Autoregressive Model

We present a discrete diffusion-based language model using Glauber dynamics from statistical physics. Our main insight is that instead of trying to train a discrete state space diffusion model using Glauber dynamics with a uniform transition kernel as the forward process, one can set up an ``energy function'' based on pretrained causal/masked language models. When viewed as the stationary distribution, this energy function allows us to significantly improve the quality of the generated text. Incorporating UL2 as the pretrained model into our diffusion pipeline, we outperform prior diffusion based LMs and perform competitively with autoregressive models of comparable model sizes. Furthermore, our models are competitive with or outperform prior diffusion models and GPT-2 style auto-regressive models on zero-shot common sense reasoning tasks as well as planning and search tasks like Sudoku and Zebra puzzles.

Coordinating multi-agent systems over spatially distributed areas requires solving a complex hierarchical problem: first distributing areas among agents (allocation) and subsequently determining the optimal visitation order (routing). Existing methods typically decouple these stages ignoring inter-stage dependencies or rely on decentralized heuristics that lack global context. In this work, we propose a centralized, fully end-to-end auto-regressive framework that jointly generates allocation decisions and routing sequences. The core contribution of our approach is a multi-stage decoding mechanism that unifies high-level allocation and low-level routing in a single autoregressive pass while maintaining a centralized global state. This enables the model to implicitly balance workload distribution with routing efficiency, avoiding local optima common in decentralized methods. Extensive experiments demonstrate that our method significantly outperforms diverse baselines, achieving up to a 20% improvement in solution quality over industrial solvers such as Google OR-Tools, IBM CPLEX, and LKH-3, while reducing computation time from hours to seconds.

Test-Time Adaptation (TTA) via entropy minimization (EM) has proven effective for classification tasks, yet its application to generative autoregressive models remains theoretically fragmented. Existing approaches typically rely on distinct heuristics, such as teacher forcing with pseudo labels or policy-gradient-based reinforcement learning, without a unified mathematical foundation. In this work, we resolve this discrepancy by deriving a rigorous formulation of EM tailored to autoregressive models. We show that the exact objective naturally decomposes into a token-level policy gradient loss and a token-level entropy loss, and we reinterpret prior methods as partial realizations of this unified formulation. Using Whisper ASR as a testbed, we demonstrate that our approach consistently improves performance across more than 20 diverse domains, including acoustic noise, accents, and multilingual settings.

In single-stream autoregressive interfaces, the same tokens both update the model state and constitute an irreversible public commitment. This coupling creates a silence tax: additional deliberation postpones the first task-relevant content, while naive early streaming risks premature commitments that bias subsequent generations. We introduce Side-by-Side (SxS) Interleaved Reasoning, which makes disclosure timing a controllable decision within standard autoregressive generation. SxS interleaves partial disclosures with continued private reasoning in the same context, but releases content only when it is supported by the reasoning so far. To learn such pacing without incentivizing filler, we construct entailment-aligned interleaved trajectories by matching answer prefixes to supporting reasoning prefixes, then train with SFT to acquire the dual-action semantics and RL to recover reasoning performance under the new format. Across two Qwen3 architectures/scales (MoE Qwen3-30B-A3B, dense Qwen3-4B) and both in-domain (AIME25) and out-of-domain (GPQA-Diamond) benchmarks, SxS improves accuracy--content-latency Pareto trade-offs under token-level proxies such as inter-update waiting.

Estimating free energy differences quantifies thermodynamic preferences in molecular interactions, which is central to chemistry and drug discovery. Despite fruitful progress, existing methods still face key limitations: classical computational approaches remain prohibitively expensive due to their reliance on extensive molecular dynamics simulations, while deep learning-based methods are constrained by either less-expressive generative models or input dimensions tied to a specific system, resulting in negligible generalization. To address these challenges, we propose CARD, a generative framework that employs a novel radix-based decomposition to bijectively convert 3D coordinates into mixed discrete-continuous sequences, enabling coarse-to-fine autoregressive modeling with enhanced expressiveness. Notably, the model corresponds to a distribution with zero free energy, serving as a proposal for absolute free energy computation of arbitrary systems without relying on alchemical pathways. Experiments across diverse tasks demonstrate that CARD matches the accuracy of classical computational methods on unseen systems with diverse topologies, while achieving an approximately 40-fold speedup in inference.

Generative AI disrupts the practice of giving credit to work that came before. Ideally, a generative model would give credit to any work on which its output depends in a significant way. \emph{Counterfactual credit attribution} (CCA) is a technical condition formalizing this goal--a relaxation of differential privacy--recently introduced by Livni, Moran, Nissim, and Pabbaraju [2024] who studied it in the PAC learning setting. We initiate the study of CCA generative models. Specifically, we consider autoregressive models giving credit to a deployment-time dataset (e.g., a RAG database). We uncover barriers to two natural approaches to CCA autoregressive models. First, we show that imposing CCA on the underlying next-token predictor does not guarantee that the model is CCA: CCA does not compose autoregressively (unlike DP). Second, we consider a different approach to building CCA models which we call \emph{retrofitting}. Retrofitting takes a model that does not attribute credit, and adds credit onto it. We prove a lower bound for CCA retrofitting under a weak optimality requirement. Given black-box access to the starting model, retrofitting requires query complexity exponential in the length of the model's outputs.

