Autoregressive Model

Generating realistic and diverse graphs is a key problem in machine learning, with applications in molecular discovery, circuit design, cybersecurity, and beyond. However, current graph generative models remain limited by scalability and novelty. Diffusion-based methods often require costly full-adjacency operations and long denoising chains, while many autoregressive and hybrid models have at least quadratic complexity. In addition, these models often imitate training graphs rather than generalize beyond them. We propose a lightweight autoregressive framework to address these issues. It uses a structure-guided topological ordering to serialize graphs into regular edge sequences, enabling near log-linear generation, and a two-phase training strategy that combines exploration-oriented augmentation with iterative refinement to reduce overfitting and promote controlled novelty. Experiments on molecular and non-molecular benchmarks show that our approach improves novelty while preserving high validity and uniqueness. The framework also supports both LSTM and Mamba-style causal sequence backbones, with large-memory accelerators enabling longer graph-sequence experiments beyond typical GPU limits.

Safety alignment in large language models (LLMs) is fragile in part because it is often shallow: fine-tuning mainly reshapes the model's behavior near the first few output tokens. We argue that this phenomenon can be understood through autoregressive consistency, the tendency of next-token prediction to preserve and extend the current response trajectory consistently. By analyzing the learning dynamics of safety alignment, we show that autoregressive consistency can concentrate alignment updates on early tokens, offering a mechanistic explanation for shallow safety alignment. The same mechanism also predicts a broader class of attacks on LLMs: attacks that induce harmful continuation states at arbitrary positions in the output trajectory. As a concrete example, we introduce random insertion attack, which inserts a short harmful span into an otherwise safe refusal trajectory and exploits autoregressive consistency to sustain the resulting harmful branch, thereby bypassing safety alignment. Notably, a short harmful span can redirect the generation to be harmful even after a long refusal prefix, highlighting autoregressive consistency as a potential broader failure mechanism. This suggests that safety alignment should also break harmful autoregressive consistency throughout the output trajectory. We therefore propose adversarial safety alignment, an initial framework based on worst-case harmful continuation states, and instantiate it with random worst-insertion training. Overall, our results suggest that autoregressive consistency should be treated as a central consideration in both safety alignment and attack design.

Time series forecasting relies on historical patterns, but real-world series often exhibit non-stationarity and regime shifts that challenge fully parametric forecasters. Inspired by Retrieval-Augmented Generation (RAG), recent work augments forecasters by retrieving relevant historical segments and using them as external evidence at inference time. However, due to the intrinsic non-stationarity of real-world time series, a highly similar past segment does not necessarily imply a similar future, rendering similarity-only retrieval brittle and prone to redundancy. We propose Stationarity-Aware Retrieval-Augmented Time Series Forecasting (SARAF), a framework that adaptively balances relevance and diversity in retrieval. SARAF first forms a candidate pool via temporal similarity with time-aligned enhancement, then applies a diversity-aware selection strategy to cover heterogeneous historical regimes, with the diversification strength automatically modulated by dataset-level stationarity. Moreover, SARAF uses stationarity-aware aggregation to fuse the retrieved futures. Extensive experiments on eight real-world datasets show that SARAF achieves competitive forecasting performance and improves average accuracy and robustness over strong baselines, with particularly clear benefits under challenging non-stationary settings. Code: https://github.com/ShiqiaoZhou/SARAF.

Untargeted liquid chromatography-high-resolution mass spectrometry (LC-HRMS) detects thousands of molecular features per sample, yet only 2-20% receive confident structural annotations. A root cause of this "dark metabolome" is that tandem MS/MS acquisition is reactive: instruments select precursors only after ions appear, blind to what elutes next. We reframe chromatographic elution as an autoregressive sequence prediction task. Because reversed-phase elution order is governed by hydrophobicity, successive features form a physically constrained sequence, like tokens in language. We discretize the mass-to-charge (m/z) axis into 110 bins and train long short-term memory (LSTM) and Transformer models to predict the next eluting m/z bin from five annotation-free per-token features: m/z bin, mass defect, retention-time gap, polarity, and intensity rank. Trained on 15,242 features from four clinical lipidomics cohorts (342 plasma samples; SCIEX TripleTOF 6600+, Waters CSH C18), the LSTM reaches 98.4% top-1 accuracy (99.99% top-5; mean absolute error 3.6 Da) and the Transformer 98.0%. Ablation shows autoregressive context accounts for 55.5 percentage points while no single feature contributes more than 0.2 pp: the sequential pattern, not molecular properties, drives prediction. Models transfer across instruments sharing the method (r=0.999 on an independent Agilent 6530 dataset) but fail under a different column chemistry (5.1% top-1) or polarity mode (2.6%), confirming method- and mode-specificity. Fine-tuning on as few as two to five quality-control injections recovers held-out accuracy from 2.6% to nearly 50%, so cross-condition deployment needs minimal calibration. These results establish that elution sequences are highly predictable and lay the groundwork for predictive MS/MS acquisition to improve annotation coverage in untargeted metabolomics.

Causal discovery with instantaneous effects in multivariate time series is challenging, as the instantaneous structure must be acyclic. Prior methods enforce this by either separating instantaneous and lagged estimation into multi-stage pipelines or imposing algebraic acyclicity constraints via complex augmented Lagrangian optimization, both of which incur high computational cost. In this work, we propose a different approach: we learn a differentiable permutation of variables using the Gumbel--Sinkhorn operator and triangularize the instantaneous coefficient matrix of a Structural Vector Autoregressive (SVAR) model in the learned order. This converts acyclicity from a hard constraint into a parameterization and keeps it valid throughout optimization. In doing so, our method enables unified, continuous optimization with gradient-based learning, leading to improved efficiency in time--series causal discovery. Across three real-world benchmarks, our method achieves the best overall performance compared with 12 baselines in both discovery accuracy and efficiency. On the large-scale benchmark, it further demonstrates strong scalability, achieving more than a 6x speedup over competing methods.

Large Language Models suffer from slow autoregressive inference. While self-speculative decoding accelerates this process, its efficiency is hampered by static configurations like fixed exit layers and speculation lengths. We reframe this optimization as a \textbf{Markov Decision Process} and propose \textbf{LEDE}, a framework that uses offline reinforcement learning. LEDE learns a policy to dynamically select the optimal exit layer and speculation length based on the local context of the generated sequence at each step, balancing computational cost and draft quality. Comprehensive evaluations on Llama-2 and Llama-3 models show LEDE achieves up to a 2.0\times$$\sim$$2.7\times speedup over autoregressive decoding and and provides an additional 17% speedup over the static speculative baselines.

Autoregressive world models have emerged as a powerful paradigm for interactive video generation, allowing users to navigate dynamically generated environments through actions. These models are typically conditioned on a text prompt and/or a single reference frame, from which the entire world is generated. Yet the moment the user navigates beyond what is visible in that frame, the unseen regions are populated by the base model's priors, with no mechanism for the user to specify what should appear and where. This is a fundamental limitation for applications such as gaming, interactive storytelling, and simulation, where controllable scene composition is essential. We refer to this missing capability as concept spawning; introducing a user-specified visual concept into a world model, analogous to spawning in a game engine. We introduce SPAWN (Swapping Pinned Anchor with Windowed iNjection), a training-free method for concept spawning. SPAWN exploits a structural property of image-to-video backbones: the first slot of the context memory is pinned to the reference frame and acts as a foundational anchor for every generated chunk. By swapping this anchor with an external concept latent over a short injection window and letting the original anchor return, we cause the concept to propagate naturally through the rollout via the model's own memory. SPAWN supports concepts from fine-grained entities such as characters and props to large-scale elements such as buildings and landmarks, and accepts either a concept image or a text description as input. Experiments show that SPAWN integrates concepts with consistent lighting, scale, and perspective while preserving identity and temporal coherence, demonstrating that controllable concept spawning is achievable in existing autoregressive world models without any training.

