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Shu Nakamura

Publications and source records attributed to Shu Nakamura.

At least 19 recordsLinked to original sources
arXiv2026

Surflo: Consistent 3D Surface Flow Model with Global State

Geometry is invariant to viewpoint, which makes any collection of images a redundant encoding of a single 3D state. Existing feed-forward reconstruction models fail to exploit this: per-view methods emit overlapping, unaligned pointmaps that grow linearly with input count, while global-latent methods commit to a fixed, low-resolution output. We introduce Surflo, which compresses a variable number of unposed RGB views into K latent tokens-one global state-and decodes oriented 3D surface points by independently transporting them from noise onto the surface via flow matching. This frees the output from any fixed grid or token budget: the same latent yields from a few thousand to a million points in a single forward pass. To suppress the local inconsistencies inherent to independent per-point decoding, an inference-time guidance term correlates nearby points by injecting a photometric gradient during ODE integration. Surflo matches or surpasses feed-forward baselines on surface metrics, runs an order of magnitude faster than optimization-based methods that require hundreds of views, and is the only feed-forward approach to combine a global latent with arbitrary-resolution decoding.

cs.CV↗
arXiv2026

REACH: Hand Pose Estimation from Room Corners

We introduce a novel 3D hand pose estimator that can accurately recover the shape and pose of people's hands in a room from afar, typically from fixed cameras at room corners, in extremely low-resolution and frequently occluded views. Our key idea is to fully leverage hand-body coordination, its temporal progression, and multiview observations. We achieve this with a novel Transformer-based model, in which hand and body configurations are modeled through correlations between their visual features expressed as per-view tokens, and their temporal coordination is exploited in an autoregressive manner. We introduce a novel dataset, which we refer to as REACH, Room-Environment dataset Annotated with Chest cameras for Hand pose estimation, to train and test our method. REACH is a first-of-its-kind large-scale hand pose dataset that captures accurate hand movements of 50 participants across a wide variety of daily activities. In order to avoid interfering with natural movements while annotating the hands with accurate shape and pose, we leverage concealed chest cameras. Through extensive experiments, including comparative studies with existing methods, we show that our model, REACH-Net, achieves highly accurate 3D hand pose estimation from afar. These results broaden the horizon of 3D hand pose estimation, especially towards "in-the-wild" continuous human behavior analysis.

cs.CV↗
arXiv2026

Action Motifs: Self-Supervised Hierarchical Representation of Human Body Movements

Effective human behavior modeling requires a representation of the human body movement that capitalizes on its compositionality. We propose a hierarchical representation consisting of Action Atoms that capture the atomic joint movements and Action Motifs that are formed by their temporal compositions and encode similar body movements found across different overall human actions. We derive A4Mer, a nested latent Transformer to learn this hierarchical representation from human pose data in a fully self-supervised manner. A4Mer splits a 3D pose sequence into variable-length segments and represents each segment as a single latent token (Action Atoms). Through bottom-up representation learning, temporal patterns composed of these Action Atoms, which capture meaningful temporal spans of reusable, semantic segments of body movements, naturally emerge (Action Motifs). A4Mer achieves this with a unified pretext task of masked token prediction in their respective latent spaces. We also introduce Action Motif Dataset (AMD), a large-scale dataset of multi-view human behavior videos with full SMPL annotations. We introduce a novel use of cameras by mounting them on the feet to achieve their frame-wise annotations despite frequent and heavy body occlusions. Experimental results demonstrate the effectiveness of A4Mer for extracting meaningful Action Motifs, which significantly benefit human behavior modeling tasks including action recognition, motion prediction, and motion interpolation.

cs.CV↗
arXiv2026

Mathematical analysis of one-layer neural network with fixed biases, a new activation function and other observations

We analyze a simple one-hidden-layer neural network with ReLU activation functions and fixed biases, with one-dimensional input and output. We study both continuous and discrete versions of the model, and we rigorously prove the convergence of the learning process with the $L^2$ squared loss function and the gradient descent procedure. We also prove the spectral bias property for this learning process. Several conclusions of this analysis are discussed; in particular, regarding the structure and properties that activation functions should possess, as well as the relationships between the spectrum of certain operators and the learning process. Based on this, we also propose an alternative activation function, the full-wave rectified exponential function (FReX), and we discuss the convergence of the gradient descent with this alternative activation function.

cs.LG↗
arXiv2024

Continuum limit of resonances for discrete Schrödinger operators

We consider complex resonances for discrete and continuous Schrödinger operators, and we show that the resonances of discrete models converge to resonances of continuous models in the continuum limit. The potential is supposed to be a sum of an exterior dilation analytic function and an exponentially decaying function, which may have local singularities. The proof employs a generalization of the norm resolvent convergence of discrete Schrödinger operators by Nakamura and Tadano (2021), combined with the complex distortion method in the Fourier space. Our results confirm that the complex resonances can be approximately computed using discrete Schrödinger operators. We also give a recipe for the construction of approximate discrete operators for Schrödinger operators with singular potentials.

math-ph↗
arXiv2024

Equivalence of the staggered fermion Hamiltonan and the discrete Hodge-Dirac operator on square lattices

We show that the free massless staggered fermion (or the KS-fermion) Hamiltonian is equivalent to a discrete Hodge-Dirac operator on the $d$-dimensional square lattice $h\mathbb{Z}^d$. In fact, they are identical operator valued matrices under suitable choices of their representations on $\ell^2(2h\mathbb{Z}^d)\otimes\mathbb{C}^{2^d}$. We employ the formulations of the staggered fermion by Nakamura (2024), and the discrete cohomology structure on the square lattices by Miranda-Parra (2023).