Speculative decoding accelerates autoregressive inference by drafting candidate tokens with a fast model and verifying them in parallel with the target. Self-speculative methods avoid the need for an external drafter but have been studied exclusively in homogeneous Transformer architectures. We introduce component-aware self-speculative decoding, the first method to exploit the internal architectural heterogeneity of hybrid language models, isolating the SSM/linear-attention subgraph as a zero-cost internal draft. We evaluate this on two architecturally distinct hybrid families: Falcon-H1 (parallel: Mamba-2 + attention per layer) and Qwen3.5 (sequential: interleaved linear and attention layers), with a pure Transformer control (Qwen2.5). Parallel hybrids achieve acceptance rates of alpha = 0.68 at draft length k=2 under greedy decoding, while sequential hybrids yield only alpha = 0.038 -- an 18x gap attributable to how each architecture integrates its components. The property is scale-invariant: Falcon-H1 at 3B reproduces the rates observed at 0.5B. We further show that perplexity degradation from a companion ablation study predicts speculative viability without running speculative decoding: a 3.15x ratio (Falcon) maps to alpha = 0.37 at k=4, while 81.96x (Qwen) maps to alpha = 0.019. For sequential hybrids, generic LayerSkip achieves 12x higher acceptance rates than the component-aware strategy. The composition pattern of hybrid models -- not merely the presence of alternative components -- determines whether component-level self-speculation is viable.

Autoregressive image modeling relies on visual tokenizers to compress images into compact latent representations. We design an end-to-end training pipeline that jointly optimizes reconstruction and generation, enabling direct supervision from generation results to the tokenizer. This contrasts with prior two-stage approaches that train tokenizers and generative models separately. We further investigate leveraging vision foundation models to improve 1D tokenizers for autoregressive modeling. Our autoregressive generative model achieves strong empirical results, including a state-of-the-art FID score of 1.48 without guidance on ImageNet 256x256 generation.

Autoregressive Neural Networks based on dense or convolutional layers have recently been shown to be a viable strategy for generating classical spin systems. Unlike these methods, sampling with transformers is commonly considered to be computationally inefficient. In this work, we propose a novel approach to transformer-based neural samplers in which we generate not a single spin per step but groups of spins. As an additional improvement, we construct a model of approximated probabilities, further improving the efficiency of the algorithm. Despite our approach being computationally heavier than dense networks or CNN-based approaches, we were able to sample larger systems of up to $180 \times 180$ spins in case of the Ising model. The Effective Sample Size of our sampler is $\sim 20$ times larger than that of the previous state-of-the-art neural sampler when trained for the $128 \times 128$ Ising model at critical temperature. Finally, we also test our algorithm on the 2D Edwards-Anderson model, where we train $64\times 64$ spin systems.

Norway's electricity market is heavily dominated by hydropower, but the 2021-2022 energy crisis and stronger integration with Continental Europe have fundamentally altered price formation, reducing the reliability of forecasting models calibrated on historical data. Despite the critical need for updated models, a unified benchmark evaluating feature contributions across all structurally diverse Norwegian bidding zones remains lacking. Here we present a comprehensive evaluation of one-step-ahead forecasting of the Nord Pool market across all five Norwegian bidding zones. We constructed a multimodal hourly dataset spanning 2019-2025 and evaluated eight forecasting model families, including Light Gradient Boosting Machine (LightGBM), autoregressive models with exogenous variables, and advanced deep learning architectures, using a strictly causal test set. We implemented robust rolling-origin backtesting, leave-one-group-out feature ablation, and conditional regime analysis to dissect model performance and feature utility. Our results show that LightGBM achieves the best performance in every zone, with mean absolute error ranging from 1.60 to 5.58 euros per megawatt-hour, while a ridge-regularized autoregressive model with exogenous variables remains a highly competitive linear benchmark in northern zones. Feature ablation reveals that models relying solely on lagged prices and calendar variables achieve high accuracy and often match or closely approach the performance of the full multimodal model. However, conditional regime analysis demonstrates that external features like reservoir levels and gas prices remain crucial to stratify forecast errors, which consistently increase under stressed market regimes. This highlights the practical value of model interpretability and regime awareness for decision makers facing structural changes in market dynamics.

Data quality assessment is an essential step that ensures the reliability of the subsequent structural health monitoring (SHM) tasks. This study proposes a prediction deviation-based SHM data quality assessment method using a univariate implicit auto-regressive model, enabling outlier diagnosis and data cleaning. The proposed conditional diffusion model (CDM) augments the standard diffusion model with a conditional embedding module to incorporate temporal context, quartile normalization to mitigate distribution skew, and a Huber loss to enhance robustness against outliers. Within this univariate implicit autoregressive framework, each data point is assigned an outlier probability, quantifying its degree of "outlier-ness", and a global quality evaluation score is computed to characterize the overall dataset quality. Extensive case studies utilizing operational data from real-world structures demonstrate that the proposed framework significantly improves the accuracy of data quality assessment, outperforming other strong baselines representative of clustering, isolation-based, and deep reconstruction methods. The effectiveness and robustness of the proposed framework are further demonstrated by the findings of ablation experiments and hyperparameter analysis.

