Daily Papers

Recovering a latent potential from observed flow on a directed graph (a discrete Poisson problem with Dirichlet boundaries) is ill-posed, and the standard fix backfires: ridge regularization shrinks toward a gauge-meaningless origin, collapsing and reversing the recovered ordering (+0.81to-0.42 rank correlation against a planted ground truth). The gauge-invariant graph Dirichlet energy removes the hazard and delivers parameter-insensitivity: the estimate is stable across four orders of magnitude in λ, whereas ridge inverts the ordering for every λ>0. We prove the reduced solve is SPD and preserves dynamic range exactly where ridge collapses it, and localize absorbing boundaries from flow alone via a Poisson residual. The H^1 seminorm is classical; what is new is the gauge diagnosis, the parameter-insensitivity it buys, and an ablation showing the result is robust to the extraction method. On three public clickstream corpora the gauge-invariant estimate retains 28--41% of the interior dynamic range while ridge collapses to as little as 0.2%. The same gauge invariance carries into graph neural networks -- neutralizing the constant mode per layer prevents the oversmoothing that collapses a deep directed GCN -- linking this classical inverse problem to a central question in graph learning.

We implement physics-informed neural networks (PINNs) to solve the time-independent Schr\"odinger equation for three canonical one-dimensional quantum potentials: an infinite square well, a finite square well, and a finite barrier. The PINN models incorporate trial wavefunctions that exactly satisfy boundary conditions (Dirichlet zeros at domain boundaries), and they optimize a loss functional combining the PDE residual with a normalization constraint. For the infinite well, the ground-state energy is known (E = pi^2 in dimensionless units) and held fixed in training, whereas for the finite well and barrier, the eigenenergy is treated as a trainable parameter. We use fully-connected neural networks with smooth activation functions to represent the wavefunction and demonstrate that PINNs can learn the ground-state eigenfunctions and eigenvalues for these quantum systems. The results show that the PINN-predicted wavefunctions closely match analytical solutions or expected behaviors, and the learned eigenenergies converge to known values. We present training logs and convergence of the energy parameter, as well as figures comparing the PINN solutions to exact results. The discussion addresses the performance of PINNs relative to traditional numerical methods, highlighting challenges such as convergence to the correct eigenvalue, sensitivity to initialization, and the difficulty of modeling discontinuous potentials. We also discuss the importance of the normalization term to resolve the scaling ambiguity of the wavefunction. Finally, we conclude that PINNs are a viable approach for quantum eigenvalue problems, and we outline future directions including extensions to higher-dimensional and time-dependent Schr\"odinger equations.

We present HyPINO, a multi-physics neural operator designed for zero-shot generalization across a broad class of parametric PDEs without requiring task-specific fine-tuning. Our approach combines a Swin Transformer-based hypernetwork with mixed supervision: (i) labeled data from analytical solutions generated via the Method of Manufactured Solutions (MMS), and (ii) unlabeled samples optimized using physics-informed objectives. The model maps PDE parametrizations to target Physics-Informed Neural Networks (PINNs) and can handle linear elliptic, hyperbolic, and parabolic equations in two dimensions with varying source terms, geometries, and mixed Dirichlet/Neumann boundary conditions, including interior boundaries. HyPINO achieves strong zero-shot accuracy on seven benchmark problems from PINN literature, outperforming U-Nets, Poseidon, and Physics-Informed Neural Operators (PINO). Further, we introduce an iterative refinement procedure that compares the physics of the generated PINN to the requested PDE and uses the discrepancy to generate a "delta" PINN. Summing their contributions and repeating this process forms an ensemble whose combined solution progressively reduces the error on six benchmarks and achieves over 100x gain in average L_2 loss in the best case, while retaining forward-only inference. Additionally, we evaluate the fine-tuning behavior of PINNs initialized by HyPINO and show that they converge faster and to lower final error than both randomly initialized and Reptile-meta-learned PINNs on five benchmarks, performing on par on the remaining two. Our results highlight the potential of this scalable approach as a foundation for extending neural operators toward solving increasingly complex, nonlinear, and high-dimensional PDE problems with significantly improved accuracy and reduced computational cost.

Dirichlet Process mixture models (DPMM) in combination with Gaussian kernels have been an important modeling tool for numerous data domains arising from biological, physical, and social sciences. However, this versatility in applications does not extend to strong theoretical guarantees for the underlying parameter estimates, for which only a logarithmic rate is achieved. In this work, we (re)introduce and investigate a metric, named Orlicz-Wasserstein distance, in the study of the Bayesian contraction behavior for the parameters. We show that despite the overall slow convergence guarantees for all the parameters, posterior contraction for parameters happens at almost polynomial rates in outlier regions of the parameter space. Our theoretical results provide new insight in understanding the convergence behavior of parameters arising from various settings of hierarchical Bayesian nonparametric models. In addition, we provide an algorithm to compute the metric by leveraging Sinkhorn divergences and validate our findings through a simulation study.

Due to the rapid development of large language models, people increasingly often encounter texts that may start as written by a human but continue as machine-generated. Detecting the boundary between human-written and machine-generated parts of such texts is a challenging problem that has not received much attention in literature. We attempt to bridge this gap and examine several ways to adapt state of the art artificial text detection classifiers to the boundary detection setting. We push all detectors to their limits, using the Real or Fake text benchmark that contains short texts on several topics and includes generations of various language models. We use this diversity to deeply examine the robustness of all detectors in cross-domain and cross-model settings to provide baselines and insights for future research. In particular, we find that perplexity-based approaches to boundary detection tend to be more robust to peculiarities of domain-specific data than supervised fine-tuning of the RoBERTa model; we also find which features of the text confuse boundary detection algorithms and negatively influence their performance in cross-domain settings.

In this work, we derive sharp non-asymptotic deviation bounds for weighted sums of Dirichlet random variables. These bounds are based on a novel integral representation of the density of a weighted Dirichlet sum. This representation allows us to obtain a Gaussian-like approximation for the sum distribution using geometry and complex analysis methods. Our results generalize similar bounds for the Beta distribution obtained in the seminal paper Alfers and Dinges [1984]. Additionally, our results can be considered a sharp non-asymptotic version of the inverse of Sanov's theorem studied by Ganesh and O'Connell [1999] in the Bayesian setting. Based on these results, we derive new deviation bounds for the Dirichlet process posterior means with application to Bayesian bootstrap. Finally, we apply our estimates to the analysis of the Multinomial Thompson Sampling (TS) algorithm in multi-armed bandits and significantly sharpen the existing regret bounds by making them independent of the size of the arms distribution support.

Transformers achieve unrivalled performance in modelling language, but remain inefficient in terms of memory and time complexity. A possible remedy is to reduce the sequence length in the intermediate layers by pooling fixed-length segments of tokens. Nevertheless, natural units of meaning, such as words or phrases, display varying sizes. To address this mismatch, we equip language models with a dynamic-pooling mechanism, which predicts segment boundaries in an autoregressive fashion. We compare several methods to infer boundaries, including end-to-end learning through stochastic re-parameterisation, supervised learning (based on segmentations from subword tokenizers or spikes in conditional entropy), as well as linguistically motivated boundaries. We perform character-level evaluation on texts from multiple datasets and morphologically diverse languages. The results demonstrate that dynamic pooling, which jointly segments and models language, is both faster and more accurate than vanilla Transformers and fixed-length pooling within the same computational budget.

With the increasing prevalence of text generated by large language models (LLMs), there is a growing concern about distinguishing between LLM-generated and human-written texts in order to prevent the misuse of LLMs, such as the dissemination of misleading information and academic dishonesty. Previous research has primarily focused on classifying text as either entirely human-written or LLM-generated, neglecting the detection of mixed texts that contain both types of content. This paper explores LLMs' ability to identify boundaries in human-written and machine-generated mixed texts. We approach this task by transforming it into a token classification problem and regard the label turning point as the boundary. Notably, our ensemble model of LLMs achieved first place in the 'Human-Machine Mixed Text Detection' sub-task of the SemEval'24 Competition Task 8. Additionally, we investigate factors that influence the capability of LLMs in detecting boundaries within mixed texts, including the incorporation of extra layers on top of LLMs, combination of segmentation loss, and the impact of pretraining. Our findings aim to provide valuable insights for future research in this area.

Discrete diffusion or flow models could enable faster and more controllable sequence generation than autoregressive models. We show that na\"ive linear flow matching on the simplex is insufficient toward this goal since it suffers from discontinuities in the training target and further pathologies. To overcome this, we develop Dirichlet flow matching on the simplex based on mixtures of Dirichlet distributions as probability paths. In this framework, we derive a connection between the mixtures' scores and the flow's vector field that allows for classifier and classifier-free guidance. Further, we provide distilled Dirichlet flow matching, which enables one-step sequence generation with minimal performance hits, resulting in O(L) speedups compared to autoregressive models. On complex DNA sequence generation tasks, we demonstrate superior performance compared to all baselines in distributional metrics and in achieving desired design targets for generated sequences. Finally, we show that our classifier-free guidance approach improves unconditional generation and is effective for generating DNA that satisfies design targets. Code is available at https://github.com/HannesStark/dirichlet-flow-matching.

Neural speaker diarization is widely used for overlap-aware speaker diarization, but it requires large multi-speaker datasets for training. To meet this data requirement, large datasets are often constructed by combining multiple corpora, including those originally designed for multi-speaker automatic speech recognition (ASR). However, ASR datasets often feature loosely defined segment boundaries that do not align with the stricter conventions of diarization benchmarks. In this work, we show that such boundary looseness significantly impacts the diarization error rate, reducing evaluation reliability. We also reveal that models trained on data with varying boundary precision tend to learn dataset-specific looseness, leading to poor generalization across out-of-domain datasets. Training with standardized tight boundaries via forced alignment improves not only diarization performance, especially in streaming scenarios, but also ASR performance when combined with simple post-processing.

Books are typically segmented into chapters and sections, representing coherent subnarratives and topics. We investigate the task of predicting chapter boundaries, as a proxy for the general task of segmenting long texts. We build a Project Gutenberg chapter segmentation data set of 9,126 English novels, using a hybrid approach combining neural inference and rule matching to recognize chapter title headers in books, achieving an F1-score of 0.77 on this task. Using this annotated data as ground truth after removing structural cues, we present cut-based and neural methods for chapter segmentation, achieving an F1-score of 0.453 on the challenging task of exact break prediction over book-length documents. Finally, we reveal interesting historical trends in the chapter structure of novels.

We study the Dirichlet problem for the weighted Schr\"odinger operator \[-\Delta u +Vu = \lambda \rho u,\] where rho is a positive weighting function and V is a potential. Such equations appear naturally in conformal geometry and in the composite membrane problem. Our primary goal is to establish concavity estimates for the principle eigenfunction with respect to conformal connections. Doing so, we obtain new bounds on the fundamental gap problem, which is the difference between the first and second eigenvalues. In particular, we partially resolve a conjecture of Nguyen, Stancu and Wei [IMRN 2022] on the fundamental gap of horoconvex domains. In addition, we obtain a power convexity estimate for solutions to the torsion problem in spherical geometry on convex domains which are not too large.

Language models provide a key framework for studying linguistic theories based on prediction, but phonological analysis using large language models (LLMs) is difficult; there are few phonological benchmarks beyond English and the standard input representation used in LLMs (subwords of graphemes) is not suitable for analyzing the representation of phonemes. In this work, we demonstrate how word segmentation can be used as a phonological probing task, allowing us to study the representations learned by phoneme-based language models trained on child-directed speech across 31 languages. Following computational models of word segmentation, we present unsupervised methods for extracting word boundaries from a trained model using the observation that prediction-error peaks at the start of words. We also use linear probes to identify that these models implicitly track word boundaries, even when they do not appear in training. This cross-lingual work corroborates statistical learning theories of acquisition and empirically motivates new methods for training subword tokenizers.

In recent years, substantial advancements have been made in the development of large language models, achieving remarkable performance across diverse tasks. To evaluate the knowledge ability of language models, previous studies have proposed lots of benchmarks based on question-answering pairs. We argue that it is not reliable and comprehensive to evaluate language models with a fixed question or limited paraphrases as the query, since language models are sensitive to prompt. Therefore, we introduce a novel concept named knowledge boundary to encompass both prompt-agnostic and prompt-sensitive knowledge within language models. Knowledge boundary avoids prompt sensitivity in language model evaluations, rendering them more dependable and robust. To explore the knowledge boundary for a given model, we propose projected gradient descent method with semantic constraints, a new algorithm designed to identify the optimal prompt for each piece of knowledge. Experiments demonstrate a superior performance of our algorithm in computing the knowledge boundary compared to existing methods. Furthermore, we evaluate the ability of multiple language models in several domains with knowledge boundary.

Interactions with large language models (LLMs) often yield long and detailed responses, leveraging both parametric knowledge and retrieval-augmented generation (RAG). While these responses can provide rich insights, they often include redundant or less engaging content not aligned with user interests. This issue becomes apparent when users specify particular subtopics to include or exclude -- termed coverage-conditioned (C^2) queries -- as LLMs often struggle to provide tailored responses. To address this challenge, we investigate the role of query outlines, sequences of subqueries designed to guide LLMs in generating responses that meet specific user requirements. To systematically create and evaluate these outlines, we introduce QTree, a dataset of 10K hierarchical sets of information-seeking subqueries that define structured boundaries for outline creation and evaluation in C^2 scenarios. Additionally, we develop QPlanner, a 7B language model trained to generate customized outlines within boundaries of QTree. We evaluate the effectiveness of the generated outlines through automatic and human judgements, focusing on their impact within retrieval-augmented generation (RAG) systems. Experimental results demonstrate that QPlanner, especially when trained with alignment techniques like DPO, generates higher-quality outlines that better fulfill diverse user needs.

