arXiv subjects

Takuya Kanazawa

Publications and source records attributed to Takuya Kanazawa.

At least 19 recordsLinked to original sources

arXiv2025

Multivariate Uncertainty Quantification with Tomographic Quantile Forests

Quantifying predictive uncertainty is essential for safe and trustworthy real-world AI deployment. Yet, fully nonparametric estimation of conditional distributions remains challenging for multivariate targets. We propose Tomographic Quantile Forests (TQF), a nonparametric, uncertainty-aware, tree-based regression model for multivariate targets. TQF learns conditional quantiles of directional projections $\mathbf{n}^{\top}\mathbf{y}$ as functions of the input $\mathbf{x}$ and the unit direction $\mathbf{n}$. At inference, it aggregates quantiles across many directions and reconstructs the multivariate conditional distribution by minimizing the sliced Wasserstein distance via an efficient alternating scheme with convex subproblems. Unlike classical directional-quantile approaches that typically produce only convex quantile regions and require training separate models for different directions, TQF covers all directions with a single model without imposing convexity restrictions. We evaluate TQF on synthetic and real-world datasets, and release the source code on GitHub.

cs.LG↗

arXiv2025

Using Distance Correlation for Efficient Bayesian Optimization

The need to collect data via expensive measurements of black-box functions is prevalent across science, engineering and medicine. As an example, hyperparameter tuning of a large AI model is critical to its predictive performance but is generally time-consuming and unwieldy. Bayesian optimization (BO) is a collection of methods that aim to address this issue by means of Bayesian statistical inference. In this work, we put forward a BO scheme named BDC, which integrates BO with a statistical measure of association of two random variables called Distance Correlation. BDC balances exploration and exploitation automatically, and requires no manual hyperparameter tuning. We evaluate BDC on a range of benchmark tests and observe that it performs on per with popular BO methods such as the expected improvement and max-value entropy search. We also apply BDC to optimization of sequential integral observations of an unknown terrain and confirm its utility.

cs.LG↗

arXiv2024

Latent-Conditioned Policy Gradient for Multi-Objective Deep Reinforcement Learning

Sequential decision making in the real world often requires finding a good balance of conflicting objectives. In general, there exist a plethora of Pareto-optimal policies that embody different patterns of compromises between objectives, and it is technically challenging to obtain them exhaustively using deep neural networks. In this work, we propose a novel multi-objective reinforcement learning (MORL) algorithm that trains a single neural network via policy gradient to approximately obtain the entire Pareto set in a single run of training, without relying on linear scalarization of objectives. The proposed method works in both continuous and discrete action spaces with no design change of the policy network. Numerical experiments in benchmark environments demonstrate the practicality and efficacy of our approach in comparison to standard MORL baselines.

cs.LG↗

arXiv2022

Sample-based Uncertainty Quantification with a Single Deterministic Neural Network

Development of an accurate, flexible, and numerically efficient uncertainty quantification (UQ) method is one of fundamental challenges in machine learning. Previously, a UQ method called DISCO Nets has been proposed (Bouchacourt et al., 2016), which trains a neural network by minimizing the energy score. In this method, a random noise vector in $\mathbb{R}^{10\text{--}100}$ is concatenated with the original input vector in order to produce a diverse ensemble forecast despite using a single neural network. While this method has shown promising performance on a hand pose estimation task in computer vision, it remained unexplored whether this method works as nicely for regression on tabular data, and how it competes with more recent advanced UQ methods such as NGBoost. In this paper, we propose an improved neural architecture of DISCO Nets that admits faster and more stable training while only using a compact noise vector of dimension $\sim \mathcal{O}(1)$. We benchmark this approach on miscellaneous real-world tabular datasets and confirm that it is competitive with or even superior to standard UQ baselines. Moreover we observe that it exhibits better point forecast performance than a neural network of the same size trained with the conventional mean squared error. As another advantage of the proposed method, we show that local feature importance computation methods such as SHAP can be easily applied to any subregion of the predictive distribution. A new elementary proof for the validity of using the energy score to learn predictive distributions is also provided.

