arXiv subjects

Bin Gao

Publications and source records attributed to Bin Gao.

At least 19 recordsLinked to original sources

arXiv2026

High-dimensional extreme eigenvalue problems: low-rank tensor parametrization and optimization

High-dimensional extreme eigenvalue problems often arise from molecular vibrational models, electronic structure calculations, and quantum mechanics. Directly solving these problems suffers from the curse of dimensionality. Instead of tackling the problem in high-dimensional ambient space, we reformulate the problem through low-rank tensor formats, which can significantly reduce the computational cost and storage. Specifically, we consider the Rayleigh--Ritz problem on bounded-rank tensors in the tensor train format, which enables a more flexible choice of rank parameters. Moreover, we consider a smooth parametrization for bounded-rank tensors by introducing slack variables, leading to a smooth manifold structure. The original Rayleigh--Ritz problem is therefore transferred to an optimization problem on the manifold. We develop the Riemannian geometry and propose optimization methods for solving extreme eigenvalue problems. In practice, the Kronecker-product structure in Hamiltonian and PDE operators is employed to simplify the computation. Numerical experiments on the harmonic oscillator, the Laplace operator, the Schrödinger equation, the layered cluster problem, and the Bose--Einstein model demonstrate that the proposed method achieves accuracy comparable to full-space eigensolvers with reduced computation time and avoids storing full vectors. The results also show numerical rank reduction during iteration and robustness when the rank parameter is over-estimated. In addition, the fixed-point iterations illustrate that the proposed methods are able to serve as an inner eigensolver for solving nonlinear eigenvalue problems.

math.NA↗

arXiv2026

Quotient geometry of tensor ring decomposition

Differential geometries derived from tensor decompositions have been extensively studied and provided the foundations for a variety of efficient numerical methods. Despite the practical success of the tensor ring (TR) decomposition, its intrinsic geometry remains less understood, primarily due to the underlying ring structure and the resulting nontrivial gauge invariance. We establish the quotient geometry and immersed-submanifold structure of TR decomposition by imposing full-rank conditions on all unfolding matrices of the core tensors and capturing the gauge invariance. The intrinsic ring structure of TR leads to an analysis that is substantially different from other tensor formats. Additionally, for the uniform TR decomposition, where all core tensors are identical and the manifold structure is known, we derive explicit parameterizations for the vertical and horizontal spaces, which enable Riemannian optimization. Numerical experiments validate the developed geometries via tensor ring completion tasks.

math.NA↗

arXiv2026

SPLASH: Co-Designing Sparse Attention with High-Bandwidth Flash for Efficient Long-Context Inference

The key-value (KV) cache has become the dominant consumer of memory in large language model (LLM) serving systems as context lengths, concurrency, and request lifetimes grow. High-bandwidth memory (HBM) provides the bandwidth attention decode needs but limited capacity, while off-package memory and storage add capacity but lack the bandwidth to sustain attention decode. High-Bandwidth Flash (HBF) is a promising substrate that combines terabyte-scale capacity with near-HBM read bandwidth. Limited write endurance makes read-only model weights its natural use, but we argue that HBF paired with HBM as a hierarchy can also hold the KV cache. Unlike prior hierarchies, whose secondary tiers are bandwidth bottlenecked, the comparable bandwidths let the two act as one logical memory for the long-context KV cache. HBF capacity enables long-context serving, and sparse attention makes it efficient by limiting KV-cache reads during memory-bound decode. Since HBF reads full flash pages and aggregates bandwidth by accessing thousands of parallel flash planes, sparse attention must be co-designed with these physical properties. We present SPLASH, an algorithm and architecture co-design that virtualizes the KV cache across HBM and HBF and adapts sparse attention to HBF's page granularity and plane-level parallelism. Across models and context lengths, SPLASH improves decode throughput per GPU by 3.5x-11.4x over the evaluated baselines under a 100 ms per-token latency objective, while keeping accuracy within 4% of dense attention across long-context suites.

cs.AR↗

arXiv2026

SAEM: Stage-Aware Expert Management for Memory-Efficient MoE Inference in Chain-of-Thought Reasoning

