Masanori Koyama

Takeru Miyato, Masanori Koyama, Kenji Fukumizu

In this study, we present meta-sequential prediction (MSP), an unsupervised framework to learn the symmetry from the time sequence of length at least three. Our method leverages the stationary property (e.g. constant velocity, constant acceleration) of the time sequence to learn the underlying equivariant structure of the dataset by simply training the encoder-decoder model to be able to predict the future observations. We will demonstrate that, with our framework, the hidden disentangled structure of the dataset naturally emerges as a by-product by applying simultaneous block-diagonalization to the transition operators in the latent space, the procedure which is commonly used in representation theory to decompose the feature-space based on the type of response to group actions. We will showcase our method from both empirical and theoretical perspectives. Our result suggests that finding a simple structured relation and learning a model with extrapolation capability are two sides of the same coin. The code is available at https://github.com/takerum/meta_sequential_prediction.

Masaaki Imaizumi, Masanori Koyama, Noboru Isobe et al.

We use a mean-field-based transformer model to theoretically investigate how auxiliary variables, such as positional encoding, prevent mode collapse of self-attention mechanisms. The use of mean-field transformers to analyze the properties of self-attention mechanisms has garnered significant attention in recent years due to their ability to comprehensively analyze token interactions. However, analysis of this simple model suggests that mode collapse, where token distributions degenerate to a single point, occurs during long inferences (i.e., many layers), indicating a discrepancy with reality. This study investigates this mean-field transformer model and demonstrates that the introduction of auxiliary variables, such as positional encoding, acts as a counterforce against theoretical mode collapse. Specifically, we show that in the theoretical scheme, the energy-maximizing distribution does not degenerate to a single point; instead, it is characterized by a pushforward of the auxiliary variable distribution, thereby avoiding concentration in the Dirac measure. Our main examples are the positional encoding and the fixed prompt insertion treated as a parallel auxiliary-variable mechanism. Furthermore, we demonstrate that positional encoding and prompt insertion possess universality of representation in the limit, meaning that the limit distribution of inference can exactly represent a wide class of distributions. We also analyze several key properties of positional encoding and metastability, and validate our theoretical results through mathematical experiments.

David F. Anderson, Masanori Koyama

The simplest, and most common, stochastic model for population processes, including those from biochemistry and cell biology, are continuous time Markov chains. Simulation of such models is often relatively straightforward as there are easily implementable methods for the generation of exact sample paths. However, when using ensemble averages to approximate expected values, the computational complexity can become prohibitive as the number of computations per path scales linearly with the number of jumps of the process. When such methods become computationally intractable, approximate methods, which introduce a bias, can become advantageous. In this paper, we provide a general framework for understanding the weak error, or bias, induced by different numerical approximation techniques in the current setting. The analysis takes into account both the natural scalings within a given system and the step-size of the numerical method. Examples are provided to demonstrate the main analytical results as well as the reduction in computational complexity achieved by the approximate methods.

Masanori Koyama, Takeru Miyato, Kenji Fukumizu

Recent years have witnessed the effectiveness of contrastive learning in obtaining the representation of dataset that is useful in interpretation and downstream tasks. However, the mechanism that describes this effectiveness have not been thoroughly analyzed, and many studies have been conducted to investigate the data structures captured by contrastive learning. In particular, the recent study of \citet{content_isolate} has shown that contrastive learning is capable of decomposing the data space into the space that is invariant to all augmentations and its complement. In this paper, we introduce the notion of invariance-adapted latent space that decomposes the data space into the intersections of the invariant spaces of each augmentation and their complements. This decomposition generalizes the one introduced in \citet{content_isolate}, and describes a structure that is analogous to the frequencies in the harmonic analysis of a group. We experimentally show that contrastive learning with lasso-type metric can be used to find an invariance-adapted latent space, thereby suggesting a new potential for the contrastive learning. We also investigate when such a latent space can be identified up to mixings within each component.