Some text generation tasks, such as Attribute Value Extraction (AVE), require decoding multiple independent sequences from the same document context. While standard autoregressive decoding is slow due to its sequential nature, the independence between output sequences offers an opportunity for parallelism. We present Hyper-Parallel Decoding, a novel decoding algorithm that accelerates offline decoding by leveraging both shared memory and computation across batches. HPD enables out-of-order token generation through position ID manipulation, significantly improving efficiency. Experiments on AVE show that attribute-value pairs are conditionally independent, enabling us to parallelize value generation within each prompt. By further stacking multiple documents within a single prompt, we can decode in parallel up to 96 tokens per prompt. HPD works with all LLMs, and reduces both inference costs and total inference time by up to 13.8X without compromising output quality, potentially saving hundreds of thousands of dollars on industry AVE tasks. Although designed for attribute extraction, HPD makes no assumptions unique to the AVE domain and can in theory be applied to other scenarios with independent output structures.

We introduce an efficient, resolution-agnostic autoregressive (AR) image synthesis approach that generalizes to arbitrary resolutions and aspect ratios, narrowing the gap to diffusion models at scale. At its core is VibeToken, a novel resolution-agnostic 1D Transformer-based image tokenizer that encodes images into a dynamic, user-controllable sequence of 32-256 tokens, achieving a state-of-the-art efficiency and performance trade-off. Building on VibeToken, we present VibeToken-Gen, a class-conditioned AR generator with out-of-the-box support for arbitrary resolutions while requiring significantly fewer compute resources. Notably, VibeToken-Gen synthesizes 1024x1024 images using only 64 tokens and achieves 3.94 gFID; by comparison, a diffusion-based state-of-the-art alternative requires 1,024 tokens and attains 5.87 gFID. In contrast to fixed-resolution AR models such as LlamaGen -- whose inference FLOPs grow quadratically with resolution (11T FLOPs at 1024x1024) -- VibeToken-Gen maintains a constant 179G FLOPs (63.4x efficient) independent of resolution. We hope VibeToken can help unlock the wide adoption of AR visual generative models in production use cases.

Long-context reasoning is a critical capability of large language models (LLMs), enabling applications such as long-document understanding, summarization, and code generation. However, efficient autoregressive inference relies on the key-value (KV) cache, whose memory footprint grows linearly with sequence length, leading to a major memory bottleneck. To mitigate this overhead, KV cache pruning methods discard cached tokens with low attention scores during inference. Most existing methods apply a uniform pruning ratio across layers, implicitly assuming that all layers contribute equally to overall model performance. We show that this assumption is suboptimal, as layers differ significantly in their sensitivity to pruning. We propose DepthKV, a layer-dependent pruning framework that allocates a fixed global KV budget across layers based on their sensitivity, rather than using a uniform allocation. Across multiple models and tasks, DepthKV consistently outperforms uniform pruning at the same global pruning ratio, demonstrating more effective utilization of the KV cache budget through layer-dependent allocation.

As the demand to integrate Artificial Intelligence into high-stakes environments continues to grow, explaining the reasoning behind neural-network predictions has shifted from a theoretical curiosity to a strict operational requirement. Our work is motivated by the explanations of autoregressive neural predictions on dynamic physical fields, as in weather forecasting. Gradient-based feature attribution methods are widely used to explain the predictions on such data, in particular due to their scalability to high-dimensional inputs. It is also interesting to remark that gradient-based techniques such as SmoothGrad are now standard on images to robustify the explanations using pointwise averages of the attribution maps obtained from several noised inputs. Our goal is to efficiently adapt this aggregation strategy to dynamic physical fields. To do so, our first contribution is to identify a fundamental failure mode when averaging perturbed attribution maps on dynamic physical fields: stochastic input perturbations do not induce stationary amplitude noise in attribution maps, but instead cause a geometric displacement of the attributions. Consequently, pointwise averaging blurs these spatially misaligned features. To tackle this issue, we introduce WassersteinGrad, which extracts a geometric consensus of perturbed attribution maps by computing their entropic Wasserstein barycenter. The results, obtained on regional weather data and a meteorologist-validated neural model, demonstrate promising explainability properties of WassersteinGrad over gradient-based baselines across both single-step and autoregressive forecasting settings.

For autoregressive modeling of chaotic dynamical systems over long time horizons, the stability of both training and inference is a major challenge in building scientific foundation models. We present a hybrid technique in which an autoregressive transformer is embedded within a novel shooting-based mixed finite element scheme, exposing topological structure that enables provable stability. For forward problems, we prove preservation of discrete energies, while for training we prove uniform bounds on gradients, provably avoiding the exploding gradient problem. Combined with a vision transformer, this yields latent tokens admitting structure-preserving dynamics. We outperform modern foundation models with a $65\times$ reduction in model parameters and long-horizon forecasting of chaotic systems. A "mini-foundation" model of a fusion component shows that 12 simulations suffice to train a real-time surrogate, achieving a $9{,}000\times$ speedup over particle-in-cell simulation.

