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.

Evolutionary Context Search for Automated Skill Acquisition

Large Language Models cannot reliably acquire new knowledge post-deployment -- even when relevant text resources exist, models fail to transform them into actionable knowledge without retraining. Retrieval-Augmented Generation attempts to bridge this gap by surfacing relevant documents at inference time, yet similarity-based retrieval often fails to identify context that actually improves task performance. We introduce Evolutionary Context Search (ECS), an evolutionary method that searches context combinations using accuracy on a small development set, requiring only inference calls without weight updates. ECS moves beyond semantic similarity to discover non-obvious context pairings that significantly boost performance. Our empirical results show that ECS improves BackendBench by 27\% and $τ$-bench airline by 7\%. The evolved contexts are model-agnostic, as those evolved with Gemini-3-Flash transfer effectively to Claude Sonnet and DeepSeek. This suggests that ECS opens a path toward automated context discovery for skill acquisition -- an efficient alternative to manual prompt engineering or costly fine-tuning.

On the Optimal Reasoning Length for RL-Trained Language Models

Reinforcement learning substantially improves reasoning in large language models, but it also tends to lengthen chain of thought outputs and increase computational cost during both training and inference. Though length control methods have been proposed, it remains unclear what the optimal output length is for balancing efficiency and performance. In this work, we compare several length control methods on two models, Qwen3-1.7B Base and DeepSeek-R1-Distill-Qwen-1.5B. Our results indicate that length penalties may hinder reasoning acquisition, while properly tuned length control can improve efficiency for models with strong prior reasoning. By extending prior work to RL trained policies, we identify two failure modes, 1) long outputs increase dispersion, and 2) short outputs lead to under-thinking.

FedPM: Federated Learning Using Second-order Optimization with Preconditioned Mixing of Local Parameters

We propose Federated Preconditioned Mixing (FedPM), a novel Federated Learning (FL) method that leverages second-order optimization. Prior methods--such as LocalNewton, LTDA, and FedSophia--have incorporated second-order optimization in FL by performing iterative local updates on clients and applying simple mixing of local parameters on the server. However, these methods often suffer from drift in local preconditioners, which significantly disrupts the convergence of parameter training, particularly in heterogeneous data settings. To overcome this issue, we refine the update rules by decomposing the ideal second-order update--computed using globally preconditioned global gradients--into parameter mixing on the server and local parameter updates on clients. As a result, our FedPM introduces preconditioned mixing of local parameters on the server, effectively mitigating drift in local preconditioners. We provide a theoretical convergence analysis demonstrating a superlinear rate for strongly convex objectives in scenarios involving a single local update. To demonstrate the practical benefits of FedPM, we conducted extensive experiments. The results showed significant improvements with FedPM in the test accuracy compared to conventional methods incorporating simple mixing, fully leveraging the potential of second-order optimization.

Optimal Sparsity of Mixture-of-Experts Language Models for Reasoning Tasks

Empirical scaling laws have driven the evolution of large language models (LLMs), yet their coefficients shift whenever the model architecture or data pipeline changes. Mixture-of-Experts (MoE) models, now standard in state-of-the-art systems, introduce a new sparsity dimension that current dense-model frontiers overlook. We investigate how MoE sparsity influences two distinct capability regimes: memorization and reasoning. We train families of MoE Transformers that systematically vary total parameters, active parameters, and top-$k$ routing while holding the compute budget fixed. For every model we record pre-training loss, downstream task loss, and task accuracy, allowing us to separate the train-test generalization gap from the loss-accuracy gap. Memorization benchmarks improve monotonically with total parameters, mirroring training loss. By contrast, reasoning performance saturates and can even regress despite continued gains in both total parameters and training loss. Altering top-$k$ alone has little effect when active parameters are constant, and classic hyperparameters such as learning rate and initialization modulate the generalization gap in the same direction as sparsity. Neither post-training reinforcement learning (GRPO) nor extra test-time compute rescues the reasoning deficit of overly sparse models. Our model checkpoints, code and logs are open-source at https://github.com/rioyokotalab/optimal-sparsity.

Improving LoRA with Variational Learning

Bayesian methods have recently been used to improve LoRA finetuning and, although they improve calibration, their effect on other metrics (such as accuracy) is marginal and can sometimes even be detrimental. Moreover, Bayesian methods also increase computational overheads and require additional tricks for them to work well. Here, we fix these issues by using a recently proposed variational algorithm called IVON. We show that IVON is easy to implement and has similar costs to AdamW, and yet it can also drastically improve many metrics by using a simple posterior pruning technique. We present extensive results on billion-scale LLMs (Llama and Qwen series) going way beyond the scale of existing applications of IVON. For example, we finetune a Llama-3.2-3B model on a set of commonsense reasoning tasks and improve accuracy over AdamW by 1.3% and reduce ECE by 5.4%, outperforming AdamW and other recent Bayesian methods like Laplace-LoRA and BLoB. Overall, our results show that variational learning with IVON can effectively improve LoRA finetuning.

