Autoregressive Modeling

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Autoregressive models represent a sequence as successive predictions conditioned on earlier elements, enabling both forecasting and generation. Common approaches include Transformer and state-space models, order-agnostic or masked prediction, coarse-to-fine generation, and continuous-latent models. They are used for tasks ranging from language and speech to weather, motion, and physical simulation, with evaluations including long-horizon rollouts and benchmarks such as ERA5, M5, and LibriSpeech. A central challenge is balancing accurate, efficient stepwise prediction with error accumulation, stability, and reliable behavior over long horizons or under distribution shift.

Latest papers

86 papers8 papers in the last four weeks, level with the four weeks before. 0.0% of all new papers.

May 5, 2026

Rethinking Entropy Minimization in Test-Time Adaptation for Autoregressive Models

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.

Wei-Ping Huang, Chee-En Yu, Guan-Ting Lin +1

Graduate Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan

Test-Time Adaptation Entropy Regularization Autoregressive Modeling

May 2, 2026

Barriers to Counterfactual Credit Attribution for Autoregressive Models

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. 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 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.

Aloni Cohen, Chenhao Zhang

Generative Modeling Counterfactual Credit Assignment Autoregressive Modeling

Apr 30, 2026

Sampling two-dimensional spin systems with transformers

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.

Piotr Białas, Piotr Korcyl, Tomasz Stebel +2

Institute of Applied Computer Science, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland · Institute of Theoretical Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland · Doctoral School of Exact and Natural Sciences, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland

Transformer Ising Model Autoregressive Modeling

Apr 30, 2026

ABC: Any-Subset Autoregression via Non-Markovian Diffusion Bridges in Continuous Time and Space

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

Gabe Guo, Thanawat Sornwanee, Lutong Hao +3

Stanford University

Autoregressive Diffusion Generative Modeling Autoregressive Video Generation Autoregressive Modeling

Apr 22, 2026

A Hybridizable Neural Time Integrator for Stable Autoregressive Forecasting

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.

Brooks Kinch, Xiaozhe Hu, Yilong Huang +6

Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, USA · Department of Mathematics, Tufts University, Medford, MA, USA · Department of Mathematics and Cybernetics, SINTEF Digital, Oslo, Norway +3

Neural Surrogate Modeling Time Series Transformers Chaotic Time-Series Prediction Autoregressive Modeling Neural Network Stability Autoregressive Transformer

Apr 13, 2026

One Scale at a Time: Scale-Autoregressive Modeling for Fluid Flow Distributions

Analyzing unsteady fluid flows often requires access to the full distribution of possible temporal states, yet conventional PDE solvers are computationally prohibitive and learned time-stepping surrogates quickly accumulate error over long rollouts. Generative models avoid compounding error by sampling states independently, but diffusion and flow-matching methods, while accurate, are limited by the cost of many evaluations over the entire mesh. We introduce scale-autoregressive modeling (SAR) for sampling flows on unstructured meshes hierarchically from coarse to fine: it first generates a low-resolution field, then refines it by progressively sampling higher resolutions conditioned on coarser predictions. This coarse-to-fine factorization improves efficiency by concentrating computation at coarser scales, where uncertainty is greatest, while requiring fewer steps at finer scales. Across unsteady-flow benchmarks of varying complexity, SAR attains substantially lower distributional error and higher per-sample accuracy than state-of-the-art diffusion models based on multi-scale GNNs, while matching or surpassing a flow-matching Transolver (a linear-time transformer) yet running 2-7x faster than this depending on the task. Overall, SAR provides a practical tool for fast and accurate estimation of statistical flow quantities (e.g., turbulent kinetic energy and two-point correlations) in real-world settings.