Diffusion large language models (dLLMs) have recently emerged as a promising alternative to autoregressive (AR) LLMs, offering faster inference through parallel or blockwise decoding. However, their masked language modeling formulation remains incompatible with standard token-level speculative decoding, one of the most effective acceleration techniques for AR models. In AR decoding, the causal mask preserves temporally valid token-level contexts, enabling a target model to verify multiple drafted tokens in a single forward pass. In contrast, dLLMs rely on mask tokens and bidirectional attention, causing the effective context to change across denoising steps and preventing direct token-level speculative verification. To bridge this gap, we propose a simple but effective speculative decoding algorithm for diffusion language models, named SimSD, which mainly adopts a plug-and-play masking strategy that equips dLLMs with temporally valid token-level contexts for speculative decoding. Our method explicitly introduces reference tokens from draft-model predictions and designs an attention mask that regulates their interaction with current-step tokens, allowing dLLMs to compute valid logits for drafted tokens in a single forward pass. This restores the key verification ability provided by causal masking in AR models while preserving the parallel decoding advantages of dLLMs. The proposed method is training-free and can be flexibly integrated with other acceleration techniques such as KV cache and blockwise decoding. Experiments on SDAR-family dLLMs across four benchmarks show that our method achieves up to 7.46x higher decoding throughput while maintaining and even improving average generation quality.

Zero-shot time series forecasting aims to predict future values for previously unseen series, requiring models to generalize temporal dynamics beyond the training distribution. While recent foundation models achieve strong in-domain performance through large-scale pretraining, their effectiveness often relies on broad data coverage and implicit pattern memorization, which can limit generalization when data are scarce or source and target domains are disjoint. In this work, we propose FSA, a feature-to-strategy framework for controlled zero-shot univariate forecasting. Instead of directly modeling raw sequences in the observation space, FSA learns a structured mapping from an interpretable feature space to an autoregressive strategy space. This design introduces explicit inductive biases that disentangle global trends, periodic components, and local temporal dynamics, enabling the model to capture transferable time-series structure with fewer data assumptions. Empirical results show that, under identical pretraining data, training protocol, and comparable parameter budgets, FSA outperforms Transformer-based architectures in our controlled zero-shot setting.

Time series forecasting often requires learning nonlinear and time-delayed dependencies. A paradigmatic class of forecasting models are nonlinear vector autoregressive processes (NVAR), also known as next-generation reservoir computers (NG-RCs). These models approximate the Koopman operator on the space spanned by their explicit feature library. We consider the identifiability problem for learning Markovian nonlinear dynamical systems and show that the training error as a function of time resolution follows characteristic (pre-)asymptotic scaling laws. These laws depend on whether the feature library can represent the early Lie-series coefficients of the flow map (propagator) exactly or merely approximately. For dynamical systems governed by polynomial vector fields, we demonstrate the mechanism for NVAR/NG-RC models with monomial and Fourier feature libraries. We determine the dependence of the training error on the temporal resolution, the involved nonlinear degree, and the number of delay terms. While delay terms reduce the optimal one-step training error, they improve long-horizon forecasts only when the library provides sufficient nonlinearity. Thus, small training error coexists with weak generalization as the model class is mismatched to the true data-generating process. Numerical experiments on various chaotic dynamical systems confirm the theoretical predictions.

The diffusion based robot navigation world models are typically trained using parallel supervision, while autoregressive inference is employed during path planning. This results in a distribution shift between training and inference, which destabilizes the performance over long-horizon prediction. We propose AR Forcing, an autoregressive training strategy, which integrates the standard diffusion loss into the autoregressive training loop. At each step, the model uses its own predictions to update the context and optimize the single step noise prediction objective, thereby explicitly exposing the model to the inference state distribution during training. Our method does not require additional discriminators or distribution-matching losses, retains the original diffusion framework and sampler, and is easy to integrate. Experiments on multi-domain navigation datasets (RECON, SCAND, HuRoN, TartanDrive) show that compared with strong baselines, AR Forcing improved the consistency of generated images during long-horizon navigation and the accuracy of predicted trajectories, enhancing robustness of the model in complex known and unknown environments. We will release the code soon.

Estimating 3D attributes directly from images has advanced rapidly with the Visual Geometry Grounded Transformer (VGGT), which predicts camera parameters, depth maps, and point clouds in a single forward pass. However, its 1.2B-parameter scale severely limits deployment on resource-constrained platforms such as UAVs and mobile AR devices. To address this limitation, we introduce QVGGT, a tailored quantization framework designed to compress VGGT. Our approach starts from the observation that transformer blocks within VGGT exhibit heterogeneous sensitivity to quantization. We thus analyze per-block quantization sensitivity and propose a selective mixed-precision strategy that allocates higher precision to the most fragile transformer blocks. To address the amplification of quantization error caused by high-variance camera and register tokens, we further introduce token filtering with camera information compensation, which removes these outliers from activation calibration and restores their geometric cues using a PCA-derived global compensation token. Finally, we develop a task-aware scale search mechanism that evaluates candidate quantization scales not only through layer reconstruction but also through multi-head supervision and cross-head geometric consistency among camera poses, depth maps, and point maps. Extensive experiments on multiple geometry perception benchmarks demonstrate that QVGGT achieves near-lossless W4A16 quantization, preserving the accuracy of all 3D prediction heads while delivering 3$\sim$4.9$\times$ memory reduction and up to 2.8$\times$ real hardware speedup over FP32. Our approach makes high-fidelity 3D perception feasible on edge devices, enabling practical deployment of feed-forward 3D reconstruction models in real-world constrained environments.

Autoregressive (AR) video generation has emerged as a promising paradigm for long-horizon video synthesis, where each frame is generated conditioned on previously generated tokens. To accelerate inference, the KV cache is used to avoid redundant recomputation across generation steps. Nevertheless, its growth with generation length introduces increasing memory and error accumulation, limiting the scalability of AR models to even longer sequences. Existing KV cache compression methods mitigate this issue by selectively retaining only video tokens deemed important. However, most existing methods assess token importance using short-horizon signals derived from the current or historical generation context, making these methods prone to overlooking tokens that appear unimportant at early steps but later become critical for future frames. In this work, we identify an important property of trained AR video models: although RoPE-modulated queries evolve across autoregressive steps, the underlying canonical pre-RoPE query distribution remains remarkably stable throughout the video generation process. This approximate stationarity implies that future query distributions are estimable from historical statistics, enabling principled future-aware cache decisions without any additional training. Building on this insight, we propose Future Forcing, a training-free future-aware KV cache policy for AR video generation. Specifically, Future Forcing first constructs a future query proxy from historical statistics, then scores KV cache tokens by their importance under this proxy, and finally merges redundant token pairs within the affine subspace induced by the future query. Extensive experiments show that Future Forcing improves long-horizon consistency under limited KV caches, achieving up to 1.49 improvement in subject consistency on VBench-Long for 60s generation over existing AR video KV cache policies.

This book provides a compact, derivation-oriented introduction to the mathematical foundations of modern generative artificial intelligence. Rather than surveying every recent architecture or implementation detail, it develops a coherent route through the ideas connecting major families of generative models, from PCA, probabilistic PCA, variational autoencoders, and diffusion models to normalising flows, autoregressive factorisations, GANs, Wasserstein GANs, and energy-based models. The aim is to make the structure of generative modelling more accessible without removing the mathematical substance needed to understand how these models are derived and related. The book is intended as a foundation-building primer for mathematically curious researchers, practitioners, and students.

Composing autoregressive models remains a core challenge in understanding how large language models can combine behaviors or skills learned across tasks. We introduce a new and principled composition strategy for autoregressive systems, inspired by composition methods developed for diffusion models. Under a factorized-conditionals assumption, we show that the resulting composition is projective: each component model preserves control over its own designated subspace of the output distribution avoiding interference between models. This property is further preserved under smooth reparameterizations of the output space, yielding a feature-space theorem. Finally, we show that composition preserves length-generalizing behavior when the factorization assumptions and component guarantees hold uniformly at the target length. These results provide a principled understanding of when model composition and merging succeed in autoregressive systems and identify conditions under which their interactions remain stable.

Causal discovery in time series is increasingly performed using nonlinear machine-learning models, yet the resulting causal relationships are almost always summarized by scalar edge scores. We argue that this practice obscures the true object learned by nonlinear autoregressive models: a state-dependent function whose effect varies across regimes, magnitudes, and contexts. We formalize function-valued causal influence for additive, contribution-decomposable architectures and show that scalar causal scores constitute a severe information bottleneck, conflating between-state variation with within-state residual noise. Using Neural Additive Vector Autoregression as a representative architecture, we introduce a practical framework based on Individual Conditional Expectation for estimating causal response functions directly from trained models. Through controlled synthetic experiments, we demonstrate that edges with indistinguishable scalar scores can exhibit qualitatively different functional behaviors, including monotonic, thresholded, saturating, and sign-changing effects. An applied case study on democratic development further shows that function-valued analysis reveals regime-specific and asymmetric causal structure systematically missed by score-centric approaches.

