arXiv subjects

Shinichi Nakajima

Publications and source records attributed to Shinichi Nakajima.

At least 37 records · Page 2Linked to original sources

arXiv2025

Explaining Bayesian Neural Networks

To advance the transparency of learning machines such as Deep Neural Networks (DNNs), the field of Explainable AI (XAI) was established to provide interpretations of DNNs' predictions. While different explanation techniques exist, a popular approach is given in the form of attribution maps, which illustrate, given a particular data point, the relevant patterns the model has used for making its prediction. Although Bayesian models such as Bayesian Neural Networks (BNNs) have a limited form of transparency built-in through their prior weight distribution, they lack explanations of their predictions for given instances. In this work, we take a step toward combining these two perspectives by examining how local attributions can be extended to BNNs. Within the Bayesian framework, network weights follow a probability distribution; hence, the standard point explanation extends naturally to an explanation distribution. Viewing explanations probabilistically, we aggregate and analyze multiple local attributions drawn from an approximate posterior to explore variability in explanation patterns. The diversity of explanations offers a way to further explore how predictive rationales may vary across posterior samples. Quantitative and qualitative experiments on toy and benchmark data, as well as on a real-world pathology dataset, illustrate that our framework enriches standard explanations with uncertainty information and may support the visualization of explanation stability.

cs.LG↗

arXiv2025

Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects

We introduce a novel technique to numerically calculate Rényi entanglement entropies in lattice quantum field theory using generative models. We describe how flow-based approaches can be combined with the replica trick using a custom neural-network architecture around a lattice defect connecting two replicas. Numerical tests for the $ϕ^4$ scalar field theory in two and three dimensions demonstrate that our technique outperforms state-of-the-art Monte Carlo calculations, and exhibit a promising scaling with the defect size.

quant-ph↗

arXiv2025

Uncovering the Structure of Explanation Quality with Spectral Analysis

As machine learning models are increasingly considered for high-stakes domains, effective explanation methods are crucial to ensure that their prediction strategies are transparent to the user. Over the years, numerous metrics have been proposed to assess quality of explanations. However, their practical applicability remains unclear, in particular due to a limited understanding of which specific aspects each metric rewards. In this paper we propose a new framework based on spectral analysis of explanation outcomes to systematically capture the multifaceted properties of different explanation techniques. Our analysis uncovers two distinct factors of explanation quality-stability and target sensitivity-that can be directly observed through spectral decomposition. Experiments on both MNIST and ImageNet show that popular evaluation techniques (e.g., pixel-flipping, entropy) partially capture the trade-offs between these factors. Overall, our framework provides a foundational basis for understanding explanation quality, guiding the development of more reliable techniques for evaluating explanations.

cs.LG↗

arXiv2025

Multilevel Generative Samplers for Investigating Critical Phenomena

Investigating critical phenomena or phase transitions is of high interest in physics and chemistry, for which Monte Carlo (MC) simulations, a crucial tool for numerically analyzing macroscopic properties of given systems, are often hindered by an emerging divergence of correlation length -- known as scale invariance at criticality (SIC) in the renormalization group theory. SIC causes the system to behave the same at any length scale, from which many existing sampling methods suffer: long-range correlations cause critical slowing down in Markov chain Monte Carlo (MCMC), and require intractably large receptive fields for generative samplers. In this paper, we propose a Renormalization-informed Generative Critical Sampler (RiGCS) -- a novel sampler specialized for near-critical systems, where SIC is leveraged as an advantage rather than a nuisance. Specifically, RiGCS builds on MultiLevel Monte Carlo (MLMC) with Heat Bath (HB) algorithms, which perform ancestral sampling from low-resolution to high-resolution lattice configurations with site-wise-independent conditional HB sampling. Although MLMC-HB is highly efficient under exact SIC, it suffers from a low acceptance rate under slight SIC violation. Notably, SIC violation always occurs in finite-size systems, and may induce long-range and higher-order interactions in the renormalized distributions, which are not considered by independent HB samplers. RiGCS enhances MLMC-HB by replacing a part of the conditional HB sampler with generative models that capture those residual interactions and improve the sampling efficiency. Our experiments show that the effective sample size of RiGCS is a few orders of magnitude higher than state-of-the-art generative model baselines in sampling configurations for 128x128 two-dimensional Ising systems.

cs.LG↗

arXiv2025

Federated Learning over Connected Modes

Statistical heterogeneity in federated learning poses two major challenges: slow global training due to conflicting gradient signals, and the need of personalization for local distributions. In this work, we tackle both challenges by leveraging recent advances in \emph{linear mode connectivity} -- identifying a linearly connected low-loss region in the parameter space of neural networks, which we call solution simplex. We propose federated learning over connected modes (\textsc{Floco}), where clients are assigned local subregions in this simplex based on their gradient signals, and together learn the shared global solution simplex. This allows personalization of the client models to fit their local distributions within the degrees of freedom in the solution simplex and homogenizes the update signals for the global simplex training. Our experiments show that \textsc{Floco} accelerates the global training process, and significantly improves the local accuracy with minimal computational overhead in cross-silo federated learning settings.