Mario Lino, Nils Thuerey

Technical University of Munich

Generative Modeling Autoregressive Modeling Computational Fluid Dynamics

Apr 9, 2026

Hidden Biases in Conditioning Autoregressive Models

Large language and music models are increasingly used for constrained generation: rhyming lines, fixed meter, inpainting or infilling, positional endings, and other global form requirements. These systems often perform strikingly well, but the induced procedures are usually not exact conditioning of the underlying autoregressive model. This creates a hidden inferential bias, distinct from the better-known notion of bias inherited from the training set: samples are distorted relative to the true constrained distribution, with no generic guarantee of complete coverage of the admissible solution space or of correct conditional probabilities over valid completions. We formalize several exact inference tasks for autoregressive models and prove corresponding hardness results. For succinctly represented autoregressive models whose next-token probabilities are computable in polynomial time, exact sentence-level maximum a posteriori (MAP) decoding is NP-hard. This hardness persists under unary and metrical constraints. On the sampling side, exact conditioned normalization is #P-hard even for regular constraints such as fixed-length terminal events. Unlike finite-state Markov models, general autoregressive models do not admit a bounded-state dynamic program for these tasks. These results formalize a standard claim in the neural decoding literature: local autoregressive sampling is easy, whereas exact decoding and exact conditioning under global form constraints are computationally intractable in general.

Francois Pachet, Pierre Roy

LIP6, Sorbonne Université · Soundtrap

Constrained Generative Modeling Constrained Decoding Autoregressive Language Modeling Autoregressive Modeling

Apr 6, 2026

Towards Scaling Law Analysis For Spatiotemporal Weather Data

Compute-optimal scaling laws are relatively well studied for NLP and CV, where objectives are typically single-step and targets are comparatively homogeneous. Weather forecasting is harder to characterize in the same framework: autoregressive rollouts compound errors over long horizons, outputs couple many physical channels with disparate scales and predictability, and globally pooled test metrics can disagree sharply with per-channel, late-lead behavior implied by short-horizon training. We extend neural scaling analysis for autoregressive weather forecasting from single-step training loss to long rollouts and per-channel metrics. We quantify (1) how prediction error is distributed across channels and how its growth rate evolves with forecast horizon, (2) if power law scaling holds for test error, relative to rollout length when error is pooled globally, and (3) how that fit varies jointly with horizon and channel for parameter, data, and compute-based scaling axes. We find strong cross-channel and cross-horizon heterogeneity: pooled scaling can look favorable while many channels degrade at late leads. We discuss implications for weighted objectives, horizon-aware curricula, and resource allocation across outputs.

Alexander Kiefer, Prasanna Balaprakash, Xiao Wang

Bredesen Center, University of Tennessee, Knoxville, Tennessee · Oak Ridge National Laboratory, Oak Ridge, Tennessee

Weather Forecasting Spatiotemporal Forecasting Neural Scaling Laws Autoregressive Modeling

Apr 4, 2026

Next-Scale Autoregressive Models for Text-to-Motion Generation

Autoregressive (AR) models offer stable and efficient training, but standard next-token prediction is not well aligned with the temporal structure required for text-conditioned motion generation. We introduce MoScale, a next-scale AR framework that generates motion hierarchically from coarse to fine temporal resolutions. By providing global semantics at the coarsest scale and refining them progressively, MoScale establishes a causal hierarchy better suited for long-range motion structure. To improve robustness under limited text-motion data, we further incorporate cross-scale hierarchical refinement for improving per-scale initial predictions and in-scale temporal refinement for selective bidirectional re-prediction. MoScale achieves SOTA text-to-motion performance with high training efficiency, scales effectively with model size, and generalizes zero-shot to diverse motion generation and editing tasks.

Zhiwei Zheng, Shibo Jin, Lingjie Liu +1

University of Pennsylvania

Text-to-Motion Generation Human Motion Generation Autoregressive Generation Autoregressive Modeling

Mar 21, 2026

From Causal Discovery to Dynamic Causal Inference in Neural Time Series

Time-varying causal models provide a powerful framework for studying dynamic scientific systems, yet most existing approaches assume that the underlying causal network is known a priori - an assumption rarely satisfied in real-world domains where causal structure is uncertain, evolving, or only indirectly observable. This limits the applicability of dynamic causal inference in many scientific settings. We propose Dynamic Causal Network Autoregression (DCNAR), a two-stage neural causal modeling framework that integrates data-driven causal discovery with time-varying causal inference. In the first stage, a neural autoregressive causal discovery model learns a sparse directed causal network from multivariate time series. In the second stage, this learned structure is used as a structural prior for a time-varying neural network autoregression, enabling dynamic estimation of causal influence without requiring pre-specified network structure. We evaluate the scientific validity of DCNAR using behavioral diagnostics that assess causal necessity, temporal stability, and sensitivity to structural change, rather than predictive accuracy alone. Experiments on multi-country panel time-series data demonstrate that learned causal networks yield more stable and behaviorally meaningful dynamic causal inferences than coefficient-based or structure-free alternatives, even when forecasting performance is comparable. These results position DCNAR as a general framework for using AI as a scientific instrument for dynamic causal reasoning under structural uncertainty.

