Issei Sato

Kento Nozawa, Issei Sato · ibm-research

Representation learning enables us to automatically extract generic feature representations from a dataset to solve another machine learning task. Recently, extracted feature representations by a representation learning algorithm and a simple predictor have exhibited state-of-the-art performance on several machine learning tasks. Despite its remarkable progress, there exist various ways to evaluate representation learning algorithms depending on the application because of the flexibility of representation learning. To understand the current representation learning, we review evaluation methods of representation learning algorithms and theoretical analyses. On the basis of our evaluation survey, we also discuss the future direction of representation learning. Note that this survey is the extended version of Nozawa and Sato (2022).

Tokio Kajitsuka, Issei Sato

Existing analyses of the expressive capacity of Transformer models have required excessively deep layers for data memorization, leading to a discrepancy with the Transformers actually used in practice. This is primarily due to the interpretation of the softmax function as an approximation of the hardmax function. By clarifying the connection between the softmax function and the Boltzmann operator, we prove that a single layer of self-attention with low-rank weight matrices possesses the capability to perfectly capture the context of an entire input sequence. As a consequence, we show that one-layer and single-head Transformers have a memorization capacity for finite samples, and that Transformers consisting of one self-attention layer with two feed-forward neural networks are universal approximators for continuous permutation equivariant functions on a compact domain.

Futoshi Futami, Tomoharu Iwata, Naonori Ueda et al.

Bayesian deep learning plays an important role especially for its ability evaluating epistemic uncertainty (EU). Due to computational complexity issues, approximation methods such as variational inference (VI) have been used in practice to obtain posterior distributions and their generalization abilities have been analyzed extensively, for example, by PAC-Bayesian theory; however, little analysis exists on EU, although many numerical experiments have been conducted on it. In this study, we analyze the EU of supervised learning in approximate Bayesian inference by focusing on its excess risk. First, we theoretically show the novel relations between generalization error and the widely used EU measurements, such as the variance and mutual information of predictive distribution, and derive their convergence behaviors. Next, we clarify how the objective function of VI regularizes the EU. With this analysis, we propose a new objective function for VI that directly controls the prediction performance and the EU based on the PAC-Bayesian theory. Numerical experiments show that our algorithm significantly improves the EU evaluation over the existing VI methods.

Keitaro Sakamoto, Issei Sato

The lottery ticket hypothesis (LTH) has attracted attention because it can explain why over-parameterized models often show high generalization ability. It is known that when we use iterative magnitude pruning (IMP), which is an algorithm to find sparse networks with high generalization ability that can be trained from the initial weights independently, called winning tickets, the initial large learning rate does not work well in deep neural networks such as ResNet. However, since the initial large learning rate generally helps the optimizer to converge to flatter minima, we hypothesize that the winning tickets have relatively sharp minima, which is considered a disadvantage in terms of generalization ability. In this paper, we confirm this hypothesis and show that the PAC-Bayesian theory can provide an explicit understanding of the relationship between LTH and generalization behavior. On the basis of our experimental findings that flatness is useful for improving accuracy and robustness to label noise and that the distance from the initial weights is deeply involved in winning tickets, we offer the PAC-Bayes bound using a spike-and-slab distribution to analyze winning tickets. Finally, we revisit existing algorithms for finding winning tickets from a PAC-Bayesian perspective and provide new insights into these methods.

Takeshi Koshizuka, Issei Sato

Population dynamics is the study of temporal and spatial variation in the size of populations of organisms and is a major part of population ecology. One of the main difficulties in analyzing population dynamics is that we can only obtain observation data with coarse time intervals from fixed-point observations due to experimental costs or measurement constraints. Recently, modeling population dynamics by using continuous normalizing flows (CNFs) and dynamic optimal transport has been proposed to infer the sample trajectories from a fixed-point observed population. While the sample behavior in CNFs is deterministic, the actual sample in biological systems moves in an essentially random yet directional manner. Moreover, when a sample moves from point A to point B in dynamical systems, its trajectory typically follows the principle of least action in which the corresponding action has the smallest possible value. To satisfy these requirements of the sample trajectories, we formulate the Lagrangian Schrödinger bridge (LSB) problem and propose to solve it approximately by modeling the advection-diffusion process with regularized neural SDE. We also develop a model architecture that enables faster computation of the loss function. Experimental results show that the proposed method can efficiently approximate the population-level dynamics even for high-dimensional data and that using the prior knowledge introduced by the Lagrangian enables us to estimate the sample-level dynamics with stochastic behavior.