Chain-of-thought (CoT) prompting improves LLM reasoning by decomposing complex problems into intermediate steps, but its sequential nature increases decoding latency and memory usage. Mixture-of-Experts (MoE) models scale capacity through sparse expert activation, yet their full expert weights often exceed GPU memory and require costly GPU-CPU transfers. Existing runtimes treat all tokens uniformly, overlooking a key structural property of CoT traces: consecutive reasoning stages exhibit coherent and predictable expert activation patterns. Ignoring this stage-level regularity leads to inefficient caching and unnecessary data movement. We propose SAEM, a stage-aware MoE inference runtime that detects reasoning stage boundaries and exploits stage-level activation coherence to guide expert placement. SAEM combines stage-aware caching, expert-aligned token repacking, and in-situ CPU execution to reduce data transfer and kernel fragmentation. On mathematical and scientific reasoning workloads, SAEM achieves an average 1.33x throughput improvement over the strongest state-of-the-art caching and offloading baselines under constrained GPU memory, rising to 1.54x when calibration data matches the workload, demonstrating the effectiveness of stage-aware, locality-driven MoE inference for CoT reasoning.

cs.AI↗

arXiv2026

Field-induced first order transitions and phase coexistence in the Kitaev quantum spin liquid candidate BaCo2(AsO4)2

BaCo2(AsO4)2 (BCAO) is an insulating Kitaev quantum spin liquid candidate with a rich low-temperature phase diagram. Below 5 K, it exhibits double-zigzag magnetic order. Upon application of an in-plane magnetic field, the magnetic structure first transforms into an up-up-down (UUD) state near 0.12 T and then enters a fully spin-polarized ferromagnetic (FM) state near 0.5 T. In the narrow field regime close to the polarized phase, a finite residual thermal conductivity has been reported, suggesting a possible field-induced quantum spin liquid phase. Using neutron scattering, we show that the field-induced double-zigzag-to-UUD transition near 0.15 T is accompanied by the emergence of a cluster of localized UUD spin excitations that coexist with conventional spin waves. Upon further increasing field, BCAO undergoes a first-order UUD-to-FM transition with coexistence of UUD and FM phases, accompanied by a sharp response in the spin Seebeck coefficient. These results do not support a quantum spin liquid scenario near the UUD-to-FM critical field. Instead, modeling indicates that the broad excitations arise from bound spin-flip pairs, while a low-lying dispersive branch near the FM phase boundary carries the same sign of magnetization as the FM order. These excitations naturally account for the observed sign of the spin Seebeck response and are likely relevant to the thermal conductivity near the critical field.

cond-mat.str-el↗

arXiv2026

Optimization over the intersection of manifolds

Optimization over the intersection of two manifolds arises in a broad range of applications, but is hindered by the coupled geometry of the feasible region. In this paper, we prove that the regularities -- clean intersection and intrinsic transversality -- are equivalent, which yields a tractable projection onto the tangent space of the intersection. Therefore, we propose a geometric method that employs a retraction on only one manifold and updates the iterate along two orthogonal directions. Specifically, the iterates stay on one manifold, and the two directions are responsible for asymptotically approaching the other manifold and decreasing the objective function, respectively. Under intrinsic transversality, we derive the convergence rate for both the feasibility and optimality measures, and show that every accumulation point is first-order stationary. Numerical experiments on problems stemming from sparse and low-rank optimization, including fitting spherical data, approximating hyperbolic embeddings on real data, and computing compressed modes, demonstrate the effectiveness of the proposed method.

math.OC↗

arXiv2026

Nyström Approximation on Manifolds

Computations on a manifold often involve constructing an operator on the tangent space and computing its inverse, which can be time-consuming in many applications. In order to reduce the computational costs and preserve the benign properties of tangent operators, we develop the Riemannian Nyström approximation on manifolds, a low-rank approximation of tangent operators through subspace projections onto the tangent space. The developed approximation is intrinsically constructed and inherits desirable properties from the classical Nyström approximation, e.g., positive semidefiniteness and approximation errors. Instead of the Gaussian sketching, we introduce the Haar--Grassmann sketching condition with a coordinate-free representation, which remains compatible under isometric vector transport across tangent spaces. Moreover, we propose a randomized Newton-type method for optimization on manifolds in which the linear system is constructed via the Riemannian Nyström approximation. Numerical experiments on the SPD and Grassmann manifolds, together with principal geodesic analysis on real data, illustrate that the proposed approximation reduces the computational cost of operators while maintaining comparable accuracy.