Dmitry Zaytsev, Valentina Kuskova, Michael Coppedge

Lucy Family Institute for Data & Society, University of Notre Dame, Notre Dame, Indiana, USA · Political Science, University of Notre Dame, Notre Dame, Indiana, USA

Causal Inference Time-Series Causal Discovery Causal Structure Learning Autoregressive Modeling

Mar 19, 2026

Revisiting Autoregressive Models for Generative Image Classification

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.

Ilia Sudakov, Artem Babenko, Dmitry Baranchuk

1HSE University · 2Yandex Research

Visual Autoregressive Models Image Classification Autoregressive Modeling

Mar 19, 2026

Fast and Interpretable Autoregressive Estimation with Neural Network Backpropagation

Autoregressive (AR) models remain widely used in time series analysis due to their interpretability, but convencional parameter estimation methods can be computationally expensive and prone to convergence issues. This paper proposes a Neural Network (NN) formulation of AR estimation by embedding the autoregressive structure directly into a feedforward NN, enabling coefficient estimation through backpropagation while preserving interpretability. Simulation experiments on 125,000 synthetic AR(p) time series with short-term dependence (1 <= p <= 5) show that the proposed NN-based method consistently recovers model coefficients for all series, while Conditional Maximum Likelihood (CML) fails to converge in approximately 55% of cases. When both methods converge, estimation accuracy is comparable with negligible differences in relative error, R2 and, perplexity/likelihood. However, when CML fails, the NN-based approach still provides reliable estimates. In all cases, the NN estimator achieves substantial computational gains, reaching a median speedup of 12.6x and up to 34.2x for higher model orders. Overall, results demonstrate that gradient-descent NN optimization can provide a fast and efficient alternative for interpretable AR parameter estimation.

Anaísa Lucena, Ana Martins, Armando J. Pinho +1

IEETA/DETI/LASI, University of Aveiro, 3810-193 Aveiro, Portugal

Autoregressive Modeling

Mar 18, 2026

Towards Infinitely Long Neural Simulations: Self-Refining Neural Surrogate Models for Dynamical Systems

Recent advances in autoregressive neural surrogate models have enabled orders-of-magnitude speedups in simulating dynamical systems. However, autoregressive models are generally prone to distribution drift: compounding errors in autoregressive rollouts that severely degrade generation quality over long time horizons. Existing work attempts to address this issue by implicitly leveraging the inherent trade-off between short-time accuracy and long-time consistency through hyperparameter tuning. In this work, we introduce a unifying mathematical framework that makes this tradeoff explicit, formalizing and generalizing hyperparameter-based strategies in existing approaches. Within this framework, we propose a robust, hyperparameter-free model implemented as a conditional diffusion model that balances short-time fidelity with long-time consistency by construction. Our model, Self-refining Neural Surrogate model (SNS), can be implemented as a standalone model that refines its own autoregressive outputs or as a complementary model to existing neural surrogates to ensure long-time consistency. We also demonstrate the numerical feasibility of SNS through high-fidelity simulations of complex dynamical systems over arbitrarily long time horizons.

Qi Liu, Laure Zanna, Joan Bruna

Courant Institute School of Mathematics, Computing, and Data Science, New York University, USA.

Neural Surrogate Modeling Autoregressive Modeling Dynamical Systems Diffusion Models

Mar 16, 2026

Scaling Autoregressive Models for Lattice Thermodynamics

Predicting how materials behave under realistic conditions requires understanding the statistical distribution of atomic configurations on crystal lattices, a problem central to alloy design, catalysis, and the study of phase transitions. Traditional Markov-chain Monte Carlo sampling suffers from slow convergence and critical slowing down near phase transitions, motivating the use of generative models that directly learn the thermodynamic distribution. Existing autoregressive models (ARMs), however, generate configurations in a fixed sequential order and incur high memory and training costs, limiting their applicability to realistic systems. Here, we develop a framework combining any-order ARMs, which generate configurations flexibly by conditioning on any known subset of lattice sites, with marginalization models (MAMs), which approximate the probability of any partial configuration in a single forward pass and substantially reduce memory requirements. This combination enables models trained on smaller lattices to be reused for sampling larger systems, while supporting expressive Transformer architectures with lattice-aware positional encodings at manageable computational cost. We demonstrate that Transformer-based any-order MAMs achieve more accurate free energies than multilayer perceptron-based ARMs on both the two-dimensional Ising model and CuAu alloys, faithfully capturing phase transitions and critical behavior. Overall, our framework scales from

10 \times 10

to

20 \times 20

Ising systems and from

2 \times 2 \times 4

to

4 \times 4 \times 8

CuAu supercells at reduced computational cost compared to conventional sampling methods.