Sentence Boundary Detection (SBD) is one of the foundational building blocks of Natural Language Processing (NLP), with incorrectly split sentences heavily influencing the output quality of downstream tasks. It is a challenging task for algorithms, especially in the legal domain, considering the complex and different sentence structures used. In this work, we curated a diverse multilingual legal dataset consisting of over 130'000 annotated sentences in 6 languages. Our experimental results indicate that the performance of existing SBD models is subpar on multilingual legal data. We trained and tested monolingual and multilingual models based on CRF, BiLSTM-CRF, and transformers, demonstrating state-of-the-art performance. We also show that our multilingual models outperform all baselines in the zero-shot setting on a Portuguese test set. To encourage further research and development by the community, we have made our dataset, models, and code publicly available.

The recent large language models (LLMs), e.g., ChatGPT, have been able to generate human-like and fluent responses when provided with specific instructions. While admitting the convenience brought by technological advancement, educators also have concerns that students might leverage LLMs to complete their writing assignments and pass them off as their original work. Although many AI content detection studies have been conducted as a result of such concerns, most of these prior studies modeled AI content detection as a classification problem, assuming that a text is either entirely human-written or entirely AI-generated. In this study, we investigated AI content detection in a rarely explored yet realistic setting where the text to be detected is collaboratively written by human and generative LLMs (i.e., hybrid text). We first formalized the detection task as identifying the transition points between human-written content and AI-generated content from a given hybrid text (boundary detection). Then we proposed a two-step approach where we (1) separated AI-generated content from human-written content during the encoder training process; and (2) calculated the distances between every two adjacent prototypes and assumed that the boundaries exist between the two adjacent prototypes that have the furthest distance from each other. Through extensive experiments, we observed the following main findings: (1) the proposed approach consistently outperformed the baseline methods across different experiment settings; (2) the encoder training process can significantly boost the performance of the proposed approach; (3) when detecting boundaries for single-boundary hybrid essays, the proposed approach could be enhanced by adopting a relatively large prototype size, leading to a 22% improvement in the In-Domain evaluation and an 18% improvement in the Out-of-Domain evaluation.

We present a novel metric for the evaluation of the morphological plausibility of subword segmentation. Unlike the typically used morpheme boundary or retrieval F-score, which requires gold segmentation data that is either unavailable or of inconsistent quality across many languages, our approach utilizes morpho-syntactic features. These are available in resources such as Universal Dependencies or UniMorph for a much wider range of languages. The metric works by probabilistically aligning subwords with morphological features through an IBM Model 1. Our experiments show that the metric correlates well with traditional morpheme boundary recall while being more broadly applicable across languages with different morphological systems.

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared representation space using contrastive learning. However, systematic evaluations reveal significant performance degradation at structural boundaries where distinct topological patterns converge, with accuracy losses exceeding 20 percentage points. This issue arises from a key limitation: current methods assume all graph structures can be encoded within a single Euclidean space. In reality, tree structures require hyperbolic geometry to preserve hierarchical branching, while cyclic patterns depend on spherical geometry for closure properties. At structural boundaries, nodes experience conflicting geometric constraints that uniform encoding spaces cannot resolve. This raises a crucial challenge: Can alignment frameworks be designed to respect the intrinsic geometric diversity of graph structures? We introduce GraphShaper, a geometry-aware framework that enhances graph encoding through multi-geometric specialization. Our approach employs expert networks tailored to different geometric spaces, dynamically computing fusion weights to adaptively integrate geometric properties based on local structural characteristics. This adaptive fusion preserves structural integrity before alignment with text embeddings. Extensive experiments demonstrate that GraphShaper achieves 9.47\% accuracy improvements on citation networks and 7.63\% on social networks in zero-shot settings.

Under standard graphical assumptions, the Markov boundary of a target variable is the smallest set of features that renders every other feature redundant. Once the boundary is observed, the target is conditionally independent of the rest of the table. This is a tempting object for tabular prediction, since it names exactly the columns a model should need. Yet modern regressors are still trained on the full feature set. We ask whether the Markov boundary is genuinely useful for prediction on SCM3K, a 3,450-task synthetic SCM benchmark with feature counts from 40 to 1000 and six SCM families, evaluated with six regressors. The answer is more nuanced than the theory suggests. Restricting a regressor to the oracle boundary often improves prediction substantially, and the improvement grows as the feature space becomes larger and sparser. But the natural pipeline of recovering the boundary with causal discovery and training on the recovered mask does not deliver. Existing estimators exhaust the compute budget before reaching the regime where the boundary helps most, and even where they run they rarely beat the full feature set. We trace this to three causes. Discovery optimizes structural recovery rather than prediction. False negatives and false positives carry sharply asymmetric predictive cost. The exact boundary is only one of many feature sets that beat all features. We then develop what these facts imply for prediction-aligned feature selection and for tabular models that learn to use causal structure.

Domain-general semantic parsing is a long-standing goal in natural language processing, where the semantic parser is capable of robustly parsing sentences from domains outside of which it was trained. Current approaches largely rely on additional supervision from new domains in order to generalize to those domains. We present a generative model of natural language utterances and logical forms and demonstrate its application to semantic parsing. Our approach relies on domain-independent supervision to generalize to new domains. We derive and implement efficient algorithms for training, parsing, and sentence generation. The work relies on a novel application of hierarchical Dirichlet processes (HDPs) for structured prediction, which we also present in this manuscript. This manuscript is an excerpt of chapter 4 from the Ph.D. thesis of Saparov (2022), where the model plays a central role in a larger natural language understanding system. This manuscript provides a new simplified and more complete presentation of the work first introduced in Saparov, Saraswat, and Mitchell (2017). The description and proofs of correctness of the training algorithm, parsing algorithm, and sentence generation algorithm are much simplified in this new presentation. We also describe the novel application of hierarchical Dirichlet processes for structured prediction. In addition, we extend the earlier work with a new model of word morphology, which utilizes the comprehensive morphological data from Wiktionary.

The Beta kernel estimator offers a theoretically superior alternative to the Gaussian kernel for unit interval data, eliminating boundary bias without requiring reflection or transformation. However, its adoption remains limited by the lack of a reliable bandwidth selector; practitioners currently rely on iterative optimization methods that are computationally expensive and prone to instability. We derive the ``Beta Reference Rule,'' a fast, closed-form bandwidth selector based on the unweighted Asymptotic Mean Integrated Squared Error (AMISE) of a beta reference distribution. To address boundary integrability issues, we introduce a principled heuristic for U-shaped and J-shaped distributions. By employing a method-of-moments approximation, we reduce the bandwidth selection complexity from iterative optimization to O(1). Extensive Monte Carlo simulations demonstrate that our rule matches the accuracy of numerical optimization while delivering a speedup of over 35,000 times. Real-world validation on socioeconomic data shows that it avoids the ``vanishing boundary'' and ``shoulder'' artifacts common to Gaussian-based methods. We provide a comprehensive, open-source Python package to facilitate the immediate adoption of the Beta kernel as a drop-in replacement for standard density estimation tools.

Consider a random uniform sample of n points in a compact region A of Euclidean d-space, d geq 2, with a smooth or (when d=2) polygonal boundary. Fix k bf N. Let T_{n,k} be the threshold r at which the geometric graph on these n vertices with distance parameter r becomes k-connected. We show that if d=2 then n (pi/|A|) T_{n,1}^2 - log n is asymptotically standard Gumbel. For (d,k) neq (2,1), it is n (theta_d/|A|) T_{n,k}^d - (2-2/d) log n - (4-2k-2/d) log log n that converges in distribution to a nondegenerate limit, where theta_d is the volume of the unit ball. The limit is Gumbel with scale parameter 2 except when (d,k)=(2,2) where the limit is two component extreme value distributed. The different cases reflect the fact that boundary effects are more more important in some cases than others. We also give similar results for the largest k-nearest neighbour link U_{n,k} in the sample, and show T_{n,k}=U_{n,k} with high probability. We provide estimates on rates of convergence and give similar results for Poisson samples in A. Finally, we give similar results even for non-uniform samples, with a less explicit sequence of centring constants.

In the age of advanced large language models (LLMs), the boundaries between human and AI-generated text are becoming increasingly blurred. We address the challenge of segmenting mixed-authorship text, that is identifying transition points in text where authorship shifts from human to AI or vice-versa, a problem with critical implications for authenticity, trust, and human oversight. We introduce a novel framework, called Info-Mask for mixed authorship detection that integrates stylometric cues, perplexity-driven signals, and structured boundary modeling to accurately segment collaborative human-AI content. To evaluate the robustness of our system against adversarial perturbations, we construct and release an adversarial benchmark dataset Mixed-text Adversarial setting for Segmentation (MAS), designed to probe the limits of existing detectors. Beyond segmentation accuracy, we introduce Human-Interpretable Attribution (HIA overlays that highlight how stylometric features inform boundary predictions, and we conduct a small-scale human study assessing their usefulness. Across multiple architectures, Info-Mask significantly improves span-level robustness under adversarial conditions, establishing new baselines while revealing remaining challenges. Our findings highlight both the promise and limitations of adversarially robust, interpretable mixed-authorship detection, with implications for trust and oversight in human-AI co-authorship.

While understanding the knowledge boundaries of LLMs is crucial to prevent hallucination, research on knowledge boundaries of LLMs has predominantly focused on English. In this work, we present the first study to analyze how LLMs recognize knowledge boundaries across different languages by probing their internal representations when processing known and unknown questions in multiple languages. Our empirical studies reveal three key findings: 1) LLMs' perceptions of knowledge boundaries are encoded in the middle to middle-upper layers across different languages. 2) Language differences in knowledge boundary perception follow a linear structure, which motivates our proposal of a training-free alignment method that effectively transfers knowledge boundary perception ability across languages, thereby helping reduce hallucination risk in low-resource languages; 3) Fine-tuning on bilingual question pair translation further enhances LLMs' recognition of knowledge boundaries across languages. Given the absence of standard testbeds for cross-lingual knowledge boundary analysis, we construct a multilingual evaluation suite comprising three representative types of knowledge boundary data. Our code and datasets are publicly available at https://github.com/DAMO-NLP-SG/LLM-Multilingual-Knowledge-Boundaries.

We investigate optimal control problems governed by the elliptic partial differential equation -Delta u=f subject to Dirichlet boundary conditions on a given domain Omega. The control variable in this setting is the right-hand side f, and the objective is to minimize a cost functional that depends simultaneously on the control f and on the associated state function u. We establish the existence of optimal controls and analyze their qualitative properties by deriving necessary conditions for optimality. In particular, when pointwise constraints of the form alphale flebeta are imposed a priori on the control, we examine situations where a {\it bang-bang} phenomenon arises, that is where the optimal control f assumes only the extremal values alpha and beta. More precisely, the control takes the form f=alpha1_E+beta1_{Omegasetminus E}, thereby placing the problem within the framework of shape optimization. Under suitable assumptions, we further establish certain regularity properties for the optimal sets E. Finally, in the last part of the paper, we present numerical simulations that illustrate our theoretical findings through a selection of representative examples.

Dialogue topic segmentation supports summarization, retrieval, memory management, and conversational continuity. Despite decades of prior work, evaluation practice in dialogue topic segmentation remains dominated by strict boundary matching and F1-based metrics, even as modern LLM-based conversational systems increasingly rely on segmentation to manage conversation history beyond the model's fixed context window, where unstructured context accumulation degrades efficiency and coherence. This paper introduces an evaluation objective for dialogue topic segmentation that treats boundary density and segment coherence as primary criteria, alongside window-tolerant F1 (W-F1). Through extensive cross-dataset empirical evaluation, we show that reported performance differences across dialogue segmentation benchmarks are driven not by model quality, but by annotation granularity mismatches and sparse boundary labels. This indicates that many reported improvements arise from evaluation artifacts rather than improved boundary detection. We evaluated multiple, structurally distinct dialogue segmentation strategies across eight dialogue datasets spanning task-oriented, open-domain, meeting-style, and synthetic interactions. Across these settings, we observe high segment coherence combined with extreme oversegmentation relative to sparse labels, producing misleadingly low exact-match F1 scores. We show that topic segmentation is best understood as selecting an appropriate granularity rather than predicting a single correct boundary set. We operationalize this view by explicitly separating boundary scoring from boundary selection.

We introduce a new functional space U designed to contain all classical arithmetic functions (Mobius, von Mangoldt, Euler phi, divisor functions, Dirichlet characters, etc.). The norm of U combines a Hilbert-type component, based on square summability of Dirichlet coefficients for every s > 1, with a Banach component controlling logarithmic averages of partial sums. We prove that U is a complete Banach space which embeds continuously all standard Hilbert spaces of Dirichlet series and allows natural actions of Dirichlet convolution and shift operators. This framework provides a unified analytic setting for classical and modern problems in multiplicative number theory.

Large-scale pre-training tasks like image classification, captioning, or self-supervised techniques do not incentivize learning the semantic boundaries of objects. However, recent generative foundation models built using text-based latent diffusion techniques may learn semantic boundaries. This is because they have to synthesize intricate details about all objects in an image based on a text description. Therefore, we present a technique for segmenting real and AI-generated images using latent diffusion models (LDMs) trained on internet-scale datasets. First, we show that the latent space of LDMs (z-space) is a better input representation compared to other feature representations like RGB images or CLIP encodings for text-based image segmentation. By training the segmentation models on the latent z-space, which creates a compressed representation across several domains like different forms of art, cartoons, illustrations, and photographs, we are also able to bridge the domain gap between real and AI-generated images. We show that the internal features of LDMs contain rich semantic information and present a technique in the form of LD-ZNet to further boost the performance of text-based segmentation. Overall, we show up to 6% improvement over standard baselines for text-to-image segmentation on natural images. For AI-generated imagery, we show close to 20% improvement compared to state-of-the-art techniques. The project is available at https://koutilya-pnvr.github.io/LD-ZNet/.

