arXiv subjects

Yuki Takezawa

Publications and source records attributed to Yuki Takezawa.

At least 19 recordsLinked to original sources

arXiv2026

Improved Convergence Analysis of Topology Dependence in Decentralized SGD

Decentralized SGD is a fundamental algorithm in decentralized learning, although the influence of an underlying network topology on its convergence behavior is not yet fully understood. Existing convergence analyses have shown that topologies with a small spectral gap significantly deteriorate the convergence rate of Decentralized SGD in both homogeneous and heterogeneous cases. However, many prior papers have reported that indeed the choice of the topology has a significant experimental impact in the heterogeneous case, but has little experimental impact on training behavior in the homogeneous case. In this paper, we present a tighter convergence analysis of Decentralized SGD, offering a more precise understanding of how topologies affect the convergence rate than the prior analysis. Specifically, unlike existing convergence analyses that used only the spectral gap as a property of the topology, our novel analysis shows that all eigenvalues of the mixing matrix affect the convergence rate. Throughout the experiments, we carefully evaluated the convergence behavior of Decentralized SGD and demonstrated that our novel convergence analysis can more accurately describe the effect of topology on the convergence rate.

cs.LG↗

arXiv2026

Delayed Momentum Aggregation: Communication-efficient Byzantine-robust Federated Learning with Partial Participation

Partial participation is essential for communication-efficient federated learning at scale, yet existing Byzantine-robust methods typically assume full client participation. In the partial participation setting, a majority of the sampled clients may be Byzantine, once Byzantine clients dominate, existing methods break down immediately. We introduce delayed momentum aggregation, a principle where the central server aggregates cached momentum from non-sampled clients along with fresh momentum from sampled clients. This principle ensures Byzantine clients remain a minority from the server's perspective even when they dominate the sampled set. We instantiate this principle in our optimizer DeMoA. We analyze the convergence rate of DeMoA, showing that DeMoA is Byzantine-robust under partial participation. Experiments show that, with 20% Byzantine ratio and only 10% partial participation rate, DeMoA achieves the best accuracy even when existing methods fail empirically.

cs.LG↗

arXiv2025

Any-stepsize Gradient Descent for Separable Data under Fenchel-Young Losses

The gradient descent (GD) has been one of the most common optimizer in machine learning. In particular, the loss landscape of a neural network is typically sharpened during the initial phase of training, making the training dynamics hover on the edge of stability. This is beyond our standard understanding of GD convergence in the stable regime where arbitrarily chosen stepsize is sufficiently smaller than the edge of stability. Recently, Wu et al. (COLT2024) have showed that GD converges with arbitrary stepsize under linearly separable logistic regression. Although their analysis hinges on the self-bounding property of the logistic loss, which seems to be a cornerstone to establish a modified descent lemma, our pilot study shows that other loss functions without the self-bounding property can make GD converge with arbitrary stepsize. To further understand what property of a loss function matters in GD, we aim to show arbitrary-stepsize GD convergence for a general loss function based on the framework of \emph{Fenchel--Young losses}. We essentially leverage the classical perceptron argument to derive the convergence rate for achieving $ε$-optimal loss, which is possible for a majority of Fenchel--Young losses. Among typical loss functions, the Tsallis entropy achieves the GD convergence rate $T=Ω(ε^{-1/2})$, and the R{é}nyi entropy achieves the far better rate $T=Ω(ε^{-1/3})$. We argue that these better rate is possible because of \emph{separation margin} of loss functions, instead of the self-bounding property.

stat.ML↗

arXiv2025

FedMuon: Federated Learning with Bias-corrected LMO-based Optimization

Recently, a new optimization method based on the linear minimization oracle (LMO), called Muon, has been attracting increasing attention since it can train neural networks faster than existing adaptive optimization methods, such as Adam. In this paper, we study how Muon can be utilized in federated learning. We first show that straightforwardly using Muon as the local optimizer of FedAvg does not converge to the stationary point since the LMO is a biased operator. We then propose FedMuon which can mitigate this issue. We also analyze how solving the LMO approximately affects the convergence rate and find that, surprisingly, FedMuon can converge for any number of Newton-Schulz iterations, while it can converge faster as we solve the LMO more accurately. Through experiments, we demonstrated that FedMuon can outperform the state-of-the-art federated learning methods.