Real-time world simulation is becoming a key infrastructure for scalable evaluation and online reinforcement learning of autonomous driving systems. Recent driving world models built on autoregressive video diffusion achieve high-fidelity, controllable multi-camera generation, but their inference cost remains a bottleneck for interactive deployment. However, existing diffusion caching methods are designed for offline video generation with multiple denoising steps, and do not transfer to this scenario. Few-step distilled models have no inter-step redundancy left for these methods to reuse, and sequence-level parallelization techniques require future conditioning that closed-loop interactive generation does not provide. We present X-Cache, a training-free acceleration method that caches along a different axis: across consecutive generation chunks rather than across denoising steps. X-Cache maintains per-block residual caches that persist across chunks, and applies a dual-metric gating mechanism over a structure- and action-aware block-input fingerprint to independently decide whether each block should recompute or reuse its cached residual. To prevent approximation errors from permanently contaminating the autoregressive KV cache, X-Cache identifies KV update chunks (the forward passes that write clean keys and values into the persistent cache) and unconditionally forces full computation on these chunks, cutting off error propagation. We implement X-Cache on X-world, a production multi-camera action-conditioned driving world model built on multi-block causal DiT with few-step denoising and rolling KV cache. X-Cache achieves 71% block skip rate with 2.6x wall-clock speedup while maintaining minimum degradation.

Failures in complex systems often emerge through gradual degradation and the propagation of stress across interacting components rather than through isolated shocks. Democratic systems exhibit similar dynamics, where weakening institutions can trigger cascading deterioration in related institutional structures. Traditional reliability and survival models typically estimate failure risk based on the current system state but do not explicitly capture how degradation propagates through institutional networks over time. This paper introduces a trajectory-aware reliability modeling framework based on Dynamic Causal Neural Autoregression (DCNAR). The framework first estimates a causal interaction structure among institutional indicators and then models their joint temporal evolution to generate forward trajectories of system states. Failure risk is defined as the probability that predicted trajectories cross predefined degradation thresholds within a fixed horizon. Using longitudinal institutional indicators, we compare DCNAR-based trajectory risk models with discrete-time hazard and Cox proportional hazards models. Results show that trajectory-aware modeling consistently outperforms Cox models and improves risk prediction for several propagation-driven institutional failures. These findings highlight the importance of modeling dynamic system interactions for reliability analysis and early detection of systemic degradation.

While generative models have set new benchmarks for Target Speaker Extraction (TSE), their inherent reliance on global context precludes deployment in real-time applications. Direct adaptation to streaming scenarios often leads to catastrophic inference performance degradation due to the severe mismatch between training and streaming inference. To bridge this gap, we present the first autoregressive (AR) models tailored for streaming TSE. Our approach introduces a Chunk-wise Interleaved Splicing Paradigm that ensures highly efficient and stable streaming inference. To ensure the coherence between the extracted speech segments, we design a historical context refinement mechanism that mitigates boundary discontinuities by leveraging historical information. Experiments on Libri2Mix show that while AR generative baseline exhibits performance degradation at low latencies, our approach maintains 100% stability and superior intelligibility. Furthermore, our streaming results are comparable to or even surpass offline baselines. Additionally, our model achieves a Real-Time-Factor (RTF) of 0.248 on consumer-level GPUs. This work provides empirical evidence that AR generative backbones are viable for latency-sensitive applications through the Chunk-wise Interleaved Splicing Paradigm.

An active challenge in developing multimodal machine learning (ML) models for healthcare is handling missing modalities during training and deployment. As clinical datasets are inherently temporal and sparse in terms of modality presence, capturing the underlying predictive signal via diagnostic multimodal ML models while retaining model explainability remains an ongoing challenge. In this work, we address this by re-framing clinical diagnosis as an autoregressive sequence modeling task, utilizing causal decoders from large language models (LLMs) to model a patient's multimodal trajectory. We first introduce a missingness-aware contrastive pre-training objective that integrates multiple modalities in datasets with missingness in a shared latent space. We then show that autoregressive sequence modeling with transformer-based architectures outperforms baselines on the MIMIC-IV and eICU fine-tuning benchmarks. Finally, we use interpretability techniques to move beyond performance boosts and find that across various patient stays, removing modalities leads to divergent behavior that our contrastive pre-training mitigates. By abstracting clinical diagnosis as sequence modeling and interpreting patient stay trajectories, we develop a framework to profile and handle missing modalities while addressing the canonical desideratum of safe, transparent clinical AI.

Accurate autoregressive prediction of 3D turbulent flows remains challenging for neural PDE solvers, as small errors in fine-scale structures can accumulate rapidly over rollout. In this paper, we propose FlowRefiner, a flow matching-based iterative refinement framework for 3D turbulent flow simulation. The method replaces stochastic denoising refinement with deterministic ODE-based correction, uses a unified velocity-field regression objective across all refinement stages, and introduces a decoupled sigma schedule that fixes the noise range independently of refinement depth. These design choices yield stable and effective refinement in the small-noise regime. Experiments on large-scale 3D turbulence with rich multi-scale structures show that FlowRefiner achieves state-of-the-art autoregressive prediction accuracy and strong physical consistency. Although developed for turbulent flow simulation, the proposed framework is broadly applicable to iterative refinement problems in scientific modeling.

In this paper, we consider the problem of extraction of most informative features from time series that are regarded as observed values of stochastic processes satisfying the It{ô} stochastic differential equations with unknown random drift and diffusion coefficients. We do not attract any additional information and use only the information contained in the time series as it is. Therefore, as additional features, we use the parameters of statistically adjusted mixture-type models of the observed regularities of the behavior of the time series. Several algorithms of construction of these parameters are discussed. These algorithms are based on statistical reconstruction of the coefficients which, in turn, is based on statistical separation of normal mixtures. We obtain two types of parameters by the techniques of the uniform and non-uniform statistical reconstruction of the coefficients of the underlying It{ô} process. The reconstructed coefficients obtained by uniform techniques do not depend on the current value of the process, while the non-uniform techniques reconstruct the coefficients with the account of their dependence on the value of the process. Actually, the non-uniform techniques used in this paper represent a stochastic analog of the Taylor expansion for the time series. The efficiency of the obtained additional features is compared by using them in the autoregressive algorithms of prediction of time series. In order to obtain pure conclusion that is not affected by unwanted factors, say, related to a special choice of the architecture of the neural network prediction methods, we used only simple autoregressive algorithms. We show that the use of additional statistical features improves the prediction.

