak signal, especially when the frequency distribution is flat, such as in long queries or short documents where the text is of sentence/passage-length. This paper proposes a Deep Contextualized Term Weighting framework that learns to map BERT's contextualized text representations to context-aware term weights for sentences and passages. When applied to passages, DeepCT-Index produces term weights that can be stored in an ordinary inverted index for passage retrieval. When applied to query text, DeepCT-Query generates a weighted bag-of-words query. Both types of term weight can be used directly by typical first-stage retrieval algorithms. This is novel because most deep neural network based ranking models have higher computational costs, and thus are restricted to later-stage rankers. Experiments on four datasets demonstrate that DeepCT's deep contextualized text understanding greatly improves the accuracy of first-stage retrieval algorithms.

Learned sparse representations form an attractive class of contextual embeddings for text retrieval. That is so because they are effective models of relevance and are interpretable by design. Despite their apparent compatibility with inverted indexes, however, retrieval over sparse embeddings remains challenging. That is due to the distributional differences between learned embeddings and term frequency-based lexical models of relevance such as BM25. Recognizing this challenge, a great deal of research has gone into, among other things, designing retrieval algorithms tailored to the properties of learned sparse representations, including approximate retrieval systems. In fact, this task featured prominently in the latest BigANN Challenge at NeurIPS 2023, where approximate algorithms were evaluated on a large benchmark dataset by throughput and recall. In this work, we propose a novel organization of the inverted index that enables fast yet effective approximate retrieval over learned sparse embeddings. Our approach organizes inverted lists into geometrically-cohesive blocks, each equipped with a summary vector. During query processing, we quickly determine if a block must be evaluated using the summaries. As we show experimentally, single-threaded query processing using our method, Seismic, reaches sub-millisecond per-query latency on various sparse embeddings of the MS MARCO dataset while maintaining high recall. Our results indicate that Seismic is one to two orders of magnitude faster than state-of-the-art inverted index-based solutions and further outperforms the winning (graph-based) submissions to the BigANN Challenge by a significant margin.

Word frequency is a key variable in psycholinguistics, useful for modeling human familiarity with words even in the era of large language models (LLMs). Frequency in film subtitles has proved to be a particularly good approximation of everyday language exposure. For many languages, however, film subtitles are not easily available, or are overwhelmingly translated from English. We demonstrate that frequencies extracted from carefully processed YouTube subtitles provide an approximation comparable to, and often better than, the best currently available resources. Moreover, they are available for languages for which a high-quality subtitle or speech corpus does not exist. We use YouTube subtitles to construct frequency norms for five diverse languages, Chinese, English, Indonesian, Japanese, and Spanish, and evaluate their correlation with lexical decision time, word familiarity, and lexical complexity. In addition to being strongly correlated with two psycholinguistic variables, a simple linear regression on the new frequencies achieves a new high score on a lexical complexity prediction task in English and Japanese, surpassing both models trained on film subtitle frequencies and the LLM GPT-4. Our code, the frequency lists, fastText word embeddings, and statistical language models are freely available at https://github.com/naist-nlp/tubelex.

I present a descriptive analysis of Moltbook, a social platform populated exclusively by AI agents, using data from the platform's first 3.5 days (6{,}159 agents; 13{,}875 posts; 115{,}031 comments). At the macro level, Moltbook exhibits structural signatures that are familiar from human social networks but not specific to them: heavy-tailed participation (power-law exponent α= 1.70) and small-world connectivity (average path length =2.91). At the micro level, patterns appear distinctly non-human. Conversations are extremely shallow (mean depth =1.07; 93.5\% of comments receive no replies), reciprocity is low (0.197), and 34.1\% of messages are exact duplicates of viral templates. Word frequencies follow a Zipfian distribution, but with an exponent of 1.70 -- notably steeper than typical English text (approx 1.0), suggesting more formulaic content. Agent discourse is dominated by identity-related language (68.1\% of unique messages) and distinctive phrasings like ``my human'' (9.4\% of messages) that have no parallel in human social media. Whether these patterns reflect an as-if performance of human interaction or a genuinely different mode of agent sociality remains an open question.

This paper proposes a novel framework for digital curation of Web corpora in order to provide robust estimation of their parameters, such as their composition and the lexicon. In recent years language models pre-trained on large corpora emerged as clear winners in numerous NLP tasks, but no proper analysis of the corpora which led to their success has been conducted. The paper presents a procedure for robust frequency estimation, which helps in establishing the core lexicon for a given corpus, as well as a procedure for estimating the corpus composition via unsupervised topic models and via supervised genre classification of Web pages. The results of the digital curation study applied to several Web-derived corpora demonstrate their considerable differences. First, this concerns different frequency bursts which impact the core lexicon obtained from each corpus. Second, this concerns the kinds of texts they contain. For example, OpenWebText contains considerably more topical news and political argumentation in comparison to ukWac or Wikipedia. The tools and the results of analysis have been released.

The word embedding space in neural models is skewed, and correcting this can improve task performance. We point out that most approaches for modeling, correcting, and measuring the symmetry of an embedding space implicitly assume that the word frequencies are uniform; in reality, word frequencies follow a highly non-uniform distribution, known as Zipf's law. Surprisingly, simply performing PCA whitening weighted by the empirical word frequency that follows Zipf's law significantly improves task performance, surpassing established baselines. From a theoretical perspective, both our approach and existing methods can be clearly categorized: word representations are distributed according to an exponential family with either uniform or Zipfian base measures. By adopting the latter approach, we can naturally emphasize informative low-frequency words in terms of their vector norm, which becomes evident from the information-geometric perspective, and in terms of the loss functions for imbalanced classification. Additionally, our theory corroborates that popular natural language processing methods, such as skip-gram negative sampling, WhiteningBERT, and headless language models, work well just because their word embeddings encode the empirical word frequency into the underlying probabilistic model.

Data collected from the real world typically exhibit long-tailed distributions, where frequent classes contain abundant data while rare ones have only a limited number of samples. While existing supervised learning approaches have been proposed to tackle such data imbalance, the requirement of label supervision would limit their applicability to real-world scenarios in which label annotation might not be available. Without the access to class labels nor the associated class frequencies, we propose Frequency-Aware Self-Supervised Learning (FASSL) in this paper. Targeting at learning from unlabeled data with inherent long-tailed distributions, the goal of FASSL is to produce discriminative feature representations for downstream classification tasks. In FASSL, we first learn frequency-aware prototypes, reflecting the associated long-tailed distribution. Particularly focusing on rare-class samples, the relationships between image data and the derived prototypes are further exploited with the introduced self-supervised learning scheme. Experiments on long-tailed image datasets quantitatively and qualitatively verify the effectiveness of our learning scheme.

Masked language models (MLM) do not explicitly define a distribution over language, i.e., they are not language models per se. However, recent work has implicitly treated them as such for the purposes of generation and scoring. This paper studies methods for deriving explicit joint distributions from MLMs, focusing on distributions over two tokens, which makes it possible to calculate exact distributional properties. We find that an approach based on identifying joints whose conditionals are closest to those of the MLM works well and outperforms existing Markov random field-based approaches. We further find that this derived model's conditionals can even occasionally outperform the original MLM's conditionals.

The distribution of subpopulations is an important property hidden within a dataset. Uncovering and analyzing the subpopulation distribution within datasets provides a comprehensive understanding of the datasets, standing as a powerful tool beneficial to various downstream tasks, including Dataset Subpopulation Organization, Subpopulation Shift, and Slice Discovery. Despite its importance, there has been no work that systematically explores the subpopulation distribution of datasets to our knowledge. To address the limitation and solve all the mentioned tasks in a unified way, we introduce a novel concept of subpopulation structures to represent, analyze, and utilize subpopulation distributions within datasets. To characterize the structures in an interpretable manner, we propose the Subpopulation Structure Discovery with Large Language Models (SSD-LLM) framework, which employs world knowledge and instruction-following capabilities of Large Language Models (LLMs) to linguistically analyze informative image captions and summarize the structures. Furthermore, we propose complete workflows to address downstream tasks, named Task-specific Tuning, showcasing the application of the discovered structure to a spectrum of subpopulation-related tasks, including dataset subpopulation organization, subpopulation shift, and slice discovery. Furthermore, we propose complete workflows to address downstream tasks, named Task-specific Tuning, showcasing the application of the discovered structure to a spectrum of subpopulation-related tasks, including dataset subpopulation organization, subpopulation shift, and slice discovery.

While textual frequency has been validated as relevant to human cognition in reading speed, its relatedness to Large Language Models (LLMs) is seldom studied. We propose a novel research direction in terms of textual data frequency, which is an understudied topic, to the best of our knowledge. Our framework is composed of three units. First, this paper proposes Textual Frequency Law (TFL), which indicates that frequent textual data should be preferred for LLMs for both prompting and fine-tuning. Since many LLMs are closed-source in their training data, we propose using online resources to estimate the sentence-level frequency. We then utilize an input paraphraser to paraphrase the input into a more frequent textual expression. Next, we propose Textual Frequency Distillation (TFD) by querying LLMs to conduct story completion by further extending the sentences in the datasets, and the resulting corpora are used to adjust the initial estimation. Finally, we propose Curriculum Textual Frequency Training (CTFT) that fine-tunes LLMs in an increasing order of sentence-level frequency. Experiments are conducted on our curated dataset Textual Frequency Paired Dataset (TFPD) on math reasoning, machine translation, commonsense reasoning and agentic tool calling. Results show the effectiveness of our framework.

Despite the non-autoregressive potential of diffusion language models (dLLMs), existing decoding strategies demonstrate positional bias, failing to fully unlock the potential of arbitrary generation. In this work, we delve into the inherent spectral characteristics of dLLMs and present the first frequency-domain analysis showing that low-frequency components in hidden states primarily encode global structural information and long-range dependencies, while high-frequency components are responsible for characterizing local details. Based on this observation, we propose FourierSampler, which leverages a frequency-domain sliding window mechanism to dynamically guide the model to achieve a "structure-to-detail" generation. FourierSampler outperforms other inference enhancement strategies on LLADA and SDAR, achieving relative improvements of 20.4% on LLaDA1.5-8B and 16.0% on LLaDA-8B-Instruct. It notably surpasses similarly sized autoregressive models like Llama3.1-8B-Instruct.

Frequency analysis is useful for understanding the mechanisms of representation learning in neural networks (NNs). Most research in this area focuses on the learning dynamics of NNs for regression tasks, while little for classification. This study empirically investigates the latter and expands the understanding of frequency shortcuts. First, we perform experiments on synthetic datasets, designed to have a bias in different frequency bands. Our results demonstrate that NNs tend to find simple solutions for classification, and what they learn first during training depends on the most distinctive frequency characteristics, which can be either low- or high-frequencies. Second, we confirm this phenomenon on natural images. We propose a metric to measure class-wise frequency characteristics and a method to identify frequency shortcuts. The results show that frequency shortcuts can be texture-based or shape-based, depending on what best simplifies the objective. Third, we validate the transferability of frequency shortcuts on out-of-distribution (OOD) test sets. Our results suggest that frequency shortcuts can be transferred across datasets and cannot be fully avoided by larger model capacity and data augmentation. We recommend that future research should focus on effective training schemes mitigating frequency shortcut learning.

Modern language models define distributions over strings, but downstream tasks often require different output formats. For instance, a model that generates byte-pair strings does not directly produce word-level predictions, and a DNA model does not directly produce amino-acid sequences. In such cases, a deterministic string-to-string transformation can convert the model's output to the desired form. This is a familiar pattern in probability theory: applying a function f to a random variable Xsim p yields a transformed random variable f(X) with an induced distribution. While such transformations are occasionally used in language modeling, prior work does not treat them as yielding new, fully functional language models. We formalize this perspective and introduce a general framework for language models derived from deterministic string-to-string transformations. We focus on transformations representable as finite-state transducers -- a commonly used state-machine abstraction for efficient string-to-string mappings. We develop algorithms that compose a language model with an FST to *marginalize* over source strings mapping to a given target, propagating probabilities through the transducer without altering model parameters and enabling *conditioning* on transformed outputs. We present an exact algorithm, an efficient approximation, and a theoretical analysis. We conduct experiments in three domains: converting language models from tokens to bytes, from tokens to words, and from DNA to amino acids. These experiments demonstrate inference-time adaptation of pretrained language models to match application-specific output requirements.

We study the relationship between vocabulary size and text length in a corpus of 75 literary works in English, authored by six writers, distinguishing between the contributions of three grammatical classes (or ``tags,'' namely, {\it nouns}, {\it verbs}, and {\it others}), and analyze the progressive appearance of new words of each tag along each individual text. While the power-law relation prescribed by Heaps' law is satisfactorily fulfilled by total vocabulary sizes and text lengths, the appearance of new words in each text is on the whole well described by the average of random shufflings of the text, which does not obey a power law. Deviations from this average, however, are statistically significant and show a systematic trend across the corpus. Specifically, they reveal that the appearance of new words along each text is predominantly retarded with respect to the average of random shufflings. Moreover, different tags are shown to add systematically distinct contributions to this tendency, with {\it verbs} and {\it others} being respectively more and less retarded than the mean trend, and {\it nouns} following instead this overall mean. These statistical systematicities are likely to point to the existence of linguistically relevant information stored in the different variants of Heaps' law, a feature that is still in need of extensive assessment.

