Hiroki Naganuma

Hiroki Naganuma, Hideaki Iiduka

One of the training strategies of generative models is to minimize the Jensen--Shannon divergence between the model distribution and the data distribution. Since data distribution is unknown, generative adversarial networks (GANs) formulate this problem as a game between two models, a generator and a discriminator. The training can be formulated in the context of game theory and the local Nash equilibrium (LNE). It does not seem feasible to derive guarantees of stability or optimality for the existing methods. This optimization problem is far more challenging than the single objective setting. Here, we use the conjugate gradient method to reliably and efficiently solve the LNE problem in GANs. We give a proof and convergence analysis under mild assumptions showing that the proposed method converges to a LNE with three different learning rate update rules, including a constant learning rate. Finally, we demonstrate that the proposed method outperforms stochastic gradient descent (SGD) and momentum SGD in terms of best Frechet inception distance (FID) score and outperforms Adam on average. The code is available at \url{https://github.com/Hiroki11x/ConjugateGradient_GAN}.

Hiroki Naganuma, Kartik Ahuja, Shiro Takagi et al.

Modern deep learning systems do not generalize well when the test data distribution is slightly different to the training data distribution. While much promising work has been accomplished to address this fragility, a systematic study of the role of optimizers and their out-of-distribution generalization performance has not been undertaken. In this study, we examine the performance of popular first-order optimizers for different classes of distributional shift under empirical risk minimization and invariant risk minimization. We address this question for image and text classification using DomainBed, WILDS, and Backgrounds Challenge as testbeds for studying different types of shifts -- namely correlation and diversity shift. We search over a wide range of hyperparameters and examine classification accuracy (in-distribution and out-of-distribution) for over 20,000 models. We arrive at the following findings, which we expect to be helpful for practitioners: i) adaptive optimizers (e.g., Adam) perform worse than non-adaptive optimizers (e.g., SGD, momentum SGD) on out-of-distribution performance. In particular, even though there is no significant difference in in-distribution performance, we show a measurable difference in out-of-distribution performance. ii) in-distribution performance and out-of-distribution performance exhibit three types of behavior depending on the dataset -- linear returns, increasing returns, and diminishing returns. For example, in the training of natural language data using Adam, fine-tuning the performance of in-distribution performance does not significantly contribute to the out-of-distribution generalization performance.

Kilian Fatras, Hiroki Naganuma, Ioannis Mitliagkas

It is common in computer vision to be confronted with domain shift: images which have the same class but different acquisition conditions. In domain adaptation (DA), one wants to classify unlabeled target images using source labeled images. Unfortunately, deep neural networks trained on a source training set perform poorly on target images which do not belong to the training domain. One strategy to improve these performances is to align the source and target image distributions in an embedded space using optimal transport (OT). However OT can cause negative transfer, i.e. aligning samples with different labels, which leads to overfitting especially in the presence of label shift between domains. In this work, we mitigate negative alignment by explaining it as a noisy label assignment to target images. We then mitigate its effect by appropriate regularization. We propose to couple the MixUp regularization \citep{zhang2018mixup} with a loss that is robust to noisy labels in order to improve domain adaptation performance. We show in an extensive ablation study that a combination of the two techniques is critical to achieve improved performance. Finally, we evaluate our method, called \textsc{mixunbot}, on several benchmarks and real-world DA problems.

Charles Guille-Escuret, Hiroki Naganuma, Kilian Fatras et al.

Understanding the optimization dynamics of neural networks is necessary for closing the gap between theory and practice. Stochastic first-order optimization algorithms are known to efficiently locate favorable minima in deep neural networks. This efficiency, however, contrasts with the non-convex and seemingly complex structure of neural loss landscapes. In this study, we delve into the fundamental geometric properties of sampled gradients along optimization paths. We focus on two key quantities, which appear in the restricted secant inequality and error bound. Both hold high significance for first-order optimization. Our analysis reveals that these quantities exhibit predictable, consistent behavior throughout training, despite the stochasticity induced by sampling minibatches. Our findings suggest that not only do optimization trajectories never encounter significant obstacles, but they also maintain stable dynamics during the majority of training. These observed properties are sufficiently expressive to theoretically guarantee linear convergence and prescribe learning rate schedules mirroring empirical practices. We conduct our experiments on image classification, semantic segmentation and language modeling across different batch sizes, network architectures, datasets, optimizers, and initialization seeds. We discuss the impact of each factor. Our work provides novel insights into the properties of neural network loss functions, and opens the door to theoretical frameworks more relevant to prevalent practice.