David F. Anderson, Masanori Koyama

This paper is concerned with elucidating a relationship between two common coupling methods for the continuous time Markov chain models utilized in the cell biology literature. The couplings considered here are primarily used in a computational framework by providing reductions in variance for different Monte Carlo estimators, thereby allowing for significantly more accurate results for a fixed amount of computational time. Common applications of the couplings include the estimation of parametric sensitivities via finite difference methods and the estimation of expectations via multi-level Monte Carlo algorithms. While a number of coupling strategies have been proposed for the models considered here, and a number of articles have experimentally compared the different strategies, to date there has been no mathematical analysis describing the connections between them. Such analyses are critical in order to determine the best use for each. In the current paper, we show a connection between the common reaction path (CRP) method and the split coupling (SC) method, which is termed coupled finite differences (CFD) in the parametric sensitivities literature. In particular, we show that the two couplings are both limits of a third coupling strategy we call the "local-CRP" coupling, with the split coupling method arising as a key parameter goes to infinity, and the common reaction path coupling arising as the same parameter goes to zero. The analysis helps explain why the split coupling method often provides a lower variance than does the common reaction path method, a fact previously shown experimentally.

Kenji Kubo, Shunsuke Kamiya, Masanori Koyama et al.

Neural network models with latent recurrent processing, where identical layers are recursively applied to the latent state, have gained attention as promising models for performing reasoning tasks. A strength of such models is that they enable test-time scaling, where the models can enhance their performance in the test phase without additional training. Models such as the Hierarchical Reasoning Model (HRM) and Artificial Kuramoto Oscillatory Neurons (AKOrN) can facilitate deeper reasoning by increasing the number of recurrent steps, thereby enabling the completion of challenging tasks, including Sudoku, Maze solving, and AGI benchmarks. In this work, we introduce confidence-based voting (C-voting), a test-time scaling strategy designed for recurrent models with multiple latent candidate trajectories. Initializing the latent state with multiple candidates using random variables, C-voting selects the one maximizing the average of top-1 probabilities of the predictions, reflecting the model's confidence. Additionally, it yields 4.9% higher accuracy on Sudoku-hard than the energy-based voting strategy, which is specific to models with explicit energy functions. An essential advantage of C-voting is its applicability: it can be applied to recurrent models without requiring an explicit energy function. Finally, we introduce a simple attention-based recurrent model with randomized initial values named ItrSA++, and demonstrate that when combined with C-voting, it outperforms HRM on Sudoku-extreme (95.2% vs. 55.0%) and Maze (78.6% vs. 74.5%) tasks.

Shota Takashiro, Masanori Koyama, Takeru Miyato et al.

We extend the recent latent recurrent modeling to sequential input streams. By interleaving fast, recurrent latent updates with self-organizational ability between slow observation updates, our method facilitates the learning of stable internal structures that evolve alongside the input. This mechanism allows the model to maintain coherent and clustered representations over long horizons, improving out-of-distribution generalization in reinforcement learning and algorithmic tasks compared to sequential baselines such as LSTM, state space models, and Transformer variants.

Kotaro Ikeda, Masanori Koyama, Jinzhe Zhang et al.

In this paper, we propose a flow-based method for learning all-to-all transfer maps among conditional distributions that approximates pairwise optimal transport. The proposed method addresses the challenge of handling the case of continuous conditions, which often involve a large set of conditions with sparse empirical observations per condition. We introduce a novel cost function that enables simultaneous learning of optimal transports for all pairs of conditional distributions. Our method is supported by a theoretical guarantee that, in the limit, it converges to the pairwise optimal transports among infinite pairs of conditional distributions. The learned transport maps are subsequently used to couple data points in conditional flow matching. We demonstrate the effectiveness of this method on synthetic and benchmark datasets, as well as on chemical datasets in which continuous physical properties are defined as conditions. The code for this project can be found at https://github.com/kotatumuri-room/A2A-FM

Takuya Akiba, Shotaro Sano, Toshihiko Yanase et al.

The purpose of this study is to introduce new design-criteria for next-generation hyperparameter optimization software. The criteria we propose include (1) define-by-run API that allows users to construct the parameter search space dynamically, (2) efficient implementation of both searching and pruning strategies, and (3) easy-to-setup, versatile architecture that can be deployed for various purposes, ranging from scalable distributed computing to light-weight experiment conducted via interactive interface. In order to prove our point, we will introduce Optuna, an optimization software which is a culmination of our effort in the development of a next generation optimization software. As an optimization software designed with define-by-run principle, Optuna is particularly the first of its kind. We will present the design-techniques that became necessary in the development of the software that meets the above criteria, and demonstrate the power of our new design through experimental results and real world applications. Our software is available under the MIT license (https://github.com/pfnet/optuna/).