Takahiro Suzuki, Shouhei Hanaoka, Issei Sato

A computer-aided detection (CAD) system based on machine learning is expected to assist radiologists in making a diagnosis. It is desirable to build CAD systems for the various types of diseases accumulating daily in a hospital. An obstacle in developing a CAD system for a disease is that the number of medical images is typically too small to improve the performance of the machine learning model. In this paper, we aim to explore ways to address this problem through a sim2real transfer approach in medical image fields. To build a platform to evaluate the performance of sim2real transfer methods in the field of medical imaging, we construct a benchmark dataset that consists of $101$ chest X-images with difficult-to-identify pneumonia lesions judged by an experienced radiologist and a simulator based on fractal Perlin noise and the X-ray principle for generating pseudo pneumonia lesions. We then develop a novel domain randomization method, called Goldilocks-curriculum domain randomization (GDR) and evaluate our method in this platform.

Akiyoshi Tomihari, Issei Sato

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

Takeshi Koshizuka, Masahiro Fujisawa, Yusuke Tanaka et al.

In this paper, we explores the expressivity and trainability of the Fourier Neural Operator (FNO). We establish a mean-field theory for the FNO, analyzing the behavior of the random FNO from an edge of chaos perspective. Our investigation into the expressivity of a random FNO involves examining the ordered-chaos phase transition of the network based on the weight distribution. This phase transition demonstrates characteristics unique to the FNO, induced by mode truncation, while also showcasing similarities to those of densely connected networks. Furthermore, we identify a connection between expressivity and trainability: the ordered and chaotic phases correspond to regions of vanishing and exploding gradients, respectively. This finding provides a practical prerequisite for the stable training of the FNO. Our experimental results corroborate our theoretical findings.

Akiyoshi Tomihari, Issei Sato

Transformers are challenging to optimize with SGD and typically require adaptive optimizers such as Adam. However, the reasons behind the superior performance of Adam over SGD remain unclear. In this study, we investigate the optimization of transformers by focusing on gradient heterogeneity, defined as the disparity in gradient norms among parameters. Our analysis shows that gradient heterogeneity hinders gradient-based optimization, including SGD, while sign-based optimization, a simplified variant of Adam, is less affected. We further examine gradient heterogeneity in transformers and show that it is influenced by the placement of layer normalization. Experimental results from fine-tuning transformers in both NLP and vision domains validate our theoretical analyses. This study provides insights into the optimization challenges of transformers and offers guidance for designing future optimization algorithms. Code is available at https://github.com/tom4649/gradient-heterogeneity.

Tokio Kajitsuka, Issei Sato

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

Kevin Xu, Issei Sato

Chain-of-Thought (CoT) elicits reasoning in large language models by explicitly generating intermediate steps in natural language. In contrast, Latent Thought in looped models operates directly in the continuous latent space, enabling computation beyond discrete linguistic representations. While both approaches exploit iterative computation, their comparative capabilities remain underexplored. In this work, we present a formal analysis showing that Latent Thought in Looped Transformers enables parallel computation, which is more efficient than the inherently sequential process of CoT. In contrast, CoT leverages stochastic decoding to approximate solutions to problems where exact computation is intractable. These separations suggest the tasks for which depth-driven recursion is more suitable, thereby offering practical guidance for choosing between reasoning paradigms. Code is available at https://github.com/kevin671/cot-vs-loop.

Shun Sato, Issei Sato

Symbolic regression aims to discover mathematical equations that fit given numerical data. It has been applied in various fields of scientific research, such as producing human-readable expressions that explain physical phenomena. Recently, Neural symbolic regression (NSR) methods that involve Transformers pre-trained on large-scale synthetic datasets have gained attention. While these methods offer advantages such as short inference time, they suffer from low performance, particularly when the number of input variables is large. In this study, we hypothesized that this limitation stems from the memorization bias of Transformers in symbolic regression. We conducted a quantitative evaluation of this bias in Transformers using a synthetic dataset and found that Transformers rarely generate expressions not present in the training data. Additional theoretical analysis reveals that this bias arises from the Transformer's inability to construct expressions compositionally while verifying their numerical validity. We finally examined if tailoring test-time strategies can lead to reduced memorization bias and better performance. We empirically demonstrate that providing additional information to the model at test time can significantly mitigate memorization bias. On the other hand, we also find that reducing memorization bias does not necessarily correlate with improved performance. These findings contribute to a deeper understanding of the limitations of NSR approaches and offer a foundation for designing more robust, generalizable symbolic regression methods. Code is available at https://github.com/Shun-0922/Mem-Bias-NSR .