Consider an auto-regressive model that produces outputs x (e.g., answers to questions, molecules) each of which can be summarized by an attribute vector y (e.g., helpfulness vs. harmlessness, or bio-availability vs. lipophilicity). An arbitrary reward function r(y) encodes tradeoffs between these properties. Typically, tilting the model's sampling distribution to increase this reward is done at training time via reinforcement learning. However, if the reward function changes, re-alignment requires re-training. In this paper, we show that a reward weighted classifier-free guidance (RCFG) can act as a policy improvement operator in this setting, approximating tilting the sampling distribution by the Q function. We apply RCFG to molecular generation, demonstrating that it can optimize novel reward functions at test time. Finally, we show that using RCFG as a teacher and distilling into the base policy to serve as a warm start significantly speeds up convergence for standard RL.

KV caching is a ubiquitous optimization in autoregressive transformer inference, long presumed to be numerically equivalent to cache-free computation. This assumption fails under standard FP16 precision: cache-ON and cache-OFF execution paths employ different floating-point accumulation orderings which, due to FP16 non-associativity, produce a deterministic divergence in decoded token sequences. Across three open-weight models (LLaMA-2-7B, Mistral-7B-v0.3, Gemma-2-2B) evaluated on GSM8K, we observe a 100% token divergence rate across all sampling strategies, including greedy decoding, which rules out sampling randomness as a cause, and also with cache-ON yielding higher accuracy in 8 of 9 conditions, where the accuracy difference serves as an indicator that the divergence direction is systematic rather than random. Controlled FP32 falsification reduces divergence by eight orders of magnitude, eliminates token flips, and drops the flip rate to exactly 0.0%, confirming FP16 non-associativity as the sole causal driver. Layer-wise drift profiling reveals architecturally predictable propagation patterns: models using Grouped-Query Attention exhibit sharp divergence at the first layer, while Gemma's larger head dimension and sliding window attention produce uniform accumulation across all layers. Finally, activation patching of the entire residual stream fails to recover the cache-free trajectory, localizing the causal variable to the stateful KV cache. These findings establish that FP16 KV cache inference is fundamentally non-equivalent to recomputation and provide a mechanistic framework for understanding numerical instability in modern LLM inference systems.

Autoregressive vision-language models (VLMs) deliver strong multimodal capability, but their token-by-token decoding imposes a fundamental inference bottleneck. Diffusion VLMs offer a more parallel decoding paradigm, yet directly converting a pretrained autoregressive VLM into a large-block diffusion VLM (dVLM) often leads to substantial quality degradation. In this work, we present BARD, a simple and effective bridging framework that converts a pretrained autoregressive VLM into a same-architecture, decoding-efficient dVLM. Our approach combines progressive supervised block merging, which gradually enlarges the decoding block size, with stage-wise intra-dVLM distillation from a fixed small-block diffusion anchor to recover performance lost at larger blocks. We further incorporate a mixed noise scheduler to improve robustness and token revision during denoising, and memory-friendly training to enable efficient training on long multimodal sequences. A key empirical finding is that direct autoregressive-to-diffusion distillation is poorly aligned and can even hurt performance, whereas distillation within the diffusion regime is consistently effective. Experimental results show that, with $\leq$ 4.4M data, BARD-VL transfers strong multimodal capability from Qwen3-VL to a large-block dVLM. Remarkably, BARD-VL establishes a new SOTA among comparable-scale open dVLMs on our evaluation suite at both 4B and 8B scales. At the same time, BARD-VL achieves up to 3$\times$ decoding throughput speedup compared to the source model. Code is available at https://github.com/fudan-generative-vision/Bard-VL.

Music accompaniment generation aims to automatically produce instrumental accompaniments that are rhythmically, harmonically, and timbrally coherent with a given vocal input, with broad applications in personalized music creation, arrangement assistance, and music education. Existing approaches, primarily operating in the symbolic domain or relying on single-stage audio generation frameworks, commonly suffer from insufficient high-level semantic structure modeling, limited acoustic detail reconstruction, and weak conditional controllability. To address these limitations, this paper proposes HAFM, a Hierarchical Autoregressive Foundation Model for vocal-conditioned music accompaniment generation. The model employs a dual-rate tokenization strategy in which $50$ Hz HuBERT semantic tokens capture high-level musical structure and $75$ Hz EnCodec acoustic tokens encode fine-grained acoustic content, enabling explicit disentanglement of semantic and acoustic representations. Building on this foundation, a three-stage cascaded generation framework is designed to progressively generate semantic tokens, coarse acoustic tokens, and fine acoustic tokens, refining the accompaniment from global structure to local detail. . Objective evaluation on the MUSDB18 dataset demonstrates that the full three-stage model achieves a Fr{é}chet Audio Distance (FAD) score of 1.71, representing an 18.6% relative improvement over the two-stage baseline (FAD = 2.10). Subjective listening tests show that the generated accompaniments achieve a 51.5% preference rate against ground-truth accompaniments in head-to-head comparisons, and substantially outperform the random baseline in terms of rhythmic alignment, harmonic compatibility, and overall musical coherence. The source code and demo are available at https://github.com/HackerHyper/HAFM.git.

