arXiv subjects

Taiji Suzuki

Publications and source records attributed to Taiji Suzuki.

At least 19 recordsLinked to original sources

arXiv2026

Test time training enhances in-context learning of nonlinear functions

Test-time training (TTT) enhances model performance by explicitly updating designated parameters prior to each prediction to adapt to the test data. While TTT has demonstrated considerable empirical success, its theoretical underpinnings remain limited, particularly for nonlinear models. In this paper, we investigate the combination of TTT with in-context learning (ICL), where the model is given a few examples from the target distribution at inference time. We analyze this framework in the setting of single-index models, where the feature vector is drawn from a hidden low-dimensional subspace. For single-layer transformers trained with gradient-based algorithms and adopting TTT, we establish an upper bound on the prediction risk. Our theory reveals that TTT enables the single-layer transformers to adapt to both the feature vector and the link function, which vary across tasks. This creates a sharp contrast with ICL alone, which is theoretically difficult to adapt to shifts in the link function. Moreover, we provide the convergence rate with respect to the data length, showing the predictive error can be driven arbitrarily close to the noise level as the context size and the network width grow.

stat.ML↗

arXiv2026

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

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↗

arXiv2026

The Geometry of Statistical Feature Learning in Mean-Field Langevin Dynamics

We introduce a geometric formulation of statistical feature learning for supervised regression. Feature learning is defined through a base--fiber decomposition: the base is the feature-side geometry produced by training, and the fiber is the learned feature space where estimation is performed. We prove this property for spherical mean-field Langevin dynamics, viewed as the Wasserstein gradient flow of a negative entropy-regularized empirical risk. In Gaussian multi-index models, the low-temperature stationary distribution concentrates near the hidden indices, forms a multi-spike structure, and yields parameter recovery with high probability, even though negative entropy regularization penalizes concentration. This concentration has a sharp transition at temperature $λ\asymp 1$. In Gaussian single-index models, the stationary measure satisfies a concentration property, with parity determining whether it lives on $S_2^{d-1}$ or $\mathbb{RP}^{d-1}$. The induced learned feature space aligns the regression signal and yields rates $d/N$ and $Md/N$, up to logarithmic factors.

math.ST↗

arXiv2026

Zero-Flow Two-Sample Tests

We propose a new approach to two-sample testing for deciding whether two sets of samples are drawn from the same distribution. The test is built on a statistical discrepancy based on the zero-flow criterion, termed zero-flow discrepancy (ZFD). We prove the validity of ZFD and propose a practical testing procedure, termed the zero-flow two-sample test (ZF2ST). The key idea is to learn how samples from the two distributions are locally misaligned and use the resulting directional pattern as evidence of distributional difference. By separating witness learning from hypothesis evaluation, ZF2ST can use flexible neural networks while maintaining valid statistical calibration. We develop both regression-based and power-maximized approaches for learning the witness. Experiments on synthetic and image datasets demonstrate that ZF2ST can achieve strong testing power for structured distributional changes while maintaining well-calibrated type-I error.

cs.LG↗

arXiv2026

In-Context Learning Is Provably Bayesian Inference: A Generalization Theory for Meta-Learning

This paper develops a finite-sample statistical theory for in-context learning (ICL), analyzed within a meta-learning framework that accommodates mixtures of diverse task types. We introduce a principled risk decomposition that separates the total ICL risk into two orthogonal components: Bayes Gap and Posterior Variance. The Bayes Gap quantifies how well the trained model approximates the Bayes-optimal in-context predictor. For a uniform-attention Transformer, we derive a non-asymptotic upper bound on this gap, which explicitly clarifies the dependence on the number of pretraining prompts and their context length. The Posterior Variance is a model-independent risk representing the intrinsic task uncertainty. Our key finding is that this term is determined solely by the difficulty of the true underlying task, while the uncertainty arising from the task mixture vanishes exponentially fast with only a few in-context examples. Together, these results provide a unified view of ICL: the Transformer selects the optimal meta-algorithm during pretraining and rapidly converges to the optimal algorithm for the true task at test time.

stat.ML↗

arXiv2026

Distributional Biases in Post-Training: A Markovian Analysis of Reasoning Trajectories

Foundation models exhibit broad knowledge but limited task-specific reasoning, motivating post-training strategies such as RL with verifiable rewards (RLVR) and test-time scaling (TTS). While recent work highlights the role of exploration in improving pass@K, empirical evidence points to a paradox: RLVR and ORM/PRM typically reinforce existing paths rather than expanding the reasoning scope, raising the question of why exploration helps if no new patterns emerge. To reconcile this paradox, we adopt the perspective of Kim et al. (2025), viewing easy (e.g., simplifying a fraction) versus hard (e.g., discovering the some symmetry) reasoning steps as low versus high probability Markov transitions. In this tractable model, pretraining corresponds to tree-graph discovering, while post-training corresponds to CoT reweighting. We provably show that, both RLVR and ORM/PRM would favor heavily to several high-probability paths, and thereby forget rare-but-crucial CoTs. Building on this, we further prove that exploration strategies such as rejecting easy instances and KL regularization help preserve rare CoTs. Empirical simulations corroborate our theoretical results.