Naoya Hasegawa, Issei Sato

Recognition problems in long-tailed data, in which the sample size per class is heavily skewed, have gained importance because the distribution of the sample size per class in a dataset is generally exponential unless the sample size is intentionally adjusted. Various methods have been devised to address these problems.Recently, weight balancing, which combines well-known classical regularization techniques with two-stage training, has been proposed. Despite its simplicity, it is known for its high performance compared with existing methods devised in various ways. However, there is a lack of understanding as to why this method is effective for long-tailed data. In this study, we analyze weight balancing by focusing on neural collapse and the cone effect at each training stage and found that it can be decomposed into an increase in Fisher's discriminant ratio of the feature extractor caused by weight decay and cross entropy loss and implicit logit adjustment caused by weight decay and class-balanced loss. Our analysis enables the training method to be further simplified by reducing the number of training stages to one while increasing accuracy. Code is available at https://github.com/HN410/Exploring-Weight-Balancing-on-Long-Tailed-Recognition-Problem.

Zeke Xie, Fengxiang He, Shaopeng Fu et al.

Deep learning is often criticized by two serious issues which rarely exist in natural nervous systems: overfitting and catastrophic forgetting. It can even memorize randomly labelled data, which has little knowledge behind the instance-label pairs. When a deep network continually learns over time by accommodating new tasks, it usually quickly overwrites the knowledge learned from previous tasks. Referred to as the {\it neural variability}, it is well-known in neuroscience that human brain reactions exhibit substantial variability even in response to the same stimulus. This mechanism balances accuracy and plasticity/flexibility in the motor learning of natural nervous systems. Thus it motivates us to design a similar mechanism named {\it artificial neural variability} (ANV), which helps artificial neural networks learn some advantages from ``natural'' neural networks. We rigorously prove that ANV plays as an implicit regularizer of the mutual information between the training data and the learned model. This result theoretically guarantees ANV a strictly improved generalizability, robustness to label noise, and robustness to catastrophic forgetting. We then devise a {\it neural variable risk minimization} (NVRM) framework and {\it neural variable optimizers} to achieve ANV for conventional network architectures in practice. The empirical studies demonstrate that NVRM can effectively relieve overfitting, label noise memorization, and catastrophic forgetting at negligible costs. \footnote{Code: \url{https://github.com/zeke-xie/artificial-neural-variability-for-deep-learning}.

Shota Fujikawa, Issei Sato

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

Shuo Wang, Issei Sato

Deep neural networks are being increasingly implemented throughout society in recent years. It is useful to identify which parameters trigger misclassification in diagnosing undesirable model behaviors. The concept of parameter saliency is proposed and used to diagnose convolutional neural networks (CNNs) by ranking convolution filters that may have caused misclassification on the basis of parameter saliency. It is also shown that fine-tuning the top ranking salient filters efficiently corrects misidentification on ImageNet. However, there is still a knowledge gap in terms of understanding why parameter saliency ranking can find the filters inducing misidentification. In this work, we attempt to bridge the gap by analyzing parameter saliency ranking from a statistical viewpoint, namely, extreme value theory. We first show that the existing work implicitly assumes that the gradient norm computed for each filter follows a normal distribution. Then, we clarify the relationship between parameter saliency and the score based on the peaks-over-threshold (POT) method, which is often used to model extreme values. Finally, we reformulate parameter saliency in terms of the POT method, where this reformulation is regarded as statistical anomaly detection and does not require the implicit assumptions of the existing parameter-saliency formulation. Our experimental results demonstrate that our reformulation can detect malicious filters as well. Furthermore, we show that the existing parameter saliency method exhibits a bias against the depth of layers in deep neural networks. In particular, this bias has the potential to inhibit the discovery of filters that cause misidentification in situations where domain shift occurs. In contrast, parameter saliency based on POT shows less of this bias.