Ryohei Suzuki, Masanori Koyama, Takeru Miyato et al.

We present a novel CNN-based image editing strategy that allows the user to change the semantic information of an image over an arbitrary region by manipulating the feature-space representation of the image in a trained GAN model. We will present two variants of our strategy: (1) spatial conditional batch normalization (sCBN), a type of conditional batch normalization with user-specifiable spatial weight maps, and (2) feature-blending, a method of directly modifying the intermediate features. Our methods can be used to edit both artificial image and real image, and they both can be used together with any GAN with conditional normalization layers. We will demonstrate the power of our method through experiments on various types of GANs trained on different datasets. Code will be available at https://github.com/pfnet-research/neural-collage.

Noboru Isobe, Masanori Koyama, Jinzhe Zhang et al.

The task of conditional generation is one of the most important applications of generative models, and numerous methods have been developed to date based on the celebrated flow-based models. However, many flow-based models in use today are not built to allow one to introduce an explicit inductive bias to how the conditional distribution to be generated changes with respect to conditions. This can result in unexpected behavior in the task of style transfer, for example. In this research, we introduce extended flow matching (EFM), a direct extension of flow matching that learns a "matrix field" corresponding to the continuous map from the space of conditions to the space of distributions. We show that we can introduce inductive bias to the conditional generation through the matrix field and demonstrate this fact with MMOT-EFM, a version of EFM that aims to minimize the Dirichlet energy or the sensitivity of the distribution with respect to conditions. We will present our theory along with experimental results that support the competitiveness of EFM in conditional generation.

Makoto Shing, Masanori Koyama, Takuya Akiba

End-to-end backpropagation requires storing activations throughout all layers, creating memory bottlenecks that limit model scalability. Existing block-wise training methods offer means to alleviate this problem, but they rely on ad-hoc local objectives and remain largely unexplored beyond classification tasks. We propose $\textit{DiffusionBlocks}$, a principled framework for transforming transformer-based networks into genuinely independent trainable blocks that maintain competitive performance with end-to-end training. Our key insight leverages the fact that residual connections naturally correspond to updates in a dynamical system. With minimal modifications to this system, we can convert the updates to those of a denoising process, where each block can be learned independently by leveraging the score matching objective. This independence enables training with gradients for only one block at a time, thereby reducing memory requirements in proportion to the number of blocks. Our experiments on a range of transformer architectures (vision, diffusion, autoregressive, recurrent-depth, and masked diffusion) demonstrate that DiffusionBlocks training matches the performance of end-to-end training while enabling scalable block-wise training on practical tasks beyond small-scale classification. DiffusionBlocks provides a theoretically grounded approach that successfully scales to modern generative tasks across diverse architectures.

Kohei Hayashi, Masanori Koyama, Julian Jorge Andrade Guerreiro

Various world model frameworks are being developed today based on autoregressive frameworks that rely on discrete representations of actions and observations, and these frameworks are succeeding in constructing interactive generative models for the target environment of interest. Meanwhile, humans demonstrate remarkable generalization abilities to combine experiences in multiple environments to mentally simulate and learn to control agents in diverse environments. Inspired by this human capability, we introduce World modeling through Lie Action (WLA), an unsupervised framework that learns continuous latent action representations to simulate across environments. WLA learns a control interface with high controllability and predictive ability by simultaneously modeling the dynamics of multiple environments using Lie group theory and object-centric autoencoder. On synthetic benchmark and real-world datasets, we demonstrate that WLA can be trained using only video frames and, with minimal or no action labels, can quickly adapt to new environments with novel action sets.

Masanori Koyama, Kenji Fukumizu, Kohei Hayashi et al.

Symmetry learning has proven to be an effective approach for extracting the hidden structure of data, with the concept of equivariance relation playing the central role. However, most of the current studies are built on architectural theory and corresponding assumptions on the form of data. We propose Neural Fourier Transform (NFT), a general framework of learning the latent linear action of the group without assuming explicit knowledge of how the group acts on data. We present the theoretical foundations of NFT and show that the existence of a linear equivariant feature, which has been assumed ubiquitously in equivariance learning, is equivalent to the existence of a group invariant kernel on the dataspace. We also provide experimental results to demonstrate the application of NFT in typical scenarios with varying levels of knowledge about the acting group.