In this work, we study the asymptotic behaviour of solutions to the heat equation in exterior domains, i.e., domains which are the complement of a smooth compact set in R^N. Different homogeneous boundary conditions are considered, including Dirichlet, Robin, and Neumann ones. In this second part of our work, we consider the case of bounded initial data and prove that, after some correction term, the solutions become close to the solutions in the whole space and show how complex behaviours appear. We also analyse the case of initial data in L^p with 1<p<infty where all solutions essentially decay to 0 and the convergence rate could be arbitrarily slow.

A realistic Chinese word segmentation tool must adapt to textual variations with minimal training input and yet robust enough to yield reliable segmentation result for all variants. Various lexicon-driven approaches to Chinese segmentation, e.g. [1,16], achieve high f-scores yet require massive training for any variation. Text-driven approach, e.g. [12], can be easily adapted for domain and genre changes yet has difficulty matching the high f-scores of the lexicon-driven approaches. In this paper, we refine and implement an innovative text-driven word boundary decision (WBD) segmentation model proposed in [15]. The WBD model treats word segmentation simply and efficiently as a binary decision on whether to realize the natural textual break between two adjacent characters as a word boundary. The WBD model allows simple and quick training data preparation converting characters as contextual vectors for learning the word boundary decision. Machine learning experiments with four different classifiers show that training with 1,000 vectors and 1 million vectors achieve comparable and reliable results. In addition, when applied to SigHAN Bakeoff 3 competition data, the WBD model produces OOV recall rates that are higher than all published results. Unlike all previous work, our OOV recall rate is comparable to our own F-score. Both experiments support the claim that the WBD model is a realistic model for Chinese word segmentation as it can be easily adapted for new variants with the robust result. In conclusion, we will discuss linguistic ramifications as well as future implications for the WBD approach.

Graph-structured knowledge systems -- from knowledge graphs to GraphRAG pipelines -- organize information into hierarchical communities, yet lack a principled mechanism for continuous resolution control: where do the qualitative boundaries between abstraction levels lie, and how should an agent navigate them? Current approaches rely on discrete community detection with manually tuned resolution parameters (e.g., Leiden γ), offering no continuous zoom and no formal guarantees. We introduce Semantic Level of Detail (SLoD), a framework that addresses both problems by defining a continuous zoom operator via heat kernel diffusion on a graph Laplacian whose kNN structure is induced by a Poincare-ball embedding. We prove hierarchical coherence in the tree limit (exact tree with Sarkar embedding), with bounded approximation error, and demonstrate consistent boundary-detection behaviour on noisy hierarchies; spectral gaps in the graph Laplacian then induce emergent scale boundaries -- scales where the representation undergoes qualitative transitions -- detectable without manual resolution tuning. On synthetic hierarchies (HSBM, 1024 nodes), spectral clustering at the BoundaryScan-detected scale recovers planted levels, with macro ARI saturating at 1.00 in the high-SNR regime (50-seed median) and meso ARI reaching 0.89 [0.86, 0.92] at r=200. On the full WordNet noun hierarchy (82K synsets), using 100 stratified leaf queries, detected boundaries align with true taxonomic depth (τ= 0.79), demonstrating meaningful abstraction-level discovery in real-world knowledge graphs without resolution-parameter tuning. The composite weights, MAD threshold, and kNN-parameter rule (k = max(10, min(lfloorNrfloor, 50))) use defaults that transferred unchanged between HSBM and WordNet; their behaviour on graphs with implicit or qualitatively different hierarchical structure is open.

We describe nonparametric deconvolution models (NDMs), a family of Bayesian nonparametric models for collections of data in which each observation is the average over the features from heterogeneous particles. For example, these types of data are found in elections, where we observe precinct-level vote tallies (observations) of individual citizens' votes (particles) across each of the candidates or ballot measures (features), where each voter is part of a specific voter cohort or demographic (factor). Like the hierarchical Dirichlet process, NDMs rely on two tiers of Dirichlet processes to explain the data with an unknown number of latent factors; each observation is modeled as a weighted average of these latent factors. Unlike existing models, NDMs recover how factor distributions vary locally for each observation. This uniquely allows NDMs both to deconvolve each observation into its constituent factors, and also to describe how the factor distributions specific to each observation vary across observations and deviate from the corresponding global factors. We present variational inference techniques for this family of models and study its performance on simulated data and voting data from California. We show that including local factors improves estimates of global factors and provides a novel scaffold for exploring data.

Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding techniques for boundary enforcement. Reflected diffusion models (Lou23) aim to enhance generalizability by generating the data distribution through a backward process governed by reflected Brownian motion. However, reflected diffusion models may not easily adapt to diverse domains without the derivation of proper diffeomorphic mappings and do not guarantee optimal transport properties. To overcome these limitations, we introduce the Reflected Schrodinger Bridge algorithm: an entropy-regularized optimal transport approach tailored for generating data within diverse bounded domains. We derive elegant reflected forward-backward stochastic differential equations with Neumann and Robin boundary conditions, extend divergence-based likelihood training to bounded domains, and explore natural connections to entropic optimal transport for the study of approximate linear convergence - a valuable insight for practical training. Our algorithm yields robust generative modeling in diverse domains, and its scalability is demonstrated in real-world constrained generative modeling through standard image benchmarks.

Named Entity Recognition (NER) is a fundamental NLP task, commonly formulated as classification over a sequence of tokens. Morphologically-Rich Languages (MRLs) pose a challenge to this basic formulation, as the boundaries of Named Entities do not necessarily coincide with token boundaries, rather, they respect morphological boundaries. To address NER in MRLs we then need to answer two fundamental questions, namely, what are the basic units to be labeled, and how can these units be detected and classified in realistic settings, i.e., where no gold morphology is available. We empirically investigate these questions on a novel NER benchmark, with parallel tokenlevel and morpheme-level NER annotations, which we develop for Modern Hebrew, a morphologically rich-and-ambiguous language. Our results show that explicitly modeling morphological boundaries leads to improved NER performance, and that a novel hybrid architecture, in which NER precedes and prunes morphological decomposition, greatly outperforms the standard pipeline, where morphological decomposition strictly precedes NER, setting a new performance bar for both Hebrew NER and Hebrew morphological decomposition tasks.

In this paper, we present a rule-based sentence boundary disambiguation Python package that works out-of-the-box for 22 languages. We aim to provide a realistic segmenter which can provide logical sentences even when the format and domain of the input text is unknown. In our work, we adapt the Golden Rules Set (a language-specific set of sentence boundary exemplars) originally implemented as a ruby gem - pragmatic_segmenter - which we ported to Python with additional improvements and functionality. PySBD passes 97.92% of the Golden Rule Set exemplars for English, an improvement of 25% over the next best open-source Python tool.

Estimating truncated density models is difficult, as these models have intractable normalising constants and hard to satisfy boundary conditions. Score matching can be adapted to solve the truncated density estimation problem, but requires a continuous weighting function which takes zero at the boundary and is positive elsewhere. Evaluation of such a weighting function (and its gradient) often requires a closed-form expression of the truncation boundary and finding a solution to a complicated optimisation problem. In this paper, we propose approximate Stein classes, which in turn leads to a relaxed Stein identity for truncated density estimation. We develop a novel discrepancy measure, truncated kernelised Stein discrepancy (TKSD), which does not require fixing a weighting function in advance, and can be evaluated using only samples on the boundary. We estimate a truncated density model by minimising the Lagrangian dual of TKSD. Finally, experiments show the accuracy of our method to be an improvement over previous works even without the explicit functional form of the boundary.

Denoising diffusion probabilistic models (DDPMs) (Ho et al. 2020) have shown impressive results on image and waveform generation in continuous state spaces. Here, we introduce Discrete Denoising Diffusion Probabilistic Models (D3PMs), diffusion-like generative models for discrete data that generalize the multinomial diffusion model of Hoogeboom et al. 2021, by going beyond corruption processes with uniform transition probabilities. This includes corruption with transition matrices that mimic Gaussian kernels in continuous space, matrices based on nearest neighbors in embedding space, and matrices that introduce absorbing states. The third allows us to draw a connection between diffusion models and autoregressive and mask-based generative models. We show that the choice of transition matrix is an important design decision that leads to improved results in image and text domains. We also introduce a new loss function that combines the variational lower bound with an auxiliary cross entropy loss. For text, this model class achieves strong results on character-level text generation while scaling to large vocabularies on LM1B. On the image dataset CIFAR-10, our models approach the sample quality and exceed the log-likelihood of the continuous-space DDPM model.

Some fractals -- for instance those associated with the Mandelbrot and quadratic Julia sets -- are computed by iterating a function, and identifying the boundary between hyperparameters for which the resulting series diverges or remains bounded. Neural network training similarly involves iterating an update function (e.g. repeated steps of gradient descent), can result in convergent or divergent behavior, and can be extremely sensitive to small changes in hyperparameters. Motivated by these similarities, we experimentally examine the boundary between neural network hyperparameters that lead to stable and divergent training. We find that this boundary is fractal over more than ten decades of scale in all tested configurations.

Boundary point detection aims to outline the external contour structure of clusters and enhance the inter-cluster discrimination, thus bolstering the performance of the downstream classification and clustering tasks. However, existing boundary point detectors are sensitive to density heterogeneity or cannot identify boundary points in concave structures and high-dimensional manifolds. In this work, we propose a robust and efficient boundary point detection method based on Local Direction Dispersion (LoDD). The core of boundary point detection lies in measuring the difference between boundary points and internal points. It is a common observation that an internal point is surrounded by its neighbors in all directions, while the neighbors of a boundary point tend to be distributed only in a certain directional range. By considering this observation, we adopt density-independent K-Nearest Neighbors (KNN) method to determine neighboring points and design a centrality metric LoDD using the eigenvalues of the covariance matrix to depict the distribution uniformity of KNN. We also develop a grid-structure assumption of data distribution to determine the parameters adaptively. The effectiveness of LoDD is demonstrated on synthetic datasets, real-world benchmarks, and application of training set split for deep learning model and hole detection on point cloud data. The datasets and toolkit are available at: https://github.com/ZPGuiGroupWhu/lodd.

Large language models (LLMs) have achieved remarkable success and demonstrated superior performance across various tasks, including natural language processing (NLP), weather forecasting, biological protein folding, text generation, and solving mathematical problems. However, many real-world data exhibit highly non-Euclidean latent hierarchical anatomy, such as protein networks, transportation networks, financial networks, brain networks, and linguistic structures or syntactic trees in natural languages. Effectively learning intrinsic semantic entailment and hierarchical relationships from these raw, unstructured input data using LLMs remains an underexplored area. Due to its effectiveness in modeling tree-like hierarchical structures, hyperbolic geometry -- a non-Euclidean space -- has rapidly gained popularity as an expressive latent representation space for complex data modeling across domains such as graphs, images, languages, and multi-modal data. Here, we provide a comprehensive and contextual exposition of recent advancements in LLMs that leverage hyperbolic geometry as a representation space to enhance semantic representation learning and multi-scale reasoning. Specifically, the paper presents a taxonomy of the principal techniques of Hyperbolic LLMs (HypLLMs) in terms of four main categories: (1) hyperbolic LLMs through exp/log maps; (2) hyperbolic fine-tuned models; (3) fully hyperbolic LLMs, and (4) hyperbolic state-space models. We also explore crucial potential applications and outline future research directions. A repository of key papers, models, datasets, and code implementations is available at https://github.com/sarangp2402/Hyperbolic-LLM-Models/tree/main.

Phoneme boundary detection plays an essential first step for a variety of speech processing applications such as speaker diarization, speech science, keyword spotting, etc. In this work, we propose a neural architecture coupled with a parameterized structured loss function to learn segmental representations for the task of phoneme boundary detection. First, we evaluated our model when the spoken phonemes were not given as input. Results on the TIMIT and Buckeye corpora suggest that the proposed model is superior to the baseline models and reaches state-of-the-art performance in terms of F1 and R-value. We further explore the use of phonetic transcription as additional supervision and show this yields minor improvements in performance but substantially better convergence rates. We additionally evaluate the model on a Hebrew corpus and demonstrate such phonetic supervision can be beneficial in a multi-lingual setting.

In this paper, we introduce a novel approach for bounding the cumulant generating function (CGF) of a Dirichlet process (DP) X sim DP(αν_0), using superadditivity. In particular, our key technical contribution is the demonstration of the superadditivity of αmapsto log E_{X sim DP(αν_0)}[exp( E_X[αf])], where E_X[f] = int f dX. This result, combined with Fekete's lemma and Varadhan's integral lemma, converts the known asymptotic large deviation principle into a practical upper bound on the CGF logE_{Xsim DP(αν_0)}{exp(E_{X}{[f]})} for any α> 0. The bound is given by the convex conjugate of the scaled reversed Kullback-Leibler divergence αKL(ν_0Vert cdot). This new bound provides particularly effective confidence regions for sums of independent DPs, making it applicable across various fields.

Unsupervised automatic speech recognition (ASR) aims to learn the mapping between the speech signal and its corresponding textual transcription without the supervision of paired speech-text data. A word/phoneme in the speech signal is represented by a segment of speech signal with variable length and unknown boundary, and this segmental structure makes learning the mapping between speech and text challenging, especially without paired data. In this paper, we propose REBORN, Reinforcement-Learned Boundary Segmentation with Iterative Training for Unsupervised ASR. REBORN alternates between (1) training a segmentation model that predicts the boundaries of the segmental structures in speech signals and (2) training the phoneme prediction model, whose input is a segmental structure segmented by the segmentation model, to predict a phoneme transcription. Since supervised data for training the segmentation model is not available, we use reinforcement learning to train the segmentation model to favor segmentations that yield phoneme sequence predictions with a lower perplexity. We conduct extensive experiments and find that under the same setting, REBORN outperforms all prior unsupervised ASR models on LibriSpeech, TIMIT, and five non-English languages in Multilingual LibriSpeech. We comprehensively analyze why the boundaries learned by REBORN improve the unsupervised ASR performance.