Naoya Hasegawa, Issei Sato

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

Keitaro Sakamoto, Issei Sato

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

Yuto Tanaka, Issei Sato

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

Keitaro Sakamoto, Issei Sato

End-to-end (E2E) training, optimizing the entire model through error backpropagation, fundamentally supports the advancements of deep learning. Despite its high performance, E2E training faces the problems of memory consumption, parallel computing, and discrepancy with the functionalities of the actual brain. Various alternative methods have been proposed to overcome these difficulties; however, no one can yet match the performance of E2E training, thereby falling short in practicality. Furthermore, there is no deep understanding regarding differences in the trained model properties beyond the performance gap. In this paper, we reconsider why E2E training demonstrates a superior performance through a comparison with layer-wise training, a non-E2E method that locally sets errors. On the basis of the observation that E2E training has an advantage in propagating input information, we analyze the information plane dynamics of intermediate representations based on the Hilbert-Schmidt independence criterion (HSIC). The results of our normalized HSIC value analysis reveal the E2E training ability to exhibit different information dynamics across layers, in addition to efficient information propagation. Furthermore, we show that this layer-role differentiation leads to the final representation following the information bottleneck principle. It suggests the need to consider the cooperative interactions between layers, not just the final layer when analyzing the information bottleneck of deep learning.

Kevin Xu, Issei Sato

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

Jinya Sakurai, Issei Sato

The proliferation of Text-to-Image (T2I) models has revolutionized content creation, providing powerful tools for diverse applications ranging from artistic expression to educational material development and marketing. Despite these technological advancements, significant ethical concerns arise from these models' reliance on large-scale datasets that often contain inherent societal biases. These biases are further amplified when AI-generated content is included in training data, potentially reinforcing and perpetuating stereotypes in the generated outputs. In this paper, we introduce FairT2I, a novel framework that harnesses large language models to detect and mitigate social biases in T2I generation. Our framework comprises two key components: (1) an LLM-based bias detection module that identifies potential social biases in generated images based on text prompts, and (2) an attribute rebalancing module that fine-tunes sensitive attributes within the T2I model to mitigate identified biases. Our extensive experiments across various T2I models and datasets show that FairT2I can significantly reduce bias while maintaining high-quality image generation. We conducted both qualitative user studies and quantitative non-parametric analyses in the generated image feature space, building upon the occupational dataset introduced in the Stable Bias study. Our results show that FairT2I successfully mitigates social biases and enhances the diversity of sensitive attributes in generated images. We further demonstrate, using the P2 dataset, that our framework can detect subtle biases that are challenging for human observers to perceive, extending beyond occupation-related prompts. On the basis of these findings, we introduce a new benchmark dataset for evaluating bias in T2I models.

Takeshi Koshizuka, Issei Sato

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

Keitaro Sakamoto, Issei Sato

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

Shuo Wang, Issei Sato

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

Daichi Hayakawa, Issei Sato

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

Soma Yokoi, Issei Sato

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

Mingcheng Hou, Issei Sato

The prototypical network is a prototype classifier based on meta-learning and is widely used for few-shot learning because it classifies unseen examples by constructing class-specific prototypes without adjusting hyper-parameters during meta-testing. Interestingly, recent research has attracted a lot of attention, showing that training a new linear classifier, which does not use a meta-learning algorithm, performs comparably with the prototypical network. However, the training of a new linear classifier requires the retraining of the classifier every time a new class appears. In this paper, we analyze how a prototype classifier works equally well without training a new linear classifier or meta-learning. We experimentally find that directly using the feature vectors, which is extracted by using standard pre-trained models to construct a prototype classifier in meta-testing, does not perform as well as the prototypical network and training new linear classifiers on the feature vectors of pre-trained models. Thus, we derive a novel generalization bound for a prototypical classifier and show that the transformation of a feature vector can improve the performance of prototype classifiers. We experimentally investigate several normalization methods for minimizing the derived bound and find that the same performance can be obtained by using the L2 normalization and minimizing the ratio of the within-class variance to the between-class variance without training a new classifier or meta-learning.

Seiya Tokui, Issei Sato

We propose a framework to analyze how multivariate representations disentangle ground-truth generative factors. A quantitative analysis of disentanglement has been based on metrics designed to compare how one variable explains each generative factor. Current metrics, however, may fail to detect entanglement that involves more than two variables, e.g., representations that duplicate and rotate generative factors in high dimensional spaces. In this work, we establish a framework to analyze information sharing in a multivariate representation with Partial Information Decomposition and propose a new disentanglement metric. This framework enables us to understand disentanglement in terms of uniqueness, redundancy, and synergy. We develop an experimental protocol to assess how increasingly entangled representations are evaluated with each metric and confirm that the proposed metric correctly responds to entanglement. Through experiments on variational autoencoders, we find that models with similar disentanglement scores have a variety of characteristics in entanglement, for each of which a distinct strategy may be required to obtain a disentangled representation.