cs.LG↗

arXiv2022

Distributional Actor-Critic Ensemble for Uncertainty-Aware Continuous Control

Uncertainty quantification is one of the central challenges for machine learning in real-world applications. In reinforcement learning, an agent confronts two kinds of uncertainty, called epistemic uncertainty and aleatoric uncertainty. Disentangling and evaluating these uncertainties simultaneously stands a chance of improving the agent's final performance, accelerating training, and facilitating quality assurance after deployment. In this work, we propose an uncertainty-aware reinforcement learning algorithm for continuous control tasks that extends the Deep Deterministic Policy Gradient algorithm (DDPG). It exploits epistemic uncertainty to accelerate exploration and aleatoric uncertainty to learn a risk-sensitive policy. We conduct numerical experiments showing that our variant of DDPG outperforms vanilla DDPG without uncertainty estimation in benchmark tasks on robotic control and power-grid optimization.

cs.LG↗

arXiv2021

Complex spacing ratios of the non-Hermitian Dirac operator in universality classes AI$^\dagger$ and AII$^\dagger$

We consider non-Hermitian Dirac operators in QCD-like theories coupled to a chiral U(1) potential or an imaginary chiral chemical potential. We show that in the continuum they fall into the recently discovered universality classes AI$^\dagger$ or AII$^\dagger$ of random matrix theory if the fermions transform in pseudoreal or real representations of the gauge group, respectively. For staggered fermions on the lattice this correspondence is reversed. We verify our predictions by computing spacing ratios of complex eigenvalues, whose distribution is universal without the need for unfolding.

hep-lat↗

arXiv2021

Unitary matrix integral for QCD with real quarks and the GOE-GUE crossover

A unitary matrix integral that appears in the low-energy limit of QCD-like theories with quarks in real representations of the gauge group at finite chemical potential is analytically evaluated and expressed as a pfaffian. Its application to the GOE-GUE crossover in random matrix theory is discussed. An analogous unitary integral for QCD-like theories with quarks in pseudoreal representations of the gauge group is also evaluated.

hep-th↗

arXiv2021

Cascade of phase transitions in a planar Dirac material

We investigate a model of interacting Dirac fermions in $2+1$ dimensions with $M$ flavors and $N$ colors having the $\mathrm{U}(M)\times \mathrm{SU}(N)$ symmetry. In the large-$N$ limit, we find that the $\mathrm{U}(M)$ symmetry is spontaneously broken in a variety of ways. In the vacuum, when the parity-breaking flavor-singlet mass is varied, the ground state undergoes a sequence of $M$ first-order phase transitions, experiencing $M+1$ phases characterized by symmetry breaking $\mathrm{U}(M)\to \mathrm{U}(M-k)\times \mathrm{U}(k)$ with $k\in\{0,1,2,\cdots,M\}$, bearing a close resemblance to the vacuum structure of three-dimensional QCD. At finite temperature and chemical potential, a rich phase diagram with first and second-order phase transitions and tricritical points is observed. Also exotic phases with spontaneous symmetry breaking of the form as $\mathrm{U}(3)\to \mathrm{U}(1)^3$, $\mathrm{U}(4)\to \mathrm{U}(2)\times \mathrm{U}(1)^2$, and $\mathrm{U}(5)\to \mathrm{U}(2)^2\times \mathrm{U}(1)$ exist. For a large flavor-singlet mass, the increase of the chemical potential $μ$ brings about $M$ consecutive first-order transitions that separate the low-$μ$ phase diagram with vanishing fermion density from the high-$μ$ region with a high fermion density.

hep-th↗

arXiv2021

One-parameter family of acquisition functions for efficient global optimization

Bayesian optimization (BO) with Gaussian processes is a powerful methodology to optimize an expensive black-box function with as few function evaluations as possible. The expected improvement (EI) and probability of improvement (PI) are among the most widely used schemes for BO. There is a plethora of other schemes that outperform EI and PI, but most of them are numerically far more expensive than EI and PI. In this work, we propose a new one-parameter family of acquisition functions for BO that unifies EI and PI. The proposed method is numerically inexpensive, is easy to implement, can be easily parallelized, and on benchmark tasks shows a performance superior to EI and GP-UCB. Its generalization to BO with Student-t processes is also presented.