In this paper, we propose DiffusionNER, which formulates the named entity recognition task as a boundary-denoising diffusion process and thus generates named entities from noisy spans. During training, DiffusionNER gradually adds noises to the golden entity boundaries by a fixed forward diffusion process and learns a reverse diffusion process to recover the entity boundaries. In inference, DiffusionNER first randomly samples some noisy spans from a standard Gaussian distribution and then generates the named entities by denoising them with the learned reverse diffusion process. The proposed boundary-denoising diffusion process allows progressive refinement and dynamic sampling of entities, empowering DiffusionNER with efficient and flexible entity generation capability. Experiments on multiple flat and nested NER datasets demonstrate that DiffusionNER achieves comparable or even better performance than previous state-of-the-art models.

Mathematical symbols and descriptions appear in various forms across document section boundaries without explicit markup. In this paper, we present a new large-scale dataset that emphasizes extracting symbols and descriptions in scientific documents. Symlink annotates scientific papers of 5 different domains (i.e., computer science, biology, physics, mathematics, and economics). Our experiments on Symlink demonstrate the challenges of the symbol-description linking task for existing models and call for further research effort in this area. We will publicly release Symlink to facilitate future research.

One important and particularly challenging step in the optical character recognition (OCR) of historical documents with complex layouts, such as newspapers, is the separation of text from non-text content (e.g. page borders or illustrations). This step is commonly referred to as page segmentation. While various rule-based algorithms have been proposed, the applicability of Deep Neural Networks (DNNs) for this task recently has gained a lot of attention. In this paper, we perform a systematic evaluation of 11 different published DNN backbone architectures and 9 different tiling and scaling configurations for separating text, tables or table column lines. We also show the influence of the number of labels and the number of training pages on the segmentation quality, which we measure using the Matthews Correlation Coefficient. Our results show that (depending on the task) Inception-ResNet-v2 and EfficientNet backbones work best, vertical tiling is generally preferable to other tiling approaches, and training data that comprises 30 to 40 pages will be sufficient most of the time.

We present NUPunkt and CharBoundary, two sentence boundary detection libraries optimized for high-precision, high-throughput processing of legal text in large-scale applications such as due diligence, e-discovery, and legal research. These libraries address the critical challenges posed by legal documents containing specialized citations, abbreviations, and complex sentence structures that confound general-purpose sentence boundary detectors. Our experimental evaluation on five diverse legal datasets comprising over 25,000 documents and 197,000 annotated sentence boundaries demonstrates that NUPunkt achieves 91.1% precision while processing 10 million characters per second with modest memory requirements (432 MB). CharBoundary models offer balanced and adjustable precision-recall tradeoffs, with the large model achieving the highest F1 score (0.782) among all tested methods. Notably, NUPunkt provides a 29-32% precision improvement over general-purpose tools while maintaining exceptional throughput, processing multi-million document collections in minutes rather than hours. Both libraries run efficiently on standard CPU hardware without requiring specialized accelerators. NUPunkt is implemented in pure Python with zero external dependencies, while CharBoundary relies only on scikit-learn and optional ONNX runtime integration for optimized performance. Both libraries are available under the MIT license, can be installed via PyPI, and can be interactively tested at https://sentences.aleainstitute.ai/. These libraries address critical precision issues in retrieval-augmented generation systems by preserving coherent legal concepts across sentences, where each percentage improvement in precision yields exponentially greater reductions in context fragmentation, creating cascading benefits throughout retrieval pipelines and significantly enhancing downstream reasoning quality.

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.

Automatic detection of phoneme or word-like units is one of the core objectives in zero-resource speech processing. Recent attempts employ self-supervised training methods, such as contrastive predictive coding (CPC), where the next frame is predicted given past context. However, CPC only looks at the audio signal's frame-level structure. We overcome this limitation with a segmental contrastive predictive coding (SCPC) framework that can model the signal structure at a higher level e.g. at the phoneme level. In this framework, a convolutional neural network learns frame-level representation from the raw waveform via noise-contrastive estimation (NCE). A differentiable boundary detector finds variable-length segments, which are then used to optimize a segment encoder via NCE to learn segment representations. The differentiable boundary detector allows us to train frame-level and segment-level encoders jointly. Typically, phoneme and word segmentation are treated as separate tasks. We unify them and experimentally show that our single model outperforms existing phoneme and word segmentation methods on TIMIT and Buckeye datasets. We analyze the impact of boundary threshold and when is the right time to include the segmental loss in the learning process.

Diffusion language models (DLMs) have recently emerged as a strong alternative to autoregressive models by enabling parallel text generation. To improve inference efficiency and KV-cache compatibility, prior work commonly adopts block-based diffusion, decoding tokens block by block. However, this paradigm suffers from a structural limitation that we term Boundary-Induced Context Truncation (BICT): undecoded tokens near block boundaries are forced to commit without access to nearby future context, even when such context could substantially reduce uncertainty. This limitation degrades decoding certainty and generation quality, especially for tasks requiring precise reasoning, such as mathematical problem solving and code generation. We propose Deferred Commitment Decoding (DCD), a novel, training-free decoding strategy that mitigates this issue. DCD maintains a certainty-aware sliding window over masked tokens, resolving low-uncertainty tokens early while deferring high-uncertainty tokens until sufficient contextual evidence becomes available. Extensive experiments across multiple diffusion language models, benchmarks, and caching configurations show that DCD improves generation accuracy by 1.73% with comparable time on average compared to fixed block-based diffusion methods, with the most significant improvement reaching 16.5%. These results demonstrate that deferring token commitment based on uncertainty is a simple yet effective principle for improving both the quality and efficiency of diffusion language model decoding.

We present an open-source benchmark and evaluation framework for assessing emotional boundary handling in Large Language Models (LLMs). Using a dataset of 1156 prompts across six languages, we evaluated three leading LLMs (GPT-4o, Claude-3.5 Sonnet, and Mistral-large) on their ability to maintain appropriate emotional boundaries through pattern-matched response analysis. Our framework quantifies responses across seven key patterns: direct refusal, apology, explanation, deflection, acknowledgment, boundary setting, and emotional awareness. Results demonstrate significant variation in boundary-handling approaches, with Claude-3.5 achieving the highest overall score (8.69/10) and producing longer, more nuanced responses (86.51 words on average). We identified a substantial performance gap between English (average score 25.62) and non-English interactions (< 0.22), with English responses showing markedly higher refusal rates (43.20% vs. < 1% for non-English). Pattern analysis revealed model-specific strategies, such as Mistral's preference for deflection (4.2%) and consistently low empathy scores across all models (< 0.06). Limitations include potential oversimplification through pattern matching, lack of contextual understanding in response analysis, and binary classification of complex emotional responses. Future work should explore more nuanced scoring methods, expand language coverage, and investigate cultural variations in emotional boundary expectations. Our benchmark and methodology provide a foundation for systematic evaluation of LLM emotional intelligence and boundary-setting capabilities.

Chain-of-Thought (CoT) reasoning has emerged as a promising approach for enhancing the performance of large language models (LLMs) on complex reasoning tasks. Recently, a series of studies attempt to explain the mechanisms underlying CoT, aiming to deepen the understanding of its efficacy. Nevertheless, the existing research faces two major challenges: (1) a lack of quantitative metrics to assess CoT capabilities and (2) a dearth of guidance on optimizing CoT performance. Motivated by this, in this work, we introduce a novel reasoning boundary framework (RBF) to address these challenges. To solve the lack of quantification, we first define a reasoning boundary (RB) to quantify the upper-bound of CoT and establish a combination law for RB, enabling a practical quantitative approach applicable to various real-world CoT tasks. To address the lack of optimization, we propose three categories of RBs. We further optimize these categories with combination laws focused on RB promotion and reasoning path optimization for CoT improvement. Through extensive experiments on 27 models and 5 tasks, the study validates the existence and rationality of the proposed framework. Furthermore, it explains the effectiveness of 10 CoT strategies and guides optimization from two perspectives. We hope this work can provide a comprehensive understanding of the boundaries and optimization strategies for reasoning in LLMs. Our code and data are available at https://github.com/LightChen233/reasoning-boundary.

In this work, we provide a systematic survey of Discrete Diffusion Language Models (dLLMs) and Discrete Diffusion Multimodal Language Models (dMLLMs). Unlike autoregressive (AR) models, dLLMs and dMLLMs adopt a multi-token, parallel decoding paradigm using full attention and a denoising-based generation strategy. This paradigm naturally enables parallel generation, fine-grained output controllability, and dynamic, response-aware perception. These capabilities are previously difficult to achieve with AR models. Recently, a growing number of industrial-scale proprietary d(M)LLMs, as well as a large number of open-source academic d(M)LLMs, have demonstrated performance comparable to their autoregressive counterparts, while achieving up to 10x acceleration in inference speed. The advancement of discrete diffusion LLMs and MLLMs has been largely driven by progress in two domains. The first is the development of autoregressive LLMs and MLLMs, which has accumulated vast amounts of data, benchmarks, and foundational infrastructure for training and inference. The second contributing domain is the evolution of the mathematical models underlying discrete diffusion. Together, these advancements have catalyzed a surge in dLLMs and dMLLMs research in early 2025. In this work, we present a comprehensive overview of the research in the dLLM and dMLLM domains. We trace the historical development of dLLMs and dMLLMs, formalize the underlying mathematical frameworks, and categorize representative models. We further analyze key techniques for training and inference, and summarize emerging applications across language, vision-language, and biological domains. We conclude by discussing future directions for research and deployment. Paper collection: https://github.com/LiQiiiii/DLLM-Survey

Every chemical language model reading SMILES begins with a tokenizer, yet the field has inherited byte-pair encoding (BPE) from natural language with little scrutiny. In natural language, BPE's principal alternative, Unigram-LM, is known to build structurally different vocabularies. Whether that contrast survives in chemistry was open. We report a controlled comparison of BPE and Unigram-LM over a fixed 165-token chemistry base, at the small vocabulary sizes where token embeddings are learnable, across three corpus typologies (diverse, drug-like, natural-products) and both pre-tokenization boundary policies. The two do not converge. In all 22 matched conditions they build near-disjoint subword vocabularies: cross-algorithm Jaccard overlap on the learned pieces never exceeds 0.161, and at most 0.05 once weighted toward the high-frequency pieces a model updates most. Unigram-LM also segments held-out molecules into 29-41% more tokens; the arms largely agree on where to cut but not how deeply, so BPE's segmentation is a strict coarsening of Unigram-LM's on 80-99% of molecules. The separation holds across corpus, boundary, and vocabulary size, persisting even at eight times that scale. The subword algorithm is therefore a modeling decision, not a free default. The study trains no language models.

Khmer text is written from left to right with optional space. Space is not served as a word boundary but instead, it is used for readability or other functional purposes. Word segmentation is a prior step for downstream tasks such as part-of-speech (POS) tagging and thus, the robustness of POS tagging highly depends on word segmentation. The conventional Khmer POS tagging is a two-stage process that begins with word segmentation and then actual tagging of each word, afterward. In this work, a joint word segmentation and POS tagging approach using a single deep learning model is proposed so that word segmentation and POS tagging can be performed spontaneously. The proposed model was trained and tested using the publicly available Khmer POS dataset. The validation suggested that the performance of the joint model is on par with the conventional two-stage POS tagging.

Large language models (LLMs) are widely explored for reasoning-intensive research tasks, yet resources for testing whether they can infer scientific conclusions from structured biomedical evidence remain limited. We introduce MedConclusion, a large-scale dataset of 5.7M PubMed structured abstracts for biomedical conclusion generation. Each instance pairs the non-conclusion sections of an abstract with the original author-written conclusion, providing naturally occurring supervision for evidence-to-conclusion reasoning. MedConclusion also includes journal-level metadata such as biomedical category and SJR, enabling subgroup analysis across biomedical domains. As an initial study, we evaluate diverse LLMs under conclusion and summary prompting settings and score outputs with both reference-based metrics and LLM-as-a-judge. We find that conclusion writing is behaviorally distinct from summary writing, strong models remain closely clustered under current automatic metrics, and judge identity can substantially shift absolute scores. MedConclusion provides a reusable data resource for studying scientific evidence-to-conclusion reasoning. Our code and data are available at: https://github.com/Harvard-AI-and-Robotics-Lab/MedConclusion.

Recent dynamic tokenisation methods operate directly on bytes and pool their latent representations into patches. This bears similarities to computational models of word segmentation that determine lexical boundaries using spikes in an autoregressive model's prediction error. Inspired by this connection, we explore whether grouping predictable bytes - rather than pooling their representations - can yield a useful fixed subword vocabulary. We propose a new information-driven subword tokeniser, ByteSpan, that uses an external byte-level LM during training to identify contiguous predictable byte sequences and group them into subwords. Experiments show that ByteSpan yields efficient vocabularies with higher morphological alignment scores than BPE for English. Multilingual experiments show similar compression and R\'enyi efficiency for 25 languages.

Document chunking is a critical task in natural language processing (NLP) that involves dividing a document into meaningful segments. Traditional methods often rely solely on semantic analysis, ignoring the spatial layout of elements, which is crucial for understanding relationships in complex documents. This paper introduces a novel hybrid approach that combines layout structure, semantic analysis, and spatial relationships to enhance the cohesion and accuracy of document chunks. By leveraging bounding box information (bbox) and text embeddings, our method constructs a weighted graph representation of document elements, which is then clustered using spectral clustering. Experimental results demonstrate that this approach outperforms traditional methods, particularly in documents with diverse layouts such as reports, articles, and multi-column designs. The proposed method also ensures that no chunk exceeds a specified token length, making it suitable for use cases where token limits are critical (e.g., language models with input size limitations)

Efforts to leverage deep learning models in low-resource regimes have led to numerous augmentation studies. However, the direct application of methods such as mixup and cutout to text data, is limited due to their discrete characteristics. While methods using pretrained language models have exhibited efficiency, they require additional considerations for robustness. Inspired by recent studies on decision boundaries, this paper proposes a decision-boundary-aware data augmentation strategy to enhance robustness using pretrained language models. The proposed technique first focuses on shifting the latent features closer to the decision boundary, followed by reconstruction to generate an ambiguous version with a soft label. Additionally, mid-K sampling is suggested to enhance the diversity of the generated sentences. This paper demonstrates the performance of the proposed augmentation strategy compared to other methods through extensive experiments. Furthermore, the ablation study reveals the effect of soft labels and mid-K sampling and the extensibility of the method with curriculum data augmentation.