Autoregressive video generators are attractive for streaming, long-horizon, and interactive applications, but distilling strong black-box teachers into causal students remains difficult. The student must learn under its own rollout distribution, whereas practical teachers may expose only prompt-conditioned completed videos and may differ in architecture, capacity, temporal design, and sampling schedule. This interface makes supervised fine-tuning off-policy, score-based distillation inapplicable, and direct adversarial imitation too sparse for denoising-time credit assignment. We propose Adversarial Flow Distillation (AFD), an on-policy framework for heterogeneous black-box video distillation. AFD queries the teacher and rolls out the current student on the same prompts, trains a prompt-paired Bradley-Terry discriminator to estimate clean-sample teacher-student discrepancy, and converts the resulting on-policy advantage into forward-process flow-matching updates on the student's own noised states. Thus, AFD provides dense velocity-field supervision while requiring no teacher scores, latents, denoising trajectories, step alignment, or reverse-chain reinforcement learning. Experiments across two causal AR student families show that AFD consistently improves motion- and physics-sensitive generation while preserving general video quality, and ablations validate the importance of adaptive on-policy feedback and forward-process credit assignment. The method requires only clean teacher videos and student rollouts, providing a practical route for distilling proprietary or heterogeneous video generators into efficient autoregressive students.

We present Channel-wise Vector Quantization (CVQ), a novel image tokenization paradigm that replaces patch-wise tokens with channel-wise tokens. Unlike conventional vector quantization, which assigns a discrete token to each patch feature vector, CVQ quantizes each channel of the feature map. This formulation represents an image as discrete levels of visual details, rather than as a grid of spatial patches. Based on CVQ, we introduce a new visual autoregressive framework with "next-channel prediction". Instead of rendering images patch by patch in raster order, our Channel-wise Autoregressive (CAR) model predicts image channels sequentially, producing progressively enriched visual details. Specifically, it first sketches global structure and then refines fine-grained attributes, akin to a human artist's workflow. Empirically, we show that: (1) CVQ achieves 100% codebook utilization with a 16K+ codebook size without any bells and whistles, and substantially improves reconstruction quality over conventional VQ; and (2) CAR attains a DPG score of 86.7 and a GenEval score of 0.79, demonstrating strong effectiveness for text-to-image generation.

3D Gaussian Splatting (3DGS) provides an efficient method for high-quality scene reconstruction using anisotropic Gaussians. Recently, 3DGS-based methods have significantly improved the rendering quality of human avatars while enabling real-time performance. However, existing methods suffer from a magnitude mismatch in the number of Gaussians generated by image-based and 3DMM-based approaches. This discrepancy results in reconstructed expressions that lack fine-grained detail. In this paper, we introduce a novel method for reconstructing an animatable head avatar from a single image. We propose a Graph splitting network to progressively generate Gaussians from coarse to fine using an autoregressive architecture. To address the graph inconsistency caused by split Gaussians, we employ a mesh topology extension method to align the GNN's connectivity with the increased Gaussian count. Furthermore, we introduce a novel density control method that includes a gating mechanism that generates soft masks for Gaussians, preventing over-densification after the splitting operation. This allows for dynamic control over Gaussian density across different facial regions. For smooth and rapid training, we employ a delayed filtering strategy to avoid re-computing the graph topology during training. Experimental results demonstrate that our autoregressive structure effectively improves expression representation ability by progressively splitting Gaussians. This process, enabled by the GNN-guided splitting, synthesizes more precise facial details and achieves higher reconstruction quality.

Generating physically buildable brick structures from 3D shapes requires more than geometric reconstruction: the output must also satisfy discrete part constraints and structural stability. Existing brick generation methods either rely on heuristic optimization, which can break down when the target 3D shape does not admit a feasible structure under predefined constraints, or generate brick sequences without explicitly modeling the underlying 3D geometry and assembly relations. In this work, we present BrickAnything, a geometry-conditioned autoregressive framework for generating buildable brick structures from diverse 3D representations. BrickAnything uses point clouds as a unified geometric interface and predicts brick sequences that reconstruct the target shape under assembly constraints. To model structural dependencies among bricks, we introduce a structure-aware tree tokenization, which represents brick structures through local attachment relations. This formulation makes sequence generation more consistent with the physical construction process, and reduces invalid intermediate states. We further introduce preference-based alignment post-training, validity-constrained decoding and adaptive rollback to improve buildability objectives such as stability and geometric fidelity. Extensive experiments demonstrate that BrickAnything produces geometrically faithful and physically realizable brick structures, and that the proposed tokenization effectively reduces rollback and regeneration compared with conventional ordering strategies.

Ocean general circulation models (OGCMs) are essential to climate science but computationally expensive, limiting ensemble size and forcing scenarios. Neural emulators promise orders-of-magnitude speedups, yet existing ocean emulators have not combined fine spatial resolution with multi-year autoregressive rollouts. Samudra, the first autoregressive neural ocean emulator to produce multi-decade global rollouts, is limited to $1^\circ$ resolution and exhibits two long-horizon failure modes: \emph{variance collapse}, the loss of temporal variability, and \emph{imprinting artifacts}, in which velocity patterns leak into deep-ocean fields. We present Samudra 2, which introduces a wider U-Net backbone with modified ConvNeXt-style blocks and a reduced block-internal expansion factor, together with a dynamic loss that reweights output channels according to their prediction errors, strengthening gradients for slow-evolving deep-ocean fields. At $1^\circ$, Samudra 2 increases upper-ocean global-mean temperature $R^2$ from 0.56 to 0.87 and reduces deep-ocean temperature error by roughly sevenfold. The same architecture scales to $1/2^\circ$ and $1/4^\circ$ over approximately 8-year autoregressive rollouts, recovering mesoscale eddies and sharp western boundary currents. Running on a single GPU, Samudra 2 enables larger ensembles for sea-level projections, ocean heat uptake, and climate variability studies. All artifacts are publicly available: project page, code, checkpoints, documentation.

Log-likelihood is a standard metric for evaluating generative models. Unfortunately, in contrast to autoregressive models (ARMs), discrete diffusion models generally do not admit exact computation of this quantity. Existing evaluations, therefore, rely on the evidence lower bound (ELBO), leaving unclear how much higher the true value may be. We address this by introducing the Tangent Upper Bound on Evidence (TUBE), a variational upper bound on log-likelihood that admits an unbiased Monte Carlo estimator. Our TUBE extends across latent-variable models, including masked diffusion models (MDMs), any-order ARMs (AO-ARMs), and block variants of both. Applied to block MDMs and block AO-ARMs, TUBE reveals our key empirical finding that these models lie strictly below the exact ARM baseline, showing that ARMs still dominate in likelihood.

Modern deep-learning models have achieved remarkable success in time-series forecasting. Yet, their performance degrades in long-term prediction due to error accumulation in autoregressive inference, where predictions are recursively used as inputs. While classical error correction mechanisms (ECMs) have long been used in statistical methods, their applicability to deep learning models remains limited or ineffective. In this work, we revisit the error accumulation problem in deep time-series forecasting and investigate the role and necessity of ECMs in this new context. We propose a simple, architecture-agnostic error correction model that can be integrated with any existing forecaster without requiring retraining. By explicitly decomposing predictions into trend and seasonal components and training the corrector to adjust each separately, we introduce the Universal Error Corrector with Seasonal-Trend Decomposition (UEC-STD), which significantly improves correction accuracy and robustness across 4 backbones and 10 datasets. Our findings provide a practical tool for enhancing forecasts while offering new insights into mitigating autoregressive errors in deep time-series models. Code is available at https://github.com/DA2I2-SLM/UEC-STD.