Masanori Koyama, Kentaro Minami, Takeru Miyato et al.

In contrastive representation learning, data representation is trained so that it can classify the image instances even when the images are altered by augmentations. However, depending on the datasets, some augmentations can damage the information of the images beyond recognition, and such augmentations can result in collapsed representations. We present a partial solution to this problem by formalizing a stochastic encoding process in which there exist a tug-of-war between the data corruption introduced by the augmentations and the information preserved by the encoder. We show that, with the infoMax objective based on this framework, we can learn a data-dependent distribution of augmentations to avoid the collapse of the representation.

Masanori Koyama, Shoichiro Yamaguchi

The goal of Out-of-Distribution (OOD) generalization problem is to train a predictor that generalizes on all environments. Popular approaches in this field use the hypothesis that such a predictor shall be an \textit{invariant predictor} that captures the mechanism that remains constant across environments. While these approaches have been experimentally successful in various case studies, there is still much room for the theoretical validation of this hypothesis. This paper presents a new set of theoretical conditions necessary for an invariant predictor to achieve the OOD optimality. Our theory not only applies to non-linear cases, but also generalizes the necessary condition used in \citet{rojas2018invariant}. We also derive Inter Gradient Alignment algorithm from our theory and demonstrate its competitiveness on MNIST-derived benchmark datasets as well as on two of the three \textit{Invariance Unit Tests} proposed by \citet{aubinlinear}.

Ruixiang Zhang, Masanori Koyama, Katsuhiko Ishiguro

Learning controllable and generalizable representation of multivariate data with desired structural properties remains a fundamental problem in machine learning. In this paper, we present a novel framework for learning generative models with various underlying structures in the latent space. We represent the inductive bias in the form of mask variables to model the dependency structure in the graphical model and extend the theory of multivariate information bottleneck to enforce it. Our model provides a principled approach to learn a set of semantically meaningful latent factors that reflect various types of desired structures like capturing correlation or encoding invariance, while also offering the flexibility to automatically estimate the dependency structure from data. We show that our framework unifies many existing generative models and can be applied to a variety of tasks including multi-modal data modeling, algorithmic fairness, and invariant risk minimization.

Shin-ichi Maeda, Toshiki Nakanishi, Masanori Koyama

Meta-Learning is a family of methods that use a set of interrelated tasks to learn a model that can quickly learn a new query task from a possibly small contextual dataset. In this study, we use a probabilistic framework to formalize what it means for two tasks to be related and reframe the meta-learning problem into the problem of Bayesian risk minimization (BRM). In our formulation, the BRM optimal solution is given by the predictive distribution computed from the posterior distribution of the task-specific latent variable conditioned on the contextual dataset, and this justifies the philosophy of Neural Process. However, the posterior distribution in Neural Process violates the way the posterior distribution changes with the contextual dataset. To address this problem, we present a novel Gaussian approximation for the posterior distribution that generalizes the posterior of the linear Gaussian model. Unlike that of the Neural Process, our approximation of the posterior distributions converges to the maximum likelihood estimate with the same rate as the true posterior distribution. We also demonstrate the competitiveness of our approach on benchmark datasets.

Shin-ichi Maeda, Hayato Watahiki, Shintarou Okada et al.

Practical reinforcement learning problems are often formulated as constrained Markov decision process (CMDP) problems, in which the agent has to maximize the expected return while satisfying a set of prescribed safety constraints. In this study, we propose a novel simulator-based method to approximately solve a CMDP problem without making any compromise on the safety constraints. We achieve this by decomposing the CMDP into a pair of MDPs; reconnaissance MDP and planning MDP. The purpose of reconnaissance MDP is to evaluate the set of actions that are safe, and the purpose of planning MDP is to maximize the return while using the actions authorized by reconnaissance MDP. RMDP can define a set of safe policies for any given set of safety constraint, and this set of safe policies can be used to solve another CMDP problem with different reward. Our method is not only computationally less demanding than the previous simulator-based approaches to CMDP, but also capable of finding a competitive reward-seeking policy in a high dimensional environment, including those involving multiple moving obstacles.

Mitsuru Kusumoto, Takuya Inoue, Gentaro Watanabe et al.

