On Computational Limits of FlowAR Models: Expressivity and Efficiency

• URL: http://arxiv.org/abs/2502.16490v1
• Date: Sun, 23 Feb 2025 08:07:35 GMT
• Title: On Computational Limits of FlowAR Models: Expressivity and Efficiency
• Authors: Chengyue Gong, Yekun Ke, Xiaoyu Li, Yingyu Liang, Zhizhou Sha, Zhenmei Shi, Zhao Song,
• Abstract summary: FlowAR is a state-of-the-art architecture that integrates flow-based and autoregressive mechanisms.<n>We show that when the largest feature map produced by the FlowAR model has dimensions $n times n times c$, the FlowAR model is simulable by a family of threshold circuits.<n>We also identify the conditions under which the FlowAR model computations can achieve almost quadratic time.
• Score: 37.56422161656334
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The expressive power and computational complexity of deep visual generative models, such as flow-based and autoregressive (AR) models, have gained considerable interest for their wide-ranging applications in generative tasks. However, the theoretical characterization of their expressiveness through the lens of circuit complexity remains underexplored, particularly for the state-of-the-art architecture like FlowAR proposed by [Ren et al., 2024], which integrates flow-based and autoregressive mechanisms. This gap limits our understanding of their inherent computational limits and practical efficiency. In this study, we address this gap by analyzing the circuit complexity of the FlowAR architecture. We demonstrate that when the largest feature map produced by the FlowAR model has dimensions $n \times n \times c$, the FlowAR model is simulable by a family of threshold circuits $\mathsf{TC}^0$, which have constant depth $O(1)$ and polynomial width $\mathrm{poly}(n)$. This is the first study to rigorously highlight the limitations in the expressive power of FlowAR models. Furthermore, we identify the conditions under which the FlowAR model computations can achieve almost quadratic time. To validate our theoretical findings, we present efficient model variant constructions based on low-rank approximations that align with the derived criteria. Our work provides a foundation for future comparisons with other generative paradigms and guides the development of more efficient and expressive implementations.

Related papers

• Normalizing Flows are Capable Models for RL [24.876149287707847]
  We propose a single Normalizing Flow architecture which integrates seamlessly into reinforcement learning algorithms.<n>Our approach leads to much simpler algorithms, and achieves higher performance in imitation learning, offline, goal conditioned RL and unsupervised RL.
  arXiv  Detail & Related papers  (2025-05-29T15:06:22Z)
• FUDOKI: Discrete Flow-based Unified Understanding and Generation via Kinetic-Optimal Velocities [76.46448367752944]
  multimodal large language models (MLLMs) unify visual understanding and image generation within a single framework.<n>Most existing MLLMs rely on autore (AR) architectures, which impose inherent limitations on future development.<n>We introduce FUDOKI, a unified multimodal model purely based on discrete flow matching.
  arXiv  Detail & Related papers  (2025-05-26T15:46:53Z)
• DSMoE: Matrix-Partitioned Experts with Dynamic Routing for Computation-Efficient Dense LLMs [70.91804882618243]
  This paper proposes DSMoE, a novel approach that achieves sparsification by partitioning pre-trained FFN layers into computational blocks.<n>We implement adaptive expert routing using sigmoid activation and straight-through estimators, enabling tokens to flexibly access different aspects of model knowledge.<n>Experiments on LLaMA models demonstrate that under equivalent computational constraints, DSMoE achieves superior performance compared to existing pruning and MoE approaches.
  arXiv  Detail & Related papers  (2025-02-18T02:37:26Z)
• Circuit Complexity Bounds for Visual Autoregressive Model [23.991344681741058]
  We investigate the circuit complexity of the Visual AutoRegressive ( VAR) model and establish a bound in this study.<n>Our primary result demonstrates that the VAR model is equivalent to a simulation by a uniform $mathsfTC0$ threshold circuit with hidden dimension $d leq O(n)$ and $mathrmpoly(n)$ precision.<n>This is the first study to rigorously highlight the limitations in the expressive power of VAR models despite their impressive performance.
  arXiv  Detail & Related papers  (2025-01-08T06:07:33Z)
• Consistency Models for Scalable and Fast Simulation-Based Inference [9.27488642055461]
  We present consistency models for posterior estimation (CMPE), a new conditional sampler for simulation-based inference ( SBI) CMPE essentially distills a continuous probability flow and enables rapid few-shot inference with an unconstrained architecture. Our empirical evaluation demonstrates that CMPE not only outperforms current state-of-the-art algorithms on hard low-dimensional benchmarks, but also achieves competitive performance with much faster sampling speed.
  arXiv  Detail & Related papers  (2023-12-09T02:14:12Z)
• Latent Variable Representation for Reinforcement Learning [131.03944557979725]
  It remains unclear theoretically and empirically how latent variable models may facilitate learning, planning, and exploration to improve the sample efficiency of model-based reinforcement learning. We provide a representation view of the latent variable models for state-action value functions, which allows both tractable variational learning algorithm and effective implementation of the optimism/pessimism principle. In particular, we propose a computationally efficient planning algorithm with UCB exploration by incorporating kernel embeddings of latent variable models.
  arXiv  Detail & Related papers  (2022-12-17T00:26:31Z)
• Multi-Scale Architectures Matter: On the Adversarial Robustness of Flow-based Lossless Compression [16.109578069331135]
  Flow-based models perform better due to their excellent probability density estimation and satisfactory inference speed. Multi-scale architecture provides a shortcut from the shallow layer to the output layer. Flows with multi-scale architecture achieve the best trade-off between coding complexity and compression efficiency.
  arXiv  Detail & Related papers  (2022-08-26T15:17:43Z)
• Closed-form Continuous-Depth Models [99.40335716948101]
  Continuous-depth neural models rely on advanced numerical differential equation solvers. We present a new family of models, termed Closed-form Continuous-depth (CfC) networks, that are simple to describe and at least one order of magnitude faster.
  arXiv  Detail & Related papers  (2021-06-25T22:08:51Z)
• Sparse Flows: Pruning Continuous-depth Models [107.98191032466544]
  We show that pruning improves generalization for neural ODEs in generative modeling. We also show that pruning finds minimal and efficient neural ODE representations with up to 98% less parameters compared to the original network, without loss of accuracy.
  arXiv  Detail & Related papers  (2021-06-24T01:40:17Z)
• Normalizing Flows with Multi-Scale Autoregressive Priors [131.895570212956]
  We introduce channel-wise dependencies in their latent space through multi-scale autoregressive priors (mAR) Our mAR prior for models with split coupling flow layers (mAR-SCF) can better capture dependencies in complex multimodal data. We show that mAR-SCF allows for improved image generation quality, with gains in FID and Inception scores compared to state-of-the-art flow-based models.
  arXiv  Detail & Related papers  (2020-04-08T09:07:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.