Hiroki Naganuma, Ryuichiro Hataya, Kotaro Yoshida et al.

In the field of computer vision, fine-tuning pre-trained models has become a prevalent strategy for out-of-distribution (OOD) generalization tasks. Different from most prior work that has focused on advancing learning algorithms, we systematically examined how pre-trained model size, pre-training dataset size, and training strategies impact generalization and confidence calibration on downstream tasks. We evaluated 100 models across diverse pre-trained model sizes, five pre-training datasets, and five data augmentations through extensive experiments on four distribution shift datasets totaling over 120,000 GPU hours. Our results demonstrate the significant impact of pre-trained model selection, with optimal choices substantially improving OOD accuracy over algorithm improvement alone. Additionally, we find that larger models and bigger pre-training datasets not only enhance OOD performance but also improve calibration, helping to mitigate overconfidence, contrary to some prior studies that found modern deep networks to calibrate worse than classical shallow models. Our work underscores the overlooked importance of pre-trained model selection for out-of-distribution generalization and calibration.

Hiroki Naganuma, Taiji Suzuki, Rio Yokota et al.

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.

Hiroki Naganuma, Atish Agarwala, Priya Kasimbeg et al.

A basic unanswered question in neural network training is: what is the best learning rate schedule shape for a given workload? The choice of learning rate schedule is a key factor in the success or failure of the training process, but beyond having some kind of warmup and decay, there is no consensus on what makes a good schedule shape. To answer this question, we designed a search procedure to find the best shapes within a parameterized schedule family. Our approach factors out the schedule shape from the base learning rate, which otherwise would dominate cross-schedule comparisons. We applied our search procedure to a variety of schedule families on three workloads: linear regression, image classification on CIFAR-10, and small-scale language modeling on Wikitext103. We showed that our search procedure indeed generally found near-optimal schedules. We found that warmup and decay are robust features of good schedules, and that commonly used schedule families are not optimal on these workloads. Finally, we explored how the outputs of our shape search depend on other optimization hyperparameters, and found that weight decay can have a strong effect on the optimal schedule shape. To the best of our knowledge, our results represent the most comprehensive results on near-optimal schedule shapes for deep neural network training, to date.

Hiroki Naganuma, Shagun Gupta, Youssef Briki et al.

To maximize hardware utilization, modern machine learning systems typically employ large constant or manually tuned batch size schedules, relying on heuristics that are brittle and costly to tune. Existing adaptive strategies based on gradient noise scale (GNS) offer a principled alternative. However, their assumption of SGD's Euclidean geometry creates a fundamental mismatch with popular optimizers based on generalized norms, such as signSGD / Signum ($\ell_\infty$) and stochastic spectral descent (specSGD) / Muon ($\mathcal{S}_\infty$). In this work, we derive gradient noise scales for signSGD and specSGD that naturally emerge from the geometry of their respective dual norms. To practically estimate these non-Euclidean metrics, we propose an efficient variance estimation procedure that leverages the local mini-batch gradients on different ranks in distributed data-parallel systems. Our experiments demonstrate that adaptive batch size strategies using non-Euclidean GNS enable us to match the validation loss of constant-batch baselines while reducing training steps by up to 66% for Signum and Muon on a 160 million parameter Llama model.

Sora Nakai, Youssef Fadhloun, Kacem Mathlouthi et al.

Generalization remains a central yet unresolved challenge in deep learning, particularly the ability to predict a model's performance beyond its training distribution using quantities available prior to test-time evaluation. Building on the large-scale study of Jiang et al. (2020). and concerns by Dziugaite et al. (2020). about instability across training configurations, we benchmark the robustness of generalization measures beyond IID regime. We train small-to-medium models over 10,000 hyperparameter configurations and evaluate more than 40 measures computable from the trained model and the available training data alone. We significantly broaden the experimental scope along multiple axes: (i) extending the evaluation beyond the standard IID setting to include benchmarking for robustness across diverse distribution shifts, (ii) evaluating multiple architectures and training recipes, and (iii) newly incorporating calibration- and information-criteria-based measures to assess their alignment with both IID and OOD generalization. We find that distribution shifts can substantially alter the predictive performance of many generalization measures, while a smaller subset remains comparatively stable across settings.

Tatsuhiro Nakamori, Laura Gomezjurado Gonzalez, Ganesh Talluri et al.