math.NA↗

arXiv2026

First-order methods on bounded-rank tensors converging to stationary points

Provably finding stationary points on bounded-rank tensors turns out to be an open problem [E. Levin, J. Kileel, and N. Boumal, Math. Program., 199 (2023), pp. 831--864] due to the inherent non-smoothness of the set of bounded-rank tensors. In contrast with bounded-rank matrices, tensors where some but not all modes are of full rank render essential difficulties in developing provable first-order methods. We resolve this problem by proposing two first-order methods with guaranteed convergence to stationary points. Specifically, we revisit the variational geometry of bounded-rank tensors and explicitly characterize its normal cones. Moreover, we propose gradient-related approximate projection methods that are provable to find stationary points, where the decisive ingredients are gradient-related vectors from tangent cones, line search along approximate projections, and rank-decreasing mechanisms near rank-deficient points. Numerical experiments on tensor completion validate that the proposed methods converge to stationary points across various rank parameters.

math.OC↗

arXiv2026

A second-order method landing on the Stiefel manifold via Newton$\unicode{x2013}$Schulz iteration

Retraction-free approaches offer attractive low-cost alternatives to Riemannian methods on the Stiefel manifold, but they are often first-order, which may limit the efficiency under high-accuracy requirements. To this end, we propose a second-order method landing on the Stiefel manifold without invoking retractions, which is proved to enjoy local quadratic (or superlinear for its inexact variant) convergence. The update consists of the sum of (i) a component tangent to the level set of the constraint-defining function that aims to reduce the objective and (ii) a component normal to the same level set that reduces the infeasibility. Specifically, we construct the normal component via Newton$\unicode{x2013}$Schulz, a fixed-point iteration for orthogonalization. Moreover, we establish a geometric connection between the Newton$\unicode{x2013}$Schulz iteration and Stiefel manifolds, in which Newton$\unicode{x2013}$Schulz moves along the normal space. For the tangent component, we formulate a modified Newton equation that incorporates Newton$\unicode{x2013}$Schulz. Numerical experiments on the orthogonal Procrustes problem, principal component analysis, and real-data independent component analysis illustrate that the proposed method performs better than the existing methods.

math.OC↗

arXiv2026

Bi-altermagnetism unveiled by sublattice-specific circular dichroism in resonant inelastic X-ray scattering

An altermagnet is a recently identified class of magnets that exhibit a zero net magnetic moment but break symmetry under the combined operations of parity and time reversal. It typically consists of two magnetic sites of opposite spins related by rotation within the unit cell. Here, we use circular dichroism (CD) in resonant inelastic X-ray scattering (RIXS) to identify a new form of altermagnetism, namely bi-altermagnetism, in the correlated insulator Fe2Mo3O8, which comprises two altermagnetic sublattices: one with alternating quasi-octahedral Fe environments and the other with alternating tetrahedral Fe environments. We experimentally revealed the emergence of CD in an achiral, zero-magnetization system, thereby probing mirror-symmetry breaking associated with altermagnetic order. Notably, the CD appeared at sublattice-specific excitations of the octahedral and tetrahedral sites, indicating symmetry breaking in both altermagnetic sublattices. Calculations based on a model with the bi-altermagnetic order along the c axis successfully reproduce the observed CD. Our findings provide compelling evidence for bi-altermagnetism in Fe2Mo3O8, and showcase the use of RIXS-CD as a probe of magnetic sublattices in systems with zero net magnetization.

cond-mat.str-el↗

arXiv2026

Spectroscopic Demarcation of Emergent Photons and Spinons in a Dipolar-Octupolar Quantum Spin Liquid

The identification of fractionalized excitations in quantum spin liquids (QSLs) remains a central challenge in condensed matter physics. In dipolar-octupolar (DO) pyrochlores, such as $\text{Ce}_2\text{Zr}_2\text{O}_7$, the candidate $π$-flux quantum spin ice (QSI) state is predicted to host both gapless emergent photons and a continuum of spinons. However, resolving these modes at zero field is complicated by their spectral overlap and the presence of nonmagnetic scattering near zero energy. Here, we report neutron scattering experiments on $\text{Ce}_2\text{Zr}_2\text{O}_7$ under a magnetic field along the $[1,1,1]$ direction. In contrast to previous unpolarized studies at zero-field that relied on high-temperature subtraction, we use a same-temperature high-field subtraction protocol to isolate the photon mode. Leveraging the selective coupling of the magnetic field to the dipolar degrees of freedom, we demonstrate the spectroscopic demarcation of these excitations. We observe that weak fields ($\approx 0.15$ T) suppress the low-energy photon weight while leaving the high-energy spinon continuum robust, albeit hardened. Our results, supported by gauge mean-field theory and exact diagonalization calculations, provide strong evidence for the $π$-flux QSI state and introduce a powerful field-tuning protocol for investigating DO-QSLs.