How should future neural reasoning systems implement extended computation? Recursive Reasoning Models (RRMs) offer a promising alternative to autoregressive sequence extension by performing iterative latent-state refinement with shared transition functions. Yet existing RRMs are largely deterministic, following a single latent trajectory and converging to a single prediction. We introduce Generative Recursive reAsoning Models (GRAM), a framework that turns recursive latent reasoning into probabilistic multi-trajectory computation. GRAM models reasoning as a stochastic latent trajectory, enabling multiple hypotheses, alternative solution strategies, and inference-time scaling through both recursive depth and parallel trajectory sampling. This yields a latent-variable generative model supporting conditional reasoning via $p_θ(y \mid x)$ and, with fixed or absent inputs, unconditional generation via $p_θ(x)$. Trained with amortized variational inference, GRAM improves over deterministic recurrent and recursive baselines on structured reasoning and multi-solution constraint satisfaction tasks, while demonstrating an unconditional generation capability. https://ahn-ml.github.io/gram-website

MRI reconstruction is an inherently ill-posed inverse problem, since incomplete measurements admit many plausible solutions. This ambiguity becomes more severe under high acceleration, where pixel-domain continuous predictors tend to average over feasible reconstructions and suppress high-frequency anatomy. We address this limitation by moving reconstruction to discrete multi-scale latent space and posing it as autoregressive next-acceleration-scale prediction. Leveraging discrete priors proven effective in visual autoregressive modeling, our method restricts the solution to compact sequences of codebook tokens, enabling sharp reconstructions even from extremely sparse measurements. This discrete autoregressive formulation also aligns naturally with modern large language model post-training techniques. Building on this observation, we introduce on-policy privileged information distillation for visual autoregressive modeling, where a teacher is provided training only privileged context that is unavailable at inference, in our case fully sampled acquisitions, and supervises a student trained on its own rollouts, leading to consistent reconstruction gains. Through extensive experiments on the fastMRI benchmark, we show that our approach delivers improved reconstruction performance across diverse sampling patterns under extreme undersampling. Project website is \href{https://yilmazkorkmaz1.github.io/discrete-mri-reconstruction-opd/}{here}.

This paper tests whether graph neural networks improve realized volatility forecasts and whether those forecasts improve portfolio performance. Using weekly realized volatility for 465 S&P 500 equities from 2015-2025, Heterogeneous Autoregressive and Long Short-Term Memory baselines are compared against GraphSAGE models built on rolling correlation, sector, and Granger-causal graphs, with and without macro regime features. The empirical finding is that the model with the lowest forecast MSE, the model with the highest cross-sectional ranking accuracy, and the model with the highest portfolio Sharpe ratio are three different models. Forecast accuracy, ranking quality, and portfolio performance are related but not interchangeable objectives. Graph volatility models add value only when the portfolio rule can exploit the cross-sectional structure they encode.

Unified autoregressive models (UAMs) are transformer models that generate text as well as image tokens within a single autoregressive pass. Shared parameters and a multimodal vocabulary simplify the training pipeline and facilitate flexible multimodal generation, yet might introduce new vulnerabilities. In particular, we are the first to show that this unified architecture enables multimodal backdoor attacks, where a trigger can propagate malicious effects across multiple output modalities. Specifically, we present the Token by Token Backdoor Attack (ToBAC), the first backdoor attack targeting UAMs, exploring both data-based and model-based poisoning strategies. We demonstrate that innocuous characters or even common words can be transformed into triggers that elicit harmful behavior in autoregressive image generation. ToBAC can jointly manipulate visual outputs and accompanying text, increasing the perceived authenticity of fabricated content. With model access, ToBAC enables attacks on the unified Liquid model in which a subtle word (e.g., ``cool'') induces modality-aligned brand promotion or ideological influence in 55% of generations. Without model access, ToBAC can be induced through data poisoning, achieving an average success rate of 63.1% against JanusPro.

Without incurring significant computational overhead, train-free long video generation aims to enable foundation video generation models to produce longer videos. Frame-level autoregressive frameworks, e.g., FIFO-diffusion, offer the advantage of generating infinitely long videos with constant memory consumption. However, the mismatch between training and inference, coupled with the challenge of maintaining long-term consistency, limits the effective utilization of foundation models. To mitigate these concerns, we propose \textbf{MIGA}, a novel infinite-frame long video generation method. Firstly, we propose an effective two-stage alignment mechanism that mitigates the training-inference gap by reducing the excessive noise span fed to the model. We then introduce an innovative dual consistency enhancement mechanism, where the self-reflection approach corrects early high-noise frames and the long-range frame guidance approach leverages later low-noise frames with broad coverage to steer generation, jointly improving temporal consistency. Extensive experiments on VBench and NarrLV demonstrate the state-of-the-art performance of MIGA. Our project page is available at https://xiaokunfeng.github.io/miga_homepage/.

Residual error propagation remains a fundamental problem in recurrent models, where small prediction inaccuracies compound over time and degrade long-horizon performance. Accurately modeling the correlation structure of such residuals is critical for reliable uncertainty quantification in probabilistic multivariate timeseries forecasting. While recent time-series deep models efficiently parametrize time-varying contemporaneous correlations, they often assume temporal independence of errors and neglect spatial correlation across the observed network. In this paper, we introduce Teger, a structured uncertainty module that overcomes the spa- tial and temporal limitations of error-correlated autoregressive forecasting. Teger proposes a spatial curvature-aware graph rewiring mechanism explicitly strengthening information-bottleneck edges identified by discrete Forman curvature. The component is integrated into a low-rank-plus-diagonal covariance head, preserving tractable inference via the Woodbury identity. Teger is backbone-agnostic, requiring only the latent state produced by any autoregressive encoder. We provide theoretical evidence of Teger, and experimentally evaluate it on LSTM, Transformer, and xLSTM backbones across four real-world spatio-temporal datasets, showing consistent improvement in Continuous Ranked Probability Score (CRPS). We further provide a formal theoretical analysis connecting curvature-aware rewiring to (i) oversquashing alleviation, (ii) improved spectral connectivity, (iii) reduced effective resistance, and (iv) improved covariance calibration bounds

Diffusion-based image synthesis has made AI-generated images (AIGI) increasingly photorealistic, raising urgent concerns about authenticity in applications such as misinformation detection, digital forensics, and content moderation. Despite the substantial advances in AIGI detection, how to correct detected AI-generated images with visible artifacts and restore realistic appearance remains largely underexplored. Moreover, few existing work has established the connection between AIGI detection and artifact correction. To fill this gap, we propose GenShield, a unified autoregressive framework that jointly performs explainable AIGI detection and controllable artifact correction in a closed loop from diagnosis to restoration, revealing a mutually reinforcing relationship between these two tasks. We further introduce a Visual Chain-of-Thought based curriculum learning strategy that enables self-explained, multi-step diagnose-then-repair'' correction with an explicit stopping criterion. A high-quality dataset with large-scale artifact-restored'' pairs is also constructed alongside a unified evaluation pipeline. Extensive experiments on our correction benchmark and mainstream AIGI detection benchmarks demonstrate state-of-the-art performance and strong generalization of our method. The code is available at https://github.com/zhipeixu/GenShield.

Recent progress in deep learning has significantly advanced CT image analysis, particularly for segmentation tasks. However, these advances are largely confined to image-level pattern recognition, with most methods lacking explicit anatomical or contextual reasoning. Large vision-language models introduce linguistic context into image analysis, yet most approaches typically focus on a single task, which is insufficient for clinical workflow analysis that requires multiple fine-grained types of analysis, such as anatomy detection and segmentation. In this paper, we propose a unified autoregressive framework that integrates language-guided visual reasoning into CT interpretation. Our method introduces task-routing tokens that trigger detection and segmentation heads conditioned on the hidden states of a large vision-language model, enabling coherent generation of visual outputs (e.g., masks and bounding boxes) and textual reasonings. To progressively enhance localisation accuracy and semantic clarity, we further design a "closer-look" mechanism that allows the model to perform progressive coarse-to-fine visits to regions of interest under refined fields of view. To support model training and evaluation, we curated a new multimodal CT dataset containing pixel-wise masks, bounding boxes, spatial prompts, and structured descriptions for visual objects constructed through an AI-assisted annotation process with human verification. Experiments on public benchmarks demonstrate consistent improvements over the SoTA, achieving up to 1.0% Dice on BTCV and 1.7% Dice on MosMed+, while additionally providing appearance reasoning outputs. The code and dataset will be available.

Aerial vision-language navigation (VLN) requires agents to follow natural-language instructions through closed-loop perception and action in 3D environments. We argue that aerial VLN can be formulated as a prediction-driven world-action problem: the agent should anticipate latent world evolution and act according to the predicted consequences. To this end, we propose WorldVLN, the first autoregressive world action model for aerial VLN. Unlike full-sequence video-generation world models that generate an entire visual clip, WorldVLN adapts a latent autoregressive video backbone to predict short-horizon world-state transitions and directly decodes them into executable waypoint actions. After each action segment is executed, newly received observations are encoded back into the autoregressive context, enabling closed-loop world-action prediction. We further introduce a two-stage training framework that first grounds the video prior in instruction-conditioned navigation dynamics and then develops Action-aware GRPO, the first reinforcement learning method tailored to autoregressive WAMs, to optimize waypoint decisions through their downstream rollout consequences. On public outdoor and indoor benchmarks, WorldVLN consistently outperforms existing Vision-Language-Action baselines with 12%+ success-rate gains and larger advantages on challenging cases. It further transfers zero-shot to real drone deployment, suggesting that the proposed WorldVLN offers a promising route for spatial action tasks. Demos and code are available at https://embodiedcity.github.io/WorldVLN/.

