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版本更新 · v4arXiv:2604.24357

DPRM: A Plug-in Doob h transform-induced Token-Ordering Module for Discrete Diffusion Models

Dake Bu, Wei Huang, Andi Han, Si Wu, Hau-San Wong, Qingfu Zhang, Taiji Suzuki, Atsushi Nitanda

原文摘要

Discrete diffusion models admit many token orders, yet most systems rely on confidence-based decoding. Confidence is a strong and efficient heuristic, but it can be myopic because local certainty does not measure a position's effect on terminal quality. We introduce DPRM (Doob h-transform Process Reward Model), a plug-in token-ordering module induced by a terminal-reward-tilted trajectory distribution. The Doob transform converts terminal reward into a process reward for each candidate position. A compact estimator indexed by generation progress, confidence, and optional positional or task state makes this correction reusable across partial states. DPRM changes only token order; the host architecture, denoising objective, supervision, and token sampler remain fixed. We derive the exact reward-tilted law and bound its shortlist and online approximations. Across nine recent open-source hosts spanning language, multimodal generation, and scientific sequences, DPRM improves reasoning, numeric VQA, visual-codebook ordering, and preference-conditioned generation. Relative to confidence, it improves PUMA GSM8K by 14.6%, Omni-Diffusion CLIP-L/14 by 13.2%, Prism voted accuracy from 82.41% to 83.85%, and RealWorldQA numeric/count accuracy by 8.97 points. Matched scientific gains include 8.3% in DCM nonzero recovery, 15.0% in GenMol QED, and 53.3% in SDPO-DNA total utility. Entropy and random-order controls show that the gains do not come from favoring uncertain tokens indiscriminately. Token-order traces and shared-state interventions instead show how terminal reward can correct a locally confident but globally poor choice. Code is available at: https://github.com/DakeBU/DPRM-DLLM.

cs.LG · cs.AI

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2510.12026

Mamba Can Learn Low-Dimensional Targets In-Context via Test-Time Feature Learning

Junsoo Oh, Wei Huang, Taiji Suzuki

原文摘要

Mamba, a recently proposed linear-time sequence model, has attracted significant attention for its computational efficiency and strong empirical performance. However, a rigorous theoretical understanding of its underlying mechanisms remains limited. In this work, we provide a theoretical analysis of Mamba's in-context learning (ICL) capability by focusing on tasks defined by low-dimensional nonlinear target functions. Specifically, we study in-context learning of a single-index model $y \approx g_*(\langle \boldsymbolβ, \boldsymbol{x} \rangle)$, which depends on only a single relevant direction $\boldsymbolβ$, referred to as feature. We prove that Mamba, pretrained by gradient-based methods, can achieve efficient ICL via test-time feature learning, extracting the relevant direction directly from context examples. Consequently, we establish a test-time sample complexity that improves upon linear Transformers -- analyzed to behave like kernel methods -- and is comparable to nonlinear Transformers, which have been shown to surpass the Correlational Statistical Query (CSQ) lower bound and achieve near information-theoretically optimal rate in previous works. Our analysis reveals the crucial role of the nonlinear gating mechanism in Mamba for feature extraction, highlighting it as the fundamental driver behind Mamba's ability to achieve both computational efficiency and high performance.

cs.LG · stat.ML

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2605.20235

Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine

Wei Huang, Andi Han, Mingyuan Bai, Huanjian Zhou, Qixin Zhang, Taiji Suzuki, Kenji Fukumizu

原文摘要

Diffusion models generate high-dimensional data with remarkable quality, yet how training discovers and exploits low-dimensional manifold structure remains incompletely understood. We analyze a two-stage collapse-and-refine procedure motivated by the small-noise score: its singular normal component identifies manifold projection as the leading denoising target, while the remaining correction encodes density and geometry. Under suitable assumptions, we prove that annealed mean-field training asymptotically recovers the population denoiser and quantify the resulting geometric alignment error. With the learned representation fixed, residual score learning reduces to convex random-feature regression. We establish generalization bounds that separate residual learning error, propagated projection error, and geometric approximation bias, with statistical exponents governed by the intrinsic dimension. Under additional structural assumptions, we further derive an end-to-end sampling guarantee. Motivated by this analysis, we develop Score-induced Latent Diffusion (SiLD), a practical two-stage framework combining low-noise denoising representation learning with latent diffusion, without requiring KL regularization of the latent representation. Experiments on Stacked MNIST and molecular generation benchmarks demonstrate competitive generation quality relative to architecture-matched VAE-based latent diffusion baselines.

cs.LG · cs.AI

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.05813

Towards the Query Complexity of Sampling under Strong Log-Concavity and Log-Sobolev Inequalities

Huanjian Zhou, Taiji Suzuki

原文摘要

We study the query complexity of sampling from smooth distributions on $\mathbb R^d$ using first-order oracles. For $d$-dimensional strongly log-concave targets with condition number $κ=2$, we prove that any randomized sampler requires $\exp({Ω(\log^{1/3} d)})$ queries even from a constant warm start. This rules out polylogarithmic dimension dependence and strictly separates strongly log-concave sampling from Gaussian sampling. For targets with $L$-smooth potentials satisfying an $α$-log-Sobolev inequality with $κ= L/α$, we prove an $Ω(κ)$ query lower bound for $d\gtrsim\log^2κ$. This shows that log-Sobolev sampling is strictly harder than strongly log-concave sampling. Our proofs construct instance-dependent tests that target samples typically pass but outputs of algorithms making few queries typically fail. For strongly log-concave targets, we embed a sequence of hidden Gaussian into high-degree tensor polynomial with smooth gates, forcing any algorithm to uncover the layers sequentially. The log-Sobolev construction hides a constant fraction of the target mass in angular caps while controlling the log-Sobolev constant via delicate estimates.

cs.CC · cs.DS · math.ST · stat.ML

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arXiv ↗PDF ↗