Futoshi Futami, Tomoharu Iwata, Naonori Ueda et al.

Bayesian model averaging, obtained as the expectation of a likelihood function by a posterior distribution, has been widely used for prediction, evaluation of uncertainty, and model selection. Various approaches have been developed to efficiently capture the information in the posterior distribution; one such approach is the optimization of a set of models simultaneously with interaction to ensure the diversity of the individual models in the same way as ensemble learning. A representative approach is particle variational inference (PVI), which uses an ensemble of models as an empirical approximation for the posterior distribution. PVI iteratively updates each model with a repulsion force to ensure the diversity of the optimized models. However, despite its promising performance, a theoretical understanding of this repulsion and its association with the generalization ability remains unclear. In this paper, we tackle this problem in light of PAC-Bayesian analysis. First, we provide a new second-order Jensen inequality, which has the repulsion term based on the loss function. Thanks to the repulsion term, it is tighter than the standard Jensen inequality. Then, we derive a novel generalization error bound and show that it can be reduced by enhancing the diversity of models. Finally, we derive a new PVI that optimizes the generalization error bound directly. Numerical experiments demonstrate that the performance of the proposed PVI compares favorably with existing methods in the experiment.

Naoki Kobayashi, Taro Sekiyama, Issei Sato et al.

We propose a novel framework of program and invariant synthesis called neural network-guided synthesis. We first show that, by suitably designing and training neural networks, we can extract logical formulas over integers from the weights and biases of the trained neural networks. Based on the idea, we have implemented a tool to synthesize formulas from positive/negative examples and implication constraints, and obtained promising experimental results. We also discuss two applications of our synthesis method. One is the use of our tool for qualifier discovery in the framework of ICE-learning-based CHC solving, which can in turn be applied to program verification and inductive invariant synthesis. Another application is to a new program development framework called oracle-based programming, which is a neural-network-guided variation of Solar-Lezama's program synthesis by sketching.

Kenshin Abe, Takanori Maehara, Issei Sato

We study the problem of modeling a binary operation that satisfies some algebraic requirements. We first construct a neural network architecture for Abelian group operations and derive a universal approximation property. Then, we extend it to Abelian semigroup operations using the characterization of associative symmetric polynomials. Both models take advantage of the analytic invertibility of invertible neural networks. For each case, by repeating the binary operations, we can represent a function for multiset input thanks to the algebraic structure. Naturally, our multiset architecture has size-generalization ability, which has not been obtained in existing methods. Further, we present modeling the Abelian group operation itself is useful in a word analogy task. We train our models over fixed word embeddings and demonstrate improved performance over the original word2vec and another naive learning method.

Kento Nozawa, Issei Sato

Instance discriminative self-supervised representation learning has been attracted attention thanks to its unsupervised nature and informative feature representation for downstream tasks. In practice, it commonly uses a larger number of negative samples than the number of supervised classes. However, there is an inconsistency in the existing analysis; theoretically, a large number of negative samples degrade classification performance on a downstream supervised task, while empirically, they improve the performance. We provide a novel framework to analyze this empirical result regarding negative samples using the coupon collector's problem. Our bound can implicitly incorporate the supervised loss of the downstream task in the self-supervised loss by increasing the number of negative samples. We confirm that our proposed analysis holds on real-world benchmark datasets.

Nan Lu, Shida Lei, Gang Niu et al.

To cope with high annotation costs, training a classifier only from weakly supervised data has attracted a great deal of attention these days. Among various approaches, strengthening supervision from completely unsupervised classification is a promising direction, which typically employs class priors as the only supervision and trains a binary classifier from unlabeled (U) datasets. While existing risk-consistent methods are theoretically grounded with high flexibility, they can learn only from two U sets. In this paper, we propose a new approach for binary classification from $m$ U-sets for $m\ge2$. Our key idea is to consider an auxiliary classification task called surrogate set classification (SSC), which is aimed at predicting from which U set each observed data is drawn. SSC can be solved by a standard (multi-class) classification method, and we use the SSC solution to obtain the final binary classifier through a certain linear-fractional transformation. We built our method in a flexible and efficient end-to-end deep learning framework and prove it to be classifier-consistent. Through experiments, we demonstrate the superiority of our proposed method over state-of-the-art methods.

Zeke Xie, Zhiqiang Xu, Jingzhao Zhang et al.