Xiaochen Du, Juno Nam, Sulin Liu +1

Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA · Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Autoregressive Modeling Computational Materials Science Free Energy Calculation

Mar 14, 2026

Data-Driven Autoregressive Power Prediction for GTernal Robots in the Robotarium

Energy-aware algorithms for multi-robot systems require accurate power consumption models, yet existing approaches rely on kinematic approximations that fail to capture the complex dynamics of real hardware. We present a lightweight autoregressive predictor for the GTernal mobile robot platform deployed in the Georgia Tech Robotarium. Through analysis of 48,000 samples collected across six motion trials, we discover that power consumption exhibits strong temporal autocorrelation (

ρ_1 = 0.95

) that dominates kinematic effects. A 7,041-parameter multi-layer perceptron (MLP) achieves

R^2 = 0.90

on held-out motion patterns by conditioning on recent power history, reaching the theoretical prediction ceiling imposed by measurement noise. Physical validation across seven robots in a collision avoidance scenario yields mean

R^2 = 0.87

, demonstrating zero-shot transfer to unseen robots and behaviors. The predictor runs in 224

μ

s per inference, enabling real-time deployment at 150

\times

the platform's 30 Hz control rate. We release the trained model and dataset to support energy-aware multi-robot algorithm development.

Yassin Abdelmeguid, Ammar Hasan

American University of Sharjah

Autoregressive Modeling Mobile Robotics Multi-Robot Systems

Mar 10, 2026

ARCHE: Autoregressive Residual Compression with Hyperprior and Excitation

Recent progress in learning-based image compression has demonstrated that end-to-end optimization can substantially outperform traditional codecs by jointly learning compact latent representations and probabilistic entropy models. However, many existing approaches achieve high rate-distortion efficiency at the expense of increased computational cost and limited parallelism. This paper presents ARCHE - Autoregressive Residual Compression with Hyperprior and Excitation, an end-to-end learned image compression framework that balances modeling accuracy and computational efficiency. The proposed architecture unifies hierarchical, spatial, and channel-based priors within a single probabilistic framework, capturing both global and local dependencies in the latent representation of the image, while employing adaptive feature recalibration and residual refinement to enhance latent representation quality. Without relying on recurrent or transformer-based components, ARCHE attains state-of-the-art rate-distortion efficiency: it reduces the BD-Rate by approximately 48% relative to the commonly used benchmark model of Balle et al., 30% relative to the channel-wise autoregressive model of Minnen & Singh and 5% against the VVC Intra codec on the Kodak benchmark dataset. The framework maintains computational efficiency with 95M parameters and 222ms running time per image. Visual comparisons confirm sharper textures and improved color fidelity, particularly at lower bit rates, demonstrating that accurate entropy modeling can be achieved through efficient convolutional designs suitable for practical deployment.

Sofia Iliopoulou, Dimitris Ampeliotis, Athanassios Skodras

Dept. of Electrical and Computer Engineering, University of Patras, Patras, Greece · Dept. of Digital Media and Communication, Ionian University, Argostoli, Greece

Learned Image Compression Autoregressive Modeling

Mar 9, 2026

On the Feasibility and Opportunity of Autoregressive 3D Object Detection

LiDAR-based 3D object detectors typically rely on proposal heads with hand-crafted components like anchor assignment and non-maximum suppression (NMS), complicating training and limiting extensibility. We present AutoReg3D, an autoregressive 3D detector that casts detection as sequence generation. Given point-cloud features, AutoReg3D emits objects in a range-causal (near-to-far) order and encodes each object as a short, discrete-token sequence consisting of its center, size, orientation, velocity, and class. This near-to-far ordering mirrors LiDAR geometry--near objects occlude far ones but not vice versa--enabling straightforward teacher forcing during training and autoregressive decoding at test time. AutoReg3D is compatible across diverse point-cloud or backbones and attains competitive nuScenes performance without anchors or NMS. Beyond parity, the sequential formulation unlocks language-model advances for 3D perception, including GRPO-style reinforcement learning for task-aligned objectives. These results position autoregressive decoding as a viable, flexible alternative for LiDAR-based detection and open a path to importing modern sequence-modeling tools into 3D perception.