cs.LG↗

arXiv2026

Zero-Flow Encoders

Flow-based methods have achieved significant success in various generative modeling tasks, capturing nuanced details within complex data distributions. However, few existing works have exploited this unique capability to resolve fine-grained structural details beyond generation tasks. This paper presents a flow-inspired framework for representation learning. First, we demonstrate that a rectified flow trained using independent coupling is zero everywhere at $t=0.5$ if and only if the source and target distributions are identical. We term this property the \emph{zero-flow criterion}. Second, we show that this criterion can certify conditional independence, thereby extracting \emph{sufficient information} from the data. Third, we translate this criterion into a tractable, simulation-free loss function that enables learning amortized Markov blankets in graphical models and latent representations in self-supervised learning tasks. Experiments on both simulated and real-world datasets demonstrate the effectiveness of our approach. The code reproducing our experiments can be found at: https://github.com/probabilityFLOW/zfe.

stat.ML↗

arXiv2026

LeanMarathon: Toward Reliable AI Co-Mathematicians through Long-Horizon Lean Autoformalization

Long-horizon autoformalization of research mathematics fails not only at hard lemmas, but at scale: statements drift, dependencies tangle, context decays, and local repairs corrupt distant work. We present LeanMarathon, a multi-agent harness for reliable research-level Lean autoformalization. Its core abstraction is an evolving blueprint: a Lean file that serves simultaneously as formal proof skeleton, natural-language proof graph, and shared system of record. Four contract-scoped agents construct, audit, prove, and repair this blueprint. These agents are coordinated by a two-stage orchestrator that first stabilizes target fidelity through adversarial review and then discharges the proof directed acyclic graph (DAG) from its dynamic leaves upward in parallel CI-gated rounds. LeanMarathon turns one brittle multi-hour run into many local, recoverable, parallel transactions. We evaluate LeanMarathon on two recent research papers spanning four Erdős problems (#1051, #1196, #164, #1217). Across three autonomous runs, it formalizes all seven target theorems with no sorry, proving 258 lemmas and theorems. These results show that reliable AI co-mathematics requires not only stronger provers, but durable harnesses that preserve target fidelity across long mathematical developments. The code can be found at https://github.com/YuanheZ/LeanMarathon.

cs.AI↗

arXiv2026

How Neural Reward Models Learn Features for Policy Optimization: A Single-Index Analysis

Reward modeling is not only a prediction problem: in KL-regularized policy optimization, the learned reward is exponentiated to define the deployed policy, so downstream value depends on errors in reward-tilted regions. We study this feedback in a Gaussian single-index model with $r^*(x) = σ^*(\langle θ^*, x\rangle)$ and $x \sim N(0, I_d)$. We analyze a two-stage neural reward model that first learns the hidden direction $θ^*$ from reward-weighted samples and then fits the readout layer by weighted ridge regression. Exponential reward weighting changes the Hermite signal available to the first layer; for any feature-learning temperature $β_1$ above a dimension-free $O(1)$ threshold, a constant fraction of neurons recover the hidden direction, with weak-recovery complexity governed by the generative exponent. After feature recovery, we derive tilted-policy value-gap bounds for an idealized label-weighted fit with weights $e^{y/β_2}$ and a more practical surrogate-weighted fit with weights $e^{r_{a_0}(x)/β_2}$. Keeping the $β_2$-dependence explicit yields an admissible set of deployment temperatures, balancing the gain from lowering $β_2$ against the learning cost amplified by exponential weighting; in the surrogate-weighted case, proxy-dependent factors shrink this admissible set.

stat.ML↗

arXiv2026

From Saddle Points Toward Global Minima: A Newton-Type Method on Wasserstein Space

We study the minimization of non-convex functionals over the Wasserstein space. While recent work has showed that perturbed Wasserstein gradient methods can avoid saddle points for benign landscapes, existing approaches remain essentially first-order and do not provide fast local convergence once the iterates enter a neighborhood of a global minimizer. We propose Wasserstein Saddle-Free Newton (WSFN), a second-order method that preconditions the Wasserstein gradient by a regularized square root of the squared Wasserstein Hessian. This construction preserves attraction toward directions of positive curvature while inducing repulsion along directions of negative curvature, thereby overcoming the tendency of standard Wasserstein Newton dynamics to be attracted to saddles. We also establish second-order sufficient optimality conditions on Wasserstein space for strict local minimality. Under regularity and benign landscape assumptions, we prove that WSFN escapes saddle regions and reaches an $α$-neighborhood of a global minimizer in polynomial time, with improved dependence on saddle parameters compared with prior perturbed first-order methods. Once inside this neighborhood, we show that WSFN converges linearly in $L^2$-Wasserstein distance to a non-degenerate global minimizer. Finally, we present a particle-based implementation of the method.