Tokenization is a pivotal design choice for neural language modeling in morphologically rich languages (MRLs) such as Turkish, where productive agglutination challenges both vocabulary efficiency and morphological fidelity. Prior studies have explored tokenizer families and vocabulary sizes but typically (i) vary vocabulary without systematically controlling the tokenizer's training corpus, (ii) provide limited intrinsic diagnostics, and (iii) evaluate a narrow slice of downstream tasks. We present the first comprehensive, principled study of Turkish subword tokenization; a "subwords manifest", that jointly varies vocabulary size and tokenizer training corpus size (data and vocabulary coupling), compares multiple tokenizer families under matched parameter budgets (WordPiece, morphology level, and character baselines), and evaluates across semantic (NLI, STS, sentiment analysis, NER), syntactic (POS, dependency parsing), and morphology-sensitive probes. To explain why tokenizers succeed or fail, we introduce a morphology-aware diagnostic toolkit that goes beyond coarse aggregates to boundary-level micro/macro F1, decoupled lemma atomicity vs. surface boundary hits, over/under-segmentation indices, character/word edit distances (CER/WER), continuation rates, and affix-type coverage and token-level atomicity. Our contributions are fourfold: (i) a systematic investigation of the vocabulary-corpus-success triad; (ii) a unified, morphology-aware evaluation framework linking intrinsic diagnostics to extrinsic outcomes; (iii) controlled comparisons identifying when character-level and morphology-level tokenization pay off; and (iv) an open-source release of evaluation code, tokenizer pipelines, and models. As the first work of its kind, this "subwords manifest" delivers actionable guidance for building effective tokenizers in MRLs and establishes a reproducible foundation for future research.

Evolvability is an important feature that impacts the ability of evolutionary processes to find interesting novel solutions and to deal with changing conditions of the problem to solve. The estimation of evolvability is not straightforward and is generally too expensive to be directly used as selective pressure in the evolutionary process. Indirectly promoting evolvability as a side effect of other easier and faster to compute selection pressures would thus be advantageous. In an unbounded behavior space, it has already been shown that evolvable individuals naturally appear and tend to be selected as they are more likely to invade empty behavior niches. Evolvability is thus a natural byproduct of the search in this context. However, practical agents and environments often impose limits on the reach-able behavior space. How do these boundaries impact evolvability? In this context, can evolvability still be promoted without explicitly rewarding it? We show that Novelty Search implicitly creates a pressure for high evolvability even in bounded behavior spaces, and explore the reasons for such a behavior. More precisely we show that, throughout the search, the dynamic evaluation of novelty rewards individuals which are very mobile in the behavior space, which in turn promotes evolvability.

Word embeddings are one of the most fundamental technologies used in natural language processing. Existing word embeddings are high-dimensional and consume considerable computational resources. In this study, we propose WordTour, unsupervised one-dimensional word embeddings. To achieve the challenging goal, we propose a decomposition of the desiderata of word embeddings into two parts, completeness and soundness, and focus on soundness in this paper. Owing to the single dimensionality, WordTour is extremely efficient and provides a minimal means to handle word embeddings. We experimentally confirmed the effectiveness of the proposed method via user study and document classification.

Diffusion models have emerged as a powerful paradigm for modern generative modeling, demonstrating strong potential for large language models (LLMs). Unlike conventional autoregressive (AR) models that generate tokens sequentially, diffusion models enable parallel token sampling, leading to faster generation and eliminating left-to-right generation constraints. Despite their empirical success, the theoretical understanding of diffusion model approaches remains underdeveloped. In this work, we develop convergence guarantees for diffusion language models from an information-theoretic perspective. Our analysis demonstrates that the sampling error, measured by the Kullback-Leibler (KL) divergence, decays inversely with the number of iterations T and scales linearly with the mutual information between tokens in the target text sequence. In particular, we establish matching upper and lower bounds, up to some constant factor, to demonstrate the tightness of our convergence analysis. These results offer novel theoretical insights into the practical effectiveness of diffusion language models.

Applying pre-trained generative denoising diffusion models (DDMs) for downstream tasks such as image semantic editing usually requires either fine-tuning DDMs or learning auxiliary editing networks in the existing literature. In this work, we present our BoundaryDiffusion method for efficient, effective and light-weight semantic control with frozen pre-trained DDMs, without learning any extra networks. As one of the first learning-free diffusion editing works, we start by seeking a comprehensive understanding of the intermediate high-dimensional latent spaces by theoretically and empirically analyzing their probabilistic and geometric behaviors in the Markov chain. We then propose to further explore the critical step for editing in the denoising trajectory that characterizes the convergence of a pre-trained DDM and introduce an automatic search method. Last but not least, in contrast to the conventional understanding that DDMs have relatively poor semantic behaviors, we prove that the critical latent space we found already exhibits semantic subspace boundaries at the generic level in unconditional DDMs, which allows us to do controllable manipulation by guiding the denoising trajectory towards the targeted boundary via a single-step operation. We conduct extensive experiments on multiple DPMs architectures (DDPM, iDDPM) and datasets (CelebA, CelebA-HQ, LSUN-church, LSUN-bedroom, AFHQ-dog) with different resolutions (64, 256), achieving superior or state-of-the-art performance in various task scenarios (image semantic editing, text-based editing, unconditional semantic control) to demonstrate the effectiveness.

We consider reinforcement learning in an environment modeled by an episodic, finite, stage-dependent Markov decision process of horizon H with S states, and A actions. The performance of an agent is measured by the regret after interacting with the environment for T episodes. We propose an optimistic posterior sampling algorithm for reinforcement learning (OPSRL), a simple variant of posterior sampling that only needs a number of posterior samples logarithmic in H, S, A, and T per state-action pair. For OPSRL we guarantee a high-probability regret bound of order at most mathcal{O}(H^3SAT) ignoring polylog(HSAT) terms. The key novel technical ingredient is a new sharp anti-concentration inequality for linear forms which may be of independent interest. Specifically, we extend the normal approximation-based lower bound for Beta distributions by Alfers and Dinges [1984] to Dirichlet distributions. Our bound matches the lower bound of order Ω(H^3SAT), thereby answering the open problems raised by Agrawal and Jia [2017b] for the episodic setting.

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.

As LLMs are increasingly used to draft public-facing arguments, they may flatten public debate by repeatedly introducing the same polished, plausible arguments. We study argument collapse, the tendency of essays generated by different LLMs to converge to a smaller set of main arguments, sub-arguments, and paragraph-level structures. We compare 1,039 human responses from 195 New York Times (NYT) debates, 448 human responses from 61 longer-form Boston Review (BR) forums, and 23,384 LLM-generated essays. In the NYT corpus, 65.3% of human main arguments are unique within a debate, compared to 3.4% of LLM main arguments. Asking LLMs to generate diverse answers adds variation, but a typical model recovers only about half of the distinct human main arguments, with much of the added variation falling outside the observed human argument space. Collapse also appears in sub-arguments, where among essays with the same main argument, 41.0% of human sub-arguments are unique versus 9.1% from LLM responses. Qualitatively, LLMs often reuse generalized and hedged sub-arguments, while humans prefer more concrete and topic-specific ones. Structure-wise, LLM-generated essays tend to follow a more fixed arc, often opening with a direct claim and moving quickly toward proposals. The same patterns hold in longer BR essays, suggesting that argument collapse extends beyond short-form responses.

Austenitic 347H stainless steel offers superior mechanical properties and corrosion resistance required for extreme operating conditions such as high temperature. The change in microstructure due to composition and process variations is expected to impact material properties. Identifying microstructural features such as grain boundaries thus becomes an important task in the process-microstructure-properties loop. Applying convolutional neural network (CNN) based deep-learning models is a powerful technique to detect features from material micrographs in an automated manner. Manual labeling of the images for the segmentation task poses a major bottleneck for generating training data and labels in a reliable and reproducible way within a reasonable timeframe. In this study, we attempt to overcome such limitations by utilizing multi-modal microscopy to generate labels directly instead of manual labeling. We combine scanning electron microscopy (SEM) images of 347H stainless steel as training data and electron backscatter diffraction (EBSD) micrographs as pixel-wise labels for grain boundary detection as a semantic segmentation task. We demonstrate that despite producing instrumentation drift during data collection between two modes of microscopy, this method performs comparably to similar segmentation tasks that used manual labeling. Additionally, we find that naïve pixel-wise segmentation results in small gaps and missing boundaries in the predicted grain boundary map. By incorporating topological information during model training, the connectivity of the grain boundary network and segmentation performance is improved. Finally, our approach is validated by accurate computation on downstream tasks of predicting the underlying grain morphology distributions which are the ultimate quantities of interest for microstructural characterization.

Language models typically tokenize text into subwords, using a deterministic, hand-engineered heuristic of combining characters into longer surface-level strings such as 'ing' or whole words. Recent literature has repeatedly shown the limitations of such a tokenization strategy, particularly for documents not written in English and for representing numbers. On the other extreme, byte/character-level language models are much less restricted but suffer from increased sequence description lengths and a subsequent quadratic expansion in self-attention computation. Recent attempts to compress and limit these context lengths with fixed size convolutions is helpful but completely ignores the word boundary. This paper considers an alternative 'learn your tokens' scheme which utilizes the word boundary to pool bytes/characters into word representations, which are fed to the primary language model, before again decoding individual characters/bytes per word in parallel. We find that our moderately expressive and moderately fast end-to-end tokenizer outperform by over 300% both subwords and byte/character models over the intrinsic language modeling metric of next-word prediction across datasets. It particularly outshines on rare words, outperforming by a factor of 30! We extensively study the language modeling setup for all three categories of tokenizers and theoretically analyze how our end-to-end models can also be a strong trade-off in efficiency and robustness.

Does text have an intrinsic curvature? Language is increasingly modeled in curved geometries - hyperbolic spaces for hierarchy, mixed-curvature manifolds for compositional structure - yet a basic scientific question remains unresolved: what does curvature mean for text itself, in a way that is native to language rather than an artifact of the embedding space we choose? We argue that text does indeed have curvature, and show how to detect it, define it, and use it. To this end, we propose Texture, a text-native, word-level discrete curvature signal, and make three contributions. (a) Existence: We provide empirical and theoretical certificates that semantic inference in natural corpora is non-flat, i.e. language has inherent curvature. (b) Definition: We define Texture by reconciling left- and right-context beliefs around a masked word through a Schrodinger bridge, yielding a curvature field that is positive where context focuses meaning and negative where it fans out into competing continuations. (c) Utility: Texture is actionable: it serves as a general-purpose measurement and control primitive enabling geometry without geometric training; we instantiate it on two representative tasks, improving long-context inference through curvature-guided compression and retrieval-augmented generation through curvature-guided routing. Together, our results establish a text-native curvature paradigm, making curvature measurable and practically useful.

This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating slab (between two parallel planes) in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the Wigner transform of the wave solution. These radiative transfer equations allow to model the transport of wave energy density, taking into account the scattering by random heterogeneities. The approach builds on the method of images, where the slab is extended to a full-space, with a periodic map of mechanical properties and a series of sources located along a periodic pattern. Two types of boundary effects, both on the (small) scale of the wavelength, are observed: one at the boundaries of the slab, and one inside the domain. The former impact the entire energy density (coherent as well as incoherent) and is also observed in half-spaces. The latter, more specific to slabs, corresponds to the constructive interference of waves that have reflected at least twice on the boundaries of the slab and only impacts the coherent part of the energy density.

Document Layout Analysis, which is the task of identifying different semantic regions inside of a document page, is a subject of great interest for both computer scientists and humanities scholars as it represents a fundamental step towards further analysis tasks for the former and a powerful tool to improve and facilitate the study of the documents for the latter. However, many of the works currently present in the literature, especially when it comes to the available datasets, fail to meet the needs of both worlds and, in particular, tend to lean towards the needs and common practices of the computer science side, leading to resources that are not representative of the humanities real needs. For this reason, the present paper introduces U-DIADS-Bib, a novel, pixel-precise, non-overlapping and noiseless document layout analysis dataset developed in close collaboration between specialists in the fields of computer vision and humanities. Furthermore, we propose a novel, computer-aided, segmentation pipeline in order to alleviate the burden represented by the time-consuming process of manual annotation, necessary for the generation of the ground truth segmentation maps. Finally, we present a standardized few-shot version of the dataset (U-DIADS-BibFS), with the aim of encouraging the development of models and solutions able to address this task with as few samples as possible, which would allow for more effective use in a real-world scenario, where collecting a large number of segmentations is not always feasible.