Weight decay is a simple yet powerful regularization technique that has been very widely used in training of deep neural networks (DNNs). While weight decay has attracted much attention, previous studies fail to discover some overlooked pitfalls on large gradient norms resulted by weight decay. In this paper, we discover that, weight decay can unfortunately lead to large gradient norms at the final phase (or the terminated solution) of training, which often indicates bad convergence and poor generalization. To mitigate the gradient-norm-centered pitfalls, we present the first practical scheduler for weight decay, called the Scheduled Weight Decay (SWD) method that can dynamically adjust the weight decay strength according to the gradient norm and significantly penalize large gradient norms during training. Our experiments also support that SWD indeed mitigates large gradient norms and often significantly outperforms the conventional constant weight decay strategy for Adaptive Moment Estimation (Adam).

Zhenghang Cui, Issei Sato

Noisy pairwise comparison feedback has been incorporated to improve the overall query complexity of interactively learning binary classifiers. The \textit{positivity comparison oracle} is used to provide feedback on which is more likely to be positive given a pair of data points. Because it is impossible to infer accurate labels using this oracle alone \textit{without knowing the classification threshold}, existing methods still rely on the traditional \textit{explicit labeling oracle}, which directly answers the label given a data point. Existing methods conduct sorting on all data points and use explicit labeling oracle to find the classification threshold. The current methods, however, have two drawbacks: (1) they needs unnecessary sorting for label inference; (2) quick sort is naively adapted to noisy feedback and negatively affects practical performance. In order to avoid this inefficiency and acquire information of the classification threshold, we propose a new pairwise comparison oracle concerning uncertainties. This oracle receives two data points as input and answers which one has higher uncertainty. We then propose an efficient adaptive labeling algorithm using the proposed oracle and the positivity comparison oracle. In addition, we also address the situation where the labeling budget is insufficient compared to the dataset size, which can be dealt with by plugging the proposed algorithm into an active learning algorithm. Furthermore, we confirm the feasibility of the proposed oracle and the performance of the proposed algorithm theoretically and empirically.

Takahiro Mimori, Keiko Sasada, Hirotaka Matsui et al.

We propose an evaluation framework for class probability estimates (CPEs) in the presence of label uncertainty, which is commonly observed as diagnosis disagreement between experts in the medical domain. We also formalize evaluation metrics for higher-order statistics, including inter-rater disagreement, to assess predictions on label uncertainty. Moreover, we propose a novel post-hoc method called $alpha$-calibration, that equips neural network classifiers with calibrated distributions over CPEs. Using synthetic experiments and a large-scale medical imaging application, we show that our approach significantly enhances the reliability of uncertainty estimates: disagreement probabilities and posterior CPEs.

Zeke Xie, Xinrui Wang, Huishuai Zhang et al.

Adaptive Moment Estimation (Adam), which combines Adaptive Learning Rate and Momentum, would be the most popular stochastic optimizer for accelerating the training of deep neural networks. However, it is empirically known that Adam often generalizes worse than Stochastic Gradient Descent (SGD). The purpose of this paper is to unveil the mystery of this behavior in the diffusion theoretical framework. Specifically, we disentangle the effects of Adaptive Learning Rate and Momentum of the Adam dynamics on saddle-point escaping and flat minima selection. We prove that Adaptive Learning Rate can escape saddle points efficiently, but cannot select flat minima as SGD does. In contrast, Momentum provides a drift effect to help the training process pass through saddle points, and almost does not affect flat minima selection. This partly explains why SGD (with Momentum) generalizes better, while Adam generalizes worse but converges faster. Furthermore, motivated by the analysis, we design a novel adaptive optimization framework named Adaptive Inertia, which uses parameter-wise adaptive inertia to accelerate the training and provably favors flat minima as well as SGD. Our extensive experiments demonstrate that the proposed adaptive inertia method can generalize significantly better than SGD and conventional adaptive gradient methods.

Kei Mukaiyama, Issei Sato, Masashi Sugiyama

The prototypical network (ProtoNet) is a few-shot learning framework that performs metric learning and classification using the distance to prototype representations of each class. It has attracted a great deal of attention recently since it is simple to implement, highly extensible, and performs well in experiments. However, it only takes into account the mean of the support vectors as prototypes and thus it performs poorly when the support set has high variance. In this paper, we propose to combine ProtoNet with local Fisher discriminant analysis to reduce the local within-class covariance and increase the local between-class covariance of the support set. We show the usefulness of the proposed method by theoretically providing an expected risk bound and empirically demonstrating its superior classification accuracy on miniImageNet and tieredImageNet.