cs.LG↗

arXiv2021

New universality classes of the non-Hermitian Dirac operator in QCD-like theories

In non-Hermitian random matrix theory there are three universality classes for local spectral correlations: the Ginibre class and the nonstandard classes $\mathrm{AI}^\dagger$ and $\mathrm{AII}^\dagger$. We show that the continuum Dirac operator in two-color QCD coupled to a chiral $\mathrm{U}(1)$ gauge field or an imaginary chiral chemical potential falls in class $\mathrm{AI}^\dagger$ ($\mathrm{AII}^\dagger$) for fermions in pseudoreal (real) representations of $\mathrm{SU}(2)$. We introduce the corresponding chiral random matrix theories and verify our predictions in lattice simulations with staggered fermions, for which the correspondence between representation and universality class is reversed. Specifically, we compute the complex eigenvalue spacing ratios introduced recently. We also derive novel spectral sum rules.

hep-th↗

arXiv2021

Efficient Bayesian Optimization using Multiscale Graph Correlation

Bayesian optimization is a powerful tool to optimize a black-box function, the evaluation of which is time-consuming or costly. In this paper, we propose a new approach to Bayesian optimization called GP-MGC, which maximizes multiscale graph correlation with respect to the global maximum to determine the next query point. We present our evaluation of GP-MGC in applications involving both synthetic benchmark functions and real-world datasets and demonstrate that GP-MGC performs as well as or even better than state-of-the-art methods such as max-value entropy search and GP-UCB.

cs.LG↗

arXiv2021

Non-Hermitian BCS-BEC crossover of Dirac fermions

We investigate chiral symmetry breaking in a model of Dirac fermions with a complexified coupling constant whose imaginary part represents dissipation. We introduce a chiral chemical potential and observe that for real coupling a relativistic BCS-BEC crossover is realized. We solve the model in the mean-field approximation and construct the phase diagram as a function of the complex coupling. It is found that the dynamical mass increases under dissipation, although the chiral symmetry gets restored if dissipation exceeds a threshold.

hep-th↗

arXiv2020

Analysis of the QCD Kondo phase using random matrices

We propose a novel random matrix model that describes the QCD Kondo phase. The model correctly implements both the chiral symmetry of light quarks and the SU(2) spin symmetry of heavy quarks. We analytically take the large-N limit with N the matrix size and show that the model has three phases: the pure Kondo phase with no chiral condensate, the pure chirally broken phase with no Kondo condensate, and the coexistence phase. The model predicts that the pairing form of the Kondo condensate in the coexistence phase is significantly altered compared to the pure Kondo phase. For each phase, we rigorously derive the low-energy effective theory of Nambu-Goldstone modes and obtain compact closed expressions for the partition function with external sources. We also include a chiral chemical potential into the model and examine the vacuum structure.

hep-th↗

arXiv2020

Chiral random matrix theory for colorful quark-antiquark condensates

In QCD at high density, the color-octet quark-antiquark condensate $\langle\overlineψγ_0(λ^A)_C (λ^A)_Fψ\rangle$ is generally nonzero and dynamically breaks the $\mathrm{SU}(3)_C\times \mathrm{SU}(3)_L\times\mathrm{SU}(3)_R$ symmetry down to the diagonal $\mathrm{SU}(3)_V$. We evaluate this condensate in the mean-field approximation and find that it is of order $μΔ^2\log(μ/Δ)$ where $Δ$ is the BCS gap of quarks. Next we propose a novel non-Hermitian chiral random matrix theory that describes the formation of colorful quark-antiquark condensates. We take the microscopic large-$N$ limit and find that three phases appear depending on the parameter of the model. They are the color-flavor locked phase, the polar phase, and the normal phase. We rigorously derive the effective theory of Nambu-Goldstone modes and determine the quark-mass dependence of the partition function.