Generative recommender systems have recently attracted attention by formulating next-item prediction as an autoregressive sequence generation task. However, most existing methods optimize standard next-token likelihood and implicitly treat all tokens as equally informative, which is misaligned with semantic-ID-based generation. Accordingly, we propose two complementary information-gain-based token-weighting strategies tailored to generative recommendation with semantic IDs. Front-Greater Weighting captures conditional semantic information gain by prioritizing early tokens that most effectively reduce candidate-item uncertainty given their prefixes and encode coarse semantics. Frequency Weighting models marginal information gain under long-tailed item and token distributions, upweighting rare tokens to counteract popularity bias. Beyond individual strategies, we introduce a multi-target learning framework with curriculum learning that jointly optimizes the two token-weighted objectives alongside standard likelihood, enabling stable optimization and adaptive emphasis across training stages. Extensive experiments on benchmark datasets show that our method consistently outperforms strong baselines and existing token-weighting approaches, with improved robustness, strong generalization across different semantic-ID constructions, and substantial gains on both head and tail items. Code is available at https://github.com/CHIUWEINING/Token-Weighted-Multi-Target-Learning-for-Generative-Recommenders-with-Curriculum-Learning.

We propose Word-Frequency-based Image-Text Pair Pruning (WFPP), a novel data pruning method that improves the efficiency of VLMs. Unlike MetaCLIP, our method does not need metadata for pruning, but selects text-image pairs to prune based on the content of the text. Specifically, WFPP prunes text-image pairs containing high-frequency words across the entire training dataset. The effect of WFPP is to reduce the dominance of frequent words. The result a better balanced word-frequency distribution in the dataset, which is known to improve the training of word embedding models. After pre-training on the pruned subset, we fine-tuned the model on the entire dataset for one additional epoch to achieve better performance. Our experiments demonstrate that applying WFPP when training a CLIP model improves performance on a wide range of downstream tasks. WFPP also provides the advantage of speeding up pre-training by using fewer samples. Additionally, we analyze the training data before and after pruning to visualize how WFPP changes the balance of word frequencies. We hope our work encourages researchers to consider the distribution of words in the training data when pre-training VLMs, not limited to CLIP.

Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability distributions. In this paper, we focus on evaluating the probabilistic reasoning capabilities of LMs using idealized and real-world statistical distributions. We perform a systematic evaluation of state-of-the-art LMs on three tasks: estimating percentiles, drawing samples, and calculating probabilities. We evaluate three ways to provide context to LMs 1) anchoring examples from within a distribution or family of distributions, 2) real-world context, 3) summary statistics on which to base a Normal approximation. Models can make inferences about distributions, and can be further aided by the incorporation of real-world context, example shots and simplified assumptions, even if these assumptions are incorrect or misspecified. To conduct this work, we developed a comprehensive benchmark distribution dataset with associated question-answer pairs that we will release publicly.

Periodic signals play an important role in daily lives. Although conventional sequential models have shown remarkable success in various fields, they still come short in modeling periodicity; they either collapse, diverge or ignore details. In this paper, we introduce a novel framework inspired by Fourier series to generate periodic signals. We first decompose the given signals into multiple sines and cosines and then conditionally generate periodic signals with the output components. We have shown our model efficacy on three tasks: reconstruction, imputation and conditional generation. Our model outperforms baselines in all tasks and shows more stable and refined results.

Large Language Models (LLMs) have recently been successfully applied to regression tasks -- such as time series forecasting and tabular prediction -- by leveraging their in-context learning abilities. However, their autoregressive decoding process may be ill-suited to continuous-valued outputs, where obtaining predictive distributions over numerical targets requires repeated sampling, leading to high computational cost and inference time. In this work, we investigate whether distributional properties of LLM predictions can be recovered without explicit autoregressive generation. To this end, we study a set of regression probes trained to predict statistical functionals (e.g., mean, median, quantiles) of the LLM's numerical output distribution directly from its internal representations. Our results suggest that LLM embeddings carry informative signals about summary statistics of their predictive distributions, including the numerical uncertainty. This investigation opens up new questions about how LLMs internally encode uncertainty in numerical tasks, and about the feasibility of lightweight alternatives to sampling-based approaches for uncertainty-aware numerical predictions.

We present the first systematic investigation of Martin's Law - the empirical relationship between word frequency and polysemy - in text generated by neural language models during training. Using DBSCAN clustering of contextualized embeddings as an operationalization of word senses, we analyze four Pythia models (70M-1B parameters) across 30 training checkpoints. Our results reveal a non-monotonic developmental trajectory: Martin's Law emerges around checkpoint 100, reaches peak correlation (r > 0.6) at checkpoint 104, then degrades by checkpoint 105. Smaller models (70M, 160M) experience catastrophic semantic collapse at late checkpoints, while larger models (410M, 1B) show graceful degradation. The frequency-specificity trade-off remains stable (r approx -0.3) across all models. These findings suggest that compliance with linguistic regularities in LLM-generated text is not monotonically increasing with training, but instead follows a balanced trajectory with an optimal semantic window. This work establishes a novel methodology for evaluating emergent linguistic structure in neural language models.

Document indexing is a key component for efficient information retrieval (IR). After preprocessing steps such as stemming and stop-word removal, document indexes usually store term-frequencies (tf). Along with tf (that only reflects the importance of a term in a document), traditional IR models use term discrimination values (TDVs) such as inverse document frequency (idf) to favor discriminative terms during retrieval. In this work, we propose to learn TDVs for document indexing with shallow neural networks that approximate traditional IR ranking functions such as TF-IDF and BM25. Our proposal outperforms, both in terms of nDCG and recall, traditional approaches, even with few positively labelled query-document pairs as learning data. Our learned TDVs, when used to filter out terms of the vocabulary that have zero discrimination value, allow to both significantly lower the memory footprint of the inverted index and speed up the retrieval process (BM25 is up to 3~times faster), without degrading retrieval quality.

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The model is instantiated as a mixture of multi-task GPs with common mean processes. A variational EM algorithm is derived for dealing with the optimisation of the hyper-parameters along with the hyper-posteriors' estimation of latent variables and processes. We establish explicit formulas for integrating the mean processes and the latent clustering variables within a predictive distribution, accounting for uncertainty on both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which enhances the performances when dealing with group-structured data. The model handles irregular grid of observations and offers different hypotheses on the covariance structure for sharing additional information across tasks. The performances on both clustering and prediction tasks are assessed through various simulated scenarios and real datasets. The overall algorithm, called MagmaClust, is publicly available as an R package.

Transformer-based foundation models have emerged as a dominant paradigm in time series analysis, offering unprecedented capabilities in tasks such as forecasting, anomaly detection, classification, trend analysis and many more time series analytical tasks. This survey provides a comprehensive overview of the current state of the art pre-trained foundation models, introducing a novel taxonomy to categorize them across several dimensions. Specifically, we classify models by their architecture design, distinguishing between those leveraging patch-based representations and those operating directly on raw sequences. The taxonomy further includes whether the models provide probabilistic or deterministic predictions, and whether they are designed to work with univariate time series or can handle multivariate time series out of the box. Additionally, the taxonomy encompasses model scale and complexity, highlighting differences between lightweight architectures and large-scale foundation models. A unique aspect of this survey is its categorization by the type of objective function employed during training phase. By synthesizing these perspectives, this survey serves as a resource for researchers and practitioners, providing insights into current trends and identifying promising directions for future research in transformer-based time series modeling.

Plenty of existing work has analyzed the abilities of the transformer architecture by describing its representational capacity with formal models of computation. However, the focus so far has been on analyzing the architecture in terms of language acceptance. We contend that this is an ill-suited problem in the study of language models (LMs), which are definitionally probability distributions over strings. In this paper, we focus on the relationship between transformer LMs and n-gram LMs, a simple and historically relevant class of language models. We show that transformer LMs using the hard or sparse attention mechanisms can exactly represent any n-gram LM, giving us a concrete lower bound on their probabilistic representational capacity. This provides a first step towards understanding the mechanisms that transformer LMs can use to represent probability distributions over strings.

Time series foundation models have demonstrated impressive performance as zero-shot forecasters. However, achieving effectively unified training on time series remains an open challenge. Existing approaches introduce some level of model specialization to account for the highly heterogeneous nature of time series data. For instance, Moirai pursues unified training by employing multiple input/output projection layers, each tailored to handle time series at a specific frequency. Similarly, TimesFM maintains a frequency embedding dictionary for this purpose. We identify two major drawbacks to this human-imposed frequency-level model specialization: (1) Frequency is not a reliable indicator of the underlying patterns in time series. For example, time series with different frequencies can display similar patterns, while those with the same frequency may exhibit varied patterns. (2) Non-stationarity is an inherent property of real-world time series, leading to varied distributions even within a short context window of a single time series. Frequency-level specialization is too coarse-grained to capture this level of diversity. To address these limitations, this paper introduces Moirai-MoE, using a single input/output projection layer while delegating the modeling of diverse time series patterns to the sparse mixture of experts (MoE) within Transformers. With these designs, Moirai-MoE reduces reliance on human-defined heuristics and enables automatic token-level specialization. Extensive experiments on 39 datasets demonstrate the superiority of Moirai-MoE over existing foundation models in both in-distribution and zero-shot scenarios. Furthermore, this study conducts comprehensive model analyses to explore the inner workings of time series MoE foundation models and provides valuable insights for future research.

Large Language Models (LLMs) offer the potential for automatic time series analysis and reporting, which is a critical task across many domains, spanning healthcare, finance, climate, energy, and many more. In this paper, we propose a framework for rigorously evaluating the capabilities of LLMs on time series understanding, encompassing both univariate and multivariate forms. We introduce a comprehensive taxonomy of time series features, a critical framework that delineates various characteristics inherent in time series data. Leveraging this taxonomy, we have systematically designed and synthesized a diverse dataset of time series, embodying the different outlined features. This dataset acts as a solid foundation for assessing the proficiency of LLMs in comprehending time series. Our experiments shed light on the strengths and limitations of state-of-the-art LLMs in time series understanding, revealing which features these models readily comprehend effectively and where they falter. In addition, we uncover the sensitivity of LLMs to factors including the formatting of the data, the position of points queried within a series and the overall time series length.

A sizeable fraction of gamma-ray burst (GRB) light curves (LCs) features a sequence of peaks, which holds information on the unknown way energy is dissipated into gamma-rays over time. Traditional searches for periodic signals in GRB LCs turned out to be inconclusive, partly because they are challenging as a consequence of the short-lived, coloured-noise, and non-stationary nature of the LCs themselves. Yet, recent claims have revived the issue. We searched for periodic components in GRB LCs through a new approach to GRBs, that avoids most of the issues faced by traditional techniques. We identified peaks through a well tested algorithm and selected GRBs with at least 10 peaks out of 5 GRB catalogues (Swift/BAT, CGRO/BATSE, Fermi/GBM, Insight-HXMT, BeppoSAX/GRBM). Each GRB was simply treated as a discrete point process, whose realisation coincides with the sequence of peak times. We searched for possible periodic recurrences based on the multinomial distribution, after accounting for the clustering of peaks due to the non-stationarity of the GRB signals. The best candidate has a p-value of 3e-4 that there is no periodic recurrence. However, accounting for the multiple trials of 555 searched GRBs, its statistical significance is demoted to 17%. The overall distribution of the p-values obtained for all GRBs is compatible with a uniform distribution in [0,1]. We found no robust evidence for multi-peaked GRBs with periodic recurrences. We can exclude that a sizeable fraction (>~ 0.75) of peaks of each GRB with at least 10 peaks are periodic. While our result does not necessarily clash with claimed periodicities based on Fourier techniques, it constrains the putative recurrent behaviour, which would not manifest itself through the sequence of peaks, but, evidently, in a more elusive way.

Accurate and efficient long-term multivariate time series forecasting requires capturing recurring temporal structure while keeping inference cheap across many variables and horizons. Frequency-space models represent long-range and periodic variation compactly, but they typically process the real and imaginary spectral components as weakly coupled streams and treat periodic cues as ordinary input features, even when such cues are unreliable. This paper proposes FRWKV-Plus, a lightweight periodic-aware frequency-space forecasting model built on the efficient FRWKV backbone. FRWKV-Plus introduces a cross-branch spectral gate that reweights each spectral branch using a summary of its sibling branch, and a trust-gated residual correction that converts compact within-period context into a bounded, sign-flexible adjustment of these gates under a learned, data-dependent trust score. By construction, the correction is identity-preserving at initialization and strictly bounded, so periodic evidence can refine but never dominate or invert the base interaction. On seven standard benchmarks, FRWKV-Plus is consistently competitive with strong linear, frequency-domain, recurrent-style, and Transformer-based forecasters while preserving the lightweight profile of the backbone. Controlled three-seed ablations show that each component contributes, that the benefit is modest on strongly periodic data and pronounced on the harder Exchange and ILI datasets, and that the within-period context is the most influential single component. The implementation is publicly available at https://github.com/yangqingyuan-byte/FRWKV-plus.

Semantic word embeddings represent the meaning of a word via a vector, and are created by diverse methods. Many use nonlinear operations on co-occurrence statistics, and have hand-tuned hyperparameters and reweighting methods. This paper proposes a new generative model, a dynamic version of the log-linear topic model of~mnih2007three. The methodological novelty is to use the prior to compute closed form expressions for word statistics. This provides a theoretical justification for nonlinear models like PMI, word2vec, and GloVe, as well as some hyperparameter choices. It also helps explain why low-dimensional semantic embeddings contain linear algebraic structure that allows solution of word analogies, as shown by~mikolov2013efficient and many subsequent papers. Experimental support is provided for the generative model assumptions, the most important of which is that latent word vectors are fairly uniformly dispersed in space.