math.OC↗

arXiv2026

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

Diffusion models generate high-dimensional data with remarkable quality, yet how their training efficiently learns the score function, bypassing the curse of dimensionality when data is supported on low-dimensional manifolds, remains theoretically unexplained. We identify a collapse-and-refine mechanism driven by the geometry of the score function itself: at small noise scales, the diverging singularity of the score drives a rapid dimensional collapse of the induced denoising map onto the data manifold projection; at moderate noise scales, training refines the intrinsic density on the learned manifold. We instantiate this principle as Score-induced Latent Diffusion (SiLD), a two-stage framework in which both manifold learning and density estimation emerge from a single denoising score matching objective, replacing the heuristic KL regularization of VAE-based latent diffusion models. We prove that the resulting sample complexity depends on the intrinsic dimension rather than the ambient dimension. Experiments on Stacked MNIST, CelebA variants, and molecular generation benchmarks show that SiLD matches or outperforms VAE-based LDMs in generation quality and consistently improves reconstruction, validating our theoretical predictions.

cs.LG↗

arXiv2026

Intrinsic Wasserstein Rates for Score-Based Generative Models on Smooth Manifolds

Score-based generative models are trained in high-dimensional ambient spaces, yet many data distributions are supported on low-dimensional nonlinear structures. We prove that, for compact $d$-dimensional smooth manifolds $\mathcal{M} \subset [0,1]^D$ with $d > 2$ and $β$-Hölder densities strictly positive on $\mathcal{M}$, a variance-preserving SGM estimator attains the intrinsic Wasserstein--1 sample exponent $\tilde{\mathcal{O}}(D^{\mathcal{O}_β(d)}n^{-(β+1)/(d+2β)})$, up to logarithmic factors and explicit geometry and density factors. The full nonasymptotic bound explicitly isolates the finite-order geometry envelope, Hölder radius, density lower bound, ambient dependence, and finite-order correction terms. The analysis separates score approximation into a large-noise tangent-cell regime and a small-noise projection-centered, de-Gaussianized Laplace regime. The key technical ingredient is a ReLU implementation of nearest-projection coordinates via finite intrinsic anchors and Gauss--Newton iterations, rather than approximating the manifold projection as a black-box high-dimensional smooth map. Consequently, for families with polynomially controlled geometry and density lower bounds, the constructed score-network parameters have polynomial ambient dependence.

cs.LG↗

arXiv2026

The Mechanism of Weak-to-Strong Generalization: Feature Elicitation from Latent Knowledge

Weak-to-strong (W2S) generalization, in which a strong model is fine-tuned on outputs of a weaker, task-specialized model, has been proposed as an approach to aligning superhuman AI systems. Existing theoretical analyses either fix the student's representations or operate in restricted settings. Whether multi-step SGD can succeed in feature learning while preserving diverse pre-trained capabilities remains open. We study W2S in the setting of reward-model learning with two-layer neural networks. The strong model has pre-trained representations organized into low-dimensional subspaces $V_k$, and is fine-tuned under the supervision of a weak model specialized on task $κ$. We prove that the strong model efficiently learns task $κ$, eliciting its pre-trained knowledge while retaining general capabilities. This establishes W2S generalization in the feature-learning regime, in the sense that the strong model acquires the target feature direction through W2S training, rather than having it given a priori. Moreover, W2S preserves pre-trained off-target features, whereas standard supervised fine-tuning causes catastrophic forgetting when off-target feature directions are correlated with the target's. Numerical experiments on synthetic data confirm our theoretical results.

stat.ML↗

arXiv2026

Provable Benefit of Curriculum in Transformer Tree-Reasoning Post-Training

Recent curriculum techniques in the post-training stage of LLMs have been empirically observed to outperform non-curriculum approaches in improving reasoning performance, yet a principled understanding of their effectiveness and limitations remains incomplete. To bridge this gap, we develop an abstract theoretical framework and identify sufficient conditions under which curriculum post-training yields exponential improvements in sample complexity. To substantiate this framework, we model the base model's Chain-of-Thought generation as a state-conditioned autoregressive reasoning tree, and formalize curriculum subtasks as either depth-increasing curricula that progressively extend reasoning horizons or hint-decreasing curricula that gradually remove partial hints. Our analysis shows that reinforcement learning finetuning with both curriculum strategies achieves high accuracy with polynomial sample complexity, whereas non-curriculum counterpart encounters an exponential complexity bottleneck. We further establish analogous guarantees for test-time scaling. Empirical simulations support our theoretical findings. Code is available at https://github.com/DakeBU/Curriculum-Post-training.