hep-th↗

arXiv2020

Chiral random matrix theory for single-flavor spin-one Cooper pairing

We propose a new non-Hermitian chiral random matrix model that describes single-flavor spin-one Cooper pairing of quarks. For three colors the model shows spontaneous breaking of color $\mathrm{SU}(3)_C$ and spin $\mathrm{SO}(3)_J$ symmetries down to the diagonal $\mathrm{SO}(3)_{C+J}$ subgroup, in striking analogy to the color-spin locked phase of one-flavor QCD at high density. For two colors, color-singlet spin-one diquarks condense and trigger symmetry breaking $\mathrm{U}(1) \times \mathrm{SO}(3)_J \to \mathrm{SO}(2)_J$. In both cases the microscopic large-$N$ limit is rigorously taken and the effective theory of Nambu-Goldstone modes is derived.

hep-th↗

arXiv2020

Relativistic Cooper pairing in the microscopic limit of chiral random matrix theory

Random matrix theory (RMT) provides a powerful framework for analyzing universal features of strongly coupled physical systems. In quantum chromodynamics (QCD), cold quark matter at asymptotically high density is expected to exhibit color superconductivity (CSC), the analogue of superconductivity in condensed-matter systems. Although CSC phases have been studied within RMT primarily in the macroscopic large-$N$ limit, where $N$ denotes the matrix size, it has remained unclear whether an RMT exists that realizes CSC in the microscopic large-$N$ limit. Here we answer this question in the affirmative by introducing a novel non-Hermitian chiral random matrix model. For three quark flavors, we show that the model exhibits spontaneous breaking of color $\mathrm{SU}(3)$ and flavor $\mathrm{SU}(3)$ symmetries down to the diagonal $\mathrm{SU}(3)$ subgroup, thereby reproducing color-flavor locking in dense QCD. For two flavors, we find that color $\mathrm{SU}(3)$ is spontaneously broken to $\mathrm{SU}(2)$ while the chiral symmetry $\mathrm{SU}(2)_{\mathrm{L}}\times\mathrm{SU}(2)_{\mathrm{R}}$ remains unbroken, consistent with the two-flavor color-superconducting phase.

hep-th↗

arXiv2019

Quantum distillation in QCD

We propose a grading protocol which assigns global symmetry associated phases to states in the Hilbert space. Without modifying the Hilbert space, this changes the state sum, a process that we call quantum distillation. We describe the image of quantum distillation in path integral in terms of (non-dynamical) flavor holonomy dependence of (dynamical) gauge holonomy potentials, in QCD with $N_f=N_c$ fundamental and one massive adjoint fermion on $\mathbb R^3 \times S^1$. The compactified theory possesses an exact zero-form color-flavor center symmetry for a special choice of flavor holonomy (under which Polyakov loop is charged), despite the absence of one-form center-symmetry. We prove that the CFC symmetry is stable at small-$β$. This is the opposite of the high-temperature limit of thermal theory and a dramatic manifestation of quantum distillation. We show chiral symmetry breaking at small $S^1$ and that the vacuum structure of the theory on $\mathbb R^4$ and $\mathbb R^3 \times S^1$ are controlled by the same mixed 't Hooft anomaly condition.

hep-th↗

arXiv2019

Accelerating small-angle scattering experiments with simulation-based machine learning

Making material experiments more efficient is a high priority for materials scientists who seek to discover new materials with desirable properties. In this paper, we investigate how to optimize the laborious sequential measurements of materials properties with data-driven methods, taking the small-angle neutron scattering (SANS) experiment as a test case. We propose two methods for optimizing sequential data sampling. These methods iteratively suggest the best target for the next measurement by performing a statistical analysis of the already acquired data, so that maximal information is gained at each step of an experiment. We conducted numerical simulations of SANS experiments for virtual materials and confirmed that the proposed methods significantly outperform baselines.

cond-mat.mtrl-sci↗