Zanming Huang, Jinsu Yoo, Sooyoung Jeon +6

The Ohio State University · Cornell University · Boston University +1

Lidar-Based 3D Object Detection 3D Object Detection Autoregressive Modeling

Mar 6, 2026

NOVA: Next-step Open-Vocabulary Autoregression for 3D Multi-Object Tracking in Autonomous Driving

Generalizing across unknown targets is critical for open-world perception, yet existing 3D Multi-Object Tracking (3D MOT) pipelines remain limited by closed-set assumptions and ``semantic-blind'' heuristics. To address this, we propose Next-step Open-Vocabulary Autoregression (NOVA), an autoregressive association formulation that shifts the data association stage from fragmented distance-based matching toward trajectory-conditioned spatio-semantic modeling. NOVA reformulates 3D trajectories as structured spatio-temporal semantic sequences, enabling the simultaneous encoding of physical motion continuity and deep linguistic priors. By leveraging the autoregressive capabilities of Large Language Models (LLMs), we transform the tracking task into a principled process of next-step sequence completion. This mechanism allows the model to explicitly utilize the hierarchical structure of language space to resolve fine-grained semantic ambiguities and maintain identity consistency across complex long-range sequences through high-level commonsense reasoning. Extensive experiments on nuScenes, V2X-Seq-SPD, and KITTI demonstrate the superior performance of NOVA. Notably, on the nuScenes dataset, NOVA achieves an AMOTA of 22.41% for Novel categories, yielding a significant 20.21% absolute improvement over the baseline. These gains are realized through a compact 0.5B autoregressive model. Code will be available at https://github.com/xifen523/NOVA.

Kai Luo, Xu Wang, Rui Fan +1

School of Artificial Intelligence and Robotics and the National Engineering Research Center of Robot Visual Perception and Control Technology, Hunan University, Changsha 410082, China · College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China · State Key Laboratory of Intelligent Autonomous Systems, Tongji University, Shanghai 201804, China

Visual Object Tracking Autonomous Driving 3D MOT Autoregressive Modeling Multi-Object Tracking

Mar 3, 2026

Spatial Autoregressive Modeling of DINOv3 Embeddings for Unsupervised Anomaly Detection

DINO models provide rich patch-level representations that have recently enabled strong performance in unsupervised anomaly detection (UAD). Most existing methods extract patch embeddings from normal images and model them independently, ignoring spatial and neighborhood relationships between patches. This implicitly assumes that self-attention and positional encodings sufficiently encode contextual information within each patch embedding. In addition, the normative distribution is often modeled as memory banks or prototype-based representations, which require storing large numbers of features and performing costly comparisons at inference time, leading to substantial memory and computational overhead. In this work, we explicitly model spatial and contextual dependencies between patch embeddings using a 2D autoregressive (AR) model, allowing us to use a simple and efficient model for normative modeling. Instead of storing embeddings or clustering prototypes, our approach learns a compact parametric model of the normative distribution via an AR convolutional neural network (CNN). At test time, anomaly detection reduces to a single forward pass through the network and enables fast and memory-efficient inference. We evaluate our method on the BMAD benchmark, comprising three medical imaging datasets, and the VisA dataset, comprising 12 industrial object categories, and compare it against existing methods, including recent DINO-based approaches. Experimental results demonstrate that explicitly modeling spatial dependencies achieves competitive anomaly detection performance while substantially reducing inference time and memory requirements. Code is available at the project page: https://eerdil.github.io/spatial-ar-dinov3-uad/

Ertunc Erdil, Nico Schulthess, Guney Tombak +1

Computer Vision Lab. ETH Zurich, Zurich, Switzerland

Medical Image Anomaly Detection Industrial Anomaly Detection Unsupervised Anomaly Detection Autoregressive Modeling

Mar 3, 2026

Embedding interpretable $\ell_1$ -regression into neural networks for uncovering temporal structure in cell imaging