cs.LG↗

arXiv2026

On the Learning Dynamics of Two-layer Linear Networks with Label Noise SGD

One crucial factor behind the success of deep learning lies in the implicit bias induced by noise inherent in gradient-based training algorithms. Motivated by empirical observations that training with noisy labels improves model generalization, we delve into the underlying mechanisms behind stochastic gradient descent (SGD) with label noise. Focusing on a two-layer over-parameterized linear network, we analyze the learning dynamics of label noise SGD, unveiling a two-phase learning behavior. In \emph{Phase I}, the magnitudes of model weights progressively diminish, and the model escapes the lazy regime; enters the rich regime. In \emph{Phase II}, the alignment between model weights and the ground-truth interpolator increases, and the model eventually converges. Our analysis highlights the critical role of label noise in driving the transition from the lazy to the rich regime and minimally explains its empirical success. Furthermore, we extend these insights to Sharpness-Aware Minimization (SAM), showing that the principles governing label noise SGD also apply to broader optimization algorithms. Extensive experiments, conducted under both synthetic and real-world setups, strongly support our theory. Our code is released at https://github.com/a-usually/Label-Noise-SGD.

cs.LG↗

arXiv2026

Takeuchi's Information Criteria as Generalization Measures for DNNs Close to NTK Regime

Generalization measures have been studied extensively in the machine learning community to better characterize generalization gaps. However, establishing a reliable generalization measure for statistically singular models such as deep neural networks (DNNs) is difficult due to their complex nature. This study focuses on Takeuchi's information criterion (TIC) to investigate the conditions under which this classical measure can effectively explain the generalization gaps of DNNs. Importantly, the developed theory indicates the applicability of TIC near the neural tangent kernel (NTK) regime. In a series of experiments, we trained more than 5,000 DNN models with 12 architectures, including large models (e.g., VGG-16), on four datasets, and estimated the corresponding TIC values to examine the relationship between the generalization gap and the TIC estimates. We applied several TIC approximation methods with feasible computational costs and assessed the accuracy trade-off. Our experimental results indicate that the estimated TIC values correlate well with the generalization gap under conditions close to the NTK regime. However, we show both theoretically and empirically that outside the NTK regime such correlation disappears. Finally, we demonstrate that TIC provides better trial pruning ability than existing methods for hyperparameter optimization.

cs.LG↗

arXiv2026

Deep Two-Way Matrix Reordering for Relational Data Analysis

Matrix reordering is a task to permute the rows and columns of a given observed matrix such that the resulting reordered matrix shows meaningful or interpretable structural patterns. Most existing matrix reordering techniques share the common processes of extracting some feature representations from an observed matrix in a predefined manner, and applying matrix reordering based on it. However, in some practical cases, we do not always have prior knowledge about the structural pattern of an observed matrix. To address this problem, we propose a new matrix reordering method, called deep two-way matrix reordering (DeepTMR), using a neural network model. The trained network can automatically extract nonlinear row/column features from an observed matrix, which can then be used for matrix reordering. Moreover, the proposed DeepTMR provides the denoised mean matrix of a given observed matrix as an output of the trained network. This denoised mean matrix can be used to visualize the global structure of the reordered observed matrix. We demonstrate the effectiveness of the proposed DeepTMR by applying it to both synthetic and practical datasets.

stat.ML↗

arXiv2026

AutoLL: Automatic Linear Layout of Graphs based on Deep Neural Network

Linear layouts are a graph visualization method that can be used to capture an entry pattern in an adjacency matrix of a given graph. By reordering the node indices of the original adjacency matrix, linear layouts provide knowledge of latent graph structures. Conventional linear layout methods commonly aim to find an optimal reordering solution based on predefined features of a given matrix and loss function. However, prior knowledge of the appropriate features to use or structural patterns in a given adjacency matrix is not always available. In such a case, performing the reordering based on data-driven feature extraction without assuming a specific structure in an adjacency matrix is preferable. Recently, a neural-network-based matrix reordering method called DeepTMR has been proposed to perform this function. However, it is limited to a two-mode reordering (i.e., the rows and columns are reordered separately) and it cannot be applied in the one-mode setting (i.e., the same node order is used for reordering both rows and columns), owing to the characteristics of its model architecture. In this study, we extend DeepTMR and propose a new one-mode linear layout method referred to as AutoLL. We developed two types of neural network models, AutoLL-D and AutoLL-U, for reordering directed and undirected networks, respectively. To perform one-mode reordering, these AutoLL models have specific encoder architectures, which extract node features from an observed adjacency matrix. We conducted both qualitative and quantitative evaluations of the proposed approach, and the experimental results demonstrate its effectiveness.

stat.ML↗