arXiv subjects

Issei Sato

Publications and source records attributed to Issei Sato.

At least 19 recordsLinked to original sources

arXiv2026

Max-pooling Network Revisited: Analyzing the Role of Semantic Probability in Multiple Instance Learning for Hallucination Detection

Hallucination detection has become increasingly important for improving the reliability of large language models (LLMs). Recently, hybrid approaches such as HaMI, which combine semantic consistency with internal model states via Multiple Instance Learning (MIL), have achieved state-of-the-art performance. However, these methods incur substantial computational overhead due to repeated sampling and costly semantic similarity computations. In this work, we first provide a theoretical analysis of HaMI in terms of decision margins, revealing that scaling internal states with semantic consistency leads to an enlarged decision margin. Motivated by this insight, we revisit classical sentence classification models from a margin enlargement perspective, aggregating token-level features via max pooling and directly estimating sentence scores using a lightweight MLP. Without requiring semantic consistency computations, our approach achieves substantial efficiency improvements while maintaining competitive performance with state-of-the-art baselines through adaptive aggregation of internal feature representations. Code is available at https://github.com/FUJI1229/Hallucination_Detection.

cs.CL↗

arXiv2026

Power Distribution Bridges Sampling, Self-Reward RL, and Self-Distillation

Recent analyses question whether reinforcement learning (RL) is responsible for strong reasoning in large language models (LLMs). At the same time, distillation and inference-time sampling, including power sampling, have emerged as effective ways to improve LLM performance. However, the relationship among RL, distillation, and sampling remains unclear. In this study, we focus on the power distribution, the target distribution of power sampling, and show that the power distribution bridges sampling, self-reward KL-regularized RL, and self-distillation. From the sampling perspective, we show that inexpensive local approximations cannot reproduce sequence-level power without information about possible suffixes. From the RL perspective, the power distribution is the closed-form optimizer of KL-regularized RL when the model's sequence-level log-probabilities are used as the reward. This identification leads to power self-distillation, an offline distillation surrogate that shares the same target distribution and amortizes the cost of power sampling into supervised training on teacher samples. We further show that power self-distillation can achieve self-reward sharpening, while improvement in a downstream true reward is governed by the covariance between true reward and self-reward under the power distribution. Experiments on reasoning tasks support our analysis: power sampling raises self-reward, true-reward gains depend on alignment with self-reward, and power self-distillation can match or exceed the performance of power sampling at much lower inference cost.

cs.LG↗

arXiv2026

Fix Initial Programs and Iteratively Refine Repair Instructions Toward Non-Elimination Multi-Turn Program Correction

Recent work on large language models (LLMs) has emphasized the importance of scaling inference compute. From this perspective, the state-of-the-art method Scattered Forest Search (SFS) has been proposed, employing Monte Carlo Tree Search with carefully crafted initial seeds and textual optimization for multi-turn program correction. However, its complexity makes it unclear what factors contribute to improvements in inference performance. To address this problem, we analyze SFS and propose a simpler method, \textsc{Iterative Refinement of Repair Instructions} (IRRI), which fixes initial programs and iteratively refines repair instructions. Because of the simplicity of IRRI, we theoretically establish the non-elimination of IRRI using Oracle-Guided Inductive Synthesis (OGIS). Experiments on several program generation benchmarks suggest that IRRI achieves inference performance comparable to state-of-the-art methods. These results indicate that, even without complex search structures, refining initial programs with high-quality repair instructions alone can effectively improve inference performance.

cs.LG↗

arXiv2025

Explaining Grokking and Information Bottleneck through Neural Collapse Emergence

The training dynamics of deep neural networks often defy expectations, even as these models form the foundation of modern machine learning. Two prominent examples are grokking, where test performance improves abruptly long after the training loss has plateaued, and the information bottleneck principle, where models progressively discard input information irrelevant to the prediction task as training proceeds. However, the mechanisms underlying these phenomena and their relations remain poorly understood. In this work, we present a unified explanation of such late-phase phenomena through the lens of neural collapse, which characterizes the geometry of learned representations. We show that the contraction of population within-class variance is a key factor underlying both grokking and information bottleneck, and relate this measure to the neural collapse measure defined on the training set. By analyzing the dynamics of neural collapse, we show that distinct time scales between fitting the training set and the progression of neural collapse account for the behavior of the late-phase phenomena. Finally, we validate our theoretical findings on multiple datasets and architectures.