math-ph↗
arXiv2023

DeePoint: Visual Pointing Recognition and Direction Estimation

In this paper, we realize automatic visual recognition and direction estimation of pointing. We introduce the first neural pointing understanding method based on two key contributions. The first is the introduction of a first-of-its-kind large-scale dataset for pointing recognition and direction estimation, which we refer to as the DP Dataset. DP Dataset consists of more than 2 million frames of 33 people pointing in various styles annotated for each frame with pointing timings and 3D directions. The second is DeePoint, a novel deep network model for joint recognition and 3D direction estimation of pointing. DeePoint is a Transformer-based network which fully leverages the spatio-temporal coordination of the body parts, not just the hands. Through extensive experiments, we demonstrate the accuracy and efficiency of DeePoint. We believe DP Dataset and DeePoint will serve as a sound foundation for visual human intention understanding.

cs.CV↗
arXiv2023

Remarks on discrete Dirac operators and their continuum limits

We discuss possible definitions of discrete Dirac operators, and discuss their continuum limits. It is well-known in the lattice field theory that the straightforward discretization of the Dirac operator introduces unwanted spectral subspaces, and it is known as the fermion doubling. In oder to overcome this difficulty, two methods were proposed. The first one is to introduce a new term, called the Wilson term, and the second one is the KS-fermion model or the staggered fermion model. We discuss mathematical formulations of these, and study their continuum limits.

math-ph↗
arXiv2023

Continuum limit for Laplace and Elliptic operators on lattices

Continuum limits of Laplace operators on general lattices are considered, and it is shown that these operators converge to elliptic operators on the Euclidean space in the sense of the generalized norm resolvent convergence. We then study operators on the hexagonal lattice, which does not apply the above general theory, but we can show its Laplace operator converges to the continuous Laplace operator in the continuum limit. We also study discrete operators on the square lattice corresponding to second order strictly elliptic operators with variable coefficients, and prove the generalized norm resolvent convergence in the continuum limit.

math-ph↗
arXiv2022

Essential self-adjointness for the Klein-Gordon type operators on asymptotically static spacetime

Let $X=\mathbb{R}\times M$ be the spacetime, where $M$ is a closed manifold equipped with a Riemannian metric $g$, and we consider a symmetric Klein-Gordon type operator $P$ on $X$, which is asymptotically converges to $\partial_t^2-\triangle_g$ as $|t|\to\infty$, where $\triangle_g$ is the Laplace-Beltrami operator on $M$. We prove the essential self-adjointness of $P$ on $C_0^\infty(X)$. The idea of the proof is closely related to a recent paper by the authors on the essential self-adjointness for Klein-Gordon operators on asymptotically flat spaces.

math-ph↗
arXiv2022

A remark on the essential self-adjointness for Klein-Gordon type operators

Here we discuss a new simplified proof of the essential self-adjointness for formally self-adjoint differential operators of real principal type, previously proved by Vasy (2020) and Nakamura-Taira (2021). For simplicity, here we discuss the second order cases, i.e., Klein-Gordon type operators only.

math-ph↗
arXiv2022

Continuum limit of the lattice quantum graph Hamiltonian

We consider the quantum graph Hamiltonian on the square lattice in Euclidean space, and we show that the spectrum of the Hamiltonian converges to the corresponding Schrödinger operator on the Euclidean space in the continuum limit, and that the corresponding eigenfunctions and eigenprojections also converge in some sense. We employ the discrete Schrödinger operator as the intermediate operator, and we use a recent result by the second and third author on the continuum limit of the discrete Schrödinger operator.

math-ph↗
arXiv2021

Quantization optimized with respect to the Haar basis

We propose a method of data quantization of finite discrete-time signals which optimizes the error estimate of low frequency Haar coefficients. We also discuss the error/noise bounds of this quantization in the Fourier space. Our result shows one can quantize any discrete-time analog signal with high precision at low frequencies. Our method is deterministic, and it employs no statistical arguments, nor any probabilistic assumptions.

eess.SP↗
arXiv2020

Resonances and viscosity limit for the Wigner-von Neumann type Hamiltonian

The resonances for the Wigner-von Neumann type Hamiltonian are defined by the periodic complex distortion in the Fourier space. Also, following Zworski, we characterize resonances as the limit points of discrete eigenvalues of the Hamiltonian with a quadratic complex absorbing potential in the viscosity type limit.

math-ph↗
arXiv2020

Remarks on scattering matrices for Schrödinger operators with critically long-range perturbations

We consider scattering matrix for Schrödinger-type operators on $\mathbb{R}^d$ with perturbation $V(x)=O(\langle x\rangle^{-1})$ as $|x|\to\infty$. We show that the scattering matrix (with time-independent modifiers) is a pseudodifferential operator, and analyze its spectrum. We present examples of which the spectrum of the scattering matrices have dense point spectrum, and absolutely continuous spectrum, respectively.

math-ph↗
arXiv2020

Long-range Scattering Matrix for Schrödinger-type Operators

We show that the scattering matrix for a class of Schrödinger-type operators with long-range perturbations is a Fourier integral operator with the phase function which is the generating function of the modified classical scattering map.

math-ph↗
arXiv2019

Essential self-adjointness of real principal type operators

We study the essential self-adjointness for real principal type differential operators. Unlike the elliptic case, we need geometric conditions even for operators on the Euclidean space with asymptotically constant coefficients, and we prove the essential self-adjointness under the null non-trapping condition.

math.AP↗