Discrete state space diffusion models have shown significant advantages in applications involving discrete data, such as text and image generation. It has also been observed that their performance is highly sensitive to the choice of rate matrices, particularly between uniform and absorbing rate matrices. While empirical results suggest that absorbing rate matrices often yield better generation quality compared to uniform rate matrices, existing theoretical works have largely focused on the uniform rate matrices case. Notably, convergence guarantees and error analyses for absorbing diffusion models are still missing. In this work, we provide the first finite-time error bounds and convergence rate analysis for discrete diffusion models using absorbing rate matrices. We begin by deriving an upper bound on the KL divergence of the forward process, introducing a surrogate initialization distribution to address the challenge posed by the absorbing stationary distribution, which is a singleton and causes the KL divergence to be ill-defined. We then establish the first convergence guarantees for both the $τ$-leaping and uniformization samplers under absorbing rate matrices, demonstrating improved rates over their counterparts using uniform rate matrices. Furthermore, under suitable assumptions, we provide convergence guarantees without early stopping. Our analysis introduces several new technical tools to address challenges unique to absorbing rate matrices. These include a Jensen-type argument for bounding forward process convergence, novel techniques for bounding absorbing score functions, and a non-divergent upper bound on the score near initialization that removes the need of early-stopping.

Discrete diffusion models have recently gained significant prominence in applications involving natural language and graph data. A key factor influencing their effectiveness is the efficiency of discretized samplers. Among these, $τ$-leaping samplers have become particularly popular due to their theoretical and empirical success. However, existing theoretical analyses of $τ$-leaping often rely on somewhat restrictive and difficult-to-verify regularity assumptions, and their convergence bounds contain quadratic dependence on the vocabulary size. In this work, we introduce a new analytical approach for discrete diffusion models that removes the need for such assumptions. For the standard $τ$-leaping method, we establish convergence guarantees in KL divergence that scale linearly with vocabulary size, improving upon prior results with quadratic dependence. Our approach is also more broadly applicable: it provides the first convergence guarantees for other widely used samplers, including the Euler method and Tweedie $τ$-leaping. Central to our approach is a novel technique based on differential inequalities, offering a more flexible alternative to the traditional Girsanov change-of-measure methods. This technique may also be of independent interest for the analysis of other stochastic processes.

Trustworthy language models should provide both correct and verifiable answers. However, citations generated directly by standalone LLMs are often unreliable. As a result, current systems insert citations by querying an external retriever at inference time, introducing latency, infrastructure dependence, and vulnerability to retrieval noise. We explore whether LLMs can be made to reliably attribute to the documents seen during continual pretraining without test-time retrieval, by revising the training process. To study this, we construct CitePretrainBench, a benchmark that mixes real-world corpora (Wikipedia, Common Crawl, arXiv) with novel documents and probes both short-form (single-fact) and long-form (multi-fact) citation tasks. Our approach follows a two-stage process: (1) continual pretraining to index factual knowledge by binding it to persistent document identifiers; and (2) instruction tuning to elicit citation behavior. We introduce Active Indexing for the first stage, which creates generalizable, source-anchored bindings by augmenting training with synthetic data that (i) restate each fact in diverse, compositional forms and (ii) enforce bidirectional training (source-to-fact and fact-to-source). This equips the model to both generate content from a cited source and attribute its own answers, improving robustness to paraphrase and composition. Experiments with Qwen-2.5-7B&3B show that Active Indexing consistently outperforms a Passive Indexing baseline, which simply appends an identifier to each document, achieving citation precision gains of up to 30.2% across all tasks and models. Our ablation studies reveal that performance continues to improve as we scale the amount of augmented data, showing a clear upward trend even at 16x the original token count. Finally, we show that internal citations complement external ones by making the model more robust to retrieval noise.

Aligning text-to-speech (TTS) system outputs with human feedback through preference optimization has been shown to effectively improve the robustness and naturalness of language model-based TTS models. Current approaches primarily require paired desirable and undesirable samples at the utterance level. However, such pairs are often limited in TTS output data, and utterance-level formulation prevents fine-grained token-level optimization needed for accurate pronunciation alignment. In this study, we propose TKTO that eliminates the need for paired data, enabling a more data-efficient training paradigm, and directly targets token-level units, automatically providing fine-grained alignment signals without token-level annotations. TKTO improves the challenging Japanese TTS accuracy by 39% and reduces CER by 54%, automatically assigning 12.8 times stronger reward to targeted tokens.

The widespread adoption of large language and vision models in real-world applications has made urgent the need to address hallucinations -- instances where models produce incorrect or nonsensical outputs. These errors can propagate misinformation during deployment, leading to both financial and operational harm. Although much research has been devoted to mitigating hallucinations, our understanding of it is still incomplete and fragmented. Without a coherent understanding of hallucinations, proposed solutions risk mitigating surface symptoms rather than underlying causes, limiting their effectiveness and generalizability in deployment. To tackle this gap, we first present a unified, multi-level framework for characterizing both image and text hallucinations across diverse applications, aiming to reduce conceptual fragmentation. We then link these hallucinations to specific mechanisms within a model's lifecycle, using a task-modality interleaved approach to promote a more integrated understanding. Our investigations reveal that hallucinations often stem from predictable patterns in data distributions and inherited biases. By deepening our understanding, this survey provides a foundation for developing more robust and effective solutions to hallucinations in real-world generative AI systems.