Time-series forecasting in real-world applications such as finance and energy often faces challenges due to limited training data and complex, noisy temporal dynamics. Existing deep forecasting models typically supervise predictions using full-length temporal windows, which include substantial high-frequency noise and obscure long-term trends. Moreover, auxiliary variables containing rich domain-specific information are often underutilized, especially in few-shot settings. To address these challenges, we propose LoFT-LLM, a frequency-aware forecasting pipeline that integrates low-frequency learning with semantic calibration via a large language model (LLM). Firstly, a Patch Low-Frequency forecasting Module (PLFM) extracts stable low-frequency trends from localized spectral patches. Secondly, a residual learner then models high-frequency variations. Finally, a fine-tuned LLM refines the predictions by incorporating auxiliary context and domain knowledge through structured natural language prompts. Extensive experiments on financial and energy datasets demonstrate that LoFT-LLM significantly outperforms strong baselines under both full-data and few-shot regimes, delivering superior accuracy, robustness, and interpretability.

As large language models (LLMs) are pretrained on massive web corpora, careful selection of data becomes essential to ensure effective and efficient learning. While perplexity (PPL)-based filtering has shown strong performance, it suffers from drawbacks: substantial time costs and inherent unreliability of the model when handling noisy or out-of-distribution samples. In this work, we propose a simple yet powerful alternative: a prior-based data filtering method that estimates token priors using corpus-level term frequency statistics, inspired by linguistic insights on word roles and lexical density. Our approach filters documents based on the mean and standard deviation of token priors, serving as a fast proxy to PPL while requiring no model inference. Despite its simplicity, the prior-based filter achieves the highest average performance across 20 downstream benchmarks, while reducing time cost by over 1000x compared to PPL-based filtering. We further demonstrate its applicability to symbolic languages such as code and math, and its dynamic adaptability to multilingual corpora without supervision

Rapid progress in the capabilities of machine learning approaches in natural language processing has culminated in the rise of large language models over the last two years. Recent works have shown unprecedented adoption of these for academic writing, especially in some fields, but their pervasiveness in astronomy has not been studied sufficiently. To remedy this, we extract words that ChatGPT uses more often than humans when generating academic text and search a total of 1 million articles for them. This way, we assess the frequency of word occurrence in published works in astronomy tracked by the NASA Astrophysics Data System since 2000. We then perform a statistical analysis of the occurrences. We identify a list of words favoured by ChatGPT and find a statistically significant increase for these words against a control group in 2024, which matches the trend in other disciplines. These results suggest a widespread adoption of these models in the writing of astronomy papers. We encourage organisations, publishers, and researchers to work together to identify ethical and pragmatic guidelines to maximise the benefits of these systems while maintaining scientific rigour.

Despite being trained specifically to follow user instructions, today's instructiontuned language models perform poorly when instructed to produce random outputs. For example, when prompted to pick a number uniformly between one and ten Llama-2-13B-chat disproportionately favors the number five, and when tasked with picking a first name at random, Mistral-7B-Instruct chooses Avery 40 times more often than we would expect based on the U.S. population. When these language models are used for real-world tasks where diversity of outputs is crucial, such as language model assisted dataset construction, their inability to produce diffuse distributions over valid choices is a major hurdle. In this work, we propose a fine-tuning method that encourages language models to output distributions that are diffuse over valid outcomes. The methods we introduce generalize across a variety of tasks and distributions and make large language models practical for synthetic dataset generation with little human intervention.

Intermittent demand forecasting poses unique challenges due to sparse observations, cold-start items, and obsolescence. Classical models such as Croston, SBA, and the Teunter-Syntetos-Babai (TSB) method provide simple heuristics but lack a principled generative foundation. Deep learning models address these limitations but often require large datasets and sacrifice interpretability. We introduce TSB-HB, a hierarchical Bayesian extension of TSB. Demand occurrence is modeled with a Beta-Binomial distribution, while nonzero demand sizes follow a Log-Normal distribution. Crucially, hierarchical priors enable partial pooling across items, stabilizing estimates for sparse or cold-start series while preserving heterogeneity. This framework yields a fully generative and interpretable model that generalizes classical exponential smoothing. On the UCI Online Retail dataset, TSB-HB achieves lower RMSE and RMSSE than Croston, SBA, TSB, ADIDA, IMAPA, ARIMA and Theta, and on a subset of the M5 dataset it outperforms all classical baselines we evaluate. The model provides calibrated probabilistic forecasts and improved accuracy on intermittent and lumpy items by combining a generative formulation with hierarchical shrinkage, while remaining interpretable and scalable.

In the real world, the frequency of occurrence of objects is naturally skewed forming long-tail class distributions, which results in poor performance on the statistically rare classes. A promising solution is to mine tail-class examples to balance the training dataset. However, mining tail-class examples is a very challenging task. For instance, most of the otherwise successful uncertainty-based mining approaches struggle due to distortion of class probabilities resulting from skewness in data. In this work, we propose an effective, yet simple, approach to overcome these challenges. Our framework enhances the subdued tail-class activations and, thereafter, uses a one-class data-centric approach to effectively identify tail-class examples. We carry out an exhaustive evaluation of our framework on three datasets spanning over two computer vision tasks. Substantial improvements in the minority-class mining and fine-tuned model's performance strongly corroborate the value of our proposed solution.

Speech processing algorithms often rely on statistical knowledge of the underlying process. Despite many years of research, however, the debate on the most appropriate statistical model for speech still continues. Speech is commonly modeled as a wide-sense stationary (WSS) process. However, the use of the WSS model for spectrally correlated processes is fundamentally wrong, as WSS implies spectral uncorrelation. In this paper, we demonstrate that voiced speech can be more accurately represented as a cyclostationary (CS) process. By employing the CS rather than the WSS model for processes that are inherently correlated across frequency, it is possible to improve the estimation of cross-power spectral densities (PSDs), source separation, and beamforming. We illustrate how the correlation between harmonic frequencies of CS processes can enhance system identification, and validate our findings using both simulated and real speech data.

This paper studies Kernel density estimation for a high-dimensional distribution rho(x). Traditional approaches have focused on the limit of large number of data points n and fixed dimension d. We analyze instead the regime where both the number n of data points y_i and their dimensionality d grow with a fixed ratio alpha=(log n)/d. Our study reveals three distinct statistical regimes for the kernel-based estimate of the density hat rho_h^{D}(x)=1{n h^d}sum_{i=1}^n Kleft(x-y_i{h}right), depending on the bandwidth h: a classical regime for large bandwidth where the Central Limit Theorem (CLT) holds, which is akin to the one found in traditional approaches. Below a certain value of the bandwidth, h_{CLT}(alpha), we find that the CLT breaks down. The statistics of hat rho_h^{D}(x) for a fixed x drawn from rho(x) is given by a heavy-tailed distribution (an alpha-stable distribution). In particular below a value h_G(alpha), we find that hat rho_h^{D}(x) is governed by extreme value statistics: only a few points in the database matter and give the dominant contribution to the density estimator. We provide a detailed analysis for high-dimensional multivariate Gaussian data. We show that the optimal bandwidth threshold based on Kullback-Leibler divergence lies in the new statistical regime identified in this paper. Our findings reveal limitations of classical approaches, show the relevance of these new statistical regimes, and offer new insights for Kernel density estimation in high-dimensional settings.

This paper introduces the multi-freq-ldpy Python package for multiple frequency estimation under Local Differential Privacy (LDP) guarantees. LDP is a gold standard for achieving local privacy with several real-world implementations by big tech companies such as Google, Apple, and Microsoft. The primary application of LDP is frequency (or histogram) estimation, in which the aggregator estimates the number of times each value has been reported. The presented package provides an easy-to-use and fast implementation of state-of-the-art solutions and LDP protocols for frequency estimation of: single attribute (i.e., the building blocks), multiple attributes (i.e., multidimensional data), multiple collections (i.e., longitudinal data), and both multiple attributes/collections. Multi-freq-ldpy is built on the well-established Numpy package -- a de facto standard for scientific computing in Python -- and the Numba package for fast execution. These features are described and illustrated in this paper with four worked examples. This package is open-source and publicly available under an MIT license via GitHub (https://github.com/hharcolezi/multi-freq-ldpy) and can be installed via PyPI (https://pypi.org/project/multi-freq-ldpy/).

We study the problem of predicting numeric labels that are constrained to the integers or to a subrange of the integers. For example, the number of up-votes on social media posts, or the number of bicycles available at a public rental station. While it is possible to model these as continuous values, and to apply traditional regression, this approach changes the underlying distribution on the labels from discrete to continuous. Discrete distributions have certain benefits, which leads us to the question whether such integer labels can be modeled directly by a discrete distribution, whose parameters are predicted from the features of a given instance. Moreover, we focus on the use case of output distributions of neural networks, which adds the requirement that the parameters of the distribution be continuous so that backpropagation and gradient descent may be used to learn the weights of the network. We investigate several options for such distributions, some existing and some novel, and test them on a range of tasks, including tabular learning, sequential prediction and image generation. We find that overall the best performance comes from two distributions: Bitwise, which represents the target integer in bits and places a Bernoulli distribution on each, and a discrete analogue of the Laplace distribution, which uses a distribution with exponentially decaying tails around a continuous mean.

We propose to extract meaning representations from autoregressive language models by considering the distribution of all possible trajectories extending an input text. This strategy is prompt-free, does not require fine-tuning, and is applicable to any pre-trained autoregressive model. Moreover, unlike vector-based representations, distribution-based representations can also model asymmetric relations (e.g., direction of logical entailment, hypernym/hyponym relations) by using algebraic operations between likelihood functions. These ideas are grounded in distributional perspectives on semantics and are connected to standard constructions in automata theory, but to our knowledge they have not been applied to modern language models. We empirically show that the representations obtained from large models align well with human annotations, outperform other zero-shot and prompt-free methods on semantic similarity tasks, and can be used to solve more complex entailment and containment tasks that standard embeddings cannot handle. Finally, we extend our method to represent data from different modalities (e.g., image and text) using multimodal autoregressive models. Our code is available at: https://github.com/tianyu139/meaning-as-trajectories

Formal and distributional semantic models offer complementary benefits in modeling meaning. The categorical compositional distributional (DisCoCat) model of meaning of Coecke et al. (arXiv:1003.4394v1 [cs.CL]) combines aspected of both to provide a general framework in which meanings of words, obtained distributionally, are composed using methods from the logical setting to form sentence meaning. Concrete consequences of this general abstract setting and applications to empirical data are under active study (Grefenstette et al., arxiv:1101.0309; Grefenstette and Sadrzadeh, arXiv:1106.4058v1 [cs.CL]). . In this paper, we extend this study by examining transitive verbs, represented as matrices in a DisCoCat. We discuss three ways of constructing such matrices, and evaluate each method in a disambiguation task developed by Grefenstette and Sadrzadeh (arXiv:1106.4058v1 [cs.CL]).

We present FineFreq, a large-scale multilingual character frequency dataset derived from the FineWeb and FineWeb2 corpora, covering over 1900 languages and spanning 2013-2025. The dataset contains frequency counts for 96 trillion characters processed from 57 TB of compressed text. For each language, FineFreq provides per-character statistics with aggregate and year-level frequencies, allowing fine-grained temporal analysis. The dataset preserves naturally occurring multilingual features such as cross-script borrowings, emoji, and acronyms without applying artificial filtering. Each character entry includes Unicode metadata (category, script, block), enabling domain-specific or other downstream filtering and analysis. The full dataset is released in both CSV and Parquet formats, with associated metadata, available on GitHub and HuggingFace. https://github.com/Bin-2/FineFreq

Generating diverse responses from large language models (LLMs) is crucial for applications such as planning/search and synthetic data generation, where diversity provides distinct answers across generations. Prior approaches rely on increasing temperature to increase diversity. However, contrary to popular belief, we show not only does this approach produce lower quality individual generations as temperature increases, but it depends on model's next-token probabilities being similar to the true distribution of answers. We propose , an alternative approach that uses the language model itself to partition the space into strata. At inference, a random stratum is selected and a sample drawn from within the strata. To measure diversity, we introduce CoverageQA, a dataset of underspecified questions with multiple equally plausible answers, and assess diversity by measuring KL Divergence between the output distribution and uniform distribution over valid ground truth answers. As computing probability per response/solution for proprietary models is infeasible, we measure recall on ground truth solutions. Our evaluation show using SimpleStrat achieves higher recall by 0.05 compared to GPT-4o and 0.36 average reduction in KL Divergence compared to Llama 3.