cs.LG↗

arXiv2025

Adaptive Observation Cost Control for Variational Quantum Eigensolvers

The objective to be minimized in the variational quantum eigensolver (VQE) has a restricted form, which allows a specialized sequential minimal optimization (SMO) that requires only a few observations in each iteration. However, the SMO iteration is still costly due to the observation noise -- one observation at a point typically requires averaging over hundreds to thousands of repeated quantum measurement shots for achieving a reasonable noise level. In this paper, we propose an adaptive cost control method, named subspace in confident region (SubsCoRe), for SMO. SubsCoRe uses the Gaussian process (GP) surrogate, and requires it to have low uncertainty over the subspace being updated, so that optimization in each iteration is performed with guaranteed accuracy. The adaptive cost control is performed by first setting the required accuracy according to the progress of the optimization, and then choosing the minimum number of measurement shots and their distribution such that the required accuracy is satisfied. We demonstrate that SubsCoRe significantly improves the efficiency of SMO, and outperforms the state-of-the-art methods.

quant-ph↗

arXiv2025

Improvement of Heatbath Algorithm in LFT using Generative models

The Heatbath Algorithm is commonly used for sampling in local lattice field theories, but performing exact updates or sampling from the local density is challenging when dealing with continuous variables. Heatbath methods rely on rejection-based sampling at each site, which can suffer from low acceptance rates if the proposal distribution is not optimally chosen a nontrivial task. In this work, we propose a novel, straightforward approach for generating proposals at each lattice site for the phi4 and XY models using generative AI models. This method learns a conditional local distribution, without requiring training samples from the target, conditioned on both neighboring sites and action parameter values.

physics.comp-ph↗

arXiv2024

Generative Fractional Diffusion Models

We introduce the first continuous-time score-based generative model that leverages fractional diffusion processes for its underlying dynamics. Although diffusion models have excelled at capturing data distributions, they still suffer from various limitations such as slow convergence, mode-collapse on imbalanced data, and lack of diversity. These issues are partially linked to the use of light-tailed Brownian motion (BM) with independent increments. In this paper, we replace BM with an approximation of its non-Markovian counterpart, fractional Brownian motion (fBM), characterized by correlated increments and Hurst index $H \in (0,1)$, where $H=0.5$ recovers the classical BM. To ensure tractable inference and learning, we employ a recently popularized Markov approximation of fBM (MA-fBM) and derive its reverse-time model, resulting in generative fractional diffusion models (GFDM). We characterize the forward dynamics using a continuous reparameterization trick and propose augmented score matching to efficiently learn the score function, which is partly known in closed form, at minimal added cost. The ability to drive our diffusion model via MA-fBM offers flexibility and control. $H \leq 0.5$ enters the regime of rough paths whereas $H>0.5$ regularizes diffusion paths and invokes long-term memory. The Markov approximation allows added control by varying the number of Markov processes linearly combined to approximate fBM. Our evaluations on real image datasets demonstrate that GFDM achieves greater pixel-wise diversity and enhanced image quality, as indicated by a lower FID, offering a promising alternative to traditional diffusion models

cs.LG↗

arXiv2024

Towards Symbolic XAI -- Explanation Through Human Understandable Logical Relationships Between Features

Explainable Artificial Intelligence (XAI) plays a crucial role in fostering transparency and trust in AI systems, where traditional XAI approaches typically offer one level of abstraction for explanations, often in the form of heatmaps highlighting single or multiple input features. However, we ask whether abstract reasoning or problem-solving strategies of a model may also be relevant, as these align more closely with how humans approach solutions to problems. We propose a framework, called Symbolic XAI, that attributes relevance to symbolic queries expressing logical relationships between input features, thereby capturing the abstract reasoning behind a model's predictions. The methodology is built upon a simple yet general multi-order decomposition of model predictions. This decomposition can be specified using higher-order propagation-based relevance methods, such as GNN-LRP, or perturbation-based explanation methods commonly used in XAI. The effectiveness of our framework is demonstrated in the domains of natural language processing (NLP), vision, and quantum chemistry (QC), where abstract symbolic domain knowledge is abundant and of significant interest to users. The Symbolic XAI framework provides an understanding of the model's decision-making process that is both flexible for customization by the user and human-readable through logical formulas.