Low-rank gradient compression reduces communication in distributed training by representing updates with rank-$r$ factors. Dion is a recent method that approximates Muon, a spectral optimizer that orthogonalizes momentum, using one step of power iteration followed by column normalization (rescaling each column of the right factor to unit length). This makes it compatible with fully sharded data parallel training, but it converges more slowly than full-rank spectral methods. We show that this gap is geometric: column normalization does not yield the rank-$r$ polar factor that Muon implicitly targets, so the resulting direction violates the dual-norm constraint of the low-rank spectral geometry, and the rate picks up an extra factor of $\sqrt{r}$ even though the low-rank approximation of the gradient itself is accurate. The same mismatch enters the smoothness term and the error-feedback recursion in the analysis, which has a knock-on effect on empirical performance. We propose Orth-Dion, which replaces column normalization with QR orthogonalization of the right factor. Under non-Euclidean smoothness, with $L_r$ the curvature constant along rank-$r$ directions, Orth-Dion attains rate $O(\sqrt{L_r/T})$, matching exact spectral methods at the same per-step communication cost as Dion. The proof removes the bounded-drift assumption common in prior error-feedback analyses via a self-consistent fixed-point argument, and uses a time-averaged contraction that only requires the error sequence to contract on average rather than at every step. Experiments on large-scale language model pre-training validate the predicted $\sqrt{r}$ scaling and show that Orth-Dion closes the convergence gap to Muon at Dion's communication cost.

Naoki Sato, Hiroki Naganuma, Hideaki Iiduka

Muon, a recently proposed optimizer that leverages the inherent matrix structure of neural network parameters, has demonstrated strong empirical performance, indicating its potential as a successor to standard optimizers such as AdamW. This paper presents theoretical analysis to support its practical success. We provide convergence proofs for Muon across four practical settings, systematically examining its behavior with and without the inclusion of Nesterov momentum and weight decay. Our analysis covers the standard configuration using both, thereby elucidating its real-world performance. We then demonstrate that the addition of weight decay yields strictly tighter theoretical bounds and clarify the interplay between the weight decay coefficient and the learning rate. Finally, we derive the critical batch size for Muon that minimizes the computational cost of training. Our analysis identifies the hyperparameters governing this value, and our experiments validate the corresponding theoretical findings across workloads including image classification and language modeling task.

Kotaro Yoshida, Hiroki Naganuma

Machine learning models traditionally assume that training and test data are independently and identically distributed. However, in real-world applications, the test distribution often differs from training. This problem, known as out-of-distribution (OOD) generalization, challenges conventional models. Invariant Risk Minimization (IRM) emerges as a solution that aims to identify invariant features across different environments to enhance OOD robustness. However, IRM's complexity, particularly its bi-level optimization, has led to the development of various approximate methods. Our study investigates these approximate IRM techniques, using the consistency and variance of calibration across environments as metrics to measure the invariance aimed for by IRM. Calibration, which measures the reliability of model prediction, serves as an indicator of whether models effectively capture environment-invariant features by showing how uniformly over-confident the model remains across varied environments. Through a comparative analysis of datasets with distributional shifts, we observe that Information Bottleneck-based IRM achieves consistent calibration across different environments. This observation suggests that information compression techniques, such as IB, are potentially effective in achieving model invariance. Furthermore, our empirical evidence indicates that models exhibiting consistent calibration across environments are also well-calibrated. This demonstrates that invariance and cross-environment calibration are empirically equivalent. Additionally, we underscore the necessity for a systematic approach to evaluating OOD generalization. This approach should move beyond traditional metrics, such as accuracy and F1 scores, which fail to account for the model's degree of over-confidence, and instead focus on the nuanced interplay between accuracy, calibration, and model invariance.

Hiroki Naganuma, Kotaro Yoshida, Laura Gomezjurado Gonzalez et al.

Model editing techniques, particularly task arithmetic using task vectors, have shown promise in efficiently modifying pre-trained models through arithmetic operations like task addition and negation. Despite computational advantages, these methods may inadvertently affect model fairness, creating risks in sensitive applications like hate speech detection. However, the fairness implications of task arithmetic remain largely unexplored, presenting a critical gap in the existing literature. We systematically examine how manipulating task vectors affects fairness metrics, including Demographic Parity and Equalized Odds. To rigorously assess these effects, we benchmark task arithmetic against full fine-tuning, a costly but widely used baseline, and Low-Rank Adaptation (LoRA), a prevalent parameter-efficient fine-tuning method. Additionally, we explore merging task vectors from models fine-tuned on demographic subgroups vulnerable to hate speech, investigating whether fairness outcomes can be controlled by adjusting task vector coefficients, potentially enabling tailored model behavior. Our results offer novel insights into the fairness implications of model editing and establish a foundation for fairness-aware and responsible model editing practices.