Masahiro Fujisawa, Takeshi Teshima, Issei Sato et al.

Approximate Bayesian computation (ABC) is a likelihood-free inference method that has been employed in various applications. However, ABC can be sensitive to outliers if a data discrepancy measure is chosen inappropriately. In this paper, we propose to use a nearest-neighbor-based $γ$-divergence estimator as a data discrepancy measure. We show that our estimator possesses a suitable theoretical robustness property called the redescending property. In addition, our estimator enjoys various desirable properties such as high flexibility, asymptotic unbiasedness, almost sure convergence, and linear-time computational complexity. Through experiments, we demonstrate that our method achieves significantly higher robustness than existing discrepancy measures.

Han Bao, Takuya Shimada, Liyuan Xu et al.

Similarity learning is a general problem to elicit useful representations by predicting the relationship between a pair of patterns. This problem is related to various important preprocessing tasks such as metric learning, kernel learning, and contrastive learning. A classifier built upon the representations is expected to perform well in downstream classification; however, little theory has been given in literature so far and thereby the relationship between similarity and classification has remained elusive. Therefore, we tackle a fundamental question: can similarity information provably leads a model to perform well in downstream classification? In this paper, we reveal that a product-type formulation of similarity learning is strongly related to an objective of binary classification. We further show that these two different problems are explicitly connected by an excess risk bound. Consequently, our results elucidate that similarity learning is capable of solving binary classification by directly eliciting a decision boundary.

Yuki Koyama, Issei Sato, Masataka Goto

Visual design tasks often involve tuning many design parameters. For example, color grading of a photograph involves many parameters, some of which non-expert users might be unfamiliar with. We propose a novel user-in-the-loop optimization method that allows users to efficiently find an appropriate parameter set by exploring such a high-dimensional design space through much easier two-dimensional search subtasks. This method, called sequential plane search, is based on Bayesian optimization to keep necessary queries to users as few as possible. To help users respond to plane-search queries, we also propose using a gallery-based interface that provides options in the two-dimensional subspace arranged in an adaptive grid view. We call this interactive framework Sequential Gallery since users sequentially select the best option from the options provided by the interface. Our experiment with synthetic functions shows that our sequential plane search can find satisfactory solutions in fewer iterations than baselines. We also conducted a preliminary user study, results of which suggest that novices can effectively complete search tasks with Sequential Gallery in a photo-enhancement scenario.

Hideaki Imamura, Nontawat Charoenphakdee, Futoshi Futami et al.

The Gaussian process bandit is a problem in which we want to find a maximizer of a black-box function with the minimum number of function evaluations. If the black-box function varies with time, then time-varying Bayesian optimization is a promising framework. However, a drawback with current methods is in the assumption that the evaluation time for every observation is constant, which can be unrealistic for many practical applications, e.g., recommender systems and environmental monitoring. As a result, the performance of current methods can be degraded when this assumption is violated. To cope with this problem, we propose a novel time-varying Bayesian optimization algorithm that can effectively handle the non-constant evaluation time. Furthermore, we theoretically establish a regret bound of our algorithm. Our bound elucidates that a pattern of the evaluation time sequence can hugely affect the difficulty of the problem. We also provide experimental results to validate the practical effectiveness of the proposed method.

Takeshi Teshima, Issei Sato, Masashi Sugiyama

We study few-shot supervised domain adaptation (DA) for regression problems, where only a few labeled target domain data and many labeled source domain data are available. Many of the current DA methods base their transfer assumptions on either parametrized distribution shift or apparent distribution similarities, e.g., identical conditionals or small distributional discrepancies. However, these assumptions may preclude the possibility of adaptation from intricately shifted and apparently very different distributions. To overcome this problem, we propose mechanism transfer, a meta-distributional scenario in which a data generating mechanism is invariant among domains. This transfer assumption can accommodate nonparametric shifts resulting in apparently different distributions while providing a solid statistical basis for DA. We take the structural equations in causal modeling as an example and propose a novel DA method, which is shown to be useful both theoretically and experimentally. Our method can be seen as the first attempt to fully leverage the structural causal models for DA.