cs.LG↗

arXiv2025

Exploiting Similarity for Computation and Communication-Efficient Decentralized Optimization

Reducing communication complexity is critical for efficient decentralized optimization. The proximal decentralized optimization (PDO) framework is particularly appealing, as methods within this framework can exploit functional similarity among nodes to reduce communication rounds. Specifically, when local functions at different nodes are similar, these methods achieve faster convergence with fewer communication steps. However, existing PDO methods often require highly accurate solutions to subproblems associated with the proximal operator, resulting in significant computational overhead. In this work, we propose the Stabilized Proximal Decentralized Optimization (SPDO) method, which achieves state-of-the-art communication and computational complexities within the PDO framework. Additionally, we refine the analysis of existing PDO methods by relaxing subproblem accuracy requirements and leveraging average functional similarity. Experimental results demonstrate that SPDO significantly outperforms existing methods.

cs.LG↗

arXiv2025

PhiNets: Brain-inspired Non-contrastive Learning Based on Temporal Prediction Hypothesis

Predictive coding is a theory which hypothesises that cortex predicts sensory inputs at various levels of abstraction to minimise prediction errors. Inspired by predictive coding, Chen et al. (2024) proposed another theory, temporal prediction hypothesis, to claim that sequence memory residing in hippocampus has emerged through predicting input signals from the past sensory inputs. Specifically, they supposed that the CA3 predictor in hippocampus creates synaptic delay between input signals, which is compensated by the following CA1 predictor. Though recorded neural activities were replicated based on the temporal prediction hypothesis, its validity has not been fully explored. In this work, we aim to explore the temporal prediction hypothesis from the perspective of self-supervised learning. Specifically, we focus on non-contrastive learning, which generates two augmented views of an input image and predicts one from another. Non-contrastive learning is intimately related to the temporal prediction hypothesis because the synaptic delay is implicitly created by StopGradient. Building upon a popular non-contrastive learner, SimSiam, we propose PhiNet, an extension of SimSiam to have two predictors explicitly corresponding to the CA3 and CA1, respectively. Through studying the PhiNet model, we discover two findings. First, meaningful data representations emerge in PhiNet more stably than in SimSiam. This is initially supported by our learning dynamics analysis: PhiNet is more robust to the representational collapse. Second, PhiNet adapts more quickly to newly incoming patterns in online and continual learning scenarios. For practitioners, we additionally propose an extension called X-PhiNet integrated with a momentum encoder, excelling in continual learning. All in all, our work reveals that the temporal prediction hypothesis is a reasonable model in terms of the robustness and adaptivity.

cs.LG↗

arXiv2025

Scalable Decentralized Learning with Teleportation

Decentralized SGD can run with low communication costs, but its sparse communication characteristics deteriorate the convergence rate, especially when the number of nodes is large. In decentralized learning settings, communication is assumed to occur on only a given topology, while in many practical cases, the topology merely represents a preferred communication pattern, and connecting to arbitrary nodes is still possible. Previous studies have tried to alleviate the convergence rate degradation in these cases by designing topologies with large spectral gaps. However, the degradation is still significant when the number of nodes is substantial. In this work, we propose TELEPORTATION. TELEPORTATION activates only a subset of nodes, and the active nodes fetch the parameters from previous active nodes. Then, the active nodes update their parameters by SGD and perform gossip averaging on a relatively small topology comprising only the active nodes. We show that by activating only a proper number of nodes, TELEPORTATION can completely alleviate the convergence rate degradation. Furthermore, we propose an efficient hyperparameter-tuning method to search for the appropriate number of nodes to be activated. Experimentally, we showed that TELEPORTATION can train neural networks more stably and achieve higher accuracy than Decentralized SGD.