Variational Learning Finds Flatter Solutions at the Edge of Stability

Variational Learning (VL) has recently gained popularity for training deep neural networks and is competitive to standard learning methods. Part of its empirical success can be explained by theories such as PAC-Bayes bounds, minimum description length and marginal likelihood, but there are few tools to unravel the implicit regularization in play. Here, we analyze the implicit regularization of VL through the Edge of Stability (EoS) framework. EoS has previously been used to show that gradient descent can find flat solutions and we extend this result to VL to show that it can find even flatter solutions. This is obtained by controlling the posterior covariance and the number of Monte Carlo samples from the posterior. These results are derived in a similar fashion as the standard EoS literature for deep learning, by first deriving a result for a quadratic problem and then extending it to deep neural networks. We empirically validate these findings on a wide variety of large networks, such as ResNet and ViT, to find that the theoretical results closely match the empirical ones. Ours is the first work to analyze the EoS dynamics in VL.

Rewriting Pre-Training Data Boosts LLM Performance in Math and Code

The performance of large language models (LLMs) in program synthesis and mathematical reasoning is fundamentally limited by the quality of their pre-training corpora. We introduce two openly licensed datasets, released under the Llama 3.3 Community License, that significantly enhance LLM performance by systematically rewriting public data. SwallowCode (approximately 16.1 billion tokens) refines Python snippets from The-Stack-v2 through a novel four-stage pipeline: syntax validation, pylint-based style filtering, and a two-stage LLM rewriting process that enforces style conformity and transforms snippets into self-contained, algorithmically efficient examples. Unlike prior methods that rely on exclusionary filtering or limited transformations, our transform-and-retain approach upgrades low-quality code, maximizing data utility. SwallowMath (approximately 2.3 billion tokens) enhances Finemath-4+ by removing boilerplate, restoring context, and reformatting solutions into concise, step-by-step explanations. Within a fixed 50 billion token training budget, continual pre-training of Llama-3.1-8B with SwallowCode boosts pass@1 by +17.0 on HumanEval and +17.7 on HumanEval+ compared to Stack-Edu, surpassing the baseline model's code generation capabilities. Similarly, substituting SwallowMath yields +12.4 accuracy on GSM8K and +7.6 on MATH. Ablation studies confirm that each pipeline stage contributes incrementally, with rewriting delivering the largest gains. All datasets, prompts, and checkpoints are publicly available, enabling reproducible research and advancing LLM pre-training for specialized domains.

Building Instruction-Tuning Datasets from Human-Written Instructions with Open-Weight Large Language Models

Instruction tuning is crucial for enabling Large Language Models (LLMs) to solve real-world tasks. Prior work has shown the effectiveness of instruction-tuning data synthesized solely from LLMs, raising a fundamental question: Do we still need human-originated signals for instruction tuning? This work answers the question affirmatively: we build state-of-the-art instruction-tuning datasets sourced from human-written instructions, by simply pairing them with LLM-generated responses. LLMs fine-tuned on our datasets consistently outperform those fine-tuned on existing ones. Our data construction approach can be easily adapted to other languages; we build datasets for Japanese and confirm that LLMs tuned with our data reach state-of-the-art performance. Analyses suggest that instruction-tuning in a new language allows LLMs to follow instructions, while the tuned models exhibit a notable lack of culture-specific knowledge in that language. The datasets and fine-tuned models will be publicly available. Our datasets, synthesized with open-weight LLMs, are openly distributed under permissive licenses, allowing for diverse use cases.

On the Relationship Between Double Descent of CNNs and Shape/Texture Bias Under Learning Process

The double descent phenomenon, which deviates from the traditional bias-variance trade-off theory, attracts considerable research attention; however, the mechanism of its occurrence is not fully understood. On the other hand, in the study of convolutional neural networks (CNNs) for image recognition, methods are proposed to quantify the bias on shape features versus texture features in images, determining which features the CNN focuses on more. In this work, we hypothesize that there is a relationship between the shape/texture bias in the learning process of CNNs and epoch-wise double descent, and we conduct verification. As a result, we discover double descent/ascent of shape/texture bias synchronized with double descent of test error under conditions where epoch-wise double descent is observed. Quantitative evaluations confirm this correlation between the test errors and the bias values from the initial decrease to the full increase in test error. Interestingly, double descent/ascent of shape/texture bias is observed in some cases even in conditions without label noise, where double descent is thought not to occur. These experimental results are considered to contribute to the understanding of the mechanisms behind the double descent phenomenon and the learning process of CNNs in image recognition.