cond-mat.str-el↗

arXiv2025

Fully analogue in-memory neural computing via quantum tunneling effect

Fully analogue neural computation requires hardware that can implement both linear and nonlinear transformations without digital assistance. While analogue in-memory computing efficiently realizes matrix-vector multiplication, the absence of learnable analogue nonlinearities remains a central bottleneck. Here we introduce KANalogue, a fully analogue realization of Kolmogorov-Arnold Networks (KANs) that instantiates univariate basis functions directly using negative-differential-resistance (NDR) devices. By mapping the intrinsic current-voltage characteristics of NDR devices to learnable coordinate-wise nonlinear functions, KANalogue embeds function approximation into device physics while preserving a fully analogue signal path. Using cold-metal tunnel diodes as a representative platform, we construct diverse nonlinear bases and combine them through crossbar-based analogue summation. Experiments on MNIST, FashionMNIST, and CIFAR-10 demonstrate that KANalogue achieves competitive accuracy with substantially fewer parameters and higher crossbar node efficiency than analogue MLPs, while approaching the performance of digital KANs under strict hardware constraints. The framework is not limited to a specific device technology and naturally generalizes to a broad class of NDR devices. These results establish a device-grounded route toward scalable, energy-efficient, fully analogue neural networks.

cs.ET↗

arXiv2025

Variational analysis of determinantal varieties

Determinantal varieties -- the sets of bounded-rank matrices or tensors -- have attracted growing interest in low-rank optimization. The tangent cone to low-rank sets is widely studied and underpins a range of geometric methods. The second-order geometry, which encodes curvature information, is more intricate. In this work, we develop a unified framework to derive explicit formulas for both first- and second-order tangent sets to various low-rank sets, including low-rank matrices, tensors, symmetric matrices, and positive semidefinite matrices. The framework also accommodates the intersection of a low-rank set and another set satisfying mild assumptions, thereby yielding a tangent intersection rule. Through the lens of tangent sets, we establish a necessary and sufficient condition under which a nonsmooth problem and its smooth parameterization share equivalent second-order stationary points. Moreover, we exploit tangent sets to characterize optimality conditions for low-rank optimization and prove that verifying second-order optimality is NP-hard. In a separate line of analysis, we investigate variational geometry of the graph of the normal cone to matrix varieties, deriving the explicit Bouligand tangent cone, Fréchet and Mordukhovich normal cones to the graph. These results are further applied to develop optimality conditions for low-rank bilevel programs.

math.OC↗

arXiv2025

Spin Excitations and Flat Electronic Bands in a Cr-based Kagome Superconductor

In the quest for topology- and correlation-driven quantum states, kagome lattice materials have garnered significant interest for their band structures, featuring flat bands (FBs) from the quantum destructive interference of the electronic wavefunction. Tuning an FB to the chemical potential could induce electronic instabilities and emergent orders. Despite extensive studies, direct evidence of FBs tuned to the chemical potential and their role in emergent orders in bulk materials remains lacking. Using angle-resolved photoemission spectroscopy, resonant inelastic X-ray scattering, and density functional theory, we show that the low-energy structure of the Cr-based kagome metal superconductor {\Cr} is dominated by FBs at the Fermi level. We also observe low-energy magnetic excitations evolving across the low-temperature transition, largely consistent with the FB shift. Our results suggest that the low-temperature order contains a magnetic origin and that the kagome FBs may play a role in the emergence of this order.