cs.LG↗

arXiv2025

Necessary and Sufficient Watermark for Large Language Models

In recent years, large language models (LLMs) have achieved remarkable performances in various NLP tasks. They can generate texts that are indistinguishable from those written by humans. Such remarkable performance of LLMs increases their risk of being used for malicious purposes, such as generating fake news articles. Therefore, it is necessary to develop methods for distinguishing texts written by LLMs from those written by humans. Watermarking is one of the most powerful methods for achieving this. Although existing watermarking methods have successfully detected texts generated by LLMs, they significantly degrade the quality of the generated texts. In this study, we propose the Necessary and Sufficient Watermark (NS-Watermark) for inserting watermarks into generated texts without degrading the text quality. More specifically, we derive minimum constraints required to be imposed on the generated texts to distinguish whether LLMs or humans write the texts. Then, we formulate the NS-Watermark as a constrained optimization problem and propose an efficient algorithm to solve it. Through the experiments, we demonstrate that the NS-Watermark can generate more natural texts than existing watermarking methods and distinguish more accurately between texts written by LLMs and those written by humans. Especially in machine translation tasks, the NS-Watermark can outperform the existing watermarking method by up to 30 BLEU scores.

cs.CL↗

arXiv2024

Parameter-free Clipped Gradient Descent Meets Polyak

Gradient descent and its variants are de facto standard algorithms for training machine learning models. As gradient descent is sensitive to its hyperparameters, we need to tune the hyperparameters carefully using a grid search. However, the method is time-consuming, particularly when multiple hyperparameters exist. Therefore, recent studies have analyzed parameter-free methods that adjust the hyperparameters on the fly. However, the existing work is limited to investigations of parameter-free methods for the stepsize, and parameter-free methods for other hyperparameters have not been explored. For instance, although the gradient clipping threshold is a crucial hyperparameter in addition to the stepsize for preventing gradient explosion issues, none of the existing studies have investigated parameter-free methods for clipped gradient descent. Therefore, in this study, we investigate the parameter-free methods for clipped gradient descent. Specifically, we propose Inexact Polyak Stepsize, which converges to the optimal solution without any hyperparameters tuning, and its convergence rate is asymptotically independent of $L$ under $L$-smooth and $(L_0, L_1)$-smooth assumptions of the loss function, similar to that of clipped gradient descent with well-tuned hyperparameters. We numerically validated our convergence results using a synthetic function and demonstrated the effectiveness of our proposed methods using LSTM, Nano-GPT, and T5.

cs.LG↗

arXiv2024

An Empirical Study of Self-supervised Learning with Wasserstein Distance

In this study, we delve into the problem of self-supervised learning (SSL) utilizing the 1-Wasserstein distance on a tree structure (a.k.a., Tree-Wasserstein distance (TWD)), where TWD is defined as the L1 distance between two tree-embedded vectors. In SSL methods, the cosine similarity is often utilized as an objective function; however, it has not been well studied when utilizing the Wasserstein distance. Training the Wasserstein distance is numerically challenging. Thus, this study empirically investigates a strategy for optimizing the SSL with the Wasserstein distance and finds a stable training procedure. More specifically, we evaluate the combination of two types of TWD (total variation and ClusterTree) and several probability models, including the softmax function, the ArcFace probability model, and simplicial embedding. We propose a simple yet effective Jeffrey divergence-based regularization method to stabilize optimization. Through empirical experiments on STL10, CIFAR10, CIFAR100, and SVHN, we find that a simple combination of the softmax function and TWD can obtain significantly lower results than the standard SimCLR. Moreover, a simple combination of TWD and SimSiam fails to train the model. We find that the model performance depends on the combination of TWD and probability model, and that the Jeffrey divergence regularization helps in model training. Finally, we show that the appropriate combination of the TWD and probability model outperforms cosine similarity-based representation learning.

stat.ML↗

arXiv2023

Beyond Exponential Graph: Communication-Efficient Topologies for Decentralized Learning via Finite-time Convergence

Decentralized learning has recently been attracting increasing attention for its applications in parallel computation and privacy preservation. Many recent studies stated that the underlying network topology with a faster consensus rate (a.k.a. spectral gap) leads to a better convergence rate and accuracy for decentralized learning. However, a topology with a fast consensus rate, e.g., the exponential graph, generally has a large maximum degree, which incurs significant communication costs. Thus, seeking topologies with both a fast consensus rate and small maximum degree is important. In this study, we propose a novel topology combining both a fast consensus rate and small maximum degree called the Base-$(k + 1)$ Graph. Unlike the existing topologies, the Base-$(k + 1)$ Graph enables all nodes to reach the exact consensus after a finite number of iterations for any number of nodes and maximum degree k. Thanks to this favorable property, the Base-$(k + 1)$ Graph endows Decentralized SGD (DSGD) with both a faster convergence rate and more communication efficiency than the exponential graph. We conducted experiments with various topologies, demonstrating that the Base-$(k + 1)$ Graph enables various decentralized learning methods to achieve higher accuracy with better communication efficiency than the existing topologies.

