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BAR: Refactor the Basis of Autoregressive Visual Generation

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 5.5Download Report PDF
Autoregressive ModelsAutoregressive Visual Generation
Abstract:

Autoregressive (AR) models, despite their remarkable successes, encounter limitations in image generation due to sequential prediction of tokens, e.g. local image patches, in a predetermined row-major raster-scan order. Prior works improve AR with various designs of prediction units and orders, however, rely on human inductive biases. This work proposes Basis Autoregressive (BAR), a novel paradigm that conceptualizes tokens as basis vectors within the image space and employs an end-to-end learnable approach to transform basis. By viewing tokens xkx_k as the projection of image x\mathbf{x} onto basis vectors eke_k, BAR's unified framework refactors fixed token sequences through the linear transform y=Ax\mathbf{y}=\mathbf{Ax}, and encompasses previous methods as specific instances of matrix A\mathbf{A}. Furthermore, BAR adaptively optimizes the transform matrix with an end-to-end AR objective, thereby discovering effective strategies beyond hand-crafted assumptions. Comprehensive experiments, notably achieving a state-of-the-art FID of 1.15 on the ImageNet-256 benchmark, demonstrate the ability of BAR to overcome human biases and significantly advance image generation, including text-to-image synthesis.

Disclaimer
This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper proposes a unified mathematical framework treating image tokens as basis vector projections and learning the transformation matrix end-to-end. According to the taxonomy, it occupies the 'End-to-End Learnable Linear Basis Optimization' leaf under 'Learnable Basis Transformation Methods'. Notably, this leaf contains only the original paper itself with zero sibling papers, indicating this is a sparse and potentially underexplored research direction. The broader parent branch 'Learnable Basis Transformation Methods' also appears relatively small compared to the overall taxonomy structure.

The taxonomy reveals three neighboring branches: 'Predefined Basis Representation Methods' using fixed transforms like DCT, 'Model Optimization and Deployment' focused on quantization and efficiency, and 'Autoregressive Neural Network Applications in Non-Visual Domains' extending to quantum physics. The paper's approach diverges sharply from predefined methods by replacing hand-crafted transformations with learned matrices. The taxonomy's scope notes explicitly distinguish learnable versus fixed basis approaches, positioning this work as fundamentally different from frequency-domain sparse representations that rely on predetermined mathematical structures.

Among nineteen candidates examined across three contributions, zero refutable pairs were found. The unified framework contribution examined five candidates with no refutations; end-to-end learnable optimization examined ten candidates with no refutations; residual training objective examined four candidates with no refutations. This suggests that within the limited search scope of top-K semantic matches and citation expansion, no prior work directly anticipates the specific combination of learnable linear basis optimization with autoregressive visual generation objectives. The absence of sibling papers in the taxonomy leaf corroborates this finding.

Based on the limited literature search of nineteen candidates, the work appears to occupy a relatively unexplored niche combining learnable basis transformations with autoregressive image generation. The taxonomy structure and contribution-level statistics both suggest novelty, though the small search scope means potentially relevant work outside top semantic matches may exist. The sparse population of the taxonomy leaf and zero refutations across all contributions provide preliminary evidence of originality.

Taxonomy

Core-task Taxonomy Papers
3
3
Claimed Contributions
19
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: autoregressive visual generation with learnable basis transformation. The field encompasses methods that generate images or visual data autoregressively by transforming representations into learned or predefined bases. The taxonomy reveals four main branches: Learnable Basis Transformation Methods, which optimize basis functions end-to-end during training; Predefined Basis Representation Methods, which rely on fixed transforms like wavelets or Fourier bases; Model Optimization and Deployment, addressing efficiency and practical implementation; and Autoregressive Neural Network Applications in Non-Visual Domains, extending similar principles beyond images. Learnable approaches such as BAR Autoregressive[0] and Adaptive Basis Neural[3] contrast with methods that use handcrafted representations like Sparse Representations[1], reflecting a trade-off between flexibility and interpretability. Works like FPQVAR[2] explore quantization and compression within these frameworks, bridging learnable transformations with deployment concerns. Recent activity centers on how to balance expressiveness of learned bases against computational cost and generalization. Some lines pursue fully end-to-end optimization of linear basis functions, aiming for maximum adaptability to data distributions, while others incorporate structured priors or hybrid strategies that blend learned and fixed components. BAR Autoregressive[0] sits within the End-to-End Learnable Linear Basis Optimization cluster, emphasizing direct optimization of basis matrices without predefined constraints. This contrasts with Adaptive Basis Neural[3], which also learns bases but may incorporate adaptive mechanisms or regularization, and with FPQVAR[2], which focuses on quantized representations for efficiency. The main open questions revolve around whether fully learnable bases consistently outperform structured alternatives across diverse visual tasks, and how to scale these methods to high-resolution generation while maintaining training stability and inference speed.

Claimed Contributions

Unified mathematical framework for autoregressive visual generation

BAR introduces a linear-space-based framework that conceptualizes tokens as projections onto basis vectors and applies a linear transform y=Ax. This framework unifies previous AR methods (VAR, xAR, RAR, PAR, FAR) as specific instances of the transform matrix A, providing a rigorous mathematical foundation where prior works lacked formal grounding.

5 retrieved papers
End-to-end learnable transform matrix optimization

BAR parameterizes the transform matrix A as a learnable parameter and optimizes it jointly with the AR model using derived training objectives equivalent to existing methods (MAR and xAR). This adaptive approach eliminates reliance on hand-crafted priors and allows the model to discover optimal transforms through training.

10 retrieved papers
Residual training objective for ordered basis learning

BAR proposes a residual objective that encourages earlier basis vectors to maximize image recovery and later ones to capture residuals. This design enables adaptive learning of coarse-to-fine generation patterns without imposing static hierarchical assumptions like those in VAR or RQ-VAE.

4 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Unified mathematical framework for autoregressive visual generation

BAR introduces a linear-space-based framework that conceptualizes tokens as projections onto basis vectors and applies a linear transform y=Ax. This framework unifies previous AR methods (VAR, xAR, RAR, PAR, FAR) as specific instances of the transform matrix A, providing a rigorous mathematical foundation where prior works lacked formal grounding.

Contribution

End-to-end learnable transform matrix optimization

BAR parameterizes the transform matrix A as a learnable parameter and optimizes it jointly with the AR model using derived training objectives equivalent to existing methods (MAR and xAR). This adaptive approach eliminates reliance on hand-crafted priors and allows the model to discover optimal transforms through training.

Contribution

Residual training objective for ordered basis learning

BAR proposes a residual objective that encourages earlier basis vectors to maximize image recovery and later ones to capture residuals. This design enables adaptive learning of coarse-to-fine generation patterns without imposing static hierarchical assumptions like those in VAR or RQ-VAE.

Table of Contents