cs.AI↗

arXiv2024

Molecular relaxation by reverse diffusion with time step prediction

Molecular relaxation, finding the equilibrium state of a non-equilibrium structure, is an essential component of computational chemistry to understand reactivity. Classical force field (FF) methods often rely on insufficient local energy minimization, while neural network FF models require large labeled datasets encompassing both equilibrium and non-equilibrium structures. As a remedy, we propose MoreRed, molecular relaxation by reverse diffusion, a conceptually novel and purely statistical approach where non-equilibrium structures are treated as noisy instances of their corresponding equilibrium states. To enable the denoising of arbitrarily noisy inputs via a generative diffusion model, we further introduce a novel diffusion time step predictor. Notably, MoreRed learns a simpler pseudo potential energy surface (PES) instead of the complex physical PES. It is trained on a significantly smaller, and thus computationally cheaper, dataset consisting of solely unlabeled equilibrium structures, avoiding the computation of non-equilibrium structures altogether. We compare MoreRed to classical FFs, equivariant neural network FFs trained on a large dataset of equilibrium and non-equilibrium data, as well as a semi-empirical tight-binding model. To assess this quantitatively, we evaluate the root-mean-square deviation between the found equilibrium structures and the reference equilibrium structures as well as their energies.

physics.chem-ph↗

arXiv2024

Physics-Informed Bayesian Optimization of Variational Quantum Circuits

In this paper, we propose a novel and powerful method to harness Bayesian optimization for Variational Quantum Eigensolvers (VQEs) -- a hybrid quantum-classical protocol used to approximate the ground state of a quantum Hamiltonian. Specifically, we derive a VQE-kernel which incorporates important prior information about quantum circuits: the kernel feature map of the VQE-kernel exactly matches the known functional form of the VQE's objective function and thereby significantly reduces the posterior uncertainty. Moreover, we propose a novel acquisition function for Bayesian optimization called Expected Maximum Improvement over Confident Regions (EMICoRe) which can actively exploit the inductive bias of the VQE-kernel by treating regions with low predictive uncertainty as indirectly ``observed''. As a result, observations at as few as three points in the search domain are sufficient to determine the complete objective function along an entire one-dimensional subspace of the optimization landscape. Our numerical experiments demonstrate that our approach improves over state-of-the-art baselines.

cs.LG↗

arXiv2024

Self-Supervised Training with Autoencoders for Visual Anomaly Detection

We focus on a specific use case in anomaly detection where the distribution of normal samples is supported by a lower-dimensional manifold. Here, regularized autoencoders provide a popular approach by learning the identity mapping on the set of normal examples, while trying to prevent good reconstruction on points outside of the manifold. Typically, this goal is implemented by controlling the capacity of the model, either directly by reducing the size of the bottleneck layer or implicitly by imposing some sparsity (or contraction) constraints on parts of the corresponding network. However, neither of these techniques does explicitly penalize the reconstruction of anomalous signals often resulting in poor detection. We tackle this problem by adapting a self-supervised learning regime that exploits discriminative information during training but focuses on the submanifold of normal examples. Informally, our training objective regularizes the model to produce locally consistent reconstructions, while replacing irregularities by acting as a filter that removes anomalous patterns. To support this intuition, we perform a rigorous formal analysis of the proposed method and provide a number of interesting insights. In particular, we show that the resulting model resembles a non-linear orthogonal projection of partially corrupted images onto the submanifold of uncorrupted samples. On the other hand, we identify the orthogonal projection as an optimal solution for a number of regularized autoencoders including the contractive and denoising variants. We support our theoretical analysis by empirical evaluation of the resulting detection and localization performance of the proposed method. In particular, we achieve a new state-of-the-art result on the MVTec AD dataset -- a challenging benchmark for visual anomaly detection in the manufacturing domain.

cs.CV↗

arXiv2024

Labeling Neural Representations with Inverse Recognition

Deep Neural Networks (DNNs) demonstrate remarkable capabilities in learning complex hierarchical data representations, but the nature of these representations remains largely unknown. Existing global explainability methods, such as Network Dissection, face limitations such as reliance on segmentation masks, lack of statistical significance testing, and high computational demands. We propose Inverse Recognition (INVERT), a scalable approach for connecting learned representations with human-understandable concepts by leveraging their capacity to discriminate between these concepts. In contrast to prior work, INVERT is capable of handling diverse types of neurons, exhibits less computational complexity, and does not rely on the availability of segmentation masks. Moreover, INVERT provides an interpretable metric assessing the alignment between the representation and its corresponding explanation and delivering a measure of statistical significance. We demonstrate the applicability of INVERT in various scenarios, including the identification of representations affected by spurious correlations, and the interpretation of the hierarchical structure of decision-making within the models.