Molecules are frequently represented as graphs, but the underlying 3D molecular geometry (the locations of the atoms) ultimately determines most molecular properties. However, most molecules are not static and at room temperature adopt a wide variety of geometries or conformations. The resulting distribution on geometries p(x) is known as the Boltzmann distribution, and many molecular properties are expectations computed under this distribution. Generating accurate samples from the Boltzmann distribution is therefore essential for computing these expectations accurately. Traditional sampling-based methods are computationally expensive, and most recent machine learning-based methods have focused on identifying modes in this distribution rather than generating true samples. Generating such samples requires capturing conformational variability, and it has been widely recognized that the majority of conformational variability in molecules arises from rotatable bonds. In this work, we present VonMisesNet, a new graph neural network that captures conformational variability via a variational approximation of rotatable bond torsion angles as a mixture of von Mises distributions. We demonstrate that VonMisesNet can generate conformations for arbitrary molecules in a way that is both physically accurate with respect to the Boltzmann distribution and orders of magnitude faster than existing sampling methods.

In this research, we aim to compare the performance of different classical machine learning models and neural networks in identifying the frequency of occurrence of each digit in a given number. It has various applications in machine learning and computer vision, e.g. for obtaining the frequency of a target object in a visual scene. We considered this problem as a hybrid of classification and regression tasks. We carefully create our own datasets to observe systematic differences between different methods. We evaluate each of the methods using different metrics across multiple datasets.The metrics of performance used were the root mean squared error and mean absolute error for regression evaluation, and accuracy for classification performance evaluation. We observe that decision trees and random forests overfit to the dataset, due to their inherent bias, and are not able to generalize well. We also observe that the neural networks significantly outperform the classical machine learning models in terms of both the regression and classification metrics for both the 6-digit and 10-digit number datasets. Dataset and code are available on github.

Recent studies indicate that NLU models are prone to rely on shortcut features for prediction, without achieving true language understanding. As a result, these models fail to generalize to real-world out-of-distribution data. In this work, we show that the words in the NLU training set can be modeled as a long-tailed distribution. There are two findings: 1) NLU models have strong preference for features located at the head of the long-tailed distribution, and 2) Shortcut features are picked up during very early few iterations of the model training. These two observations are further employed to formulate a measurement which can quantify the shortcut degree of each training sample. Based on this shortcut measurement, we propose a shortcut mitigation framework LTGR, to suppress the model from making overconfident predictions for samples with large shortcut degree. Experimental results on three NLU benchmarks demonstrate that our long-tailed distribution explanation accurately reflects the shortcut learning behavior of NLU models. Experimental analysis further indicates that LTGR can improve the generalization accuracy on OOD data, while preserving the accuracy on in-distribution data.

Large Language Models (LLMs) are increasingly being used to simulate human-like decision making in agent-based financial market models (ABMs). As models become more powerful and accessible, researchers can now incorporate individual LLM decisions into ABM environments. However, integration may introduce inherent biases that need careful evaluation. In this paper we test three state-of-the-art GPT models for bias using two model sampling approaches: one-shot and few-shot API queries. We observe significant variations in distributions of outputs between specific models, and model sub versions, with GPT-4o-Mini-2024-07-18 showing notably better performance (32-43% yes responses) compared to GPT-4-0125-preview's extreme bias (98-99% yes responses). We show that sampling methods and model sub-versions significantly impact results: repeated independent API calls produce different distributions compared to batch sampling within a single call. While no current GPT model can simultaneously achieve a uniform distribution and Markovian properties in one-shot testing, few-shot sampling can approach uniform distributions under certain conditions. We explore the Temperature parameter, providing a definition and comparative results. We further compare our results to true random binary series and test specifically for the common human bias of Negative Recency - finding LLMs have a mixed ability to 'beat' humans in this one regard. These findings emphasise the critical importance of careful LLM integration into ABMs for financial markets and more broadly.

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.

Recently, information retrieval has seen the emergence of dense retrievers, using neural networks, as an alternative to classical sparse methods based on term-frequency. These models have obtained state-of-the-art results on datasets and tasks where large training sets are available. However, they do not transfer well to new applications with no training data, and are outperformed by unsupervised term-frequency methods such as BM25. In this work, we explore the limits of contrastive learning as a way to train unsupervised dense retrievers and show that it leads to strong performance in various retrieval settings. On the BEIR benchmark our unsupervised model outperforms BM25 on 11 out of 15 datasets for the Recall@100. When used as pre-training before fine-tuning, either on a few thousands in-domain examples or on the large MS~MARCO dataset, our contrastive model leads to improvements on the BEIR benchmark. Finally, we evaluate our approach for multi-lingual retrieval, where training data is even scarcer than for English, and show that our approach leads to strong unsupervised performance. Our model also exhibits strong cross-lingual transfer when fine-tuned on supervised English data only and evaluated on low resources language such as Swahili. We show that our unsupervised models can perform cross-lingual retrieval between different scripts, such as retrieving English documents from Arabic queries, which would not be possible with term matching methods.

Language models (LMs) are increasingly used as simulacra for people, yet their ability to match the distribution of views of a specific demographic group and be distributionally aligned remains uncertain. This notion of distributional alignment is complex, as there is significant variation in the types of attributes that are simulated. Prior works have underexplored the role of three critical variables -- the question domain, steering method, and distribution expression method -- which motivates our contribution of a benchmark explicitly addressing these dimensions. We construct a dataset expanding beyond political values, create human baselines for this task, and evaluate the extent to which an LM can align with a particular group's opinion distribution to inform design choices of such simulation systems. Our analysis reveals open problems regarding if, and how, LMs can be used to simulate humans, and that LLMs can more accurately describe the opinion distribution than simulate such distributions.

Text-to-image (T2I) models are remarkable at generating realistic images based on textual descriptions. However, textual prompts are inherently underspecified: they do not specify all possible attributes of the required image. This raises two key questions: Do T2I models generate diverse outputs on underspecified prompts? How can we automatically measure diversity? We propose GRADE: Granular Attribute Diversity Evaluation, an automatic method for quantifying sample diversity. GRADE leverages the world knowledge embedded in large language models and visual question-answering systems to identify relevant concept-specific axes of diversity (e.g., ``shape'' and ``color'' for the concept ``cookie''). It then estimates frequency distributions of concepts and their attributes and quantifies diversity using (normalized) entropy. GRADE achieves over 90% human agreement while exhibiting weak correlation to commonly used diversity metrics. We use GRADE to measure the overall diversity of 12 T2I models using 400 concept-attribute pairs, revealing that all models display limited variation. Further, we find that these models often exhibit default behaviors, a phenomenon where the model consistently generates concepts with the same attributes (e.g., 98% of the cookies are round). Finally, we demonstrate that a key reason for low diversity is due to underspecified captions in training data. Our work proposes a modern, semantically-driven approach to measure sample diversity and highlights the stunning homogeneity in outputs by T2I models.

Understanding what kinds of factual knowledge large language models (LLMs) memorize is essential for evaluating their reliability and limitations. Entity-based QA is a common framework for analyzing non-verbatim memorization, but typical evaluations query each entity using a single canonical surface form, making it difficult to disentangle fact memorization from access through a particular name. We introduce RedirectQA, an entity-based QA dataset that uses Wikipedia redirect information to associate Wikidata factual triples with categorized surface forms for each entity, including alternative names, abbreviations, spelling variants, and common erroneous forms. Across 13 LLMs, we examine surface-conditioned factual memorization and find that prediction outcomes often change when only the entity surface form changes. This inconsistency is category-dependent: models are more robust to minor orthographic variations than to larger lexical variations such as aliases and abbreviations. Frequency analyses further suggest that both entity- and surface-level frequencies are associated with accuracy, and that entity frequency often contributes beyond surface frequency. Overall, factual memorization appears neither purely surface-specific nor fully surface-invariant, highlighting the importance of surface-form diversity in evaluating non-verbatim memorization.

In recent years, diffusion based methods have emerged as a powerful paradigm for generative modeling. Although discrete diffusion for natural language processing has been explored to a lesser extent, it shows promise for tasks requiring iterative denoising of token based data. In standard approaches to text generation, transformers dominate, but their reliance on self attention often incurs high computational costs. This paper introduces a fully diffusion driven discrete text generation model built without any transformer or large convolution modules. Instead, the model integrates structured state space dynamics in the time domain with a novel Complex Fourier Multi Layer Perceptron module that operates in the frequency domain. The forward noising process randomly samples the vocabulary to replace tokens with a controlled probability, while the learned reverse model systematically reverts corrupted sequences toward their original states. By composing local state space updates with global Fourier based mixing, the approach effectively captures both short and long range dependencies.

This paper introduces a continuous-time stochastic dynamical framework for understanding how large language models (LLMs) may self-amplify latent biases or toxicity through their own chain-of-thought reasoning. The model posits an instantaneous "severity" variable x(t) in [0,1] evolving under a stochastic differential equation (SDE) with a drift term μ(x) and diffusion σ(x). Crucially, such a process can be consistently analyzed via the Fokker--Planck approach if each incremental step behaves nearly Markovian in severity space. The analysis investigates critical phenomena, showing that certain parameter regimes create phase transitions from subcritical (self-correcting) to supercritical (runaway severity). The paper derives stationary distributions, first-passage times to harmful thresholds, and scaling laws near critical points. Finally, it highlights implications for agents and extended LLM reasoning models: in principle, these equations might serve as a basis for formal verification of whether a model remains stable or propagates bias over repeated inferences.

We develop an econometric framework integrating heavy-tailed Student's t distributions with behavioral probability weighting while preserving infinite divisibility. Using 432{,}752 observations across 86 assets (2004--2024), we demonstrate Student's t specifications outperform Gaussian models in 88.4\% of cases. Bounded probability-weighting transformations preserve mathematical properties required for dynamic pricing. Gaussian models underestimate 99\% Value-at-Risk by 19.7\% versus 3.2\% for our specification. Joint estimation procedures identify tail and behavioral parameters with established asymptotic properties. Results provide robust inference for asset-pricing applications where heavy tails and behavioral distortions coexist.

Arbitrary style transfer (AST) and domain generalization (DG) are important yet challenging visual learning tasks, which can be cast as a feature distribution matching problem. With the assumption of Gaussian feature distribution, conventional feature distribution matching methods usually match the mean and standard deviation of features. However, the feature distributions of real-world data are usually much more complicated than Gaussian, which cannot be accurately matched by using only the first-order and second-order statistics, while it is computationally prohibitive to use high-order statistics for distribution matching. In this work, we, for the first time to our best knowledge, propose to perform Exact Feature Distribution Matching (EFDM) by exactly matching the empirical Cumulative Distribution Functions (eCDFs) of image features, which could be implemented by applying the Exact Histogram Matching (EHM) in the image feature space. Particularly, a fast EHM algorithm, named Sort-Matching, is employed to perform EFDM in a plug-and-play manner with minimal cost. The effectiveness of our proposed EFDM method is verified on a variety of AST and DG tasks, demonstrating new state-of-the-art results. Codes are available at https://github.com/YBZh/EFDM.

Speculative sampling has emerged as an important technique for accelerating the auto-regressive generation process of large language models (LLMs) by utilizing a draft-then-verify mechanism to produce multiple tokens per forward pass. While state-of-the-art speculative sampling methods use only a single layer and a language modeling (LM) head as the draft model to achieve impressive layer compression, their efficiency gains are substantially reduced for large-vocabulary LLMs, such as Llama-3-8B with a vocabulary of 128k tokens. To address this, we present FR-Spec, a frequency-ranked speculative sampling framework that optimizes draft candidate selection through vocabulary space compression. By constraining the draft search to a frequency-prioritized token subset, our method reduces LM Head computation overhead by 75% while ensuring the equivalence of the final output distribution. Experiments across multiple datasets demonstrate an average of 1.12times speedup over the state-of-the-art speculative sampling method EAGLE-2.

This paper introduces a structural equation formulation that gives rise to a new family of quasi-periodic Gaussian processes, useful to process a broad class of natural and physiological signals. The proposed formulation simplifies generation and forecasting, and provides hyperparameter estimates, which we exploit in a convergent and consistent iterative estimation algorithm. A bootstrap approach for standard error estimation and confidence intervals is also provided. We demonstrate the computational and scaling benefits of the proposed approach on a broad class of problems, including water level tidal analysis, CO_{2} emission data, and sunspot numbers data. By leveraging the structural equations, our method reduces the cost of likelihood evaluations and predictions from O(k^2 p^2) to O(p^2), significantly improving scalability.

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.

We study the problem of estimating the distribution of the return of a policy using an offline dataset that is not generated from the policy, i.e., distributional offline policy evaluation (OPE). We propose an algorithm called Fitted Likelihood Estimation (FLE), which conducts a sequence of Maximum Likelihood Estimation (MLE) and has the flexibility of integrating any state-of-the-art probabilistic generative models as long as it can be trained via MLE. FLE can be used for both finite-horizon and infinite-horizon discounted settings where rewards can be multi-dimensional vectors. Our theoretical results show that for both finite-horizon and infinite-horizon discounted settings, FLE can learn distributions that are close to the ground truth under total variation distance and Wasserstein distance, respectively. Our theoretical results hold under the conditions that the offline data covers the test policy's traces and that the supervised learning MLE procedures succeed. Experimentally, we demonstrate the performance of FLE with two generative models, Gaussian mixture models and diffusion models. For the multi-dimensional reward setting, FLE with diffusion models is capable of estimating the complicated distribution of the return of a test policy.