Zeke Xie, Issei Sato, Masashi Sugiyama

Stochastic Gradient Descent (SGD) and its variants are mainstream methods for training deep networks in practice. SGD is known to find a flat minimum that often generalizes well. However, it is mathematically unclear how deep learning can select a flat minimum among so many minima. To answer the question quantitatively, we develop a density diffusion theory (DDT) to reveal how minima selection quantitatively depends on the minima sharpness and the hyperparameters. To the best of our knowledge, we are the first to theoretically and empirically prove that, benefited from the Hessian-dependent covariance of stochastic gradient noise, SGD favors flat minima exponentially more than sharp minima, while Gradient Descent (GD) with injected white noise favors flat minima only polynomially more than sharp minima. We also reveal that either a small learning rate or large-batch training requires exponentially many iterations to escape from minima in terms of the ratio of the batch size and learning rate. Thus, large-batch training cannot search flat minima efficiently in a realistic computational time.

Soma Yokoi, Issei Sato

The current interpretation of stochastic gradient descent (SGD) as a stochastic process lacks generality in that its numerical scheme restricts continuous-time dynamics as well as the loss function and the distribution of gradient noise. We introduce a simplified scheme with milder conditions that flexibly interprets SGD as a discrete-time approximation of an Ito process. The scheme also works as a common foundation of SGD and stochastic gradient Langevin dynamics (SGLD), providing insights into their asymptotic properties. We investigate the convergence of SGD with biased gradient in terms of the equilibrium mode and the overestimation problem of the second moment of SGLD.

Zhenghang Cui, Nontawat Charoenphakdee, Issei Sato et al.

Learning from triplet comparison data has been extensively studied in the context of metric learning, where we want to learn a distance metric between two instances, and ordinal embedding, where we want to learn an embedding in an Euclidean space of the given instances that preserves the comparison order as well as possible. Unlike fully-labeled data, triplet comparison data can be collected in a more accurate and human-friendly way. Although learning from triplet comparison data has been considered in many applications, an important fundamental question of whether we can learn a classifier only from triplet comparison data has remained unanswered. In this paper, we give a positive answer to this important question by proposing an unbiased estimator for the classification risk under the empirical risk minimization framework. Since the proposed method is based on the empirical risk minimization framework, it inherently has the advantage that any surrogate loss function and any model, including neural networks, can be easily applied. Furthermore, we theoretically establish an estimation error bound for the proposed empirical risk minimizer. Finally, we provide experimental results to show that our method empirically works well and outperforms various baseline methods.

Toby Chong Long Hin, I-Chao Shen, Issei Sato et al.

Generative image modeling techniques such as GAN demonstrate highly convincing image generation result. However, user interaction is often necessary to obtain the desired results. Existing attempts add interactivity but require either tailored architectures or extra data. We present a human-in-the-optimization method that allows users to directly explore and search the latent vector space of generative image modeling. Our system provides multiple candidates by sampling the latent vector space, and the user selects the best blending weights within the subspace using multiple sliders. In addition, the user can express their intention through image editing tools. The system samples latent vectors based on inputs and presents new candidates to the user iteratively. An advantage of our formulation is that one can apply our method to arbitrary pre-trained model without developing specialized architecture or data. We demonstrate our method with various generative image modeling applications, and show superior performance in a comparative user study with prior art iGAN.

Kenshin Abe, Zijian Xu, Issei Sato et al.

There have been increasing challenges to solve combinatorial optimization problems by machine learning. Khalil et al. proposed an end-to-end reinforcement learning framework, S2V-DQN, which automatically learns graph embeddings to construct solutions to a wide range of problems. To improve the generalization ability of their Q-learning method, we propose a novel learning strategy based on AlphaGo Zero which is a Go engine that achieved a superhuman level without the domain knowledge of the game. Our framework is redesigned for combinatorial problems, where the final reward might take any real number instead of a binary response, win/lose. In experiments conducted for five kinds of NP-hard problems including {\sc MinimumVertexCover} and {\sc MaxCut}, our method is shown to generalize better to various graphs than S2V-DQN. Furthermore, our method can be combined with recently-developed graph neural network (GNN) models such as the \emph{Graph Isomorphism Network}, resulting in even better performance. This experiment also gives an interesting insight into a suitable choice of GNN models for each task.

Xi Yang, Bojian Wu, Issei Sato et al.

Deep neural networks (DNNs) have a high accuracy on image classification tasks. However, DNNs trained by such dataset with co-occurrence bias may rely on wrong features while making decisions for classification. It will greatly affect the transferability of pre-trained DNNs. In this paper, we propose an interactive method to direct classifiers paying attentions to the regions that are manually specified by the users, in order to mitigate the influence of co-occurrence bias. We test on CelebA dataset, the pre-trained AlexNet is fine-tuned to focus on the specific facial attributes based on the results of Grad-CAM.