cs.LG↗

arXiv2023

Embarrassingly Simple Text Watermarks

We propose Easymark, a family of embarrassingly simple yet effective watermarks. Text watermarking is becoming increasingly important with the advent of Large Language Models (LLM). LLMs can generate texts that cannot be distinguished from human-written texts. This is a serious problem for the credibility of the text. Easymark is a simple yet effective solution to this problem. Easymark can inject a watermark without changing the meaning of the text at all while a validator can detect if a text was generated from a system that adopted Easymark or not with high credibility. Easymark is extremely easy to implement so that it only requires a few lines of code. Easymark does not require access to LLMs, so it can be implemented on the user-side when the LLM providers do not offer watermarked LLMs. In spite of its simplicity, it achieves higher detection accuracy and BLEU scores than the state-of-the-art text watermarking methods. We also prove the impossibility theorem of perfect watermarking, which is valuable in its own right. This theorem shows that no matter how sophisticated a watermark is, a malicious user could remove it from the text, which motivate us to use a simple watermark such as Easymark. We carry out experiments with LLM-generated texts and confirm that Easymark can be detected reliably without any degradation of BLEU and perplexity, and outperform state-of-the-art watermarks in terms of both quality and reliability.

cs.LG↗

arXiv2023

Momentum Tracking: Momentum Acceleration for Decentralized Deep Learning on Heterogeneous Data

SGD with momentum is one of the key components for improving the performance of neural networks. For decentralized learning, a straightforward approach using momentum is Distributed SGD (DSGD) with momentum (DSGDm). However, DSGDm performs worse than DSGD when the data distributions are statistically heterogeneous. Recently, several studies have addressed this issue and proposed methods with momentum that are more robust to data heterogeneity than DSGDm, although their convergence rates remain dependent on data heterogeneity and deteriorate when the data distributions are heterogeneous. In this study, we propose Momentum Tracking, which is a method with momentum whose convergence rate is proven to be independent of data heterogeneity. More specifically, we analyze the convergence rate of Momentum Tracking in the setting where the objective function is non-convex and the stochastic gradient is used. Then, we identify that it is independent of data heterogeneity for any momentum coefficient $β\in [0, 1)$. Through experiments, we demonstrate that Momentum Tracking is more robust to data heterogeneity than the existing decentralized learning methods with momentum and can consistently outperform these existing methods when the data distributions are heterogeneous.

cs.LG↗

arXiv2022

Improving the Robustness to Variations of Objects and Instructions with a Neuro-Symbolic Approach for Interactive Instruction Following

An interactive instruction following task has been proposed as a benchmark for learning to map natural language instructions and first-person vision into sequences of actions to interact with objects in 3D environments. We found that an existing end-to-end neural model for this task tends to fail to interact with objects of unseen attributes and follow various instructions. We assume that this problem is caused by the high sensitivity of neural feature extraction to small changes in vision and language inputs. To mitigate this problem, we propose a neuro-symbolic approach that utilizes high-level symbolic features, which are robust to small changes in raw inputs, as intermediate representations. We verify the effectiveness of our model with the subtask evaluation on the ALFRED benchmark. Our experiments show that our approach significantly outperforms the end-to-end neural model by 9, 46, and 74 points in the success rate on the ToggleObject, PickupObject, and SliceObject subtasks in unseen environments respectively.

cs.AI↗

arXiv2022

Theoretical Analysis of Primal-Dual Algorithm for Non-Convex Stochastic Decentralized Optimization