Singular limits for the following indirect signalling chemotaxis system align* \left\{ array{lllllll} \partial_t n = \Delta n - \nabla \cdot (n \nabla c ) & in \Omega\times(0,\infty) , \varepsilon \partial_t c = \Delta c - c + w & in \Omega\times(0,\infty), \varepsilon \partial_t w = \tau \Delta w - w + n & in \Omega\times (0,\infty), \partial_\nu n = \partial_\nu c = \partial_\nu w = 0, &on \partial\Omega\times (0,\infty) %(n,c,w)_{t=0} = (n_0,c_0,w_0) & on \Omega, array \right. align* are investigated. More precisely, we study parabolic-elliptic simplification, or PES, varepsilonto 0^+ with fixed tau>0 up to the critical dimension N=4, and indirect-direct simplification, or IDS, (varepsilon,tau)to (0^+,0^+) up to the critical dimension N=2. These are relevant in biological situations where the signalling process is on a much faster time scale compared to the species diffusion and all interactions. Showing singular limits in critical dimensions is challenging. To deal with the PES, we carefully combine the entropy function, an Adam-type inequality, the regularisation of slow evolution, and an energy equation method to obtain strong convergence in representative spaces. For the IDS, a bootstrap argument concerning the L^p-energy function is devised, which allows us to obtain suitable uniform bounds for the singular limits. Moreover, in both scenarios, we also present the convergence rates, where the effect of the initial layer and the convergence to the critical manifold are also revealed.

Large language models have transformed natural language processing, yet supervised fine-tuning (SFT) remains computationally intensive. This paper formally proves that capabilities acquired through SFT can be approximated by a base transformer model using inference-time techniques, specifically in-context learning (ICL), without altering model parameters, under idealized assumptions including unbounded computational resources and access to the fine-tuning dataset. We extend these results to practical scenarios with finite context lengths and partial dataset access. For text generation tasks with fixed output length l, datasets of size Oleft( m V{varepsilon^2} log m{delta} right) or, with bounded context, Oleft( l log V{varepsilon^2} log 1{delta} right) suffice to approximate fine-tuned behavior across m contexts within error varepsilon, where V is the vocabulary size and delta is the failure probability. For linear classification, datasets of size Oleft( d{varepsilon} right) or, with fixed context, Oleft( 1{varepsilon^2} log 1{delta} right) are sufficient, where d is the input dimension. Grounded in the Turing completeness of transformers, these results provide a theoretical foundation for resource-efficient deployment of large language models, with practical techniques like retrieval-augmented generation bridging theory to real-world applications.

While numerous architectures for long-range language models (LRLMs) have recently been proposed, a meaningful evaluation of their discourse-level language understanding capabilities has not yet followed. To this end, we introduce ChapterBreak, a challenge dataset that provides an LRLM with a long segment from a narrative that ends at a chapter boundary and asks it to distinguish the beginning of the ground-truth next chapter from a set of negative segments sampled from the same narrative. A fine-grained human annotation reveals that our dataset contains many complex types of chapter transitions (e.g., parallel narratives, cliffhanger endings) that require processing global context to comprehend. Experiments on ChapterBreak show that existing LRLMs fail to effectively leverage long-range context, substantially underperforming a segment-level model trained directly for this task. We publicly release our ChapterBreak dataset to spur more principled future research into LRLMs.

We propose a hierarchical attention mechanism based on two-level overlapping Schwarz domain decomposition. The method is motivated by the observation that two-level Schwarz domain decomposition methods combine local subdomain corrections with a coarse level that communicates global, long-range information. We test its usefulness in the context of finite-dimensional operator learning using a simple, one-dimensional diffusion problem with homogeneous Dirichlet boundary conditions. Although elementary, this problem provides a controlled sequence-to-sequence setting in which the exact nonlocal solution operator is known. After discretization, learning the solution operator amounts to approximating the inverse of a symmetric positive definite matrix. As a baseline, we use a global softmax-free low-rank attention operator of the form QK^T. The proposed construction replaces this dense global factorization by a two-level additive structure: local low-rank attention blocks on overlapping subdomains are combined with a coarse attention block. The resulting operator has the form $M_θ^{-1} = ΦQ_0 K_0^T Φ^T + sum_{i=1}^{N} R_i^T D_i^{1/2} Q_i K_i^T D_i^{1/2} R_i. Here R_i restricts to an overlapping subdomain, D_i is a partition-of-unity weight, and Φ$ is a coarse interpolation (or prolongation) matrix. Numerical experiments for synthetic Fourier right-hand sides indicate that the domain-decomposition attention operator is able to train faster and can give more accurate approximations than a global low-rank attention baseline while using significantly fewer parameters.

The topology of the hyperlink graph among pages expressing different opinions may influence the exposure of readers to diverse content. Structural bias may trap a reader in a polarized bubble with no access to other opinions. We model readers' behavior as random walks. A node is in a polarized bubble if the expected length of a random walk from it to a page of different opinion is large. The structural bias of a graph is the sum of the radii of highly-polarized bubbles. We study the problem of decreasing the structural bias through edge insertions. Healing all nodes with high polarized bubble radius is hard to approximate within a logarithmic factor, so we focus on finding the best k edges to insert to maximally reduce the structural bias. We present RePBubLik, an algorithm that leverages a variant of the random walk closeness centrality to select the edges to insert. RePBubLik obtains, under mild conditions, a constant-factor approximation. It reduces the structural bias faster than existing edge-recommendation methods, including some designed to reduce the polarization of a graph.

We consider the scattering of acoustic perturbations in a presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl-Glauert transformation to recover the Helmholtz equation. The well-known setting of boundary element method for the Helmholtz equation is available. In the second zone, the flow quantities are space dependent, we have to consider a local resolution, namely the finite element method. Herein, we carry out the coupling of these two methods and present various applications and validation test cases. The source term is given through the decomposition of an incident acoustic field on a section of the computational domain's boundary.

We develop the Itô calculus of Brownian motion, machine-checked in Lean~4 over Mathlib and the BrownianMotion package. On a bounded interval [0,T] the Itô integral is built as a Hilbert-space isometry, from a predictable-rectangle π-system through the density of simple adapted processes. Realized as a process, it is a continuous L^2 martingale. One structural identity drives this: the integral at time t is the conditional-expectation projection of its terminal value onto F_t, and from it adaptedness, the martingale property, the contraction bound, and both the terminal and time-indexed Itô isometries follow as corollaries. On this integral we prove Itô's formula for C^3 functions with bounded derivatives, including the time-dependent form df = f_x,dB + (f_t + tfrac12 f_{xx}),dt, by a discrete-to-continuous argument through weighted quadratic variation with explicit L^2 remainder bounds. We then pass from the L^2 theory to the pathwise. The integral process has an almost-surely continuous modification, and its everywhere-continuous representative is a local martingale for the null-augmented Brownian filtration; gluing the bounded-horizon representatives along the half-line yields the Itô integral as a continuous local martingale on all of R_{ge 0}, the form it takes in the classical theory. To our knowledge these are the first machine-checked constructions of the Itô integral and of Itô's formula in any proof assistant, and the first to reach a pathwise-continuous local martingale. The boundary is explicit. The L^2 integral and Itô's formula are developed on [0,T] with bounded-derivative integrands; the unrestricted C^2 formula, integrators beyond brownian motion, and right-continuity of the filtration lie outside the development.

Textual domain is a crucial property within the Natural Language Processing (NLP) community due to its effects on downstream model performance. The concept itself is, however, loosely defined and, in practice, refers to any non-typological property, such as genre, topic, medium or style of a document. We investigate the core notion of domains via human proficiency in identifying related intrinsic textual properties, specifically the concepts of genre (communicative purpose) and topic (subject matter). We publish our annotations in *TGeGUM*: A collection of 9.1k sentences from the GUM dataset (Zeldes, 2017) with single sentence and larger context (i.e., prose) annotations for one of 11 genres (source type), and its topic/subtopic as per the Dewey Decimal library classification system (Dewey, 1979), consisting of 10/100 hierarchical topics of increased granularity. Each instance is annotated by three annotators, for a total of 32.7k annotations, allowing us to examine the level of human disagreement and the relative difficulty of each annotation task. With a Fleiss' kappa of at most 0.53 on the sentence level and 0.66 at the prose level, it is evident that despite the ubiquity of domains in NLP, there is little human consensus on how to define them. By training classifiers to perform the same task, we find that this uncertainty also extends to NLP models.

In this work, we leverage the intrinsic segmentation of language sequences and design a new positional encoding method called Bilevel Positional Encoding (BiPE). For each position, our BiPE blends an intra-segment encoding and an inter-segment encoding. The intra-segment encoding identifies the locations within a segment and helps the model capture the semantic information therein via absolute positional encoding. The inter-segment encoding specifies the segment index, models the relationships between segments, and aims to improve extrapolation capabilities via relative positional encoding. Theoretical analysis shows this disentanglement of positional information makes learning more effective. The empirical results also show that our BiPE has superior length extrapolation capabilities across a wide range of tasks in diverse text modalities.

This study provides a methodological framework for the computer to classify tweets according to variables of the Theory of Planned Behavior. We present a sequential process of automated text analysis which combined supervised approach and unsupervised approach in order to make the computer to detect one of TPB variables in each tweet. We conducted Latent Dirichlet Allocation (LDA), Nearest Neighbor, and then assessed "typicality" of newly labeled tweets in order to predict classification boundary. Furthermore, this study reports findings from a content analysis of suicide-related tweets which identify traits of information environment in Twitter. Consistent with extant literature about suicide coverage, the findings demonstrate that tweets often contain information which prompt perceived behavior control of committing suicide, while rarely provided deterring information on suicide. We conclude by highlighting implications for methodological advances and empirical theory studies.

It is important for Large Language Models to be aware of the boundary of their knowledge, the mechanism of identifying known and unknown queries. This type of awareness can help models perform adaptive inference, such as invoking RAG, engaging in slow and deep thinking, or adopting the abstention mechanism, which is beneficial to the development of efficient and trustworthy AI. In this work, we propose a method to detect knowledge boundaries via Query-Level Uncertainty, which aims to determine if the model is able to address a given query without generating any tokens. To this end, we introduce a novel and training-free method called Internal Confidence, which leverages self-evaluations across layers and tokens. Empirical results on both factual QA and mathematical reasoning tasks demonstrate that our internal confidence can outperform several baselines. Furthermore, we showcase that our proposed method can be used for efficient RAG and model cascading, which is able to reduce inference costs while maintaining performance.

Foundation models, pre-trained on a large amount of data have demonstrated impressive zero-shot capabilities in various downstream tasks. However, in object detection and instance segmentation, two fundamental computer vision tasks heavily reliant on extensive human annotations, foundation models such as SAM and DINO struggle to achieve satisfactory performance. In this study, we reveal that the devil is in the object boundary, i.e., these foundation models fail to discern boundaries between individual objects. For the first time, we probe that CLIP, which has never accessed any instance-level annotations, can provide a highly beneficial and strong instance-level boundary prior in the clustering results of its particular intermediate layer. Following this surprising observation, we propose Zip which Zips up CLip and SAM in a novel classification-first-then-discovery pipeline, enabling annotation-free, complex-scene-capable, open-vocabulary object detection and instance segmentation. Our Zip significantly boosts SAM's mask AP on COCO dataset by 12.5% and establishes state-of-the-art performance in various settings, including training-free, self-training, and label-efficient finetuning. Furthermore, annotation-free Zip even achieves comparable performance to the best-performing open-vocabulary object detecters using base annotations. Code is released at https://github.com/ChengShiest/Zip-Your-CLIP

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.

The magnitude of a finite metric space has recently emerged as a novel invariant quantity, allowing to measure the effective size of a metric space. Despite encouraging first results demonstrating the descriptive abilities of the magnitude, such as being able to detect the boundary of a metric space, the potential use cases of magnitude remain under-explored. In this work, we investigate the properties of the magnitude on images, an important data modality in many machine learning applications. By endowing each individual images with its own metric space, we are able to define the concept of magnitude on images and analyse the individual contribution of each pixel with the magnitude vector. In particular, we theoretically show that the previously known properties of boundary detection translate to edge detection abilities in images. Furthermore, we demonstrate practical use cases of magnitude for machine learning applications and propose a novel magnitude model that consists of a computationally efficient magnitude computation and a learnable metric. By doing so, we address the computational hurdle that used to make magnitude impractical for many applications and open the way for the adoption of magnitude in machine learning research.

Most existing text summarization datasets are compiled from the news domain, where summaries have a flattened discourse structure. In such datasets, summary-worthy content often appears in the beginning of input articles. Moreover, large segments from input articles are present verbatim in their respective summaries. These issues impede the learning and evaluation of systems that can understand an article's global content structure as well as produce abstractive summaries with high compression ratio. In this work, we present a novel dataset, BIGPATENT, consisting of 1.3 million records of U.S. patent documents along with human written abstractive summaries. Compared to existing summarization datasets, BIGPATENT has the following properties: i) summaries contain a richer discourse structure with more recurring entities, ii) salient content is evenly distributed in the input, and iii) lesser and shorter extractive fragments are present in the summaries. Finally, we train and evaluate baselines and popular learning models on BIGPATENT to shed light on new challenges and motivate future directions for summarization research.

Language barriers in scientific documents hinder the diffusion and development of science and technologies. However, prior efforts in translating such documents largely overlooked the information in layouts. To bridge the gap, we introduce PDFMathTranslate, the world's first open-source software for translating scientific documents while preserving layouts. Leveraging the most recent advances in large language models and precise layout detection, we contribute to the community with key improvements in precision, flexibility, and efficiency. The work has been open-sourced at https://github.com/byaidu/pdfmathtranslate with more than 222k downloads.

The scientific literature's exponential growth makes it increasingly challenging to navigate and synthesize knowledge across disciplines. Large language models (LLMs) are powerful tools for understanding scientific text, but they fail to capture detailed relationships across large bodies of work. Unstructured approaches, like retrieval augmented generation, can sift through such corpora to recall relevant facts; however, when millions of facts influence the answer, unstructured approaches become cost prohibitive. Structured representations offer a natural complement -- enabling systematic analysis across the whole corpus. Recent work enhances LLMs with unstructured or semistructured representations of scientific concepts; to complement this, we try extracting structured representations using LLMs. By combining LLMs' semantic understanding with a schema of scientific concepts, we prototype a system that answers precise questions about the literature as a whole. Our schema applies across scientific fields and we extract concepts from it using only 20 manually annotated abstracts. To demonstrate the system, we extract concepts from 30,000 papers on arXiv spanning astrophysics, fluid dynamics, and evolutionary biology. The resulting database highlights emerging trends and, by visualizing the knowledge graph, offers new ways to explore the ever-growing landscape of scientific knowledge. Demo: abby101/surveyor-0 on HF Spaces. Code: https://github.com/chiral-carbon/kg-for-science.