Anomaly detection in multivariate time series is challenging as heterogeneous subsequence anomalies may occur. Reconstruction-based methods, which focus on learning normal patterns in the frequency domain to detect diverse abnormal subsequences, achieve promising results, while still falling short on capturing fine-grained frequency characteristics and channel correlations. To contend with the limitations, we introduce CATCH, a framework based on frequency patching. We propose to patchify the frequency domain into frequency bands, which enhances its ability to capture fine-grained frequency characteristics. To perceive appropriate channel correlations, we propose a Channel Fusion Module (CFM), which features a patch-wise mask generator and a masked-attention mechanism. Driven by a bi-level multi-objective optimization algorithm, the CFM is encouraged to iteratively discover appropriate patch-wise channel correlations, and to cluster relevant channels while isolating adverse effects from irrelevant channels. Extensive experiments on 10 real-world datasets and 12 synthetic datasets demonstrate that CATCH achieves state-of-the-art performance. We make our code and datasets available at https://github.com/decisionintelligence/CATCH.

We introduce UnpredictaBench, an evaluation that tests the ability of large language models (LLMs) to capture true underlying distributions. As LLMs are increasingly used as substitutes for other entities (e.g., for humans in economic simulations), the tendency of many models to collapse towards a single plausible answer means a failure to capture the unpredictability of real systems. Recent work on improving output diversity is insufficient for this setting: simulation requires samples that are calibrated to a target distribution, not merely varied outputs. UnpredictaBench isolates a simplified but fundamental version of this problem: sampling outcomes from individual target distributions, including canonical statistical distributions, distributions induced by stochastic programs, and natural-language scenarios that describe random processes. We introduce 448 such problems together with KS@N, a general-purpose evaluation metric that quantifies how well a model outputs approximate black-box target distributions via the Kolmogorov-Smirnov statistical test. This is the rate at which we fail to reject model samples of size N against ground-truth samples, with larger N indicating greater difficulty. Tested across open and proprietary models, we find a large spread in distributional capabilities. For instance, when models generate samples of size 100 (KS@100, our standard metric), scores range from near 0 to over 20%. No model is able to achieve over 40% at KS@100, showing significant headroom in distributional sampling as a capability. Although adding reasoning can somewhat increase scores, we find no immediate solution for this issue. UnpredictaBench shows that even simple distributional simulation remains challenging, making it a necessary first step toward using LLMs as stand-ins for complex systems.

Diffusion models have achieved remarkable success in generative modeling, yet how to effectively adapt large pretrained models to new tasks remains challenging. We revisit the reconstruction behavior of diffusion models during denoising to unveil the underlying frequency energy mechanism governing this process. Building upon this observation, we propose FeRA, a frequency driven fine tuning framework that aligns parameter updates with the intrinsic frequency energy progression of diffusion. FeRA establishes a comprehensive frequency energy framework for effective diffusion adaptation fine tuning, comprising three synergistic components: (i) a compact frequency energy indicator that characterizes the latent bandwise energy distribution, (ii) a soft frequency router that adaptively fuses multiple frequency specific adapter experts, and (iii) a frequency energy consistency regularization that stabilizes diffusion optimization and ensures coherent adaptation across bands. Routing operates in both training and inference, with inference time routing dynamically determined by the latent frequency energy. It integrates seamlessly with adapter based tuning schemes and generalizes well across diffusion backbones and resolutions. By aligning adaptation with the frequency energy mechanism, FeRA provides a simple, stable, and compatible paradigm for effective and robust diffusion model adaptation.

Being probabilistic models, during inference large language models (LLMs) display rare events: behaviour that is far from typical but highly significant. By definition all rare events are hard to see, but the enormous scale of LLM usage means that events completely unobserved during development are likely to become prominent in deployment. Here we present an end-to-end framework for the systematic analysis of rare events in LLMs. We provide a practical implementation spanning theory, efficient generation strategies, probability estimation and error analysis, which we illustrate with concrete examples. We outline extensions and applications to other models and contexts, highlighting the generality of the concepts and techniques presented here.

This work lists and describes the main recent strategies for building fixed-length, dense and distributed representations for words, based on the distributional hypothesis. These representations are now commonly called word embeddings and, in addition to encoding surprisingly good syntactic and semantic information, have been proven useful as extra features in many downstream NLP tasks.

Large language models (LLMs) have proven to be remarkably efficient, both across a wide range of natural language processing tasks and well beyond them. However, a comprehensive theoretical analysis of the origins of their impressive performance remains elusive. In this paper, we approach this challenging task by drawing an equivalence between generic autoregressive language models with vocabulary of size T and context window of size K and Markov chains defined on a finite state space of size O(T^K). We derive several surprising findings related to the existence of a stationary distribution of Markov chains that capture the inference power of LLMs, their speed of convergence to it, and the influence of the temperature on the latter. We then prove pre-training and in-context generalization bounds and show how the drawn equivalence allows us to enrich their interpretation. Finally, we illustrate our theoretical guarantees with experiments on several recent LLMs to highlight how they capture the behavior observed in practice.

Reward models are crucial for aligning large language models (LLMs) with human values and intentions. Existing approaches follow either Generative (GRMs) or Discriminative (DRMs) paradigms, yet both suffer from limitations: GRMs typically demand costly point-wise supervision, while DRMs produce uncalibrated relative scores that lack probabilistic interpretation. To address these challenges, we introduce a novel reward modeling paradigm: Probabilistic Reward Model (PRM). Instead of modeling reward as a deterministic scalar, our approach treats it as a random variable, learning a full probability distribution for the quality of each response. To make this paradigm practical, we present its closed-form, discrete realization: the Ordinal Probabilistic Reward Model (OPRM), which discretizes the quality score into a finite set of ordinal ratings. Building on OPRM, we propose a data-efficient training strategy called Region Flooding Tuning (RgFT). It enables rewards to better reflect absolute text quality by incorporating quality-level annotations, which guide the model to concentrate the probability mass within corresponding rating sub-regions. Experiments on various reward model benchmarks show that our method improves accuracy by 2.9%sim7.4% compared to prior reward models, demonstrating strong performance and data efficiency. Analysis of the score distribution provides evidence that our method captures not only relative rankings but also absolute quality.

Large language models (LLMs) memorize a vast amount of factual knowledge, exhibiting strong performance across diverse tasks and domains. However, it has been observed that the performance diminishes when dealing with less-popular or low-frequency concepts and entities, for example in domain specific applications. The two prominent approaches to enhance the performance of LLMs on low-frequent topics are: Retrieval Augmented Generation (RAG) and fine-tuning (FT) over synthetic data. This paper explores and evaluates the impact of RAG and FT on customizing LLMs in handling low-frequency entities on question answering task. Our findings indicate that FT significantly boosts the performance across entities of varying popularity, especially in the most and least popular groups, while RAG surpasses other methods. Additionally, the success of both RAG and FT approaches is amplified by advancements in retrieval and data augmentation techniques. We release our data and code at https://github.com/informagi/RAGvsFT.

Large pre-trained time series foundation models (TSFMs) have demonstrated promising zero-shot performance across a wide range of domains. However, a question remains: Do TSFMs succeed solely by memorizing training patterns, or do they possess the ability to reason? While reasoning is a topic of great interest in the study of Large Language Models (LLMs), it is undefined and largely unexplored in the context of TSFMs. In this work, inspired by language modeling literature, we formally define compositional reasoning in forecasting and distinguish it from in-distribution generalization. We evaluate the reasoning and generalization capabilities of 23 popular deep learning forecasting models on multiple synthetic and real-world datasets. Additionally, through controlled studies, we systematically examine which design choices in TSFMs contribute to improved reasoning abilities. Our study yields key insights into the impact of TSFM architecture design on compositional reasoning and generalization. We find that patch-based Transformers have the best reasoning performance, closely followed by residualized MLP-based architectures, which are 97\% less computationally complex in terms of FLOPs and 86\% smaller in terms of the number of trainable parameters. Interestingly, in some zero-shot out-of-distribution scenarios, these models can outperform moving average and exponential smoothing statistical baselines trained on in-distribution data. Only a few design choices, such as the tokenization method, had a significant (negative) impact on Transformer model performance.

Most applications of machine learning to classification assume a closed set of balanced classes. This is at odds with the real world, where class occurrence statistics often follow a long-tailed power-law distribution and it is unlikely that all classes are seen in a single sample. Nonparametric Bayesian models naturally capture this phenomenon, but have significant practical barriers to widespread adoption, namely implementation complexity and computational inefficiency. To address this, we present a method for extracting the inductive bias from a nonparametric Bayesian model and transferring it to an artificial neural network. By simulating data with a nonparametric Bayesian prior, we can metalearn a sequence model that performs inference over an unlimited set of classes. After training, this "neural circuit" has distilled the corresponding inductive bias and can successfully perform sequential inference over an open set of classes. Our experimental results show that the metalearned neural circuit achieves comparable or better performance than particle filter-based methods for inference in these models while being faster and simpler to use than methods that explicitly incorporate Bayesian nonparametric inference.

Diffusion models have shown promising ability in generating high-quality time series (TS) data. Despite the initial success, existing works mostly focus on the authenticity of data at the individual level, but pay less attention to preserving the population-level properties on the entire dataset. Such population-level properties include value distributions for each dimension and distributions of certain functional dependencies (e.g., cross-correlation, CC) between different dimensions. For instance, when generating house energy consumption TS data, the value distributions of the outside temperature and the kitchen temperature should be preserved, as well as the distribution of CC between them. Preserving such TS population-level properties is critical in maintaining the statistical insights of the datasets, mitigating model bias, and augmenting downstream tasks like TS prediction. Yet, it is often overlooked by existing models. Hence, data generated by existing models often bear distribution shifts from the original data. We propose Population-aware Diffusion for Time Series (PaD-TS), a new TS generation model that better preserves the population-level properties. The key novelties of PaD-TS include 1) a new training method explicitly incorporating TS population-level property preservation, and 2) a new dual-channel encoder model architecture that better captures the TS data structure. Empirical results in major benchmark datasets show that PaD-TS can improve the average CC distribution shift score between real and synthetic data by 5.9x while maintaining a performance comparable to state-of-the-art models on individual-level authenticity.

Recently, universal waveform generation tasks have been investigated conditioned on various out-of-distribution scenarios. Although GAN-based methods have shown their strength in fast waveform generation, they are vulnerable to train-inference mismatch scenarios such as two-stage text-to-speech. Meanwhile, diffusion-based models have shown their powerful generative performance in other domains; however, they stay out of the limelight due to slow inference speed in waveform generation tasks. Above all, there is no generator architecture that can explicitly disentangle the natural periodic features of high-resolution waveform signals. In this paper, we propose PeriodWave, a novel universal waveform generation model. First, we introduce a period-aware flow matching estimator that can capture the periodic features of the waveform signal when estimating the vector fields. Additionally, we utilize a multi-period estimator that avoids overlaps to capture different periodic features of waveform signals. Although increasing the number of periods can improve the performance significantly, this requires more computational costs. To reduce this issue, we also propose a single period-conditional universal estimator that can feed-forward parallel by period-wise batch inference. Additionally, we utilize discrete wavelet transform to losslessly disentangle the frequency information of waveform signals for high-frequency modeling, and introduce FreeU to reduce the high-frequency noise for waveform generation. The experimental results demonstrated that our model outperforms the previous models both in Mel-spectrogram reconstruction and text-to-speech tasks. All source code will be available at https://github.com/sh-lee-prml/PeriodWave.

We propose an alternate approach to quantifying how well language models learn natural language: we ask how well they match the statistical tendencies of natural language. To answer this question, we analyze whether text generated from language models exhibits the statistical tendencies present in the human-generated text on which they were trained. We provide a framework--paired with significance tests--for evaluating the fit of language models to these trends. We find that neural language models appear to learn only a subset of the tendencies considered, but align much more closely with empirical trends than proposed theoretical distributions (when present). Further, the fit to different distributions is highly-dependent on both model architecture and generation strategy. As concrete examples, text generated under the nucleus sampling scheme adheres more closely to the type--token relationship of natural language than text produced using standard ancestral sampling; text from LSTMs reflects the natural language distributions over length, stopwords, and symbols surprisingly well.

Scaling laws offer valuable insights into the design of time series foundation models (TSFMs). However, previous research has largely focused on the scaling laws of TSFMs for in-distribution (ID) data, leaving their out-of-distribution (OOD) scaling behavior and the influence of model architectures less explored. In this work, we examine two common TSFM architectures, encoder-only and decoder-only Transformers, and investigate their scaling behavior on both ID and OOD data. These models are trained and evaluated across varying parameter counts, compute budgets, and dataset sizes. Our experiments reveal that the log-likelihood loss of TSFMs exhibits similar scaling behavior in both OOD and ID settings. We further compare the scaling properties across different architectures, incorporating two state-of-the-art TSFMs as case studies, showing that model architecture plays a significant role in scaling. The encoder-only Transformers demonstrate better scalability than the decoder-only Transformers, while the architectural enhancements in the two advanced TSFMs primarily improve ID performance but reduce OOD scalability. While scaling up TSFMs is expected to drive performance breakthroughs, the lack of a comprehensive understanding of TSFM scaling laws has hindered the development of a robust framework to guide model scaling. We fill this gap in this work by synthesizing our findings and providing practical guidelines for designing and scaling larger TSFMs with enhanced model capabilities.