cs.LG↗

arXiv2025

A Formal Comparison Between Chain of Thought and Latent Thought

Chain of thought (CoT) elicits reasoning in large language models by explicitly generating intermediate tokens. In contrast, latent thought reasoning operates directly in the continuous latent space, enabling computation beyond discrete linguistic representations. While both approaches exploit iterative computation, their comparative capabilities remain underexplored. In this work, we present a formal analysis showing that latent thought admits more efficient parallel computation than inherently sequential CoT. In contrast, CoT enables approximate counting and sampling through stochastic decoding. These separations suggest the tasks for which depth-driven recursion is more suitable, thereby offering practical guidance for choosing between reasoning paradigms.

cs.AI↗

arXiv2025

Can Test-time Computation Mitigate Reproduction Bias in Neural Symbolic Regression?

Mathematical expressions play a central role in scientific discovery. Symbolic regression aims to automatically discover such expressions from given numerical data. Recently, Neural symbolic regression (NSR) methods that involve Transformers pre-trained on synthetic datasets have gained attention for their fast inference, but they often perform poorly, especially with many input variables. In this study, we analyze NSR from both theoretical and empirical perspectives and show that (1) ordinary token-by-token generation is ill-suited for NSR, as Transformers cannot compositionally generate tokens while validating numerical consistency, and (2) the search space of NSR methods is greatly restricted due to reproduction bias, where the majority of generated expressions are merely copied from the training data. We further examine whether tailored test-time strategies can reduce reproduction bias and show that providing additional information at test time effectively mitigates it. These findings contribute to a deeper understanding of the limitation of NSR approaches and provide guidance for designing more robust and generalizable methods. Code is available at https://github.com/Shun-0922/Mem-Bias-NSR .

cs.LG↗

arXiv2025

To CoT or To Loop? A Formal Comparison Between Chain-of-Thought and Looped Transformers

Chain-of-Thought (CoT) and Looped Transformers have been shown to empirically improve performance on reasoning tasks and to theoretically enhance expressivity by recursively increasing the number of computational steps. However, their comparative capabilities are still not well understood. In this paper, we provide a formal analysis of their respective strengths and limitations. We show that Looped Transformers can efficiently simulate parallel computations for deterministic tasks, which we formalize as evaluation over directed acyclic graphs. In contrast, CoT with stochastic decoding excels at approximate inference for compositional structures, namely self-reducible problems. These separations suggest the tasks for which depth-driven recursion is more suitable, thereby offering practical cues for choosing between reasoning paradigms.

cs.LG↗

arXiv2025

FairT2I: Mitigating Social Bias in Text-to-Image Generation via Large Language Model-Assisted Detection and Attribute Rebalancing

Text-to-image (T2I) models have advanced creative content generation, yet their reliance on large uncurated datasets often reproduces societal biases. We present FairT2I, a training-free and interactive framework grounded in a mathematically principled latent variable guidance formulation. This formulation decomposes the generative score function into attribute-conditioned components and reweights them according to a defined distribution, providing a unified and flexible mechanism for bias-aware generation that also subsumes many existing ad hoc debiasing approaches as special cases. Building upon this foundation, FairT2I incorporates (1) latent variable guidance as the core mechanism, (2) LLM-based bias detection to automatically infer bias-prone categories and attributes from text prompts as part of the latent structure, and (3) attribute resampling, which allows users to adjust or redefine the attribute distribution based on uniform, real-world, or user-specified statistics. The accompanying user interface supports this pipeline by enabling users to inspect detected biases, modify attributes or weights, and generate debiased images in real time. Experimental results show that LLMs outperform average human annotators in the number and granularity of detected bias categories and attributes. Moreover, FairT2I achieves superior performance to baseline models in both societal bias mitigation and image diversity, while preserving image quality and prompt fidelity.

cs.CV↗

arXiv2025

Understanding Generalization in Physics Informed Models through Affine Variety Dimensions