Generative models are often trained with a next-token prediction objective, yet many downstream applications require the ability to estimate or control sequence-level properties. Next-token prediction can lead to overfitting of local patterns during training, underfitting of global structure, and requires significant downstream modifications or expensive sampling to guide or predict the global attributes of generated samples at inference time. Here, we introduce Conditional Attribute Transformers, a novel method for jointly estimating the next-token probability and the value of an attribute conditional on each potential next token selection. This framework enables three critical capabilities within a single forward pass, without modification of the input sequence: (1) per-token credit assignment across an entire sequence, by identifying how each token in a sequence is associated with an attribute's value; (2) counterfactual analysis, by quantifying attribute differences conditional on alternative next token choices; (3) steerable generation, by decoding sequences based on a combination of next-token and attribute likelihoods. Our approach achieves state of the art performance on sparse reward tasks, improves next-token prediction at sufficient model sizes, estimates attribute probabilities orders of magnitude faster than sampling, and can guide decoding of autoregressive sequence models on a range of language tasks.

We introduce a family of synthetic languages with hierarchical structure -- generated by a broadcast process on trees -- for which the role of context length and reasoning in autoregressive generation can be analyzed precisely. At the heart of our analytic approach is an \emph{exact $k$-gram ansatz} in place of transformers with context length $k$, a substitution we then validate empirically. Using this ansatz we derive explicit asymptotic predictions for distributional statistics of the sequences produced by a trained model, instantiated in two settings. For the \emph{Ising broadcast process} (a soft-constrained language), we prove that the variance of the generated sum scales log-linearly in the context depth and its kurtosis converges to that of a Gaussian -- both deviating from the true language for any sublinear context. For the \emph{coloring broadcast process} (a hard-constrained language) in the freezing regime, bounded-context autoregression produces sequences that, with high probability, are inconsistent with \emph{any} valid coloring of the underlying tree. Together these results imply an $Ω(n)$ lower bound on the context length required to faithfully sample length-$n$ sequences. In contrast, we prove that an autoregressive \emph{reasoning} model with only $Θ(\log n)$ working memory can sample exactly from the true language -- an exponential improvement. We confirm both the lower-bound predictions and the reasoning-based upper bound empirically with transformers trained on the synthetic language; the trained models track our asymptotic predictions quantitatively across a wide range of context sizes.

While autoregressive (AR) Vision-Language-Action (VLA) models have demonstrated formidable reasoning capabilities in robotic tasks, their sequential decoding process often incurs high inference latency and may amplify error accumulation during long-horizon execution. Discrete Diffusion Language Models (dLLMs) provide a promising alternative through parallel token refinement, but their practical deployment in robotics remains limited by repeated denoising function evaluations (NFEs) and the difficulty of directly applying standard KV caching to bidirectional iterative decoding. To bridge these paradigms, we propose BlockVLA, a framework that adapts pretrained AR backbones into an efficient discrete diffusion policy through a block diffusion paradigm. BlockVLA maintains autoregressive dependencies at the block level while enabling parallel denoising within each block, thereby combining global causal coherence with local parallel generation. This design enables prefix KV-cache reuse across completed blocks, reduces the effective cost of iterative denoising, and provides a smoother transition from AR pretraining to diffusion-based policy fine-tuning. We conduct extensive evaluations on the LIBERO and SimplerEnv benchmarks. Experimental results demonstrate that our BlockVLA achieves a 3.3$\times$ inference acceleration over standard discrete diffusion baselines. Furthermore, our model exhibits superior training efficiency, with success rates converging substantially faster than baselines, a gain that is particularly pronounced in complex, long-horizon tasks, where BlockVLA achieves significant performance gains in the early stages of training. This work establishes Block Diffusion as a robust bridge between large-scale pretrained AR models and efficient, high-frequency real-time robotic control.

While EEG foundation models have shown significant potential in universal neural decoding across tasks, their advancement remains constrained by the inadequacy modeling of complex spatiotemporal topology, as well as the inherent modality gap between low-level physiological signals and high-level textual semantics. To address these challenges, we propose a Knowledge-Anchored Semantically-Dynamic Topology Brain Autoregressive Model (KAST-BAR), which dynamically aligns physiological representations derived from multi-level brain topology with an expert-level semantic space. Specifically, we design a Dual-Stream Hierarchical Attention (DSHA) encoder that accurately captures the brain's intrinsic non-Euclidean topology by modeling local temporal dynamics with global spatial contexts. On this basis, a Knowledge-Anchored Semantic Profiler (KASP) is proposed to synthesize physically-grounded and instance-level textual profiles, which subsequently drive a Semantic Text-Aware Refiner (STAR) to dynamically reconstruct EEG representations using Latent Expert Queries. By conducting large-scale pre-training on 21 diverse datasets to build a foundation model, KAST-BAR effectively integrates expert-level medical knowledge into EEG signal representations, consistently achieving superior performance across six downstream tasks. Our code is available at https://github.com/KAST-BAR/KAST-BAR

Neural population models, which predict the joint firing of many simultaneously recorded neurons forward in time, are typically evaluated by a single aggregate Pearson correlation $r$ between predicted and actual spike counts, a number that masks critical structure. We argue that how we evaluate spike forecasting matters as much as what we build, and introduce SpikeProphecy, the first large-scale benchmark for causal, autoregressive spike-count forecasting on real electrophysiology recordings. Our core contribution is a population metric decomposition that separates aggregate performance into temporal fidelity, spatial pattern accuracy, and magnitude-invariant alignment. The decomposition surfaces aspects of the underlying data that an aggregate scalar collapses together. We apply the protocol to 105 Neuropixels sessions (Steinmetz 2019 + IBL Repeated Site; ~89,800 neurons) with seven architecture baselines spanning four structural families: four SSMs (three diagonal and one non-diagonal), a Transformer, an LSTM, and a spiking network. The decomposition surfaces a brain-region predictability ranking that reproduces across all seven baselines and survives ANCOVA correction for firing-statistics constraints (region $ΔR^2 = 0.018$ above the firing-statistics covariates). It also exposes a sub-Poisson evaluation floor where rigorous metrics combine with genuine biophysical constraints on regular spike trains, and yields a negative result on KL-on-output-rates distillation for ANN-to-SNN transfer in this Poisson count domain.

This paper introduces a physics-informed generative framework that resolves the fundamental conflict between the statistical flexibility of deep learning and the rigorous theoretical constraints of fixed-income modeling. We demonstrate that standard generative models and unconstrained statistical extrapolations suffer from "manifold collapse" and severe arbitrage violations when forecasting term structures across diverse macroeconomic regimes. To overcome this, we propose a two-stage architecture. First, a Student-t Conditional Variational Autoencoder with Dynamic Level Injection (CVAEsT+LS) extracts a robust, heavy-tailed term structure manifold, effectively decoupling macroeconomic shape dynamics from absolute base rates. Second, the latent dynamic evolution is governed by a continuous-time Neural Stochastic Differential Equation (SDE) strictly penalized by a No-Arbitrage Partial Differential Equation (PDE). Empirical results across multiple sovereign currencies (USD, GBP, JPY) confirm that our synergistic approach drastically reduces out-of-sample forecasting errors -- achieving an exceptional 6.58 bps Mean Tenor RMSE -- and successfully overcomes the massive parallel drift and zero-lower-bound violations exhibited by the classical HJM model in extreme environments. Furthermore, through phase space vector field analysis, we demonstrate the model's superior capability in unsupervised macroeconomic regime detection and high-quality continuous-time scenario generation. Ultimately, this research provides a highly scalable, mathematically sound evolutionary engine for term structure modeling.

We study the fundamental and timely problem of learning long sequences in autoregressive modeling and next-token prediction under model misspecification, measured by the joint Kullback--Leibler (KL) divergence. Our goal is to characterize how the sequence horizon $H$ affects both approximation and estimation errors in this joint-distribution, sequence-level regime. By establishing matching upper and lower bounds, we provide, to our knowledge, the first complete characterization of long-horizon error behavior under the natural joint KL objective, with improved rates and optimality justification relative to existing work. On the approximation side, we show that joint KL admits a horizon-free approximation factor, in sharp contrast to Hellinger-based analyses that exhibit an $Ω(H)$ dependence for computationally efficient methods; this isolates the choice of divergence as the source of approximation amplification. On the estimation side, we prove a fundamental information-theoretic lower bound of order $Ω(H)$ that holds for both decomposable policy classes and fully shared policies, matching the $\widetilde O(H)$ upper bounds achieved by computationally efficient algorithms. Our analysis clarifies the landscape of recent autoregressive learning results by aligning the log-loss training objective, the sequence-level evaluation metric, and the approximation metric {\color{black}through a sharp joint-KL oracle theory}. We further show that these joint-KL guarantees imply policy learning regret bounds at rates matching prior imitation learning literature.