Recomputation algorithms collectively refer to a family of methods that aims to reduce the memory consumption of the backpropagation by selectively discarding the intermediate results of the forward propagation and recomputing the discarded results as needed. In this paper, we will propose a novel and efficient recomputation method that can be applied to a wider range of neural nets than previous methods. We use the language of graph theory to formalize the general recomputation problem of minimizing the computational overhead under a fixed memory budget constraint, and provide a dynamic programming solution to the problem. Our method can reduce the peak memory consumption on various benchmark networks by 36%~81%, which outperforms the reduction achieved by other methods.

Amir Najafi, Shin-ichi Maeda, Masanori Koyama et al.

What is the role of unlabeled data in an inference problem, when the presumed underlying distribution is adversarially perturbed? To provide a concrete answer to this question, this paper unifies two major learning frameworks: Semi-Supervised Learning (SSL) and Distributionally Robust Learning (DRL). We develop a generalization theory for our framework based on a number of novel complexity measures, such as an adversarial extension of Rademacher complexity and its semi-supervised analogue. Moreover, our analysis is able to quantify the role of unlabeled data in the generalization under a more general condition compared to the existing theoretical works in SSL. Based on our framework, we also present a hybrid of DRL and EM algorithms that has a guaranteed convergence rate. When implemented with deep neural networks, our method shows a comparable performance to those of the state-of-the-art on a number of real-world benchmark datasets.

Yoshihiro Nagano, Shoichiro Yamaguchi, Yasuhiro Fujita et al.

Hyperbolic space is a geometry that is known to be well-suited for representation learning of data with an underlying hierarchical structure. In this paper, we present a novel hyperbolic distribution called \textit{pseudo-hyperbolic Gaussian}, a Gaussian-like distribution on hyperbolic space whose density can be evaluated analytically and differentiated with respect to the parameters. Our distribution enables the gradient-based learning of the probabilistic models on hyperbolic space that could never have been considered before. Also, we can sample from this hyperbolic probability distribution without resorting to auxiliary means like rejection sampling. As applications of our distribution, we develop a hyperbolic-analog of variational autoencoder and a method of probabilistic word embedding on hyperbolic space. We demonstrate the efficacy of our distribution on various datasets including MNIST, Atari 2600 Breakout, and WordNet.

Katsuhiko Ishiguro, Shin-ichi Maeda, Masanori Koyama

Graph Neural Network (GNN) is a popular architecture for the analysis of chemical molecules, and it has numerous applications in material and medicinal science. Current lines of GNNs developed for molecular analysis, however, do not fit well on the training set, and their performance does not scale well with the complexity of the network. In this paper, we propose an auxiliary module to be attached to a GNN that can boost the representation power of the model without hindering with the original GNN architecture. Our auxiliary module can be attached to a wide variety of GNNs, including those that are used commonly in biochemical applications. With our auxiliary architecture, the performances of many GNNs used in practice improve more consistently, achieving the state-of-the-art performance on popular molecular graph datasets.

Masaki Saito, Shunta Saito, Masanori Koyama et al.

Training of Generative Adversarial Network (GAN) on a video dataset is a challenge because of the sheer size of the dataset and the complexity of each observation. In general, the computational cost of training GAN scales exponentially with the resolution. In this study, we present a novel memory efficient method of unsupervised learning of high-resolution video dataset whose computational cost scales only linearly with the resolution. We achieve this by designing the generator model as a stack of small sub-generators and training the model in a specific way. We train each sub-generator with its own specific discriminator. At the time of the training, we introduce between each pair of consecutive sub-generators an auxiliary subsampling layer that reduces the frame-rate by a certain ratio. This procedure can allow each sub-generator to learn the distribution of the video at different levels of resolution. We also need only a few GPUs to train a highly complex generator that far outperforms the predecessor in terms of inception scores.

Takeru Miyato, Toshiki Kataoka, Masanori Koyama et al.

One of the challenges in the study of generative adversarial networks is the instability of its training. In this paper, we propose a novel weight normalization technique called spectral normalization to stabilize the training of the discriminator. Our new normalization technique is computationally light and easy to incorporate into existing implementations. We tested the efficacy of spectral normalization on CIFAR10, STL-10, and ILSVRC2012 dataset, and we experimentally confirmed that spectrally normalized GANs (SN-GANs) is capable of generating images of better or equal quality relative to the previous training stabilization techniques.