In recent years, decentralized learning has emerged as a powerful tool not only for large-scale machine learning, but also for preserving privacy. One of the key challenges in decentralized learning is that the data distribution held by each node is statistically heterogeneous. To address this challenge, the primal-dual algorithm called the Edge-Consensus Learning (ECL) was proposed and was experimentally shown to be robust to the heterogeneity of data distributions. However, the convergence rate of the ECL is provided only when the objective function is convex, and has not been shown in a standard machine learning setting where the objective function is non-convex. Furthermore, the intuitive reason why the ECL is robust to the heterogeneity of data distributions has not been investigated. In this work, we first investigate the relationship between the ECL and Gossip algorithm and show that the update formulas of the ECL can be regarded as correcting the local stochastic gradient in the Gossip algorithm. Then, we propose the Generalized ECL (G-ECL), which contains the ECL as a special case, and provide the convergence rates of the G-ECL in both (strongly) convex and non-convex settings, which do not depend on the heterogeneity of data distributions. Through synthetic experiments, we demonstrate that the numerical results of both the G-ECL and ECL coincide with the convergence rate of the G-ECL.

math.OC↗

arXiv2022

Approximating 1-Wasserstein Distance with Trees

Wasserstein distance, which measures the discrepancy between distributions, shows efficacy in various types of natural language processing (NLP) and computer vision (CV) applications. One of the challenges in estimating Wasserstein distance is that it is computationally expensive and does not scale well for many distribution comparison tasks. In this paper, we aim to approximate the 1-Wasserstein distance by the tree-Wasserstein distance (TWD), where TWD is a 1-Wasserstein distance with tree-based embedding and can be computed in linear time with respect to the number of nodes on a tree. More specifically, we propose a simple yet efficient L1-regularized approach to learning the weights of the edges in a tree. To this end, we first show that the 1-Wasserstein approximation problem can be formulated as a distance approximation problem using the shortest path distance on a tree. We then show that the shortest path distance can be represented by a linear model and can be formulated as a Lasso-based regression problem. Owing to the convex formulation, we can obtain a globally optimal solution efficiently. Moreover, we propose a tree-sliced variant of these methods. Through experiments, we demonstrated that the weighted TWD can accurately approximate the original 1-Wasserstein distance.

stat.ML↗

arXiv2022

Communication Compression for Decentralized Learning with Operator Splitting Methods

In decentralized learning, operator splitting methods using a primal-dual formulation (e.g., the Edge-Consensus Learning (ECL)) has been shown to be robust to heterogeneous data and has attracted significant attention in recent years. However, in the ECL, a node needs to exchange dual variables with its neighbors. These exchanges incur significant communication costs. For the Gossip-based algorithms, many compression methods have been proposed, but these Gossip-based algorithm do not perform well when the data distribution held by each node is statistically heterogeneous. In this work, we propose the novel framework of the compression methods for the ECL, called the Communication Compressed ECL (C-ECL). Specifically, we reformulate the update formulas of the ECL, and propose to compress the update values of the dual variables. We demonstrate experimentally that the C-ECL can achieve a nearly equivalent performance with fewer parameter exchanges than the ECL. Moreover, we demonstrate that the C-ECL is more robust to heterogeneous data than the Gossip-based algorithms.

cs.LG↗

arXiv2022

Fixed Support Tree-Sliced Wasserstein Barycenter

The Wasserstein barycenter has been widely studied in various fields, including natural language processing, and computer vision. However, it requires a high computational cost to solve the Wasserstein barycenter problem because the computation of the Wasserstein distance requires a quadratic time with respect to the number of supports. By contrast, the Wasserstein distance on a tree, called the tree-Wasserstein distance, can be computed in linear time and allows for the fast comparison of a large number of distributions. In this study, we propose a barycenter under the tree-Wasserstein distance, called the fixed support tree-Wasserstein barycenter (FS-TWB) and its extension, called the fixed support tree-sliced Wasserstein barycenter (FS-TSWB). More specifically, we first show that the FS-TWB and FS-TSWB problems are convex optimization problems and can be solved by using the projected subgradient descent. Moreover, we propose a more efficient algorithm to compute the subgradient and objective function value by using the properties of tree-Wasserstein barycenter problems. Through real-world experiments, we show that, by using the proposed algorithm, the FS-TWB and FS-TSWB can be solved two orders of magnitude faster than the original Wasserstein barycenter.

cs.AI↗