Physics-informed machine learning is gaining significant traction for enhancing statistical performance and sample efficiency through the integration of physical knowledge. However, current theoretical analyses often presume complete prior knowledge in non-hybrid settings, overlooking the crucial integration of observational data, and are frequently limited to linear systems, unlike the prevalent nonlinear nature of many real-world applications. To address these limitations, we introduce a unified residual form that unifies collocation and variational methods, enabling the incorporation of incomplete and complex physical constraints in hybrid learning settings. Within this formulation, we establish that the generalization performance of physics-informed regression in such hybrid settings is governed by the dimension of the affine variety associated with the physical constraint, rather than by the number of parameters. This enables a unified analysis that is applicable to both linear and nonlinear equations. We also present a method to approximate this dimension and provide experimental validation of our theoretical findings.

cs.LG↗

arXiv2025

Gradient Heterogeneity Complements Hessian Heterogeneity in Transformer Optimization

Transformers are difficult to optimize with stochastic gradient descent (SGD) and largely rely on adaptive optimizers such as Adam. Despite extensive efforts, the mechanisms behind Adam's advantage over SGD in Transformer optimization are still not fully understood. In this study, we analyze the optimization of Transformer models in the fine-tuning setting through the lens of gradient heterogeneity, defined as the variation in gradient norms across parameter blocks. We provide a theoretical analysis showing that gradient heterogeneity, together with Hessian heterogeneity, degrades the convergence of gradient-based methods such as SGD, while sign-based methods are substantially less sensitive to this effect. Adam and SignSGD both perform coordinate-wise updates and are less sensitive to the scale of individual gradient coordinates than SGD. This motivates our use of SignSGD as an analytically tractable proxy for Adam-like behavior. Our analysis uses the fact that SGD and SignSGD follow steepest descent directions under different norms, and derives upper bounds on the iteration complexity with implications for learning-rate scaling for SignSGD. We further investigate the origin of gradient heterogeneity in Transformer architectures and show that it is strongly influenced by the placement of layer normalization, with Post-LN architectures exhibiting particularly pronounced heterogeneity. Experimental results from fine-tuning Transformers in both NLP and vision domains validate our theoretical analysis.

cs.LG↗

arXiv2024

Rethinking Associative Memory Mechanism in Induction Head

Induction head mechanism is a part of the computational circuits for in-context learning (ICL) that enable large language models (LLMs) to adapt to new tasks without fine-tuning. Most existing work explains the training dynamics behind acquiring such a powerful mechanism. However, the model's ability to coordinate in-context information over long contexts and global knowledge acquired during pretraining remains poorly understood. This paper investigates how a two-layer transformer thoroughly captures in-context information and balances it with pretrained bigram knowledge in next token prediction, from the viewpoint of associative memory. We theoretically analyze the representation of weight matrices in attention layers and the resulting logits when a transformer is given prompts generated by a bigram model. In the experiments, we design specific prompts to evaluate whether the outputs of the trained transformer align with the theoretical results.

cs.CL↗

arXiv2024

Theoretical Analysis of Hierarchical Language Recognition and Generation by Transformers without Positional Encoding

In this study, we provide constructive proof that Transformers can recognize and generate hierarchical language efficiently with respect to model size, even without the need for a specific positional encoding. Specifically, we show that causal masking and a starting token enable Transformers to compute positional information and depth within hierarchical structures. We demonstrate that Transformers without positional encoding can generate hierarchical languages. Furthermore, we suggest that explicit positional encoding might have a detrimental effect on generalization with respect to sequence length.

cs.CL↗

arXiv2024

On Expressive Power of Looped Transformers: Theoretical Analysis and Enhancement via Timestep Encoding

Looped Transformers provide advantages in parameter efficiency, computational capabilities, and generalization for reasoning tasks. However, their expressive power regarding function approximation remains underexplored. In this paper, we establish the approximation rate of Looped Transformers by defining the modulus of continuity for sequence-to-sequence functions. This reveals a limitation specific to the looped architecture. That is, the analysis prompts the incorporation of scaling parameters for each loop, conditioned on timestep encoding. Experiments validate the theoretical results, showing that increasing the number of loops enhances performance, with further gains achieved through the timestep encoding.

cs.LG↗

arXiv2024

Multiplicative Logit Adjustment Approximates Neural-Collapse-Aware Decision Boundary Adjustment

Real-world data distributions are often highly skewed. This has spurred a growing body of research on long-tailed recognition, aimed at addressing the imbalance in training classification models. Among the methods studied, multiplicative logit adjustment (MLA) stands out as a simple and effective method. What theoretical foundation explains the effectiveness of this heuristic method? We provide a justification for the effectiveness of MLA with the following two-step process. First, we develop a theory that adjusts optimal decision boundaries by estimating feature spread on the basis of neural collapse. Second, we demonstrate that MLA approximates this optimal method. Additionally, through experiments on long-tailed datasets, we illustrate the practical usefulness of MLA under more realistic conditions. We also offer experimental insights to guide the tuning of MLA hyperparameters.