Autoregressive (AR)-Diffusion hybrid paradigms combine AR's structured semantic modeling with diffusion's high-fidelity synthesis, yet suffer from a dual speed bottleneck: the sequential AR stage and the iterative multi-step denoising of the diffusion vision decode stage. Existing methods address each in isolation without a unified principle design. We observe that the per-position \emph{prediction entropy} of continuous-space AR models naturally encodes spatially varying generation uncertainty, which simultaneously governing draft prediction quality in the AR stage and reflecting the corrective effort required by vision decoding stage, which is not fully explored before. Since entropy is inherently tied to both bottlenecks, it serves as a natural unifying signal for joint acceleration. In this work, we propose \textbf{Drift-AR}, which leverages entropy signal to accelerate both stages: 1) for AR acceleration, we introduce Entropy-Informed Speculative Decoding that align draft-target entropy distributions via a causal-normalized entropy loss, resolving the entropy mismatch that causes excessive draft rejection; 2) for visual decoder acceleration, we reinterpret entropy as the \emph{physical variance} of the initial state for an anti-symmetric drifting field -- high-entropy positions activate stronger drift toward the data manifold while low-entropy positions yield vanishing drift -- enabling single-step (1-NFE) decoding without iterative denoising or distillation. Moreover, both stages share the same entropy signal, which is computed once with no extra cost. Experiments on MAR, TransDiff, and NextStep-1 demonstrate 3.8-5.5$\times$ speedup with genuine 1-NFE decoding, matching or surpassing original quality. Code will be available at https://github.com/aSleepyTree/Drift-AR.

Deep spatially selective filters achieve high-quality enhancement with real-time capable architectures for stationary speakers of known directions. To retain this level of performance in dynamic scenarios where only the speakers' initial directions are given, accurate, yet computationally lightweight tracking algorithms become necessary. Assuming a frame-wise causal processing style, temporal feedback allows for leveraging the enhanced speech signal to improve tracking performance. In this work, we investigate strategies to incorporate the enhanced signal into lightweight tracking algorithms and autoregressively guide deep spatial filters. Our proposed Bayesian tracking algorithms are compatible with arbitrary deep spatial filters. To increase the realism of simulated trajectories during development and evaluation, we develop a synthetic data generation framework based on the social force model. Results validate that the autoregressive incorporation significantly improves the accuracy of our Bayesian trackers, resulting in superior enhancement with none or only negligibly increased computational overhead. Real-world recordings complement these findings and demonstrate the generalizability of our methods to unseen acoustic conditions.

Class-conditional generative models have emerged as accurate and robust classifiers, with diffusion models demonstrating clear advantages over other visual generative paradigms, including autoregressive (AR) models. In this work, we revisit visual AR-based generative classifiers and identify an important limitation of prior approaches: their reliance on a fixed token order, which imposes a restrictive inductive bias for image understanding. We observe that single-order predictions rely more on partial discriminative cues, while averaging over multiple token orders provides a more comprehensive signal. Based on this insight, we leverage recent any-order AR models to estimate order-marginalized predictions, unlocking the high classification potential of AR models. Our approach consistently outperforms diffusion-based classifiers across diverse image classification benchmarks, while being up to 25x more efficient. Compared to state-of-the-art self-supervised discriminative models, our method delivers competitive classification performance - a notable achievement for generative classifiers.

Accurate time series forecasting underpins decision-making in many domains, yetconventional ML development often faces data scarcity, distribution shift, anddiminishing returns from manual iteration. We propose Self-Evolving Agent forTime Series Algorithms (SEATS), a framework that autonomously generates, val-idates, and optimizes forecasting algorithm code through an iterative self-evolutionloop. Our design combines three mechanisms: (1) Metric-Advantage MCTS(MA-MCTS), which replaces fixed rewards with a statistically normalized advan-tage score for search guidance, (2) code review with running prompt refinement,so every successfully executed solution is reviewed and the running prompt encodescorrective patterns for later iterations, and (3) global steerable reasoning, whichcompares each evaluated node to global best- and worst-performing solutions forcross-trajectory transfer. A MAP-Elites archive maintains architectural diversity.Across four datasets and two metrics, SEATS wins seven of eight comparisonsagainst strong baselines TimeMixer, Timer, and SEMixer

Offline goal-conditioned reinforcement learning remains challenging for long-horizon tasks. While hierarchical approaches mitigate this issue by decomposing tasks, most existing methods rely on separate high- and low-level networks and generate only a single intermediate subgoal, leaving several structural limitations in long-horizon decision-making. To address this limitation, we draw inspiration from chain-of-thought reasoning and propose the Chain-of-Goals Hierarchical Policy (CoGHP), a novel framework that reformulates hierarchical decision-making as autoregressive sequence modeling within a unified architecture. Given a state and a final goal, CoGHP autoregressively generates a sequence of latent subgoals followed by the primitive action, where each latent subgoal acts as a reasoning step that conditions subsequent predictions. To implement this efficiently, we introduce an MLP-Mixer backbone, which supports cross-token communication and captures structural relationships among state, goal, latent subgoals, and action. Across challenging navigation and manipulation benchmarks, CoGHP consistently outperforms strong offline baselines, demonstrating improved performance on long-horizon tasks. Project page: https://wlsdn9350.github.io/projects/coghp/