While artificial neural networks excel in unsupervised learning of non-sparse structure, classical statistical regression techniques offer better interpretability, in particular when sparseness is enforced by

\ell_1

regularization, enabling identification of which factors drive observed dynamics. We investigate how these two types of approaches can be optimally combined, exemplarily considering two-photon calcium imaging data where sparse autoregressive dynamics are to be extracted. We propose embedding a vector autoregressive (VAR) model as an interpretable regression technique into a convolutional autoencoder, which provides dimension reduction for tractable temporal modeling. A skip connection separately addresses non-sparse static spatial information, selectively channeling sparse structure into the

\ell_1

-regularized VAR.

\ell_1

-estimation of regression parameters is enabled by differentiating through the piecewise linear solution path. This is contrasted with approaches where the autoencoder does not adapt to the VAR model. Having an embedded statistical model also enables a testing approach for comparing temporal sequences from the same observational unit. Additionally, contribution maps visualize which spatial regions drive the learned dynamics.

Fabian Kabus, Maren Hackenberg, Julia Hindel +6

Institute of Medical Biometry and Statistics (IMBI), Faculty of Medicine and Medical Center, University of Freiburg, Germany · Department of Computer Science, University of Freiburg, Germany · Institute of Physiology I, Faculty of Medicine, University of Freiburg, Germany +2

Autoregressive Modeling Neural Network Interpretability Microscopy Image Analysis Convolutional Autoencoder

Feb 26, 2026

Switch-Hurdle: A MoE Encoder with AR Hurdle Decoder for Intermittent Demand Forecasting

Intermittent demand, a pattern characterized by long sequences of zero sales punctuated by sporadic, non-zero values, poses a persistent challenge in retail and supply chain forecasting. Both traditional methods, such as ARIMA, exponential smoothing, or Croston variants, as well as modern neural architectures such as DeepAR and Transformer-based models often underperform on such data, as they treat demand as a single continuous process or become computationally expensive when scaled across many sparse series. To address these limitations, we introduce Switch-Hurdle: a new framework that integrates a Mixture-of-Experts (MoE) encoder with a Hurdle-based probabilistic decoder. The encoder uses a sparse Top-1 expert routing during the forward pass yet approximately dense in the backward pass via a straight-through estimator (STE). The decoder follows a cross-attention autoregressive design with a shared hurdle head that explicitly separates the forecasting task into two components: a binary classification component estimating the probability of a sale, and a conditional regression component, predicting the quantity given a sale. This structured separation enables the model to capture both occurrence and magnitude processes inherent to intermittent demand. Empirical results on the M5 benchmark and a large proprietary retail dataset show that Switch-Hurdle achieves state-of-the-art prediction performance while maintaining scalability.

Fabian Muşat, Simona Căbuz

eMAG, Romania

Time Series Forecasting Probabilistic Time Series Forecasting Autoregressive Modeling

Feb 23, 2026

Selecting Optimal Variable Order in Autoregressive Ising Models

Autoregressive models enable tractable sampling from learned probability distributions, but their performance critically depends on the variable ordering used in the factorization via complexities of the resulting conditional distributions. We propose to learn the Markov random field describing the underlying data, and use the inferred graphical model structure to construct optimized variable orderings. We illustrate our approach on two-dimensional image-like models where a structure-aware ordering leads to restricted conditioning sets, thereby reducing model complexity. Numerical experiments on Ising models with discrete data demonstrate that graph-informed orderings yield higher-fidelity generated samples compared to naive variable orderings.

Shiba Biswal, Marc Vuffray, Andrey Y. Lokhov

Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545.

Autoregressive Modeling Ising Model

Feb 18, 2026

BrainRVQ: A High-Fidelity EEG Foundation Model via Dual-Domain Residual Quantization and Hierarchical Autoregression