Generating realistic and user-preferred advertisements is a key challenge in e-commerce. Existing approaches utilize multiple independent models driven by click-through-rate (CTR) to controllably create attractive image or text advertisements. However, their pipelines lack cross-modal perception and rely on CTR that only reflects average preferences. Therefore, we explore jointly generating personalized image-text advertisements from historical click behaviors. We first design a Unified Advertisement Generative model (Uni-AdGen) that employs a single autoregressive framework to produce both advertising images and texts. By incorporating a foreground perception module and instruction tuning, Uni-AdGen enhances the realism of the generated content. To further personalize advertisements, we equip Uni-AdGen with a coarse-to-fine preference understanding module that effectively captures user interests from noisy multimodal historical behaviors to drive personalized generation. Additionally, we construct the first large-scale Personalized Advertising image-text dataset (PAd1M) and introduce a Product Background Similarity (PBS) metric to facilitate training and evaluation. Extensive experiments show that our method outperforms baselines in general and personalized advertisement generation. Our project is available at https://github.com/JD-GenX/Uni-AdGen.

We present ScaleMoGen, a scale-wise autoregressive framework for text-driven human motion generation. Unlike conventional autoregressive approaches that rely on standard next-token prediction, ScaleMoGen frames motion generation as a coarse-to-fine process. We quantize 3D motions into compositional discrete tokens across multiple skeletal-emporal scales of increasing granularity, learning to generate motion by autoregressively predicting next-scale token maps. To maintain structural integrity, our motion tokenizers and quantizers are explicitly designed so that discrete tokens at every scale strictly preserve the skeletal hierarchy. Additionally, we employ bitwise quantization and prediction, which efficiently scale up the tokenizer vocabulary to preserve motion details and stabilize optimization. Extensive experiments demonstrate that ScaleMoGen achieves state-of-the-art performance, establishing an FID of 0.030 (vs. 0.045 for MoMask) on HumanML3D and a CLIP Score of 0.693 (vs. 0.685 for MoMask++) on the SnapMoGen dataset. Furthermore, we demonstrate that our skeletal-temporal multi-scale representation naturally facilitates training-free, text-guided motion editing.

Closed-loop driving simulation requires real-time interaction beyond short offline clips, pushing current driving world models toward autoregressive (AR) rollout. Existing AR distillation approaches typically rely on frame sinks or student-side degradation training. The former transfers poorly to driving due to fast ego-motion and rapid scene changes, while the latter remains bounded by the teacher's single-pass output length and thus provides only a limited supervision horizon. A natural question is: can the teacher itself be extended via AR rollout to provide unbounded-horizon supervision at bounded memory cost? The key difficulty is that a standard teacher drifts under its own predictions, contaminating the supervision it provides. Our key insight is to make the teacher rollout-capable, ensuring reliable supervision from its own AR rollouts. This is instantiated as HorizonDrive, an anti-drifting training-and-distillation framework for AR driving simulation. First, scheduled rollout recovery (SRR) trains the base model to reconstruct ground-truth future clips from prediction-corrupted histories, yielding a teacher that remains stable across long AR rollouts. Second, the rollout-capable teacher is extended via AR rollout, providing long-horizon distribution-matching supervision under bounded memory, while a short-window student aligns to it with teacher rollout DMD (TRD) for efficient real-time deployment. HorizonDrive natively supports minute-scale AR rollout under bounded memory; on nuScenes, HorizonDrive reduces FID by 52% and FVD by 37%, and lowers ARE and DTW by 21% and 9% relative to the strongest long-horizon streaming baselines, while remaining competitive with single-pass driving video generators.

Learning transferable representations for electroencephalography (EEG) remains challenging because EEG signals are inherently multi-channel and non-stationary. Channels observed at the same time provide coupled measurements of neural activity, while the relevant temporal dynamics vary across contexts. This structure is poorly matched by architectures that apply uniform computation across time or route each channel patch independently. To this end, we propose TRACE, an autoregressive EEG pre-training framework that predicts future EEG patches from causal context while performing temporally adaptive and cross-channel coherent computation. At each temporal step, TRACE derives an expert routing decision from the causal cross-channel history and applies it jointly to all channels at that step. This preserves instantaneous cross-channel coherence while allowing different temporal regimes to activate different computation. Since routing is defined over the available channel set and causal temporal context, TRACE is compatible with heterogeneous pre-training across corpora with different channel counts, montages, sequence lengths, and recording domains. Across eight downstream EEG benchmarks, TRACE is evaluated in both settings: when downstream domains are seen only as unlabeled pre-training data and when downstream datasets are completely unseen during pre-training. It obtains the best results on several benchmarks while remaining competitive on motor imagery and clinical event classification tasks, with ablations supporting the importance of cross-channel temporal routing.

Selecting a coherent sequence or subset of elements is a fundamental problem in structured prediction, arising in tasks such as detection, trajectory forecasting, and representative subset selection. In many such settings, the target is inherently ambiguous: each input admits multiple valid outputs, while supervision provides only a single sampled instance. This induces a mismatch between the underlying multi-modal target distribution and the observed training signal. We propose Contextual Plackett-Luce (CPL), a structured probabilistic model for sequence selection that extends the classical Plackett-Luce model to a context-dependent setting following an Ising-style parameterization with unary and pairwise interaction terms. CPL can be viewed as a hybrid between fully autoregressive prediction and parallel sequence selection: autoregressive models effectively capture uncertainty but are computationally expensive on modern parallel hardware such as GPUs, while parallel methods are efficient but struggle to represent multi-modal dependencies. CPL combines the strengths of both by constructing the parameters of a probabilistic selection model in a fully parallel manner, followed by a lightweight autoregressive selection process in which each step applies incremental updates to contextual logits. This decoupling of parallel scoring and sequential selection enables efficient computation without sacrificing expressivity. We evaluate CPL on two structured selection tasks: multi-modal path prediction and representative subset selection. CPL achieves improved structural consistency and robustness under ambiguous supervision compared to strong parallel baselines.

We present TailedTS, a large-scale benchmark dataset derived from Wikipedia hourly page view observations throughout 2024, specifically designed to test time series forecasting models under heavy-tailed, zero-inflated, and non-Gaussian conditions. The dataset comprises approximately 24.69 billion data points spanning roughly 3 million unique Wikipedia pages per month, stored in high-efficiency Apache Parquet format. Wikipedia traffic follows a pronounced power-law distribution where roughly 5% of pages account for over 70% of total page views, creating a natural and rigorous testbed for model robustness against extreme volatility that are absent from or underrepresented in existing benchmarks such as M4, M5, and UCI electricity datasets. TailedTS enables several research tasks. First, we introduce a periodicity quantification framework based on sparse autoregression with sparsity and non-negativity constraints, revealing that frequently-viewed pages exhibit significantly weaker periodic structure than their less-viewed counterparts, showing direct implications for server allocation and traffic forecasting on large digital platforms. Second, we provide standardized prediction benchmarks evaluated under a suite of non-Gaussian loss functions, including $\ell_1$-norm, Huber, quantile, and $\ell_p$-norm losses, demonstrating that standard Gaussian-based estimators degrade substantially on high-volume page categories, while robust alternatives provide consistent gains across all traffic scales. TailedTS is publicly available at https://doi.org/10.5281/zenodo.17070469.

Autoregressive inference is typically assumed to scale predictably with decoding length, with latency increasing smoothly as generated sequence length grows. In this work, we identify unexpected non-monotonic latency behavior in the Apple MPS backend, where latency changes abruptly across nearby decoding configurations during transformer decoding. Using multiple model families (GPT-2, BLOOM, and OPT), we observe latency spikes of up to 21x within specific decoding-budget intervals, followed by recovery at neighboring configurations. Controlled experiments show that these anomalies originate primarily during the decode phase rather than prefill, are not explained by memory pressure alone, and remain absent on CPU and NVIDIA CUDA backends under identical conditions. We further show that key-value (KV) cache interacts strongly with these pathological execution regimes: KV caching remains beneficial overall, but its practical speedup collapses sharply within anomalous configurations, while cache-disabled decoding still exhibits residual non-monotonic behavior. These findings suggest that autoregressive decoding on MPS enters discrete execution regimes that are not captured by coarse-grained benchmarking, highlighting the importance of hardware-aware evaluation for long-context inference.