Handwritten mathematical expression recognition (HMER) requires reasoning over diverse symbols and structures, yet autoregressive models struggle with exposure bias and syntax inconsistency. We present GryphOne, a discrete diffusion framework which reformulates HMER as iterative symbolic refinement instead of sequential generation. GryphOne progressively refines symbols and relations, removing autoregression and improving consistency. Symbol-aware tokenization and random-masking mutual learning further enhance robustness to handwriting diversity. On the MathWriting benchmark, GryphOne achieves 5.51% CER and 59.9% EM (ExpRate), outperforming all reimplemented models in the matched setting as well as the commercial HMER system. Held-out evaluation on CROHME 2014-2023 further shows strong cross-dataset generalization.

Post-training pretrained autoregressive models (ARMs) into masked diffusion models (MDMs) provides an efficient route to diffusion language modeling, but it remains unclear whether the resulting models reuse inherited autoregressive computation or reorganize it for non-autoregressive generation. We compare two 7B ARM-MDM families across four controlled diagnostic tasks and find a task-dependent mechanism shift. On prefix-dominant tasks, MDMs largely preserve inherited high-attribution pathways or exhibit only modest changes in where computation occurs. On globally constrained tasks, the reorganization is substantially stronger, with task-relevant computation shifting toward earlier layers. This depth-wise pattern persists across prompt resampling, circuit budgets, and tested inference budgets, while targeted ablations support the functional importance of the identified structures under the tested intervention protocols. At the component level, diagnostic probes suggest that ARMs rely more strongly on sharply specialized components, whereas MDMs exhibit weaker single-component specialization and more diffuse output-space alignment. Together, these results suggest that diffusion post-training selectively preserves or reorganizes inherited computation according to task structure, rather than uniformly replacing autoregressive mechanisms.

We present Spanning Tree Autoregressive (STAR) modeling, which can incorporate prior knowledge of images, such as center bias and locality, to maintain sampling performance while also providing sufficiently flexible sequence orders to accommodate image editing at inference time. Approaches that expose conventional autoregressive (AR) models in visual generation to arbitrary sequence orders via random permutation suffer from degraded sampling performance or compromise the flexibility in sequence order choice at inference time. Instead, STAR utilizes traversal orders of uniform spanning trees in a lattice defined by the positions of image patches. Traversal orders are obtained via breadth-first search, allowing us to efficiently construct a spanning tree via rejection sampling whose traversal order ensures that the connected partial observation of the image appears as a prefix for native image inpainting support. Through the tailored yet structured sequence order randomization strategy, STAR preserves the capability of postfix completion while maintaining sampling performance, without any significant changes to the model architecture widely adopted in language AR modeling.

Neural audio codecs have largely promoted the application of language models (LMs) for speech applications. However, the effectiveness of autoregressive LM-based models in unifying speech enhancement (SE) tasks remains underexplored. In this work, we propose UniSE, a unified decoder-only LM-based framework to handle different SE tasks including speech restoration, target speaker extraction, and speech separation. Conditioned on input speech features, it autoregressively generates target discrete tokens, facilitating compatibility between distinct learning patterns of multiple tasks. To further optimize speech quality, we introduce a progressive reinforcement learning strategy with multiple assessment criteria. Experiments on several benchmarks show that UniSE achieves competitive performance compared to discriminative and generative baselines, demonstrating the capacity of LMs in unifying SE tasks. The code and demo are available at: https://github.com/alibaba/unified-audio/tree/main/QuarkAudio-UniSE.

We present HunyuanImage 3.0, a native multimodal model that unifies multimodal understanding and generation within an autoregressive framework, with its image generation module publicly available. The achievement of HunyuanImage 3.0 relies on several key components, including meticulous data curation, advanced architecture design, a native Chain-of-Thoughts schema, progressive model pre-training, aggressive model post-training, and an efficient infrastructure that enables large-scale training and inference. With these advancements, we successfully trained a Mixture-of-Experts (MoE) model comprising over 80 billion parameters in total, with 13 billion parameters activated per token during inference, making it the largest and most powerful open-source image generative model to date. We conducted extensive experiments and the results of automatic and human evaluation of text-image alignment and visual quality demonstrate that HunyuanImage 3.0 rivals previous state-of-the-art models. By releasing the code and weights of HunyuanImage 3.0, we aim to enable the community to explore new ideas with a state-of-the-art foundation model, fostering a dynamic and vibrant multimodal ecosystem. All open source assets are publicly available at https://github.com/Tencent-Hunyuan/HunyuanImage-3.0

Multimodal large language models (MLLMs) have achieved strong vision-language performance, yet their token-level visual evidence remains difficult to inspect. Recent logit-lens attribution methods project each visual-token hidden state into the vocabulary space to explain generated words, but this token-wise readout introduces a mismatch: visual tokens are context-mixed by the model, while the attribution score is decoded independently at each token location. This often produces fragmented attribution maps and can be further affected by autoregressive context signals from preceding text tokens. We propose ERCR, an attribution framework built from Evidence Recomposition (ER) and Predictive Context Residualization (PCR). ER aggregates target evidence across multiple views with different token-to-region assignments, reducing attribution fragmentation caused by a single readout grid. PCR estimates a preceding-token context map with RBO-based rank relevance and subtracts its fitted component from the ER map to suppress context-token interference. Experiments on LLaVA, Qwen2-VL, and InternVL families across COCO Caption, GranDf, and OpenPSG show that ERCR improves visual evidence for target tokens and mitigates preceding-token context interference under the existing evaluation protocol. On Qwen2-VL-2B, ERCR improves TAM F1-IoU from 39.10 to 44.45 on COCO Caption and from 30.83 to 37.20 on GranDf. Overall, ERCR provides a practical refinement for token-level visual evidence inspection.