Developing foundation models for electroencephalography (EEG) remains challenging due to the signal's low signal-to-noise ratio and complex spectro-temporal non-stationarity. Existing approaches often overlook the hierarchical latent structure inherent in neural dynamics, leading to suboptimal reconstruction of fine-grained information. In this work, we propose BrainRVQ, a general-purpose EEG foundation model pre-trained on a large-scale corpus of clinical EEG data. Unlike standard masked modeling, BrainRVQ features a Dual-Domain Residual Vector Quantization (DD-RVQ) tokenizer that disentangles temporal waveforms and spectral patterns into hierarchical discrete codes. We further introduce a hierarchical autoregressive pre-training objective that learns to reconstruct these codes in a coarse-to-fine manner, utilizing an importance-guided curriculum masking strategy to prioritize information-rich neural events over background noise. Extensive experiments across 8 diverse downstream datasets demonstrate that BrainRVQ consistently outperforms state-of-the-art baselines, validating its effectiveness in learning robust and generalizable neural representations. Our code and model weights are available:https://github.com/keqicmz/BrainRVQ

Mingzhe Cui, Tao Chen, Yang Jiao +4

State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, China · Department of Electronics, Information and Bioengineering, Politecnico di Milano, Milan, Italy · Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China

EEG Foundation Models Self-Supervised Time Series Representation Learning Residual VQ Autoregressive Modeling

Feb 17, 2026

Why Any-Order Autoregressive Models Need Two-Stream Attention: A Structural-Semantic Tradeoff

Any-order autoregressive models (AO-ARMs) offer a promising path toward efficient masked diffusion by enabling native key-value caching, but competitive performance has so far required two-stream attention, typically motivated as a means of decoupling token content from position. In this work, we argue that two-stream attention may be serving a more subtle role. We identify a structural-semantic tradeoff in any-order generation: the hidden representation at each step must simultaneously attend to semantically informative tokens for prediction and structurally recent tokens for summarization, objectives that compete for attention capacity in a single stream but can specialize across two streams. To isolate this tradeoff from position-content separation, we propose Decoupled RoPE, a modification to rotary position embeddings that provides target position information without revealing target content. Decoupled RoPE performs competitively at short sequence lengths--where semantic and structural proximity coincide--but degrades as sequence length increases and the two orderings diverge. These results suggest that the success of two-stream attention stems not merely from separating position from content, but from circumventing the deeper structural-semantic tradeoff inherent to any-order generation.

Patrick Pynadath, Ruqi Zhang

Department of Computer Science, Purdue University

Autoregressive Modeling Self-Attention Autoregressive Diffusion Rotary Positional Embeddings

Sep 19, 2025

ArchesClimate: Probabilistic Decadal Ensemble Generation With Flow Matching

Internal variability is a dominant contributor to the uncertainty of predictions at the interannual to decadal timescale. A typical approach to separating the internal variability from forced climate responses is to generate large ensembles of simulations under different initial conditions. Due to the complexity of Earth System Models, generating these large ensembles is computationally expensive. In this work, we present ArchesClimate, a deep learning-based climate model emulator designed to reduce the cost of exploring internal variability at timescales ranging from monthly to decadal. ArchesClimate is trained on decadal hindcasts of the IPSL-CM6A-LR climate model. We train a flow matching model following ArchesWeatherGen, which we adapt to predict near-term climate. Once trained, the model generates states at a one-month lead time from the states of the two preceding months, and can be used to auto-regressively emulate climate model simulations. We show that for up to 10 years, these generations are stable and physically consistent. We also show that for several important climate variables, ArchesClimate generates simulations that are interchangeable with the IPSL model. This work suggests that climate model emulators could reduce the cost of generating large ensembles with climate models.

Graham Clyne, Guillaume Couairon, Guillaume Gastineau +2

ARCHES, INRIA, Paris, France · UMR LOCEAN, IPSL, Sorbonne Universit´e, IRD, CNRS, MNHN, Paris, France · Department of Computer Science, University of Colorado Boulder, USA

Neural Surrogate Modeling Climate Science Climate Modeling Conditional Generative Modeling Autoregressive Modeling Climate Emulation

Jun 4, 2025

Temporal horizons in forecasting: a performance-learnability trade-off

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.

Pau Vilimelis Aceituno, Jack William Miller, Noah Marti +2

Institute of Neuroinformatics, ETH Zürich and University of Zürich, Winterhurerstrasse 190, Zürich 8057, Switzerland · School of Computing, National Australian University, 108 North Rd, Acton ACT 2601, Australia · Unit of Land Change Science, Swiss Federal Research Institute for Forest, Snow and Landscape Zürcherstrasse 111, Birmensdorf 8903, Switzerland

Long-Term Time Series Forecasting Time Series Forecasting Loss Landscape Geometry Hyperparameter Optimization Autoregressive Modeling