Takeru Miyato, Masanori Koyama

We propose a novel, projection based way to incorporate the conditional information into the discriminator of GANs that respects the role of the conditional information in the underlining probabilistic model. This approach is in contrast with most frameworks of conditional GANs used in application today, which use the conditional information by concatenating the (embedded) conditional vector to the feature vectors. With this modification, we were able to significantly improve the quality of the class conditional image generation on ILSVRC2012 (ImageNet) 1000-class image dataset from the current state-of-the-art result, and we achieved this with a single pair of a discriminator and a generator. We were also able to extend the application to super-resolution and succeeded in producing highly discriminative super-resolution images. This new structure also enabled high quality category transformation based on parametric functional transformation of conditional batch normalization layers in the generator.

Takeru Miyato, Shin-ichi Maeda, Masanori Koyama et al.

We propose a new regularization method based on virtual adversarial loss: a new measure of local smoothness of the conditional label distribution given input. Virtual adversarial loss is defined as the robustness of the conditional label distribution around each input data point against local perturbation. Unlike adversarial training, our method defines the adversarial direction without label information and is hence applicable to semi-supervised learning. Because the directions in which we smooth the model are only "virtually" adversarial, we call our method virtual adversarial training (VAT). The computational cost of VAT is relatively low. For neural networks, the approximated gradient of virtual adversarial loss can be computed with no more than two pairs of forward- and back-propagations. In our experiments, we applied VAT to supervised and semi-supervised learning tasks on multiple benchmark datasets. With a simple enhancement of the algorithm based on the entropy minimization principle, our VAT achieves state-of-the-art performance for semi-supervised learning tasks on SVHN and CIFAR-10.

Takeru Miyato, Shin-ichi Maeda, Masanori Koyama et al.

We propose local distributional smoothness (LDS), a new notion of smoothness for statistical model that can be used as a regularization term to promote the smoothness of the model distribution. We named the LDS based regularization as virtual adversarial training (VAT). The LDS of a model at an input datapoint is defined as the KL-divergence based robustness of the model distribution against local perturbation around the datapoint. VAT resembles adversarial training, but distinguishes itself in that it determines the adversarial direction from the model distribution alone without using the label information, making it applicable to semi-supervised learning. The computational cost for VAT is relatively low. For neural network, the approximated gradient of the LDS can be computed with no more than three pairs of forward and back propagations. When we applied our technique to supervised and semi-supervised learning for the MNIST dataset, it outperformed all the training methods other than the current state of the art method, which is based on a highly advanced generative model. We also applied our method to SVHN and NORB, and confirmed our method's superior performance over the current state of the art semi-supervised method applied to these datasets.

Sotetsu Koyamada, Yumi Shikauchi, Ken Nakae et al.

As a technology to read brain states from measurable brain activities, brain decoding are widely applied in industries and medical sciences. In spite of high demands in these applications for a universal decoder that can be applied to all individuals simultaneously, large variation in brain activities across individuals has limited the scope of many studies to the development of individual-specific decoders. In this study, we used deep neural network (DNN), a nonlinear hierarchical model, to construct a subject-transfer decoder. Our decoder is the first successful DNN-based subject-transfer decoder. When applied to a large-scale functional magnetic resonance imaging (fMRI) database, our DNN-based decoder achieved higher decoding accuracy than other baseline methods, including support vector machine (SVM). In order to analyze the knowledge acquired by this decoder, we applied principal sensitivity analysis (PSA) to the decoder and visualized the discriminative features that are common to all subjects in the dataset. Our PSA successfully visualized the subject-independent features contributing to the subject-transferability of the trained decoder.

Sotetsu Koyamada, Masanori Koyama, Ken Nakae et al.

We present a novel algorithm (Principal Sensitivity Analysis; PSA) to analyze the knowledge of the classifier obtained from supervised machine learning techniques. In particular, we define principal sensitivity map (PSM) as the direction on the input space to which the trained classifier is most sensitive, and use analogously defined k-th PSM to define a basis for the input space. We train neural networks with artificial data and real data, and apply the algorithm to the obtained supervised classifiers. We then visualize the PSMs to demonstrate the PSA's ability to decompose the knowledge acquired by the trained classifiers.