arXiv subjects

Yutian Tao

Publications and source records attributed to Yutian Tao.

6 recordsLinked to original sources

arXiv2026

Quantum Nonlinearity for Optical Neural Computing

The rapid scaling of deep neural networks comes at the cost of unsustainable power consumption. While optical neural networks offer an alternative, their capabilities remain constrained by the lack of efficient optical nonlinearities. To address this, we propose an optical neural computing architecture by embedding quantum emitters in inverse-designed nanophotonic structures. Due to their saturability, quantum emitters exhibit exceptionally strong nonlinearity compared with conventional materials. Using physics-aware training, we numerically demonstrate that the proposed architecture can solve complex tasks, including nonlinear classification and reinforcement learning, within all-optical neural networks. To enable fair comparison across different platforms, we introduce a framework that quantitatively links nonlinearity to a network's expressive power. Analysis shows that our quantum activation operates at $\text{nW}/μ\text{m}^2$ intensity, which is seven orders of magnitude below the nonlinearity threshold of conventional optical materials. Looking ahead to large language models, we estimate the nonlinearity-limited optical power, which scales sublinearly with model size. Our results indicate that quantum nanophotonics may provide a route toward sustainable AI inference.

physics.optics↗

arXiv2026

Learning Visual Feature-Based World Models via Residual Latent Action

World models predict future transitions from observations and actions. Existing works predominantly focus on image generation only. Visual feature-based world models, on the other hand, predict future visual features instead of raw video pixels, offering a promising alternative that is more efficient and less prone to hallucination. However, current feature-based approaches rely on direct regression, which leads to blurry or collapsed predictions in complex interactions, while generative modeling in high-dimensional feature spaces still remains challenging. In this work, we discover that a new type of latent action representation, which we refer to as *Residual Latent Action* (RLA), can be easily learned from DINO residuals. We also show that RLA is predictive, generalizable, and encodes temporal progression. Building on RLA, we propose *RLA World Model* (RLA-WM), which predicts RLA values via flow matching. RLA-WM outperforms both state-of-the-art feature-based and video-diffusion world models on simulation and real-world datasets, while being orders of magnitude faster than video diffusion. Furthermore, we develop two robot learning techniques that use RLA-WM to improve policy learning. The first one is a minimalist world action model with RLA that learns from actionless demonstration videos. The second one is the first visual RL framework trained entirely inside a world model learned from offline videos only, using a video-aligned reward and no online interactions or handcrafted rewards. Project page: https://mlzxy.github.io/rla-wm

cs.CV↗

arXiv2025

Interpolated Adaptive Linear Reduced Order Modeling for Deformation Dynamics

Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that allows the reduced mapping to vary dynamically in response to the evolving deformation state, significantly improving accuracy over traditional linear approaches. To further handle large deformations, we introduce a historical displacement basis combined with Grassmann interpolation, enabling the system to recover robustly even in challenging scenarios. We evaluate our method through quantitative online-error analysis and qualitative comparisons with principal component analysis (PCA)-based linear ROM simulations, demonstrating substantial accuracy gains while preserving comparable computational costs.

cs.GR↗

arXiv2025

Retrieval-Augmented Generation as Noisy In-Context Learning: A Unified Theory and Risk Bounds

Retrieval-augmented generation (RAG) has seen many empirical successes in recent years by aiding the LLM with external knowledge. However, its theoretical aspect has remained mostly unexplored. In this paper, we propose the first finite-sample generalization bound for RAG in in-context linear regression and derive an exact bias-variance tradeoff. Our framework views the retrieved texts as query-dependent noisy in-context examples and recovers the classical in-context learning (ICL) and standard RAG as the limit cases. Our analysis suggests that an intrinsic ceiling on generalization error exists on RAG as opposed to the ICL. Furthermore, our framework is able to model retrieval both from the training data and from external corpora by introducing uniform and non-uniform RAG noise. In line with our theory, we show the sample efficiency of ICL and RAG empirically with experiments on common QA benchmarks, such as Natural Questions and TriviaQA.

cs.LG↗

arXiv2024

A Symmetric Multigrid-Preconditioned Krylov Subspace Solver for Stokes Equations

Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and convergence. Multigrid is an approach with excellent applicability to elliptic problems such as the Stokes equations, and can be a solution to such challenges of scalability and efficiency. The degree of success of such methods, however, is highly contingent on the design of key components of a multigrid scheme, including the hierarchy of discretizations, and the relaxation scheme used. Additionally, in many practical cases, it may be more effective to use a multigrid scheme as a preconditioner to an iterative Krylov subspace solver, as opposed to striving for maximum efficacy of the relaxation scheme in all foreseeable settings. In this paper, we propose an efficient symmetric multigrid preconditioner for the Stokes Equations on a staggered finite-difference discretization. Our contribution is focused on crafting a preconditioner that (a) is symmetric indefinite, matching the property of the Stokes system itself, (b) is appropriate for preconditioning the SQMR iterative scheme, and (c) has the requisite symmetry properties to be used in this context. In addition, our design is efficient in terms of computational cost and facilitates scaling to large domains.

math.NA↗

arXiv2020

Optimized Processing of Localized Collisions in Projective Dynamics

We present a method for the efficient processing of contact and collision in volumetric elastic models simulated using the Projective Dynamics paradigm. Our approach enables interactive simulation of tetrahedral meshes with more than half a million elements, provided that the model satisfies two fundamental properties: the region of the model's surface that is susceptible to collision events needs to be known in advance, and the simulation degrees of freedom associated with that surface region should be limited to a small fraction (e.g. 5\%) of the total simulation nodes. Despite this conscious delineation of scope, our hypotheses hold true for common animation subjects, such as simulated models of the human face and parts of the body. In such scenarios, a partial Cholesky factorization can abstract away the behavior of the collision-safe subset of the face into the Schur Complement matrix with respect to the collision-prone region. We demonstrate how fast and accurate updates of penalty-based collision terms can be incorporated into this representation, and solved with high efficiency on the GPU. We also demonstrate the opportunity to iterate a partial update of the element rotations, akin to a selective application of the local step, specifically on the smaller collision-prone region without explicitly paying the cost associated with the rest of the simulation mesh. We demonstrate efficient and robust interactive simulation in detailed models from animation and medical applications.

cs.GR↗