Autoregressive neural simulators now match classical solvers on short-horizon prediction of physical systems, yet their accuracy degrades rapidly when rolled out over long horizons. In this work, we identify transient amplification of perturbations around rollout trajectories as a structural mechanism driving rollout error. Using a linearization analysis we show that when the Jacobians along an autoregressive trajectory are non-normal and non-commuting, the model amplifies errors transiently, resulting in model rollout drift even when the overall system is asymptotically stable. Building on the analysis, we propose commutativity regularization: a combination of two penalties designed to reduce the normality defect of individual Jacobians and the commutator norm of Jacobians across steps. The penalties are estimated with Jacobian-vector products and have no inference-time cost. We show a propagator bound that quantifies rollout error under approximate commutativity and normality. We evaluate UNet and FNO variants with commutativity regularization on 1D and 2D spatio-temporal data in synthetic and real settings, showing successful long-horizon rollouts over thousands of steps. Further, we show that the method improves FourCastNet climate forecasts on ERA5 without using any new data. The gain is most pronounced out-of-distribution: trained on trajectories of a few hundred steps, regularized models remain in-distribution for thousands of rollout steps on initial conditions where baselines diverge.

Hair is a rich medium of visual and cultural expression, yet its digital modeling remains challenging due to the duality of fluidity and structure. Many existing generative approaches rely primarily on continuous diffusion fields, which entangle global topology with local texture and obscure the semantic and structural organization of hairstyles. To address this, we propose HairGPT, a strand-centric framework that treats strands as generative primitives and formulates realistic 3D hairstyle synthesis as a dual-decoupled autoregressive sequence modeling problem. Our method applies spatial decoupling across semantic scalp regions and structural decoupling along a hierarchical strand representation, progressing from global layout to fine-grained style. We further introduce a geometric tokenizer and region-aware semantic annotations to guide strand-level generation, enabling compositional editing, synthesis of rare and complex hairstyles, and adaptation to stylized domains. By aligning generative modeling with the workflow of digital grooming, HairGPT turns hair generation from opaque texture synthesis into a structured and semantically controllable authoring process, supporting robust semantic conditioning and high-fidelity results across realistic and stylized domains. Project Page: https://haiminluo.github.io/hairgpt/

Autoregressive scientific forecasters often enforce physical or structural constraints by repairing each predicted state before feeding it back into the model. However, it remains unclear when stronger physical rule enforcement becomes reliable and when it becomes a source of distribution shift. We study this question through operator exactness, meaning whether the repair map is the identity on the target manifold and is aligned with the target geometry. We compare raw forecasting, post hoc repair, and in-loop repair across periodic incompressible Navier--Stokes, non-periodic CFDBench flows, and a hierarchical-forecasting support task. In the exact periodic regime, Fourier projection substantially improves rollout accuracy. On the NS-128 benchmark, a strong Raw-FNO has a final-step rollout MSE at horizon 100 of $(9.390 \pm 6.290)\times 10^{-5}$, and post hoc and in-loop projection reduce it to $(1.130 \pm 0.165)\times 10^{-6}$ and $(5.370 \pm 0.113)\times 10^{-7}$. However, once an exact projection is unavailable and only approximate boundary-preserving cleanup is available, the ordering changes. Across cavity, tube, dam, and cylinder flow, stronger Poisson-based cleanup can reduce divergence while worsening rollout error; target-distortion MSE predicts this harm far better than a linear-system residual. Controlled mismatch, screened cleanup, adaptive gating, and external-backbone checks show that the best approximate-regime operating point can be raw or near-identity. Hierarchical forecasting gives the same broader pattern. Exact forecast reconciliation is a stable baseline, whereas blended top-down repair, a validation-tuned interpolation toward historical-proportion top-down reconciliation, is dataset-dependent. Thus, constraint enforcement should be benchmarked by operator--data alignment before enforcement strength.

Diffusion language models (DLMs) have recently demonstrated capabilities that complement standard autoregressive (AR) models, particularly in non-sequential generation and bidirectional editing. Although recent work has shown that pretrained autoregressive checkpoints can be converted into diffusion language models, existing recipes primarily transfer parameters through continued denoising training with objective- and attention-level modifications. We instead ask whether the internal representation geometry learned by next-token prediction can be explicitly preserved during AR-to-DLM conversion. We hypothesize that much of the semantic structure learned by AR pretraining can transfer across generation orders, and thus DLM training should be viewed as relearning the decoding path rather than relearning language representations. To investigate this, we introduce REPR-ALIGN, a representation alignment objective that adapts a bidirectional masked diffusion model to reuse representations from a pretrained AR model of identical architecture. Concretely, we align the hidden states of the DLM to the frozen AR model at every layer using cosine similarity, while optimizing the standard masked denoising objective. This simple alignment, with no adapters and no architectural changes beyond the attention mask, yields up to 4x training acceleration in our setting and is particularly effective in low-data regimes. Our results suggest that linguistic representations can transfer across generation order, and that representation alignment provides a simple and effective technique for training diffusion language models. Code is available at https://github.com/pengzhangzhi/Open-dLLM.

Order-Agnostic autoregressive models have demonstrated strong performance in deep generative modeling, yet their use in settings with incomplete data remains largely unexplored. In this work, we reinterpret them through the lens of missing data. First, we show that their standard training procedure on fully observed data implicitly performs imputation under a missing completely at random mechanism, resulting in robust out-of-sample imputation performance in settings with high missingness. Second, we introduce the first principled framework for training them directly on incomplete datasets under general missingness mechanisms. Third, we leverage their amortized conditional density estimation to perform active information acquisition, i.e., sequentially selecting the most informative missing variables for downstream prediction or inference. Across a suite of real-world benchmarks, our Missingness-Aware Order-Agnostic Autoregressive Model (MO-ARM) consistently outperforms established imputation baselines.

Discrete image tokenizers are commonly trained in two stages: first for reconstruction, and then with a prior model fitted to the frozen token sequences. This decoupling leaves the tokenizer unaware of the model that will later generate its tokens. As a result, the learned tokens may preserve image information well but still be difficult for an autoregressive (AR) prior to predict from left to right. We analyze this mismatch using Tripartite Variational Consistency (TVC), which decomposes latent-variable learning into three consistency conditions: conditional-likelihood consistency, prior consistency, and posterior consistency. TVC shows that two-stage training preserves the reconstruction side but leaves prior consistency outside the tokenizer objective: the overall token distribution is fixed before the AR prior participates in training. Motivated by this view, we add a distribution-level prior-matching signal during tokenizer training, while keeping the reconstruction objective unchanged. We optimize this signal with a Wasserstein-gradient-flow update. For hard categorical tokens, the update reduces to a token-level contrast between an auxiliary AR model that tracks the tokenizer's current token distribution and the target AR prior. It requires only forward passes through the two AR models and does not backpropagate through either of them. The resulting tokenizer, wAR-Tok, reduces AR loss and improves generation FID on CIFAR-10 and ImageNet at comparable reconstruction quality.

In this work, we propose Prologue, an approach to bridging the reconstruction-generation gap in autoregressive (AR) image generation. Instead of modifying visual tokens to satisfy both reconstruction and generation, Prologue generates a small set of prologue tokens prepended to the visual token sequence. These prologue tokens are trained exclusively with the AR cross-entropy (CE) loss, while visual tokens remain dedicated to reconstruction. This decoupled design lets us optimize generation through the AR model's true distribution without affecting reconstruction quality, which we further formalize from an ELBO perspective. On ImageNet 256x256, Prologue-Base reduces gFID from 21.01 to 10.75 without classifier-free guidance while keeping reconstruction almost unchanged; Prologue-Large reaches a competitive rFID of 0.99 and gFID of 1.46 using a standard AR model without auxiliary semantic supervision. Interestingly, driven only by AR gradients, prologue tokens exhibit emergent semantic structure: linear probing on 16 prologue tokens reaches 35.88% Top-1, far above the 23.71% of the first 16 tokens from a standard tokenizer; resampling with fixed prologue tokens preserves a similar high-level semantic layout. Our results suggest a new direction: generation quality can be improved by introducing a separate learned generative representation while leaving the original representation intact.