Multilingual generative language models (LMs) are increasingly fluent in a large variety of languages. Trained on the concatenation of corpora in multiple languages, they enable powerful transfer from high-resource languages to low-resource ones. However, it is still unknown what cultural biases are induced in the predictions of these models. In this work, we focus on one language property highly influenced by culture: formality. We analyze the formality distributions of XGLM and BLOOM's predictions, two popular generative multilingual language models, in 5 languages. We classify 1,200 generations per language as formal, informal, or incohesive and measure the impact of the prompt formality on the predictions. Overall, we observe a diversity of behaviors across the models and languages. For instance, XGLM generates informal text in Arabic and Bengali when conditioned with informal prompts, much more than BLOOM. In addition, even though both models are highly biased toward the formal style when prompted neutrally, we find that the models generate a significant amount of informal predictions even when prompted with formal text. We release with this work 6,000 annotated samples, paving the way for future work on the formality of generative multilingual LMs.

Recent studies have suggested frequency-domain Data augmentation (DA) is effec tive for time series prediction. Existing frequency-domain augmentations disturb the original data with various full-spectrum noises, leading to excess domain gap between augmented and original data. Although impressive performance has been achieved in certain cases, frequency-domain DA has yet to be generalized to time series prediction datasets. In this paper, we found that frequency-domain augmentations can be significantly improved by two modifications that limit the perturbations. First, we found that limiting the perturbation to only dominant frequencies significantly outperforms full-spectrum perturbations. Dominant fre quencies represent the main periodicity and trends of the signal and are more important than other frequencies. Second, we found that simply shuffling the dominant frequency components is superior over sophisticated designed random perturbations. Shuffle rearranges the original components (magnitudes and phases) and limits the external noise. With these two modifications, we proposed dominant shuffle, a simple yet effective data augmentation for time series prediction. Our method is very simple yet powerful and can be implemented with just a few lines of code. Extensive experiments with eight datasets and six popular time series models demonstrate that our method consistently improves the baseline performance under various settings and significantly outperforms other DA methods. Code can be accessed at https://kaizhao.net/time-series.

Word embeddings are an essential component in a wide range of natural language processing applications. However, distributional semantic models are known to struggle when only a small number of context sentences are available. Several methods have been proposed to obtain higher-quality vectors for these words, leveraging both this context information and sometimes the word forms themselves through a hybrid approach. We show that the current tasks do not suffice to evaluate models that use word-form information, as such models can easily leverage word forms in the training data that are related to word forms in the test data. We introduce 3 new tasks, allowing for a more balanced comparison between models. Furthermore, we show that hyperparameters that have largely been ignored in previous work can consistently improve the performance of both baseline and advanced models, achieving a new state of the art on 4 out of 6 tasks.

We explore the relations between the zeta distribution and algorithmic information theory via a new model of the transfer learning problem. The program distribution is approximated by a zeta distribution with parameter near 1. We model the training sequence as a stochastic process. We analyze the upper temporal bound for learning a training sequence and its entropy rates, assuming an oracle for the transfer learning problem. We argue from empirical evidence that power-law models are suitable for natural processes. Four sequence models are proposed. Random typing model is like no-free lunch where transfer learning does not work. Zeta process independently samples programs from the zeta distribution. A model of common sub-programs inspired by genetics uses a database of sub-programs. An evolutionary zeta process samples mutations from Zeta distribution. The analysis of stochastic processes inspired by evolution suggest that AI may be feasible in nature, countering no-free lunch sort of arguments.

Distributional word representation methods exploit word co-occurrences to build compact vector encodings of words. While these representations enjoy widespread use in modern natural language processing, it is unclear whether they accurately encode all necessary facets of conceptual meaning. In this paper, we evaluate how well these representations can predict perceptual and conceptual features of concrete concepts, drawing on two semantic norm datasets sourced from human participants. We find that several standard word representations fail to encode many salient perceptual features of concepts, and show that these deficits correlate with word-word similarity prediction errors. Our analyses provide motivation for grounded and embodied language learning approaches, which may help to remedy these deficits.

LLM-generated stories are a popular use case, but they show very low variability. We sample 20,000 total stories from four current models using five prompts. We find that 11 words occur in 88.3% of generated stories, with little difference between models. These words include names (Elias, Mara, Elara), settings (lighthouses), and professions (clockmaker, librarian). These tokens do not often occur in published literature nor pre-training data, but they are found in preference data that is likely to have been used by all current models. Surprisingly, these "lighthouse" stories are infrequent when compared with the average post-training story, much of which contains references to copyrighted characters or adult content. This result demonstrates the potentially disproportionate impact of small datasets combined with powerful alignment algorithms.

Large Language Models (LLMs) and Foundation Models (FMs) have recently become prevalent for time series forecasting tasks. While fine-tuning LLMs enables domain adaptation, they often struggle to generalize across diverse and unseen datasets. Moreover, existing Time Series Foundation Models (TSFMs) still face challenges in handling non-stationary dynamics and distribution shifts, largely due to the lack of effective mechanisms for adaptation. To this end, we present TS-RAG, a retrieval-augmented generation framework for time series forecasting that enhances the generalization and interpretability of TSFMs. Specifically, TS-RAG leverages pre-trained time series encoders to retrieve semantically relevant segments from a dedicated knowledge base, enriching the contextual representation of the input query. Furthermore, we propose an Adaptive Retrieval Mixer (ARM) module that dynamically fuses the retrieved patterns with the TSFM's internal representation, improving forecasting accuracy without requiring task-specific fine-tuning. Thorough empirical studies on seven public benchmark datasets demonstrate that TS-RAG achieves state-of-the-art zero-shot forecasting performance, outperforming the existing TSFMs by up to 6.84% across diverse domains while also providing desirable interpretability. Our code and data are available at: https://github.com/UConn-DSIS/TS-RAG

Human processing of idioms relies on understanding the contextual sentences in which idioms occur, as well as language-intrinsic features such as frequency and speaker-intrinsic factors like familiarity. While LLMs have shown high performance on idiomaticity detection tasks, this success may be attributed to reasoning shortcuts in existing datasets. To this end, we construct a novel, controlled contrastive dataset designed to test whether LLMs can effectively use context to disambiguate idiomatic meaning. Additionally, we explore how collocational frequency and sentence probability influence model performance. Our findings reveal that LLMs often fail to resolve idiomaticity when it is required to attend to the surrounding context, and that models perform better on sentences that have higher likelihood. The collocational frequency of expressions also impacts performance. We make our code and dataset publicly available.

Rigorous statistical evaluations of large language models (LLMs), including valid error bars and significance testing, are essential for meaningful and reliable performance assessment. Currently, when such statistical measures are reported, they typically rely on the Central Limit Theorem (CLT). In this position paper, we argue that while CLT-based methods for uncertainty quantification are appropriate when benchmarks consist of thousands of examples, they fail to provide adequate uncertainty estimates for LLM evaluations that rely on smaller, highly specialized benchmarks. In these small-data settings, we demonstrate that CLT-based methods perform very poorly, usually dramatically underestimating uncertainty (i.e. producing error bars that are too small). We give recommendations for alternative frequentist and Bayesian methods that are both easy to implement and more appropriate in these increasingly common scenarios. We provide a simple Python library for these Bayesian methods at https://github.com/sambowyer/bayes_evals .

Distributed representations of words encode lexical semantic information, but what type of information is encoded and how? Focusing on the skip-gram with negative-sampling method, we found that the squared norm of static word embedding encodes the information gain conveyed by the word; the information gain is defined by the Kullback-Leibler divergence of the co-occurrence distribution of the word to the unigram distribution. Our findings are explained by the theoretical framework of the exponential family of probability distributions and confirmed through precise experiments that remove spurious correlations arising from word frequency. This theory also extends to contextualized word embeddings in language models or any neural networks with the softmax output layer. We also demonstrate that both the KL divergence and the squared norm of embedding provide a useful metric of the informativeness of a word in tasks such as keyword extraction, proper-noun discrimination, and hypernym discrimination.

Time series modeling presents unique challenges due to autocorrelation in both historical data and future sequences. While current research predominantly addresses autocorrelation within historical data, the correlations among future labels are often overlooked. Specifically, modern forecasting models primarily adhere to the Direct Forecast (DF) paradigm, generating multi-step forecasts independently and disregarding label autocorrelation over time. In this work, we demonstrate that the learning objective of DF is biased in the presence of label autocorrelation. To address this issue, we propose the Frequency-enhanced Direct Forecast (FreDF), which mitigates label autocorrelation by learning to forecast in the frequency domain, thereby reducing estimation bias. Our experiments show that FreDF significantly outperforms existing state-of-the-art methods and is compatible with a variety of forecast models. Code is available at https://github.com/Master-PLC/FreDF.

The advent of universal time series forecasting models has revolutionized zero-shot forecasting across diverse domains, yet the critical role of data diversity in training these models remains underexplored. Existing large-scale time series datasets often suffer from inherent biases and imbalanced distributions, leading to suboptimal model performance and generalization. To address this gap, we introduce BLAST, a novel pre-training corpus designed to enhance data diversity through a balanced sampling strategy. First, BLAST incorporates 321 billion observations from publicly available datasets and employs a comprehensive suite of statistical metrics to characterize time series patterns. Then, to facilitate pattern-oriented sampling, the data is implicitly clustered using grid-based partitioning. Furthermore, by integrating grid sampling and grid mixup techniques, BLAST ensures a balanced and representative coverage of diverse patterns. Experimental results demonstrate that models pre-trained on BLAST achieve state-of-the-art performance with a fraction of the computational resources and training tokens required by existing methods. Our findings highlight the pivotal role of data diversity in improving both training efficiency and model performance for the universal forecasting task.

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

By encoding time series as a string of numerical digits, we can frame time series forecasting as next-token prediction in text. Developing this approach, we find that large language models (LLMs) such as GPT-3 and LLaMA-2 can surprisingly zero-shot extrapolate time series at a level comparable to or exceeding the performance of purpose-built time series models trained on the downstream tasks. To facilitate this performance, we propose procedures for effectively tokenizing time series data and converting discrete distributions over tokens into highly flexible densities over continuous values. We argue the success of LLMs for time series stems from their ability to naturally represent multimodal distributions, in conjunction with biases for simplicity, and repetition, which align with the salient features in many time series, such as repeated seasonal trends. We also show how LLMs can naturally handle missing data without imputation through non-numerical text, accommodate textual side information, and answer questions to help explain predictions. While we find that increasing model size generally improves performance on time series, we show GPT-4 can perform worse than GPT-3 because of how it tokenizes numbers, and poor uncertainty calibration, which is likely the result of alignment interventions such as RLHF.

The task of discovering topics in text corpora has been dominated by Latent Dirichlet Allocation and other Topic Models for over a decade. In order to apply these approaches to massive text corpora, the vocabulary needs to be reduced considerably and large computer clusters and/or GPUs are typically required. Moreover, the number of topics must be provided beforehand but this depends on the corpus characteristics and it is often difficult to estimate, especially for massive text corpora. Unfortunately, both topic quality and time complexity are sensitive to this choice. This paper describes an alternative approach to discover topics based on Min-Hashing, which can handle massive text corpora and large vocabularies using modest computer hardware and does not require to fix the number of topics in advance. The basic idea is to generate multiple random partitions of the corpus vocabulary to find sets of highly co-occurring words, which are then clustered to produce the final topics. In contrast to probabilistic topic models where topics are distributions over the complete vocabulary, the topics discovered by the proposed approach are sets of highly co-occurring words. Interestingly, these topics underlie various thematics with different levels of granularity. An extensive qualitative and quantitative evaluation using the 20 Newsgroups (18K), Reuters (800K), Spanish Wikipedia (1M), and English Wikipedia (5M) corpora shows that the proposed approach is able to consistently discover meaningful and coherent topics. Remarkably, the time complexity of the proposed approach is linear with respect to corpus and vocabulary size; a non-parallel implementation was able to discover topics from the entire English edition of Wikipedia with over 5 million documents and 1 million words in less than 7 hours.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

This work studies discrete diffusion probabilistic models with applications to natural language generation. We derive an alternative yet equivalent formulation of the sampling from discrete diffusion processes and leverage this insight to develop a family of reparameterized discrete diffusion models. The derived generic framework is highly flexible, offers a fresh perspective of the generation process in discrete diffusion models, and features more effective training and decoding techniques. We conduct extensive experiments to evaluate the text generation capability of our model, demonstrating significant improvements over existing diffusion models.

Time series foundation models (TSFMs) have emerged as a powerful paradigm for time series analysis, driven by large-scale pretraining on diverse data corpora. However, time series inherently exhibit heterogeneous information density over time, influenced by system states and signal complexity, presenting significant modeling challenges especially in a zero-shot scenario. Current TSFMs rely on non-adaptive processing pipelines that fail to capture this dynamic nature. For example, common tokenization strategies such as fixed-size patching enforce rigid observational granularity, limiting their ability to adapt to varying information densities. Similarly, conventional positional encodings impose a uniform temporal scale, making it difficult to model diverse periodicities and trends across series. To overcome these limitations, we propose Kairos, a flexible TSFM framework that integrates a dynamic patching tokenizer and an instance-adaptive positional embedding. Kairos adaptively selects tokenization granularity and tailors positional encodings to the unique characteristics of each time series instance. Trained on a large-scale Predictability-Stratified Time Series (PreSTS) corpus comprising over 300 billion time points and adopting a multi-patch prediction strategy in the inference stage, Kairos achieves superior performance with much fewer parameters on two common zero-shot benchmarks, GIFT-Eval and the Time-Series-Library benchmark, consistently outperforming established methods across diverse tasks. The project page is at https://foundation-model-research.github.io/Kairos .