Document layout analysis is essential for downstream tasks such as information retrieval, extraction, OCR, and digitization. However, existing large-scale datasets like PubLayNet and DocBank lack fine-grained region labels and multilingual diversity, making them insufficient for representing complex document layouts. In contrast, human-annotated datasets such as M6Doc and D4LA offer richer labels and greater domain diversity, but are too small to train robust models and lack adequate multilingual coverage. This gap is especially pronounced for Indic documents, which encompass diverse scripts yet remain underrepresented in current datasets, further limiting progress in this space. To address these shortcomings, we introduce IndicDLP, a large-scale foundational document layout dataset spanning 11 representative Indic languages alongside English and 12 common document domains. Additionally, we curate UED-mini, a dataset derived from DocLayNet and M6Doc, to enhance pretraining and provide a solid foundation for Indic layout models. Our experiments demonstrate that fine-tuning existing English models on IndicDLP significantly boosts performance, validating its effectiveness. Moreover, models trained on IndicDLP generalize well beyond Indic layouts, making it a valuable resource for document digitization. This work bridges gaps in scale, diversity, and annotation granularity, driving inclusive and efficient document understanding.

Verifying the provenance of content is crucial to the function of many organizations, e.g., educational institutions, social media platforms, firms, etc. This problem is becoming increasingly difficult as text generated by Large Language Models (LLMs) becomes almost indistinguishable from human-generated content. In addition, many institutions utilize in-house LLMs and want to ensure that external, non-sanctioned LLMs do not produce content within the institution. In this paper, we answer the following question: Given a piece of text, can we identify whether it was produced by LLM A or B (where B can be a human)? We model LLM-generated text as a sequential stochastic process with complete dependence on history and design zero-shot statistical tests to distinguish between (i) the text generated by two different sets of LLMs A (in-house) and B (non-sanctioned) and also (ii) LLM-generated and human-generated texts. We prove that the type I and type II errors for our tests decrease exponentially in the text length. In designing our tests, we derive concentration inequalities on the difference between log-perplexity and the average entropy of the string under A. Specifically, for a given string, we demonstrate that if the string is generated by A, the log-perplexity of the string under A converges to the average entropy of the string under A, except with an exponentially small probability in string length. We also show that if B generates the text, except with an exponentially small probability in string length, the log-perplexity of the string under A converges to the average cross-entropy of B and A. Lastly, we present preliminary experimental results to support our theoretical results. By enabling guaranteed (with high probability) finding of the origin of harmful LLM-generated text with arbitrary size, we can help combat misinformation.

The success of pre-trained contextualized representations has prompted researchers to analyze them for the presence of linguistic information. Indeed, it is natural to assume that these pre-trained representations do encode some level of linguistic knowledge as they have brought about large empirical improvements on a wide variety of NLP tasks, which suggests they are learning true linguistic generalization. In this work, we focus on intrinsic probing, an analysis technique where the goal is not only to identify whether a representation encodes a linguistic attribute but also to pinpoint where this attribute is encoded. We propose a novel latent-variable formulation for constructing intrinsic probes and derive a tractable variational approximation to the log-likelihood. Our results show that our model is versatile and yields tighter mutual information estimates than two intrinsic probes previously proposed in the literature. Finally, we find empirical evidence that pre-trained representations develop a cross-lingually entangled notion of morphosyntax.

Do the Spratly Islands belong to China, the Philippines, or Vietnam? A pretrained large language model (LLM) may answer differently if asked in the languages of each claimant country: Chinese, Tagalog, or Vietnamese. This contrasts with a multilingual human, who would likely answer consistently. In this paper, we show that LLMs recall certain geographical knowledge inconsistently when queried in different languages -- a phenomenon we term geopolitical bias. As a targeted case study, we consider territorial disputes, an inherently controversial and multilingual task. We introduce BorderLines, a dataset of territorial disputes which covers 251 territories, each associated with a set of multiple-choice questions in the languages of each claimant country (49 languages in total). We also propose a suite of evaluation metrics to precisely quantify bias and consistency in responses across different languages. We then evaluate various multilingual LLMs on our dataset and metrics to probe their internal knowledge and use the proposed metrics to discover numerous inconsistencies in how these models respond in different languages. Finally, we explore several prompt modification strategies, aiming to either amplify or mitigate geopolitical bias, which highlights how brittle LLMs are and how they tailor their responses depending on cues from the interaction context. Our code and data are available at https://github.com/manestay/borderlines

Despite a growing interest in diffusion-based language models, existing work has not shown that these models can attain nontrivial likelihoods on standard language modeling benchmarks. In this work, we take the first steps towards closing the likelihood gap between autoregressive and diffusion-based language models, with the goal of building and releasing a diffusion model which outperforms a small but widely-known autoregressive model. We pursue this goal through algorithmic improvements, scaling laws, and increased compute. On the algorithmic front, we introduce several methodological improvements for the maximum-likelihood training of diffusion language models. We then study scaling laws for our diffusion models and find compute-optimal training regimes which differ substantially from autoregressive models. Using our methods and scaling analysis, we train and release Plaid 1B, a large diffusion language model which outperforms GPT-2 124M in likelihood on benchmark datasets and generates fluent samples in unconditional and zero-shot control settings.

Large language models (LLMs) have been reported to linearly encode truthfulness, yet recent work questions this finding's generality. We reconcile these views with the truthfulness spectrum hypothesis: the representational space contains directions ranging from broadly domain-general to narrowly domain-specific. To test this hypothesis, we systematically evaluate probe generalization across five truth types (definitional, empirical, logical, fictional, and ethical), sycophantic and expectation-inverted lying, and existing honesty benchmarks. Linear probes generalize well across most domains but fail on sycophantic and expectation-inverted lying. Yet training on all domains jointly recovers strong performance, confirming that domain-general directions exist despite poor pairwise transfer. The geometry of probe directions explains these patterns: Mahalanobis cosine similarity between probes near-perfectly predicts cross-domain generalization (R^2=0.98). Concept-erasure methods further isolate truth directions that are (1) domain-general, (2) domain-specific, or (3) shared only across particular domain subsets. Causal interventions reveal that domain-specific directions steer more effectively than domain-general ones. Finally, post-training reshapes truth geometry, pushing sycophantic lying further from other truth types, suggesting a representational basis for chat models' sycophantic tendencies. Together, our results support the truthfulness spectrum hypothesis: truth directions of varying generality coexist in representational space, with post-training reshaping their geometry. Code for all experiments is provided in https://github.com/zfying/truth_spec.

High-quality instance and panoptic segmentation has traditionally relied on dense instance-level annotations such as masks, boxes, or points, which are costly, inconsistent, and difficult to scale. Unsupervised and weakly-supervised approaches reduce this burden but remain constrained by semantic backbone constraints and human bias, often producing merged or fragmented outputs. We present TRACE (TRAnsforming diffusion Cues to instance Edges), showing that text-to-image diffusion models secretly function as instance edge annotators. TRACE identifies the Instance Emergence Point (IEP) where object boundaries first appear in self-attention maps, extracts boundaries through Attention Boundary Divergence (ABDiv), and distills them into a lightweight one-step edge decoder. This design removes the need for per-image diffusion inversion, achieving 81x faster inference while producing sharper and more connected boundaries. On the COCO benchmark, TRACE improves unsupervised instance segmentation by +5.1 AP, and in tag-supervised panoptic segmentation it outperforms point-supervised baselines by +1.7 PQ without using any instance-level labels. These results reveal that diffusion models encode hidden instance boundary priors, and that decoding these signals offers a practical and scalable alternative to costly manual annotation. Project Page: https://shjo-april.github.io/TRACE/

Recent breakthroughs in large language modeling have facilitated rigorous exploration of their application in diverse tasks related to tabular data modeling, such as prediction, tabular data synthesis, question answering, and table understanding. Each task presents unique challenges and opportunities. However, there is currently a lack of comprehensive review that summarizes and compares the key techniques, metrics, datasets, models, and optimization approaches in this research domain. This survey aims to address this gap by consolidating recent progress in these areas, offering a thorough survey and taxonomy of the datasets, metrics, and methodologies utilized. It identifies strengths, limitations, unexplored territories, and gaps in the existing literature, while providing some insights for future research directions in this vital and rapidly evolving field. It also provides relevant code and datasets references. Through this comprehensive review, we hope to provide interested readers with pertinent references and insightful perspectives, empowering them with the necessary tools and knowledge to effectively navigate and address the prevailing challenges in the field.

In this paper, we present a novel framework for the analysis of Riemann Hypothesis [27], which is composed of three key components: a) probabilistic modeling with cross entropy optimization and reasoning; b) the application of the law of large numbers; c) the application of mathematical inductions. The analysis is mainly conducted by virtue of probabilistic modeling of cross entropy optimization and reasoning with rare event simulation techniques. The application of the law of large numbers [2, 3, 6] and the application of mathematical inductions make the analysis of Riemann Hypothesis self-contained and complete to make sure that the whole complex plane is covered as conjectured in Riemann Hypothesis. We also discuss the method of enhanced top-p sampling with large language models (LLMs) for reasoning, where next token prediction is not just based on the estimated probabilities of each possible token in the current round but also based on accumulated path probabilities among multiple top-k chain of thoughts (CoTs) paths. The probabilistic modeling of cross entropy optimization and reasoning may suit well with the analysis of Riemann Hypothesis as Riemann Zeta functions are inherently dealing with the sums of infinite components of a complex number series. We hope that our analysis in this paper could shed some light on some of the insights of Riemann Hypothesis. The framework and techniques presented in this paper, coupled with recent developments with chain of thought (CoT) or diagram of thought (DoT) reasoning in large language models (LLMs) with reinforcement learning (RL) [1, 7, 18, 21, 24, 34, 39-41], could pave the way for eventual proof of Riemann Hypothesis [27].

We present three innovations in tokenization and subword segmentation. First, we propose to use unsupervised morphological analysis with Morfessor as pre-tokenization. Second, we present an algebraic method for obtaining subword embeddings grounded in a word embedding space. Based on that, we design a novel subword segmentation algorithm that uses the embeddings, ensuring that the procedure considers lexical meaning. Third, we introduce an efficient segmentation algorithm based on a subword bigram model that can be initialized with the lexically aware segmentation method to avoid using Morfessor and large embedding tables at inference time. We evaluate the proposed approaches using two intrinsic metrics and measure their performance on two downstream tasks: part-of-speech tagging and machine translation. Our experiments show significant improvements in the morphological plausibility of the segmentation when evaluated using segmentation precision on morpheme boundaries and improved R\'enyi efficiency in 8 languages. Although the proposed tokenization methods do not have a large impact on automatic translation quality, we observe consistent performance gains in the arguably more morphological task of part-of-speech tagging.

To compare autoregressive language models at scale, we propose using log-likelihood vectors computed on a predefined text set as model features. This approach has a solid theoretical basis: when treated as model coordinates, their squared Euclidean distance approximates the Kullback-Leibler divergence of text-generation probabilities. Our method is highly scalable, with computational cost growing linearly in both the number of models and text samples, and is easy to implement as the required features are derived from cross-entropy loss. Applying this method to over 1,000 language models, we constructed a "model map," providing a new perspective on large-scale model analysis.

As a sub-discipline of evolutionary and computational linguistics, emergent communication (EC) studies communication protocols, called emergent languages, arising in simulations where agents communicate. A key goal of EC is to give rise to languages that share statistical properties with natural languages. In this paper, we reinterpret Lewis's signaling game, a frequently used setting in EC, as beta-VAE and reformulate its objective function as ELBO. Consequently, we clarify the existence of prior distributions of emergent languages and show that the choice of the priors can influence their statistical properties. Specifically, we address the properties of word lengths and segmentation, known as Zipf's law of abbreviation (ZLA) and Harris's articulation scheme (HAS), respectively. It has been reported that the emergent languages do not follow them when using the conventional objective. We experimentally demonstrate that by selecting an appropriate prior distribution, more natural segments emerge, while suggesting that the conventional one prevents the languages from following ZLA and HAS.

Punctuation plays a vital role in structuring meaning, yet current models often struggle to restore it accurately in transcripts of spontaneous speech, especially in the presence of disfluencies such as false starts and backtracking. These limitations hinder the performance of downstream tasks like translation, text to speech, summarization, etc. where sentence boundaries are critical for preserving quality. In this work, we introduce Cadence, a generalist punctuation restoration model adapted from a pretrained large language model. Cadence is designed to handle both clean written text and highly spontaneous spoken transcripts. It surpasses the previous state of the art in performance while expanding support from 14 to all 22 Indian languages and English. We conduct a comprehensive analysis of model behavior across punctuation types and language families, identifying persistent challenges under domain shift and with rare punctuation marks. Our findings demonstrate the efficacy of utilizing pretrained language models for multilingual punctuation restoration and highlight Cadence practical value for low resource NLP pipelines at scale.

Given a complex of groups G(Y) = (G_sigma, psi_a, g_{a,b}) where all G_sigma are relatively hyperbolic, the psi_a are inclusions of full relatively quasiconvex subgroups, and the universal cover X is CAT(0) and delta--hyperbolic, we show pi_1(G(Y)) is relatively hyperbolic. The proof extends the work of Dahmani and Martin by constructing a model for the Bowditch boundary of pi_1(G(Y)). We prove the model is a compact metrizable space on which G acts as a geometrically finite convergence group, and a theorem of Yaman then implies the result. More generally, this model shows how any suitable action of a relatively hyperbolic group on a simply connected cell complex encodes a decomposition of the Bowditch boundary into the boundary of the cell complex and the boundaries of cell stabilizers. We hope this decomposition will be helpful in answering topological questions about Bowditch boundaries.

Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three levels: 1) The "atomic" small-scale structure contains "crystals" whose faces are parallelograms or trapezoids, generalizing well-known examples such as (man-woman-king-queen). We find that the quality of such parallelograms and associated function vectors improves greatly when projecting out global distractor directions such as word length, which is efficiently done with linear discriminant analysis. 2) The "brain" intermediate-scale structure has significant spatial modularity; for example, math and code features form a "lobe" akin to functional lobes seen in neural fMRI images. We quantify the spatial locality of these lobes with multiple metrics and find that clusters of co-occurring features, at coarse enough scale, also cluster together spatially far more than one would expect if feature geometry were random. 3) The "galaxy" scale large-scale structure of the feature point cloud is not isotropic, but instead has a power law of eigenvalues with steepest slope in middle layers. We also quantify how the clustering entropy depends on the layer.

Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations: (1) hallucination, (2) context compression, (3) reasoning degradation, (4) retrieval fragility, and (5) multimodal misalignment. While existing surveys describe these phenomena empirically, they lack a rigorous theoretical synthesis connecting them to the foundational limits of computation, information, and learning. This work closes that gap by presenting a unified, proof-informed framework that formalizes the innate theoretical ceilings of LLM scaling. First, computability and uncomputability imply an irreducible residue of error: for any computably enumerable model family, diagonalization guarantees inputs on which some model must fail, and undecidable queries (e.g., halting-style tasks) induce infinite failure sets for all computable predictors. Second, information-theoretic and statistical constraints bound attainable accuracy even on decidable tasks, finite description length enforces compression error, and long-tail factual knowledge requires prohibitive sample complexity. Third, geometric and computational effects compress long contexts far below their nominal size due to positional under-training, encoding attenuation, and softmax crowding. We further show how likelihood-based training favors pattern completion over inference, how retrieval under token limits suffers from semantic drift and coupling noise, and how multimodal scaling inherits shallow cross-modal alignment. Across sections, we pair theorems and empirical evidence to outline where scaling helps, where it saturates, and where it cannot progress, providing both theoretical foundations and practical mitigation paths like bounded-oracle retrieval, positional curricula, and sparse or hierarchical attention.

We propose the Bayes-UCBVI algorithm for reinforcement learning in tabular, stage-dependent, episodic Markov decision process: a natural extension of the Bayes-UCB algorithm by Kaufmann et al. (2012) for multi-armed bandits. Our method uses the quantile of a Q-value function posterior as upper confidence bound on the optimal Q-value function. For Bayes-UCBVI, we prove a regret bound of order O(H^3SAT) where H is the length of one episode, S is the number of states, A the number of actions, T the number of episodes, that matches the lower-bound of Ω(H^3SAT) up to poly-log terms in H,S,A,T for a large enough T. To the best of our knowledge, this is the first algorithm that obtains an optimal dependence on the horizon H (and S) without the need for an involved Bernstein-like bonus or noise. Crucial to our analysis is a new fine-grained anti-concentration bound for a weighted Dirichlet sum that can be of independent interest. We then explain how Bayes-UCBVI can be easily extended beyond the tabular setting, exhibiting a strong link between our algorithm and Bayesian bootstrap (Rubin, 1981).

Language models can perceive visual properties of text despite receiving only sequences of tokens-we mechanistically investigate how Claude 3.5 Haiku accomplishes one such task: linebreaking in fixed-width text. We find that character counts are represented on low-dimensional curved manifolds discretized by sparse feature families, analogous to biological place cells. Accurate predictions emerge from a sequence of geometric transformations: token lengths are accumulated into character count manifolds, attention heads twist these manifolds to estimate distance to the line boundary, and the decision to break the line is enabled by arranging estimates orthogonally to create a linear decision boundary. We validate our findings through causal interventions and discover visual illusions--character sequences that hijack the counting mechanism. Our work demonstrates the rich sensory processing of early layers, the intricacy of attention algorithms, and the importance of combining feature-based and geometric views of interpretability.

In the present article we study diffuse interface models for two-phase biomembranes. We will do so by starting off with a diffuse interface model on R^n defined by two coupled phase fields u,v. The first phase field u is the diffuse approximation of the interior of the membrane; the second phase field v is the diffuse approximation of the two phases of the membrane. We prove a compactness result and a lower bound in the sense of Gamma-convergence for pairs of phase functions (u_varepsilon,v_varepsilon). As an application of this first result, we consider a diffuse approximation of a two-phase Willmore functional plus line tension energy.

Electoral boundaries in Malaysia are not publicly available in machine-readable form. This prevents rigorous analysis of geography-centric issues such as malapportionment and gerrymandering, and constrains spatial perspectives on electoral outcomes. We present the second component of the Malaysian Election Corpus (MECo), an open-access collection of digital electoral boundaries covering all 19 approved delimitation exercises in Malaysia's history, from the first set of Malayan boundaries in 1954 until the 2019 Sabah delimitation. We also auto-generate election-time maps for all federal and state elections up to 2025, and include equal-area and electorate-weighted cartograms to support deeper geospatial analysis. This is the first complete, publicly-available, and machine-readable record of Malaysia's electoral boundaries, and fills a critical gap in the country's electoral data infrastructure.

As academic paper publication numbers grow exponentially, conducting in-depth surveys with LLMs automatically has become an inevitable trend. Outline writing, which aims to systematically organize related works, is critical for automated survey generation. Yet existing automatic survey methods treat outline writing as mere workflow steps in the overall pipeline. Such template-based workflows produce outlines that lack in-depth understanding of the survey topic and fine-grained styles. To address these limitations, we propose Meow, the first metadata-driven outline writing framework that produces organized and faithful outlines efficiently. Specifically, we first formulate outline writing as an end-to-end task that generates hierarchical structured outlines from paper metadata. We then curate a high-quality dataset of surveys from arXiv, bioRxiv, and medRxiv, and establish systematic evaluation metrics for outline quality assessment. Finally, we employ a two-stage training approach combining supervised fine-tuning and reinforcement learning. Our 8B reasoning model demonstrates strong performance with high structural fidelity and stylistic coherence.

Today's probabilistic language generators fall short when it comes to producing coherent and fluent text despite the fact that the underlying models perform well under standard metrics, e.g., perplexity. This discrepancy has puzzled the language generation community for the last few years. In this work, we posit that the abstraction of natural language generation as a discrete stochastic process--which allows for an information-theoretic analysis--can provide new insights into the behavior of probabilistic language generators, e.g., why high-probability texts can be dull or repetitive. Humans use language as a means of communicating information, aiming to do so in a simultaneously efficient and error-minimizing manner; in fact, psycholinguistics research suggests humans choose each word in a string with this subconscious goal in mind. We formally define the set of strings that meet this criterion: those for which each word has an information content close to the expected information content, i.e., the conditional entropy of our model. We then propose a simple and efficient procedure for enforcing this criterion when generating from probabilistic models, which we call locally typical sampling. Automatic and human evaluations show that, in comparison to nucleus and top-k sampling, locally typical sampling offers competitive performance (in both abstractive summarization and story generation) in terms of quality while consistently reducing degenerate repetitions.

Discrete diffusion models offer a promising alternative to autoregressive generation through parallel decoding, but they suffer from a sampling wall: once categorical sampling occurs, rich distributional information collapses into one-hot vectors and cannot be propagated across steps, forcing subsequent steps to operate with limited information. To mitigate this problem, we introduce Loopholing, a novel and simple mechanism that preserves this information via a deterministic latent pathway, leading to Loopholing Discrete Diffusion Models (LDDMs). Trained efficiently with a self-conditioning strategy, LDDMs achieve substantial gains-reducing generative perplexity by up to 61% over prior baselines, closing (and in some cases surpassing) the gap with autoregressive models, and producing more coherent text. Applied to reasoning tasks, LDDMs also improve performance on arithmetic benchmarks such as Countdown and Game of 24. These results also indicate that loopholing mitigates idle steps and oscillations, providing a scalable path toward high-quality non-autoregressive text generation.

Text Summarization is a popular task and an active area of research for the Natural Language Processing community. By definition, it requires to account for long input texts, a characteristic which poses computational challenges for neural models. Moreover, real-world documents come in a variety of complex, visually-rich, layouts. This information is of great relevance, whether to highlight salient content or to encode long-range interactions between textual passages. Yet, all publicly available summarization datasets only provide plain text content. To facilitate research on how to exploit visual/layout information to better capture long-range dependencies in summarization models, we present LoRaLay, a collection of datasets for long-range summarization with accompanying visual/layout information. We extend existing and popular English datasets (arXiv and PubMed) with layout information and propose four novel datasets -- consistently built from scholar resources -- covering French, Spanish, Portuguese, and Korean languages. Further, we propose new baselines merging layout-aware and long-range models -- two orthogonal approaches -- and obtain state-of-the-art results, showing the importance of combining both lines of research.

Deep neural networks can approximate functions on different types of data, from images to graphs, with varied underlying structure. This underlying structure can be viewed as the geometry of the data manifold. By extending recent advances in the theoretical understanding of neural networks, we study how a randomly initialized neural network with piece-wise linear activation splits the data manifold into regions where the neural network behaves as a linear function. We derive bounds on the density of boundary of linear regions and the distance to these boundaries on the data manifold. This leads to insights into the expressivity of randomly initialized deep neural networks on non-Euclidean data sets. We empirically corroborate our theoretical results using a toy supervised learning problem. Our experiments demonstrate that number of linear regions varies across manifolds and the results hold with changing neural network architectures. We further demonstrate how the complexity of linear regions is different on the low dimensional manifold of images as compared to the Euclidean space, using the MetFaces dataset.

Accurate document layout analysis is a key requirement for high-quality PDF document conversion. With the recent availability of public, large ground-truth datasets such as PubLayNet and DocBank, deep-learning models have proven to be very effective at layout detection and segmentation. While these datasets are of adequate size to train such models, they severely lack in layout variability since they are sourced from scientific article repositories such as PubMed and arXiv only. Consequently, the accuracy of the layout segmentation drops significantly when these models are applied on more challenging and diverse layouts. In this paper, we present DocLayNet, a new, publicly available, document-layout annotation dataset in COCO format. It contains 80863 manually annotated pages from diverse data sources to represent a wide variability in layouts. For each PDF page, the layout annotations provide labelled bounding-boxes with a choice of 11 distinct classes. DocLayNet also provides a subset of double- and triple-annotated pages to determine the inter-annotator agreement. In multiple experiments, we provide baseline accuracy scores (in mAP) for a set of popular object detection models. We also demonstrate that these models fall approximately 10\% behind the inter-annotator agreement. Furthermore, we provide evidence that DocLayNet is of sufficient size. Lastly, we compare models trained on PubLayNet, DocBank and DocLayNet, showing that layout predictions of the DocLayNet-trained models are more robust and thus the preferred choice for general-purpose document-layout analysis.

Large language models (LLMs) have achieved great success, but their occasional content fabrication, or hallucination, limits their practical application. Hallucination arises because LLMs struggle to admit ignorance due to inadequate training on knowledge boundaries. We call it a limitation of LLMs that they can not accurately express their knowledge boundary, answering questions they know while admitting ignorance to questions they do not know. In this paper, we aim to teach LLMs to recognize and express their knowledge boundary, so they can reduce hallucinations caused by fabricating when they do not know. We propose CoKE, which first probes LLMs' knowledge boundary via internal confidence given a set of questions, and then leverages the probing results to elicit the expression of the knowledge boundary. Extensive experiments show CoKE helps LLMs express knowledge boundaries, answering known questions while declining unknown ones, significantly improving in-domain and out-of-domain performance.

We show that two properly embedded compact surfaces in an orientable 4-manifold are cobordant if and only if they are Z/2-homologous and either the 4-manifold has boundary or the surfaces have the same normal Euler number. If the 4-manifold is simply-connected and the surfaces are closed, non-orientable, and cobordant, we show that they are in fact concordant. This completes the classification of closed surfaces in simply-connected 4-manifolds up to concordance. Our methods give new constructions of cobordisms with prescribed boundaries, and completely determine when a given cobordism between the boundaries extends to a cobordism or concordance between the surfaces. We obtain our concordance results by extending Sunukjian's method of ambient surgery to the unoriented case using Pin^--structures. We also discuss conditions for an arbitrary codimension 2 properly embedded submanifold to admit an unoriented spanning manifold with prescribed boundary. All results hold in both the smooth and topological categories.

The common practice in coreference resolution is to identify and evaluate the maximum span of mentions. The use of maximum spans tangles coreference evaluation with the challenges of mention boundary detection like prepositional phrase attachment. To address this problem, minimum spans are manually annotated in smaller corpora. However, this additional annotation is costly and therefore, this solution does not scale to large corpora. In this paper, we propose the MINA algorithm for automatically extracting minimum spans to benefit from minimum span evaluation in all corpora. We show that the extracted minimum spans by MINA are consistent with those that are manually annotated by experts. Our experiments show that using minimum spans is in particular important in cross-dataset coreference evaluation, in which detected mention boundaries are noisier due to domain shift. We will integrate MINA into https://github.com/ns-moosavi/coval for reporting standard coreference scores based on both maximum and automatically detected minimum spans.

Universal Dependencies is an open community effort to create cross-linguistically consistent treebank annotation for many languages within a dependency-based lexicalist framework. The annotation consists in a linguistically motivated word segmentation; a morphological layer comprising lemmas, universal part-of-speech tags, and standardized morphological features; and a syntactic layer focusing on syntactic relations between predicates, arguments and modifiers. In this paper, we describe version 2 of the guidelines (UD v2), discuss the major changes from UD v1 to UD v2, and give an overview of the currently available treebanks for 90 languages.