Decision Transformer (DT) formulates offline reinforcement learning as autoregressive sequence modeling, achieving promising results by predicting actions from a sequence of Return-to-Go (RTG), state, and action tokens. However, RTG is a scalar that summarizes future rewards, containing far less information than typical state or action vectors, yet it consumes the same computational budget per token. Worse, the self-attention cost of Transformers grows quadratically with sequence length, so including RTG as a separate token adds unnecessary overhead. We propose SlimDT, which removes RTG from the autoregressive sequence. Instead, we inject RTG information into the state representations before the sequential modeling step, allowing the Transformer to process only a compact (state, action) sequence. This reduces the sequence length by one-third, directly improving inference efficiency. On the D4RL benchmark, SlimDT surpasses standard DT across various tasks and achieves performance comparable to existing state-of-the-art methods. Decoupling a sparse conditioning signal from an information-rich sequence thus yields both computational gains and higher task performance.

Synthetic data has transformed language model training, yet its role in time series forecasting remains poorly understood. We present a large-scale empirical study: nine experiment groups, 4,218 runs systematically evaluating synthetic time series augmentation across five architectures, four synthetic signals and seven datasets. The effect is sharply architecture-conditional: channel-mixing models (TimesNet, iTransformer) benefit in the majority of trials, while channel-independent models (DLinear, PatchTST) are consistently degraded. In selected low-resource settings the gains are striking: TimesNet trained on only 10% of Weather data with synthetic augmentation surpasses the full-data baseline (4 of 16 sparsity-dataset combinations). Averaged across all architectures, augmentation hurts in 67% of trials. We further find that only the Seasonal-Trend generator reliably helps across the tested benchmarks, and that hard curriculum switching is actively harmful (+24% MSE degradation). These results provide concrete, actionable guidelines on how to use synthetic data: use synthetic augmentation with channel-mixing architectures, use gradual annealing schedules, and treat low-resource augmentation as architecture- and dataset-dependent. Code is available at \href{https://github.com/hugoiscracked/synthetic-ts/tree/main}

Sequence-level evaluations in autoregressive Large Language Models (LLMs) rely on highly dependent token generation. Establishing tight concentration bounds for these processes remains a challenge due to two fundamental bottlenecks in existing frameworks: (i) classical inequalities typically separate dependency structures from target sensitivities, leading to a scalar collapse that inflates the variance proxy to a suboptimal $\mathcal{O}(N)$ for sparse terminal rewards; (ii) conversely, while certain spatial methods achieve tighter bounds, they lack the strictly causal filtration required by sequential generation, rendering them inapplicable to the autoregressive setting. To resolve both bottlenecks, we establish a sharp McDiarmid-type inequality for dependent sequences, governed strictly by the exact matrix-vector multiplication of the causal dependency resolvent and the target sensitivity vector. This Matrix-Decoupled Concentration (MDC) framework natively recovers optimal constants for Markov chains and exploits directed $d$-separation to yield order-optimal bounds for causal trees. Crucially, by exactly preserving the coordinate-wise sparsity of rewards within a strictly causal framework, MDC mathematically prevents scalar collapse, guaranteeing a dimension-free $\mathcal{O}(1)$ variance proxy and providing a rigorous mathematical justification for the stability of long-context reasoning.

Standard knowledge distillation for autoregressive models often suffers from distribution mismatch. While on-policy methods mitigate this by leveraging student-generated outputs, they rely on computationally expensive Reinforcement Learning (RL) frameworks. To improve efficiency, we propose Near-Policy Distillation (NPD), an asynchronous approach that decouples student generation from training. This reformulation enables Supervised Fine-Tuning (SFT) with sequence packing. However, asynchronous updates inevitably introduce policy lag and sample noise, which can cause the behavior to drift from near-policy toward off-policy. To counteract this without sacrificing efficiency, NPD integrates sparse student updates and the $Δ$-IFD filtering mechanism, a heuristic sample selection mechanism that empirically stabilizes the optimization trajectory. By filtering extreme out-of-distribution samples, $Δ$-IFD prevents noise from dominating the gradients, ensuring updates remain within a safe proximal learning zone. Empirically, the NPD framework achieves a 8.1x speedup over on-policy baselines and outperforms SFT by 8.09%. Crucially, by effectively narrowing the exploration space for subsequent RL, our method enables openPangu-Embedded-1B to reach a state-of-the-art score of 68.73%, outperforming the substantially larger Qwen3-1.7B. Codes will be released soon.

Vector quantization (VQ) with autoregressive (AR) token modeling is a widely adopted and highly competitive paradigm for time-series generation. However, such models are fundamentally limited by exposure bias: during inference, errors can accumulate across sequential predictions, leading to pronounced quality degradation in long-horizon generation. To address this, we propose SDFlow ($\textbf{S}$imilarity-$\textbf{D}$riven $\textbf{Flow}$ Matching), a non-autoregressive framework that operates entirely in the frozen VQ latent space and enables parallel sequence generation via flow matching. We tackle three key challenges in making this transition: (1) eliminating exposure bias by replacing step-wise token prediction with a global transport map; (2) mitigating the high-dimensionality of VQ token spaces via a low-rank manifold decomposition with a learned anchor prior over the latent manifold; and (3) incorporating discrete supervision into continuous transport dynamics by introducing a categorical posterior over codebook indices within a variational flow-matching formulation. Extensive experiments show that SDFlow achieves state-of-the-art performance, improving Discriminative Score and substantially reducing Context-FID, particularly for challenging long-sequence generation. Moreover, SDFlow provides significant inference speedups over autoregressive baselines, offering both high fidelity and computational efficiency. Code is available at https://anonymous.4open.science/r/SDFlow-D6F3/

Fast surrogate modeling for high-dimensional physical dynamics requires more than low short-term error: useful models must roll out efficiently while preserving the statistical structure of long trajectories. Neural operators provide inexpensive autoregressive forecasts but can drift in turbulent regimes, whereas rolling diffusion and latent generative surrogates can represent stochastic transitions at the cost of multi-step denoising, noise-schedule design, or auxiliary compression models. We propose MeanFlow Long-term Invariant Spatiotemporal Consistency Autoregressive Models (MeLISA), a latent-free autoregressive generative surrogate built on pixel-space MeanFlow. MeLISA defines a blockwise stochastic transition kernel that generates each forecast block with a single model evaluation, avoiding latent encoders and iterative diffusion solvers at inference time. To stabilize long-horizon rollouts, MeLISA combines a Window-Consistency MeanFlow objective that learns conditional spatiotemporal generation from partially observed temporal windows with a Time Increment Consistency loss that constrains multi-lag finite increments and targets temporal-correlation structure. We evaluate MeLISA with compact UNet and scalable DiT backbones on two high-resolution benchmarks, extended 2D Kolmogorov flow at $256 \times 256$ and turbulent channel-flow slice at $192 \times 192$. MeLISA outperforms neural-operator baselines on short-term forecasting accuracy and long-horizon statistical metrics, including energy spectra, turbulent kinetic energy, and mixing-rate-related dynamics, while achieving inference speeds comparable to, and in some cases faster than, neural operators. Compact 3.7-5.7M-parameter variants already deliver strong parameter efficiency, and DiT variants provide a scalable path up to 150M parameters. Overall, MeLISA benefits both rollout efficiency and long-horizon statistical accuracy.

While Separate Source-Channel Coding (SSCC) retains the practical benefits of modular system design, its effectiveness in noisy text transmission is fundamentally constrained by the fragility of autoregressive source decoding. In low-SNR regimes, even a small number of residual bit errors after channel decoding may derail the subsequent lossless reconstruction process, especially when Arithmetic Coding (AC) relies on Large Language Model (LLM)-based probability estimation. Existing remedies either strengthen channel decoding based solely on channel observations or introduce contextual information only at the receiver for post-hoc correction, yet neither fully addresses the fragility of source probability modeling under residual channel errors. To this end, this paper proposes a Memory-Augmented Source Coding (MASC) scheme for robust SSCC-based transmission. Rather than treating context as external side information, MASC internalizes contextual patterns into a source model shared by both the transmitter-side source encoder and the receiver-side source decoder. Specifically, MASC employs a shared Parameterized Contextual Memory (PCM) to encode multi-order $n$-gram patterns, and further introduces a Mixture-of-Memory-Experts Router (MMER) to perform sparse, hidden-state-dependent routing over memory experts during autoregressive source modeling. By adaptively activating only the most relevant memories at each coding step, MASC refines source probability estimation, shortens average codelength, and mitigates the sensitivity of source decoding to residual channel errors. Extensive experiments over Rayleigh fading and AWGN channels demonstrate the effectiveness of the proposed scheme compared with state-of-the-art methods.