The uprising of deep learning methodology and practice in recent years has brought about a severe consequence of increasing carbon footprint due to the insatiable demand for computational resources and power. The field of text analytics also experienced a massive transformation in this trend of monopolizing methodology. In this paper, the original TF-IDF algorithm has been modified, and Clement Term Frequency-Inverse Document Frequency (CTF-IDF) has been proposed for data preprocessing. This paper primarily discusses the effectiveness of classical machine learning techniques in text analytics with CTF-IDF and a faster IRLBA algorithm for dimensionality reduction. The introduction of both of these techniques in the conventional text analytics pipeline ensures a more efficient, faster, and less computationally intensive application when compared with deep learning methodology regarding carbon footprint, with minor compromise in accuracy. The experimental results also exhibit a manifold of reduction in time complexity and improvement of model accuracy for the classical machine learning methods discussed further in this paper.

We present significant extensions to diffusion-based sequence generation models, blurring the line with autoregressive language models. We introduce hyperschedules, which assign distinct noise schedules to individual token positions, generalizing both autoregressive models (e.g., GPT) and conventional diffusion models (e.g., SEDD, MDLM) as special cases. Second, we propose two hybrid token-wise noising processes that interpolate between absorbing and uniform processes, enabling the model to fix past mistakes, and we introduce a novel inference algorithm that leverages this new feature in a simplified context inspired from MDLM. To support efficient training and inference, we design attention masks compatible with KV-caching. Our methods achieve state-of-the-art perplexity and generate diverse, high-quality sequences across standard benchmarks, suggesting a promising path for autoregressive diffusion-based sequence generation.

This paper revisits the problem of computing empirical cumulative distribution functions (ECDF) efficiently on large, multivariate datasets. Computing an ECDF at one evaluation point requires O(N) operations on a dataset composed of N data points. Therefore, a direct evaluation of ECDFs at N evaluation points requires a quadratic O(N^2) operations, which is prohibitive for large-scale problems. Two fast and exact methods are proposed and compared. The first one is based on fast summation in lexicographical order, with a O(N{log}N) complexity and requires the evaluation points to lie on a regular grid. The second one is based on the divide-and-conquer principle, with a O(Nlog(N)^{(d-1){vee}1}) complexity and requires the evaluation points to coincide with the input points. The two fast algorithms are described and detailed in the general d-dimensional case, and numerical experiments validate their speed and accuracy. Secondly, the paper establishes a direct connection between cumulative distribution functions and kernel density estimation (KDE) for a large class of kernels. This connection paves the way for fast exact algorithms for multivariate kernel density estimation and kernel regression. Numerical tests with the Laplacian kernel validate the speed and accuracy of the proposed algorithms. A broad range of large-scale multivariate density estimation, cumulative distribution estimation, survival function estimation and regression problems can benefit from the proposed numerical methods.

Knowledge-intensive language tasks require NLP systems to both provide the correct answer and retrieve supporting evidence for it in a given corpus. Autoregressive language models are emerging as the de-facto standard for generating answers, with newer and more powerful systems emerging at an astonishing pace. In this paper we argue that all this (and future) progress can be directly applied to the retrieval problem with minimal intervention to the models' architecture. Previous work has explored ways to partition the search space into hierarchical structures and retrieve documents by autoregressively generating their unique identifier. In this work we propose an alternative that doesn't force any structure in the search space: using all ngrams in a passage as its possible identifiers. This setup allows us to use an autoregressive model to generate and score distinctive ngrams, that are then mapped to full passages through an efficient data structure. Empirically, we show this not only outperforms prior autoregressive approaches but also leads to an average improvement of at least 10 points over more established retrieval solutions for passage-level retrieval on the KILT benchmark, establishing new state-of-the-art downstream performance on some datasets, while using a considerably lighter memory footprint than competing systems. Code and pre-trained models at https://github.com/facebookresearch/SEAL.

This paper will present textual corpora for Serbian (and Serbo-Croatian), usable for the training of large language models and publicly available at one of the several notable online repositories. Each corpus will be classified using multiple methods and its characteristics will be detailed. Additionally, the paper will introduce three new corpora: a new umbrella web corpus of Serbo-Croatian, a new high-quality corpus based on the doctoral dissertations stored within National Repository of Doctoral Dissertations from all Universities in Serbia, and a parallel corpus of abstract translation from the same source. The uniqueness of both old and new corpora will be accessed via frequency-based stylometric methods, and the results will be briefly discussed.

The paper considers the use of GPT models with retrieval-augmented generation (RAG) for qualitative and quantitative analytics on NATO sentiments, NATO unity and NATO Article 5 trust opinion scores in different web sources: news sites found via Google Search API, Youtube videos with comments, and Reddit discussions. A RAG approach using GPT-4.1 model was applied to analyse news where NATO related topics were discussed. Two levels of RAG analytics were used: on the first level, the GPT model generates qualitative news summaries and quantitative opinion scores using zero-shot prompts; on the second level, the GPT model generates the summary of news summaries. Quantitative news opinion scores generated by the GPT model were analysed using Bayesian regression to get trend lines. The distributions found for the regression parameters make it possible to analyse an uncertainty in specified news opinion score trends. Obtained results show a downward trend for analysed scores of opinion related to NATO unity. This approach does not aim to conduct real political analysis; rather, it consider AI based approaches which can be used for further analytics as a part of a complex analytical approach. The obtained results demonstrate that the use of GPT models for news analysis can give informative qualitative and quantitative analytics, providing important insights. The dynamic model based on neural ordinary differential equations was considered for modelling public opinions. This approach makes it possible to analyse different scenarios for evolving public opinions.

Customer Lifetime Value (CLTV) prediction is a critical task in business applications. Accurately predicting CLTV is challenging in real-world business scenarios, as the distribution of CLTV is complex and mutable. Firstly, there is a large number of users without any consumption consisting of a long-tailed part that is too complex to fit. Secondly, the small set of high-value users spent orders of magnitude more than a typical user leading to a wide range of the CLTV distribution which is hard to capture in a single distribution. Existing approaches for CLTV estimation either assume a prior probability distribution and fit a single group of distribution-related parameters for all samples, or directly learn from the posterior distribution with manually predefined buckets in a heuristic manner. However, all these methods fail to handle complex and mutable distributions. In this paper, we propose a novel optimal distribution selection model OptDist for CLTV prediction, which utilizes an adaptive optimal sub-distribution selection mechanism to improve the accuracy of complex distribution modeling. Specifically, OptDist trains several candidate sub-distribution networks in the distribution learning module (DLM) for modeling the probability distribution of CLTV. Then, a distribution selection module (DSM) is proposed to select the sub-distribution for each sample, thus making the selection automatically and adaptively. Besides, we design an alignment mechanism that connects both modules, which effectively guides the optimization. We conduct extensive experiments on both two public and one private dataset to verify that OptDist outperforms state-of-the-art baselines. Furthermore, OptDist has been deployed on a large-scale financial platform for customer acquisition marketing campaigns and the online experiments also demonstrate the effectiveness of OptDist.

Masked diffusion models (MDMs) have emerged as a popular research topic for generative modeling of discrete data, thanks to their superior performance over other discrete diffusion models, and are rivaling the auto-regressive models (ARMs) for language modeling tasks. The recent effort in simplifying the masked diffusion framework further leads to alignment with continuous-space diffusion models and more principled training and sampling recipes. In this paper, however, we reveal that both training and sampling of MDMs are theoretically free from the time variable, arguably the key signature of diffusion models, and are instead equivalent to masked models. The connection on the sampling aspect is drawn by our proposed first-hitting sampler (FHS). Specifically, we show that the FHS is theoretically equivalent to MDMs' original generation process while significantly alleviating the time-consuming categorical sampling and achieving a 20times speedup. In addition, our investigation raises doubts about whether MDMs can truly beat ARMs. We identify, for the first time, an underlying numerical issue, even with the commonly used 32-bit floating-point precision, which results in inaccurate categorical sampling. We show that the numerical issue lowers the effective temperature both theoretically and empirically, and the resulting decrease in token diversity makes previous evaluations, which assess the generation quality solely through the incomplete generative perplexity metric, somewhat unfair.

Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are strictly more expressive efficient than many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework that unifies vastly different existing models, but also show great potential in modeling realistic data. We exhibit a simple class of PGCs that are not trivially subsumed by simple combinations of PCs and DPPs, and obtain competitive performance on a suite of density estimation benchmarks. We also highlight PGCs' connection to the theory of strongly Rayleigh distributions.

Vector space word representations are learned from distributional information of words in large corpora. Although such statistics are semantically informative, they disregard the valuable information that is contained in semantic lexicons such as WordNet, FrameNet, and the Paraphrase Database. This paper proposes a method for refining vector space representations using relational information from semantic lexicons by encouraging linked words to have similar vector representations, and it makes no assumptions about how the input vectors were constructed. Evaluated on a battery of standard lexical semantic evaluation tasks in several languages, we obtain substantial improvements starting with a variety of word vector models. Our refinement method outperforms prior techniques for incorporating semantic lexicons into the word vector training algorithms.

Languages are not created randomly but rather to communicate information. There is a strong association between languages and their underlying meanings, resulting in a sparse joint distribution that is heavily peaked according to their correlations. Moreover, these peak values happen to match with the marginal distribution of languages due to the sparsity. With the advent of LLMs trained on big data and large models, we can now precisely assess the marginal distribution of languages, providing a convenient means of exploring the sparse structures in the joint distribution for effective inferences. In this paper, we categorize languages as either unambiguous or {\epsilon}-ambiguous and present quantitative results to demonstrate that the emergent abilities of LLMs, such as language understanding, in-context learning, chain-of-thought prompting, and effective instruction fine-tuning, can all be attributed to Bayesian inference on the sparse joint distribution of languages.

Heaps' law is an empirical relation in text analysis that predicts vocabulary growth as a function of corpus size. While this law has been validated in diverse human-authored text corpora, its applicability to large language model generated text remains unexplored. This study addresses this gap, focusing on the emulation of corpora using the suite of GPT-Neo large language models. To conduct our investigation, we emulated corpora of PubMed abstracts using three different parameter sizes of the GPT-Neo model. Our emulation strategy involved using the initial five words of each PubMed abstract as a prompt and instructing the model to expand the content up to the original abstract's length. Our findings indicate that the generated corpora adhere to Heaps' law. Interestingly, as the GPT-Neo model size grows, its generated vocabulary increasingly adheres to Heaps' law as as observed in human-authored text. To further improve the richness and authenticity of GPT-Neo outputs, future iterations could emphasize enhancing model size or refining the model architecture to curtail vocabulary repetition.

Language model (LM) decoding is based on the next-token prediction (NTP) probability distribution. For neural LMs (e.g., Transformer-based), NTP distribution is essentially a softmax-regularized dot product between an encoded input context (query) and fixed vocabulary representations (keys). In this paper, we study the effect of the key distribution on the NTP distribution, with a focus on whether the similarity between keys will trigger spurious correlations in NTP. Through knowledge-probing tasks, we show that in the NTP distribution, the few top-ranked tokens are typically accurate. However, the middle-ranked prediction is highly biased towards the tokens that are distributionally (not necessarily semantically) similar to these top ones. For instance, if "P" is predicted as the top-1 token, "A"-"Z" will all be ranked high in NTP, no matter whether they can lead to correct decoding results. This hurts the sampling diversity and makes the sampling of correct, long-tail results hopeless and noisy. We attempt to alleviate this issue via a novel in-context method that iteratively pushes the query representation away from explored regions. Specifically, we include the explored decoding results in the context and prompt the LM to generate something else, which encourages the LM to produce a query representation that has small dot products with explored keys. Experiments on knowledge-probing tasks show that our method leads to efficient navigation away from explored keys to correct new keys. We further extend our method to open-ended and chain-of-thought (for reasoning) generation. Experiment results show that ICN contributes to better generation diversity and improved self-consistency voting performance. Finally, we discuss potential training issues caused by the fixed key space together with the challenges and possible ways to address them in future research.

We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic, Burr type XII, Weibull, Gompertz), and includes defective distributions (i.e., cure models). This generality is achieved using four basic distributional parameters: two scale-type parameters and two shape parameters. Generalising to covariate dependence, the scale-type regression components correspond to accelerated failure time (AFT) and proportional hazards (PH) models. Therefore, this general formulation unifies the most popular survival models which allows us to consider the practical value of possible modelling choices for survival data. Furthermore, in line with our proposed flexible baseline distribution, we advocate the use of multi-parameter regression in which more than one distributional parameter depends on covariates - rather than the usual convention of having a single covariate-dependent (scale) parameter. While many choices are available, we suggest introducing covariates through just one or other of the two scale parameters, which covers AFT and PH models, in combination with a `power' shape parameter, which allows for more complex non-AFT/non-PH effects, while the other shape parameter remains covariate-independent, and handles automatic selection of the baseline distribution. We explore inferential issues in simulations, both with and without a covariate, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by investigating differences between treatment groups using data from a lung cancer study and a melanoma study. Censoring is accommodated throughout.