cs.LG↗

arXiv2024

Benign Overfitting in Token Selection of Attention Mechanism

Attention mechanism is a fundamental component of the transformer model and plays a significant role in its success. However, the theoretical understanding of how attention learns to select tokens is still an emerging area of research. In this work, we study the training dynamics and generalization ability of the attention mechanism under classification problems with label noise. We show that, with the characterization of signal-to-noise ratio (SNR), the token selection of attention mechanism achieves benign overfitting, i.e., maintaining high generalization performance despite fitting label noise. Our work also demonstrates an interesting delayed acquisition of generalization after an initial phase of overfitting. Finally, we provide experiments to support our theoretical analysis using both synthetic and real-world datasets.

cs.LG↗

arXiv2024

On the Optimal Memorization Capacity of Transformers

Recent research in the field of machine learning has increasingly focused on the memorization capacity of Transformers, but how efficient they are is not yet well understood. We demonstrate that Transformers can memorize labels with $\tilde{O}(\sqrt{N})$ parameters in a next-token prediction setting for $N$ input sequences of length $n$, which is proved to be optimal up to logarithmic factors. This indicates that Transformers can efficiently perform memorization with little influence from the input length $n$ owing to the benefit of parameter sharing. We also analyze the memorization capacity in the sequence-to-sequence setting, and find that $\tilde{O}(\sqrt{nN})$ parameters are not only sufficient, but also necessary at least for Transformers with hardmax. These results suggest that while self-attention mechanisms can efficiently identify input sequences, the feed-forward network becomes a bottleneck when associating a label to each token.

cs.LG↗

arXiv2024

Top-Down Bayesian Posterior Sampling for Sum-Product Networks

Sum-product networks (SPNs) are probabilistic models characterized by exact and fast evaluation of fundamental probabilistic operations. Its superior computational tractability has led to applications in many fields, such as machine learning with time constraints or accuracy requirements and real-time systems. The structural constraints of SPNs supporting fast inference, however, lead to increased learning-time complexity and can be an obstacle to building highly expressive SPNs. This study aimed to develop a Bayesian learning approach that can be efficiently implemented on large-scale SPNs. We derived a new full conditional probability of Gibbs sampling by marginalizing multiple random variables to expeditiously obtain the posterior distribution. The complexity analysis revealed that our sampling algorithm works efficiently even for the largest possible SPN. Furthermore, we proposed a hyperparameter tuning method that balances the diversity of the prior distribution and optimization efficiency in large-scale SPNs. Our method has improved learning-time complexity and demonstrated computational speed tens to more than one hundred times faster and superior predictive performance in numerical experiments on more than 20 datasets.

stat.ML↗

arXiv2024

Understanding Linear Probing then Fine-tuning Language Models from NTK Perspective

The two-stage fine-tuning (FT) method, linear probing (LP) then fine-tuning (LP-FT), outperforms linear probing and FT alone. This holds true for both in-distribution (ID) and out-of-distribution (OOD) data. One key reason for its success is the preservation of pre-trained features, achieved by obtaining a near-optimal linear head during LP. However, despite the widespread use of large language models, there has been limited exploration of more complex architectures such as Transformers. In this paper, we analyze the training dynamics of LP-FT for classification tasks on the basis of the neural tangent kernel (NTK) theory. Our analysis decomposes the NTK matrix into two components. This decomposition highlights the importance of the linear head norm alongside the prediction accuracy at the start of the FT stage. We also observe a significant increase in the linear head norm during LP, which stems from training with the cross-entropy (CE) loss. This increase in the linear head norm effectively reduces changes in learned features. Furthermore, we find that this increased norm can adversely affect model calibration, which can be corrected using temperature scaling. Additionally, we extend our analysis with the NTK to the low-rank adaptation (LoRA) method and validate its effectiveness. Our experiments using a Transformer-based model on multiple natural language processing datasets confirm our theoretical analysis. Our study demonstrates the effectiveness of LP-FT for fine-tuning language models. Code is available at https://github.com/tom4649/lp-ft_ntk.

cs.LG↗