As large language models (LLMs) scale, the question is not only how large they become, but how much of their capacity is effectively utilized. Existing scaling laws relate model size to loss, yet overlook how components exploit their latent space. We study feed-forward networks (FFNs) and recast width selection as a spectral utilization problem. Using a lightweight diagnostic suite -- Hard Rank (participation ratio), Soft Rank (Shannon rank), Spectral Concentration, and the composite Spectral Utilization Index (SUI) -- we quantify how many latent directions are meaningfully activated across LLaMA, GPT-2, and nGPT families. Our key finding is an asymmetric spectral scaling law: soft rank follows an almost perfect power law with FFN width, while hard rank grows only sublinearly and with high variance. This asymmetry suggests that widening FFNs mostly adds low-energy tail directions, while dominant-mode subspaces saturate early. Moreover, at larger widths, variance further collapses into a narrow subspace, leaving much of the latent space under-utilized. These results recast FFN width selection as a principled trade-off between tail capacity and dominant-mode capacity, offering concrete guidance for inference-efficient LLM design.

Weak-to-strong generalization (W2SG) refers to the phenomenon where a strong student model, trained on a dataset labeled by a weak teacher, ultimately outperforms the teacher on the target task. Recent studies attribute this performance gain to the prediction misfit between the student and teacher models. In this work, we theoretically investigate the emergence of W2SG through a generalized bias-variance decomposition of Bregman divergence. Specifically, we show that the expected population risk gap between the student and teacher is quantified by the expected misfit between the two models. While this aligns with previous results, our analysis removes several restrictive assumptions, most notably, the convexity of the student's hypothesis class, required in earlier works. Moreover, we show that W2SG is more likely to emerge when the student model approximates its posterior mean teacher, rather than mimicking an individual teacher. Using a concrete example, we demonstrate that if the student model size is sufficiently large, it can indeed converge to the posterior mean teacher in expectation. Our analysis also suggests that avoiding overfitting to the teacher's supervision and reducing the entropy of student's prediction further facilitate W2SG. In addition, we show that the reverse cross-entropy loss, unlike the standard forward cross-entropy, is less sensitive to the predictive uncertainty of the teacher. Finally, we empirically verify our theoretical insights and demonstrate that incorporating the reverse cross-entropy loss consistently improves student performance.

The rise of agentic AI workflows unlocks novel opportunities for computer systems design and optimization. However, for specialized domains such as program synthesis, the relative scarcity of HDL and proprietary EDA resources online compared to more common programming tasks introduces challenges, often necessitating task-specific fine-tuning, high inference costs, and manually-crafted agent orchestration. In this work, we present VeriMaAS, a multi-agent framework designed to automatically compose agentic workflows for RTL code generation. Our key insight is to integrate formal verification feedback from HDL tools directly into workflow generation, reducing the cost of gradient-based updates or prolonged reasoning traces. Our method improves synthesis performance by 5-7% for pass@k over fine-tuned baselines, while requiring only a few hundred training examples, representing an order-of-magnitude reduction in supervision cost.

Large language models increasingly rely on explicit reasoning chains and can produce multiple plausible responses for a given context. We study the candidate sampler that produces the set of plausible responses contrasting the ancestral (parallel) sampling against two alternatives: enumeration, which asks the model to produce $n$ candidates in one pass, and iterative sampling, which proposes candidates sequentially while conditioning on the currently generated response set. Under matched budgets, we compare these samplers on quality, lexical and computation flow diversity, and efficiency. Our empirical results demonstrate that enumeration and iterative strategies result in higher diversity at comparable quality. Our findings highlight the potential of simple non-independent sampling strategies to improve response diversity without sacrificing generation quality.

We study the problem of learning a neural sampler to generate samples from discrete state spaces where the target probability mass function $π\propto\mathrm{e}^{-U}$ is known up to a normalizing constant, which is an important task in fields such as statistical physics, machine learning, combinatorial optimization, etc. To better address this challenging task when the state space has a large cardinality and the distribution is multi-modal, we propose $\textbf{M}$asked $\textbf{D}$iffusion $\textbf{N}$eural $\textbf{S}$ampler ($\textbf{MDNS}$), a novel framework for training discrete neural samplers by aligning two path measures through a family of learning objectives, theoretically grounded in the stochastic optimal control of the continuous-time Markov chains. We validate the efficiency and scalability of MDNS through extensive experiments on various distributions with distinct statistical properties, where MDNS learns to accurately sample from the target distributions despite the extremely high problem dimensions and outperforms other learning-based baselines by a large margin. A comprehensive study of ablations and extensions is also provided to demonstrate the efficacy and potential of the proposed framework.