Masanari Kimura, Hiroki Naganuma

The key factor in implementing machine learning algorithms in decision-making situations is not only the accuracy of the model but also its confidence level. The confidence level of a model in a classification problem is often given by the output vector of a softmax function for convenience. However, these values are known to deviate significantly from the actual expected model confidence. This problem is called model calibration and has been studied extensively. One of the simplest techniques to tackle this task is focal loss, a generalization of cross-entropy by introducing one positive parameter. Although many related studies exist because of the simplicity of the idea and its formalization, the theoretical analysis of its behavior is still insufficient. In this study, our objective is to understand the behavior of focal loss by reinterpreting this function geometrically. Our analysis suggests that focal loss reduces the curvature of the loss surface in training the model. This indicates that curvature may be one of the essential factors in achieving model calibration. We design numerical experiments to support this conjecture to reveal the behavior of focal loss and the relationship between calibration performance and curvature.

Kotaro Yoshida, Yuji Naraki, Takafumi Horie et al.

Model merging has emerged as an efficient and flexible paradigm for multi-task learning, with numerous methods being proposed in recent years. However, these state-of-the-art techniques are typically evaluated on benchmark suites that are highly favorable to model merging, and their robustness in more realistic settings remains largely unexplored. In this work, we first investigate the vulnerabilities of model-merging methods and pinpoint the source-model characteristics that critically underlie them. Specifically, we identify two factors that are particularly harmful to the merging process: (1) disparities in task vector norms, and (2) the low confidence of the source models. To address this issue, we propose DisTaC (Distillation for Task vector Conditioning), a novel method that pre-conditions these problematic task vectors before the merge. DisTaC leverages knowledge distillation to adjust a task vector's norm and increase source-model confidence while preserving its essential task-specific knowledge. Our extensive experiments demonstrate that by pre-conditioning task vectors with DisTaC, state-of-the-art merging techniques can successfully integrate models exhibiting the harmful traits -- where they would otherwise fail -- achieving significant performance gains.

Hiroki Naganuma, Xinzhi Zhang, Man-Chung Yue et al.

Following AI scaling trends, frontier models continue to grow in size and continue to be trained on larger datasets. Training these models requires huge investments in exascale computational resources, which has in turn driven developtment of distributed deep learning methods. Data parallelism is an essential approach to speed up training, but it requires frequent global communication between workers, which can bottleneck training at the largest scales. In this work, we propose a method called Pseudo-Asynchronous Local SGD (PALSGD) to improve the efficiency of data-parallel training. PALSGD is an extension of Local SGD (Stich, 2018) and DiLoCo (Douillard et al., 2023), designed to further reduce communication frequency by introducing a pseudo-synchronization mechanism. PALSGD allows the use of longer synchronization intervals compared to standard Local SGD. Despite the reduced communication frequency, the pseudo-synchronization approach ensures that model consistency is maintained, leading to performance results comparable to those achieved with more frequent synchronization. Furthermore, we provide a theoretical analysis of PALSGD, establishing its convergence and deriving its convergence rate. This analysis offers insights into the algorithm's behavior and performance guarantees. We evaluated PALSGD on image classification and language modeling tasks. Our results show that PALSGD achieves better performance in less time compared to existing methods like Distributed Data Parallel (DDP), and DiLoCo. Notably, PALSGD trains 18.4% faster than DDP on ImageNet-1K with ResNet-50, 24.4% faster than DDP on TinyStories with GPT-Neo-125M, and 21.1% faster than DDP on TinyStories with GPT-Neo-8M.

Yuji Naraki, Ryosuke Yamaki, Yoshikazu Ikeda et al.

In the field of Natural Language Processing (NLP), Named Entity Recognition (NER) is recognized as a critical technology, employed across a wide array of applications. Traditional methodologies for annotating datasets for NER models are challenged by high costs and variations in dataset quality. This research introduces a novel hybrid annotation approach that synergizes human effort with the capabilities of Large Language Models (LLMs). This approach not only aims to ameliorate the noise inherent in manual annotations, such as omissions, thereby enhancing the performance of NER models, but also achieves this in a cost-effective manner. Additionally, by employing a label mixing strategy, it addresses the issue of class imbalance encountered in LLM-based annotations. Through an analysis across multiple datasets, this method has been consistently shown to provide superior performance compared to traditional annotation methods, even under constrained budget conditions. This study illuminates the potential of leveraging LLMs to improve dataset quality, introduces a novel technique to mitigate class imbalances, and demonstrates the feasibility of achieving high-performance NER in a cost-effective way.