cs.LG↗

arXiv2023

Local Function Complexity for Active Learning via Mixture of Gaussian Processes

Inhomogeneities in real-world data, e.g., due to changes in the observation noise level or variations in the structural complexity of the source function, pose a unique set of challenges for statistical inference. Accounting for them can greatly improve predictive power when physical resources or computation time is limited. In this paper, we draw on recent theoretical results on the estimation of local function complexity (LFC), derived from the domain of local polynomial smoothing (LPS), to establish a notion of local structural complexity, which is used to develop a model-agnostic active learning (AL) framework. Due to its reliance on pointwise estimates, the LPS model class is not robust and scalable concerning large input space dimensions that typically come along with real-world problems. Here, we derive and estimate the Gaussian process regression (GPR)-based analog of the LPS-based LFC and use it as a substitute in the above framework to make it robust and scalable. We assess the effectiveness of our LFC estimate in an AL application on a prototypical low-dimensional synthetic dataset, before taking on the challenging real-world task of reconstructing a quantum chemical force field for a small organic molecule and demonstrating state-of-the-art performance with a significantly reduced training demand.

cs.LG↗

arXiv2023

Visualizing the Diversity of Representations Learned by Bayesian Neural Networks

Explainable Artificial Intelligence (XAI) aims to make learning machines less opaque, and offers researchers and practitioners various tools to reveal the decision-making strategies of neural networks. In this work, we investigate how XAI methods can be used for exploring and visualizing the diversity of feature representations learned by Bayesian Neural Networks (BNNs). Our goal is to provide a global understanding of BNNs by making their decision-making strategies a) visible and tangible through feature visualizations and b) quantitatively measurable with a distance measure learned by contrastive learning. Our work provides new insights into the \emph{posterior} distribution in terms of human-understandable feature information with regard to the underlying decision making strategies. The main findings of our work are the following: 1) global XAI methods can be applied to explain the diversity of decision-making strategies of BNN instances, 2) Monte Carlo dropout with commonly used Dropout rates exhibit increased diversity in feature representations compared to the multimodal posterior approximation of MultiSWAG, 3) the diversity of learned feature representations highly correlates with the uncertainty estimate for the output and 4) the inter-mode diversity of the multimodal posterior decreases as the network width increases, while the intra mode diversity increases. These findings are consistent with the recent Deep Neural Networks theory, providing additional intuitions about what the theory implies in terms of humanly understandable concepts.

cs.LG↗

arXiv2023

Detecting and Mitigating Mode-Collapse for Flow-based Sampling of Lattice Field Theories

We study the consequences of mode-collapse of normalizing flows in the context of lattice field theory. Normalizing flows allow for independent sampling. For this reason, it is hoped that they can avoid the tunneling problem of local-update MCMC algorithms for multi-modal distributions. In this work, we first point out that the tunneling problem is also present for normalizing flows but is shifted from the sampling to the training phase of the algorithm. Specifically, normalizing flows often suffer from mode-collapse for which the training process assigns vanishingly low probability mass to relevant modes of the physical distribution. This may result in a significant bias when the flow is used as a sampler in a Markov-Chain or with Importance Sampling. We propose a metric to quantify the degree of mode-collapse and derive a bound on the resulting bias. Furthermore, we propose various mitigation strategies in particular in the context of estimating thermodynamic observables, such as the free energy.

hep-lat↗

arXiv2022

Domain-Specific Word Embeddings with Structure Prediction

Complementary to finding good general word embeddings, an important question for representation learning is to find dynamic word embeddings, e.g., across time or domain. Current methods do not offer a way to use or predict information on structure between sub-corpora, time or domain and dynamic embeddings can only be compared after post-alignment. We propose novel word embedding methods that provide general word representations for the whole corpus, domain-specific representations for each sub-corpus, sub-corpus structure, and embedding alignment simultaneously. We present an empirical evaluation on New York Times articles and two English Wikipedia datasets with articles on science and philosophy. Our method, called Word2Vec with Structure Prediction (W2VPred), provides better performance than baselines in terms of the general analogy tests, domain-specific analogy tests, and multiple specific word embedding evaluations as well as structure prediction performance when no structure is given a priori. As a use case in the field of Digital Humanities we demonstrate how to raise novel research questions for high literature from the German Text Archive.

cs.CL↗

arXiv2022

Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flows

We propose an algorithm to estimate the path-gradient of both the reverse and forward Kullback-Leibler divergence for an arbitrary manifestly invertible normalizing flow. The resulting path-gradient estimators are straightforward to implement, have lower variance, and lead not only to faster convergence of training but also to better overall approximation results compared to standard total gradient estimators. We also demonstrate that path-gradient training is less susceptible to mode-collapse. In light of our results, we expect that path-gradient estimators will become the new standard method to train normalizing flows for variational inference.

cs.LG↗