Discrete Diffusion Language Models progressed rapidly as an alternative to autoregressive (AR) models, motivated by their parallel generation abilities. However, for tractability, discrete diffusion models sample from a factorized distribution, which is less expressive than AR. Recent Flow Language Models (FLMs) apply continuous flows to language, transporting noise to data with a deterministic ODE that avoids factorized sampling. FLMs operate on one-hot vectors whose dimension scales with the vocabulary size, making FLMs costly to train. Moreover, since all distinct one-hot embeddings are equidistant in ell_2, adding Gaussian noise does not have a clear semantic interpretation (unlike images, where Gaussian noise progressively degrades structure). We introduce S-FLM, a latent FLM in the hypersphere. S-FLM generates sequences by rotating vectors in S^{d-1} along a velocity field learned with cross-entropy, avoiding the overhead of materializing one-hot vectors. Previous FLMs match AR in Generative Perplexity (Gen.\ PPL), but samples with high likelihood are not necessarily correct in verifiable domains such as math and code. S-FLM substantially improves continuous flow language models on large-vocabulary reasoning and closes the gap to masked diffusion under standard-temperature sampling (T=1), while a gap remains under optimized low-temperature (T=0.1) decoding.

We apply the Weibull distribution -- a two-parameter family from extreme-value theory -- as a diagnostic framework for element-wise weight magnitude distributions in transformers. At initialization, i.i.d. Gaussian weights give |w| ~ HalfNormal, yielding k ~ 1.20 via middle-80% probability-plot fit (the protocol used throughout this work). This anchor makes k a principled, architecture-independent measuring stick for training dynamics; fitting each weight matrix independently at every layer at every checkpoint enables per-component, per-layer, and per-step diagnostics that aggregate statistics cannot resolve. Applying this framework to 12 model entries spanning 7 architectural families (Pythia, OLMo-1/2, LLaMA-3, Mistral, Qwen2.5/3) reveals three findings. First, FFN modules and the attention output projection W_o -- the Transmission Class -- fall in a narrow k band: median terminal k in [1.186, 1.204] across 12 entries (cross-family CV = 0.51%), shared across SwiGLU/GeLU activations, Pre-LN/QK-Norm placements, and 70M-14B sizes. Second, the attention input projections W_q, W_k -- the Selection Class -- depart from the Weibull family, with severity shaped by storage: separately-stored Q/K (OLMo-1, OLMo-2) yields k in [0.76, 0.99] (deep); GQA models yield k in [1.10, 1.16] (mild); Pythia's merged W_qkv occupies a transitional zone tracking training budget T/tau monotonically. Third, lambda grows substantially during training and scales with sqrt(eta/lambda_wd) within the Pythia family (Pearson r = 0.94, three Transmission kinds), directionally consistent with Fan et al. (2025). The two parameters carry independent information: k labels the functional class, lambda labels training progress. We release npm-weibull-py v0.4 (Python library) and DATABASE_v9_1 at https://github.com/tiexinding/NPM-Weibull-public .

We design a new technique for the distributional semantic modeling with a neural network-based approach to learn distributed term representations (or term embeddings) - term vector space models as a result, inspired by the recent ontology-related approach (using different types of contextual knowledge such as syntactic knowledge, terminological knowledge, semantic knowledge, etc.) to the identification of terms (term extraction) and relations between them (relation extraction) called semantic pre-processing technology - SPT. Our method relies on automatic term extraction from the natural language texts and subsequent formation of the problem-oriented or application-oriented (also deeply annotated) text corpora where the fundamental entity is the term (includes non-compositional and compositional terms). This gives us an opportunity to changeover from distributed word representations (or word embeddings) to distributed term representations (or term embeddings). This transition will allow to generate more accurate semantic maps of different subject domains (also, of relations between input terms - it is useful to explore clusters and oppositions, or to test your hypotheses about them). The semantic map can be represented as a graph using Vec2graph - a Python library for visualizing word embeddings (term embeddings in our case) as dynamic and interactive graphs. The Vec2graph library coupled with term embeddings will not only improve accuracy in solving standard NLP tasks, but also update the conventional concept of automated ontology development. The main practical result of our work is the development kit (set of toolkits represented as web service APIs and web application), which provides all necessary routines for the basic linguistic pre-processing and the semantic pre-processing of the natural language texts in Ukrainian for future training of term vector space models.

Composition models of distributional semantics are used to construct phrase representations from the representations of their words. Composition models are typically situated on two ends of a spectrum. They either have a small number of parameters but compose all phrases in the same way, or they perform word-specific compositions at the cost of a far larger number of parameters. In this paper we propose transformation weighting (TransWeight), a composition model that consistently outperforms existing models on nominal compounds, adjective-noun phrases and adverb-adjective phrases in English, German and Dutch. TransWeight drastically reduces the number of parameters needed compared to the best model in the literature by composing similar words in the same way.

Understanding how machine learning models respond to distributional shifts is a key research challenge. Mazes serve as an excellent testbed due to varied generation algorithms offering a nuanced platform to simulate both subtle and pronounced distributional shifts. To enable systematic investigations of model behavior on out-of-distribution data, we present maze-dataset, a comprehensive library for generating, processing, and visualizing datasets consisting of maze-solving tasks. With this library, researchers can easily create datasets, having extensive control over the generation algorithm used, the parameters fed to the algorithm of choice, and the filters that generated mazes must satisfy. Furthermore, it supports multiple output formats, including rasterized and text-based, catering to convolutional neural networks and autoregressive transformer models. These formats, along with tools for visualizing and converting between them, ensure versatility and adaptability in research applications.

Conventional wisdom holds that autoregressive models for image generation are typically accompanied by vector-quantized tokens. We observe that while a discrete-valued space can facilitate representing a categorical distribution, it is not a necessity for autoregressive modeling. In this work, we propose to model the per-token probability distribution using a diffusion procedure, which allows us to apply autoregressive models in a continuous-valued space. Rather than using categorical cross-entropy loss, we define a Diffusion Loss function to model the per-token probability. This approach eliminates the need for discrete-valued tokenizers. We evaluate its effectiveness across a wide range of cases, including standard autoregressive models and generalized masked autoregressive (MAR) variants. By removing vector quantization, our image generator achieves strong results while enjoying the speed advantage of sequence modeling. We hope this work will motivate the use of autoregressive generation in other continuous-valued domains and applications.

Real-world datasets follow an imbalanced distribution, which poses significant challenges in rare-category object detection. Recent studies tackle this problem by developing re-weighting and re-sampling methods, that utilise the class frequencies of the dataset. However, these techniques focus solely on the frequency statistics and ignore the distribution of the classes in image space, missing important information. In contrast to them, we propose FRActal CALibration (FRACAL): a novel post-calibration method for long-tailed object detection. FRACAL devises a logit adjustment method that utilises the fractal dimension to estimate how uniformly classes are distributed in image space. During inference, it uses the fractal dimension to inversely downweight the probabilities of uniformly spaced class predictions achieving balance in two axes: between frequent and rare categories, and between uniformly spaced and sparsely spaced classes. FRACAL is a post-processing method and it does not require any training, also it can be combined with many off-the-shelf models such as one-stage sigmoid detectors and two-stage instance segmentation models. FRACAL boosts the rare class performance by up to 8.6% and surpasses all previous methods on LVIS dataset, while showing good generalisation to other datasets such as COCO, V3Det and OpenImages. We provide the code at https://github.com/kostas1515/FRACAL.

Long-term Time Series Forecasting (LTSF) is critical for numerous real-world applications, such as electricity consumption planning, financial forecasting, and disease propagation analysis. LTSF requires capturing long-range dependencies between inputs and outputs, which poses significant challenges due to complex temporal dynamics and high computational demands. While linear models reduce model complexity by employing frequency domain decomposition, current approaches often assume stationarity and filter out high-frequency components that may contain crucial short-term fluctuations. In this paper, we introduce MMFNet, a novel model designed to enhance long-term multivariate forecasting by leveraging a multi-scale masked frequency decomposition approach. MMFNet captures fine, intermediate, and coarse-grained temporal patterns by converting time series into frequency segments at varying scales while employing a learnable mask to filter out irrelevant components adaptively. Extensive experimentation with benchmark datasets shows that MMFNet not only addresses the limitations of the existing methods but also consistently achieves good performance. Specifically, MMFNet achieves up to 6.0% reductions in the Mean Squared Error (MSE) compared to state-of-the-art models designed for multivariate forecasting tasks.

We study the fractal structure of language, aiming to provide a precise formalism for quantifying properties that may have been previously suspected but not formally shown. We establish that language is: (1) self-similar, exhibiting complexities at all levels of granularity, with no particular characteristic context length, and (2) long-range dependent (LRD), with a Hurst parameter of approximately H=0.70. Based on these findings, we argue that short-term patterns/dependencies in language, such as in paragraphs, mirror the patterns/dependencies over larger scopes, like entire documents. This may shed some light on how next-token prediction can lead to a comprehension of the structure of text at multiple levels of granularity, from words and clauses to broader contexts and intents. We also demonstrate that fractal parameters improve upon perplexity-based bits-per-byte (BPB) in predicting downstream performance. We hope these findings offer a fresh perspective on language and the mechanisms underlying the success of LLMs.

Terms and conditions for online shopping websites often contain terms that can have significant financial consequences for customers. Despite their impact, there is currently no comprehensive understanding of the types and potential risks associated with unfavorable financial terms. Furthermore, there are no publicly available detection systems or datasets to systematically identify or mitigate these terms. In this paper, we take the first steps toward solving this problem with three key contributions. First, we introduce TermMiner, an automated data collection and topic modeling pipeline to understand the landscape of unfavorable financial terms. Second, we create ShopTC-100K, a dataset of terms and conditions from shopping websites in the Tranco top 100K list, comprising 1.8 million terms from 8,251 websites. Consequently, we develop a taxonomy of 22 types from 4 categories of unfavorable financial terms -- spanning purchase, post-purchase, account termination, and legal aspects. Third, we build TermLens, an automated detector that uses Large Language Models (LLMs) to identify unfavorable financial terms. Fine-tuned on an annotated dataset, TermLens achieves an F1 score of 94.6\% and a false positive rate of 2.3\% using GPT-4o. When applied to shopping websites from the Tranco top 100K, we find that 42.06\% of these sites contain at least one unfavorable financial term, with such terms being more prevalent on less popular websites. Case studies further highlight the financial risks and customer dissatisfaction associated with unfavorable financial terms, as well as the limitations of existing ecosystem defenses.

Masked language model and autoregressive language model are two types of language models. While pretrained masked language models such as BERT overwhelm the line of natural language understanding (NLU) tasks, autoregressive language models such as GPT are especially capable in natural language generation (NLG). In this paper, we propose a probabilistic masking scheme for the masked language model, which we call probabilistically masked language model (PMLM). We implement a specific PMLM with a uniform prior distribution on the masking ratio named u-PMLM. We prove that u-PMLM is equivalent to an autoregressive permutated language model. One main advantage of the model is that it supports text generation in arbitrary order with surprisingly good quality, which could potentially enable new applications over traditional unidirectional generation. Besides, the pretrained u-PMLM also outperforms BERT on a set of downstream NLU tasks.

Frequent itemset mining is a popular data mining technique. Apriori, Eclat, and FP-Growth are among the most common algorithms for frequent itemset mining. Considerable research has been performed to compare the relative performance between these three algorithms, by evaluating the scalability of each algorithm as the dataset size increases. While scalability as data size increases is important, previous papers have not examined the performance impact of similarly sized datasets that contain different itemset characteristics. This paper explores the effects that two dataset characteristics can have on the performance of these three frequent itemset algorithms. To perform this empirical analysis, a dataset generator is created to measure the effects of frequent item density and the maximum transaction size on performance. The generated datasets contain the same number of rows. This provides some insight into dataset characteristics that are conducive to each algorithm. The results of this paper's research demonstrate Eclat and FP-Growth both handle increases in maximum transaction size and frequent itemset density considerably better than the Apriori algorithm. This paper explores the effects that two dataset characteristics can have on the performance of these three frequent itemset algorithms. To perform this empirical analysis, a dataset generator is created to measure the effects of frequent item density and the maximum transaction size on performance. The generated datasets contain the same number of rows. This provides some insight into dataset characteristics that are conducive to each algorithm. The results of this paper's research demonstrate Eclat and FP-Growth both handle increases in maximum transaction size and frequent itemset density considerably better than the Apriori algorithm.

Residential electricity demand forecasting is critical for efficient energy management and grid stability. Accurate predictions enable utility companies to optimize planning and operations. However, real-world residential electricity demand data often exhibit intricate temporal variability, including multiple seasonalities, periodicities, and abrupt fluctuations, which pose significant challenges for forecasting models. Previous models that rely on statistical methods, recurrent, convolutional neural networks, and transformers often struggle to capture these intricate temporal dynamics. To address these challenges, we propose the Seasonal-Periodic Decomposition Network (SPDNet), a novel deep learning framework consisting of two main modules. The first is the Seasonal-Trend Decomposition Module (STDM), which decomposes the input data into trend, seasonal, and residual components. The second is the Periodical Decomposition Module (PDM), which employs the Fast Fourier Transform to identify the dominant periods. For each dominant period, 1D input data is reshaped into a 2D tensor, where rows represent periods and columns correspond to frequencies. The 2D representations are then processed through three submodules: a 1D convolution to capture sharp fluctuations, a transformer-based encoder to model global patterns, and a 2D convolution to capture interactions between periods. Extensive experiments conducted on real-world residential electricity load data demonstrate that SPDNet outperforms traditional and advanced models in both forecasting accuracy and computational efficiency. The code is available in this repository: https://github.com/Tims2D/SPDNet.