cond-mat.str-el↗

arXiv2025

Optimization without Retraction on the Random Generalized Stiefel Manifold

Optimization over the set of matrices $X$ that satisfy $X^\top B X = I_p$, referred to as the generalized Stiefel manifold, appears in many applications involving sampled covariance matrices such as the canonical correlation analysis (CCA), independent component analysis (ICA), and the generalized eigenvalue problem (GEVP). Solving these problems is typically done by iterative methods that require a fully formed $B$. We propose a cheap stochastic iterative method that solves the optimization problem while having access only to random estimates of $B$. Our method does not enforce the constraint in every iteration; instead, it produces iterations that converge to critical points on the generalized Stiefel manifold defined in expectation. The method has lower per-iteration cost, requires only matrix multiplications, and has the same convergence rates as its Riemannian optimization counterparts that require the full matrix $B$. Experiments demonstrate its effectiveness in various machine learning applications involving generalized orthogonality constraints, including CCA, ICA, and the GEVP.

cs.LG↗

arXiv2025

Normalized tensor train decomposition

Tensors with unit Frobenius norm are fundamental objects in many fields, including scientific computing and quantum physics, which are able to represent normalized eigenvectors and pure quantum states. While the tensor train decomposition provides a powerful low-rank format for tackling high-dimensional problems, it does not intrinsically enforce the unit-norm constraint. To address this, we introduce the normalized tensor train (NTT) decomposition, which aims to approximate a tensor by unit-norm tensors in tensor train format. The low-rank structure of NTT decomposition not only saves storage and computational cost but also preserves the underlying unit-norm structure. We prove that the set of fixed-rank NTT tensors forms a smooth manifold, and the corresponding Riemannian geometry is derived, paving the way for geometric methods. We propose NTT-based methods for low-rank tensor recovery, high-dimensional eigenvalue problem, estimation of stabilizer rank, and calculation of the minimum output Rényi 2-entropy of quantum channels. Numerical experiments demonstrate the superior efficiency and scalability of the proposed NTT-based methods.

math.NA↗

arXiv2025

Interacting spin and charge density waves in kagome metal FeGe

Unveiling the interplay between spin density wave (SDW) and charge density wave (CDW) orders in correlated electron materials is important to obtain a comprehensive understanding of their electronic, structural, and magnetic properties. Kagome lattice materials are interesting because their flat electronic bands, Dirac points, and van Hove singularities can enable a variety of exotic electronic and magnetic phenomena. The kagome metal FeGe, which exhibits a CDW order deep within an A-type antiferromagnetic (AFM) phase, was found to respond dramatically to post-growth annealing - with the ability to tune the CDW repeatedly from long-range order to no (or extremely weak) order. Additionally, neutron scattering studies suggest that incommensurate magnetic peaks that onsets at $T_{Canting}$ = $T_{SDW} \approx$ 60 K in the system arise from a SDW order instead of the AFM double cone structure. Here we use inelastic neutron scattering to show two distinct spin excitations exist below $T_{Canting}$ corresponding to two coexisting magnetic orders in the system in both sets of annealed samples with and without CDW. While CDW order or no order can dramatically affect the onset temperature of $T_{Canting}$ and elastic incommensurate magnetic scattering, its impact on low-energy spin fluctuations is more limited. In both samples, a pair of gapless incommensurate spin excitations arising from the SDW order wavevector coexist with gapped commensurate spin waves from the A-type AFM order across $T_{Canting}$. Low-energy spin excitations for both samples couple dynamically to the lattice through enhanced magnetic scattering intensity on cooling below $T_{CDW}$, regardless the status of the static long-range CDW order. The incommensurate SDW order in the long-range CDW ordered sample also induces a tiny in-plane lattice distortion of the kagome lattice that is absent in the no CDW ordered sample.

cond-mat.str-el↗

arXiv2025

A space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints

Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure and makes the problem intricate. To this end, we propose a space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints. The "space-decoupling" is reflected in several ways. We show that the tangent cone of coupled constraints is the intersection of tangent cones of each constraint. Moreover, we decouple the intertwined bounded-rank and orthogonally invariant constraints into two spaces, leading to optimization on a smooth manifold. Implementing Riemannian algorithms on this manifold is painless as long as the geometry of additional constraints is known. In addition, we unveil the equivalence between the reformulated problem and the original problem. Numerical experiments on real-world applications -- spherical data fitting, graph similarity measuring, low-rank SDP, model reduction of Markov processes, reinforcement learning, and deep learning -- validate the superiority of the proposed framework.

math.OC↗