Efficiently scaling Large Language Models (LLMs) necessitates exploring alternatives to dominant autoregressive (AR) methods, with Masked Diffusion Models (MDMs) emerging as candidates. However, comparing AR (typically decoder-only) and MDM (often encoder-only) paradigms is confounded by differing architectures, obscuring true algorithmic and efficiency trade-offs. This research decouples these factors by evaluating MDMs within a decoder-only framework to: (1) Equitably compare MDM (as Any-Order AR) and standard AR paradigms through discrepancies on orders. (2) Investigate MDM architectural impacts on computational efficiency. We show decoder-only MDMs, despite a larger modeling space, can achieve significant inference speedups ($\sim25\times$) and comparable perplexity with techniques like temperature annealing, offering a path to reduced inference compute. This work provides insights for developing more computationally efficient foundation models by disentangling core modeling choices from architectural influences. Code is available at https://github.com/scxue/AO-GPT-MDM.

When training autoregressive models to forecast dynamical systems, a critical question arises: how far into the future should the model be trained to predict for optimal performance? In this work, we address this question by analyzing the relationship between the geometry of the loss landscape and the training time horizon. Using dynamical systems theory, we prove that loss minima for long horizons generalize well to short-term forecasts, whereas minima found on short horizons result in worse long-term predictions. However, we also prove that the loss landscape becomes rougher as the training horizon grows, making long-horizon training inherently challenging. We validate our theory through numerical experiments and discuss practical implications for selecting training horizons. Our results provide a principled foundation for hyperparameter optimization in autoregressive forecasting models.

In this work, we propose Dimple, the first Discrete Diffusion Multimodal Large Language Model (DMLLM). We observe that training with a purely discrete diffusion approach leads to significant training instability, suboptimal performance, and severe length bias issues. To address these challenges, we design a novel training paradigm that combines an initial autoregressive phase with a subsequent diffusion phase. This approach yields the Dimple-7B model, trained on the same dataset and using a similar training pipeline as LLaVA-NEXT. Dimple-7B ultimately surpasses LLaVA-NEXT in performance by 3.9%, demonstrating that DMLLM can achieve performance comparable to that of autoregressive models. To improve inference efficiency, we propose a decoding strategy termed confident decoding, which dynamically adjusts the number of tokens generated at each step, significantly reducing the number of generation iterations. In autoregressive models, the number of forward iterations during generation equals the response length. With confident decoding, however, the number of iterations needed by Dimple is even only $\frac{\text{response length}}{3}$. We also re-implement the prefilling technique in autoregressive models and demonstrate that it does not significantly impact performance on most benchmark evaluations, while offering a speedup of 1.5x to 7x. Additionally, we explore Dimple's capability to precisely control its response using structure priors. These priors enable structured responses in a manner distinct from instruction-based or chain-of-thought prompting, and allow fine-grained control over response format and length, which is difficult to achieve in autoregressive models. Overall, this work validates the feasibility and advantages of DMLLM and enhances its inference efficiency and controllability. Code and models are available at https://github.com/yu-rp/Dimple.

We introduce MolMiner, a fragment-based, geometry-aware, and order-agnostic autoregressive model for molecular design. MolMiner supports high-dimensional conditional control over twelve physicochemical and structural properties from partial specifications, constructs molecules via symmetry-aware fragment attachments, and conditions each generation step on force-field-relaxed three-dimensional geometry of the partial structure. Conditional control emerges without auxiliary property losses. On targeted property windows, conditioning lifts hit rates by up to 5.25x over unconditional generation and 3.5x over the training distribution itself -- overriding the model's intrinsic biases -- at the cost of a small reduction in unconditional distributional fidelity. MolMiner unifies dynamic geometry, symmetry handling, order-agnostic generation, and scalable multi-property conditioning within a single framework.

We pose uncertainty quantification and exploration in online decision-making as a problem of training and generation from an autoregressive sequence model, an area experiencing rapid innovation. Our approach rests on viewing uncertainty as arising from missing future outcomes that could be revealed through action choices, rather than from unobservable latent parameters of the environment. This reformulation aligns naturally with modern machine learning capabilities: we can i) train generative models through next-outcome prediction rather than fit explicit priors, ii) assess uncertainty through autoregressive generation rather than sampling latent parameters from posteriors, and iii) adapt to new information by extending the sequence model's context rather than explicit posterior updating. Our main theoretical result establishes a reduction from online decision-making to offline next-outcome prediction: Bayesian regret is controlled directly by the sequence model's offline prediction loss, without requiring an explicit latent-variable posterior. Experiments, including a semi-synthetic news recommendation task, show that autoregressive generation produces calibrated epistemic uncertainty and enables effective exploration by using article text as prior information to focus exploration on resolving remaining uncertainties.