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Ao Cai

Publications and source records attributed to Ao Cai.

14 recordsLinked to original sources

ROCS: Request-Oriented Compute Sharing for Efficient Large-Scale Recommendation

Modern recommendation models gain prediction quality by scaling feature-interaction and sequence modules, but production cost constraints cap how far systems can scale. In this work, we propose Request-Oriented Compute Sharing (ROCS), a modeling and inference paradigm that exploits a unique property of recommendation inference: each user request is evaluated against many candidates, while request-side features are shared across candidates. ROCS defers request-candidate interactions as late as possible, isolates candidate-dependent representations, and evaluates substantial portions of the model once per request rather than once per candidate, significantly improving inference efficiency while maintaining or improving prediction quality. To realize this paradigm, we develop Generalized Layer Masking (GLM) to enforce candidate isolation in feature-interaction architectures, and Deep Cross Attention (DCA) to extend request-oriented sharing to sequence architectures. To support efficient GPU deployment, we co-design In-Kernel Broadcast Optimization (IKBO) that significantly accelerates ROCS model execution. Experiments on public benchmarks show that ROCS consistently improves the quality-efficiency tradeoff across recommendation backbones. On production-scale workloads, ROCS achieves up to a 3x QPS improvement on retrieval models without quality degradation and a 0.5% relative LogLoss improvement with a 50% QPS gain on a short-form video ranking model. ROCS has been deployed across large-scale recommendation systems spanning ads and organic surfaces, retrieval and ranking stages, and more than two orders of magnitude in inference complexity, delivering significant online gains at reduced infrastructure cost.

cs.LG

StructureClaw: Traceable LLM Agents and an Executable Benchmark for Structural Engineering Workflows

Addressing a structural-engineering request requires more than a single answer; it requires a chain of interdependent artifacts: interpreted requirements, a computable model, validation records, solver outputs, applicable engineering checks, and a final report. Evaluations centered on question answering or script generation may therefore reward fluent outputs even when the underlying workflow is incomplete, inconsistent, or non-executable. We present StructureClaw, an artifact-centered workbench in which LLM agents operate through governed engineering skills, typed tools, shared artifact state, and local analysis backends, together with StructureClaw-Bench, an executable benchmark of 150 controlled scenarios spanning standard workflows, interactive robustness, and multimodal structural-model reconstruction. Its analyzable standard and multimodal cases require both strict one-to-one structural-model matching and numerical-response agreement with frozen reference responses from the selected analysis engine; interactive cases instead require positive clarification or recovery evidence together with safe non-execution when appropriate. A trial succeeds only when every fixture-required assertion passes. Across nine text-agent configurations, generic-only execution passed the model-artifact check in 87.0% of retained outcomes but achieved only 22.0% E2E Success, whereas automatic StructureClaw reached 82.9%. Interactive and multimodal evaluations further identify semantic state consistency and executable model reconstruction as the dominant remaining bottlenecks. The code and benchmark are available at https://github.com/structureclaw/structureclaw.

cs.SE

Abstract Continuity Theorem for the Lyapunov Exponents of linear cocycles

We prove the H\"older continuity of Lyapunov exponents for general linear cocycles when the base measures vary in Wasserstein distance, under the assumption of uniform large deviations type (LDT) estimates. This is a measure version of the abstract continuity theorem (ACT) established by Duarte-Klein [Duarte, P. and Klein, S. (2016). Lyapunov exponents of linear cocycles: Continuity via large deviations. Atlantis Studies in Dynamical Systems, 3]. The main obstacle here lies in the fact that the magnitude of the exceptional sets in LDT estimates is constantly changing when the base measures deviate. We overcome this via a combination of a Urysohn-type lemma and properties of Wasserstein distance in every iteration step. Our measure version of ACT, combined with the original work of Duarte-Klein, provides a complete scheme for proving joint H\"older continuity of Lyapunov exponents with respect to both measure and fiber which resolves all parameter dependence. This continuity theorem is general and applicable to a wide range of mathematical models, including product of random matrices and cocycles essentially generated by shifts. In particular, it applies to associated Schr\"odinger operators which are central objects in the study of mathematical physics.

math.DS

Quantitative Reducibility of $C^k$ Quasi-Periodic Cocycles

This paper establishes an extreme $C^k$ reducibility theorem of quasi-periodic $SL(2, \mathbb{R})$ cocycles in the local perturbative region, revealing both the essence of Eliasson [Commun.Math.Phys.1992] and Hou-You [Invent.Math.2012] in respectively the non-resonant and resonant cases. By paralleling further the reducibility process with the almost reducibility, we are able to acquire the least initial regularity as well as the least loss of regularity for the whole KAM iterations. This, in return, makes various spectral applications of quasi-periodic Schr\"odinger operators wide open.

math.DS

Randomness versus quasi-periodicity

This paper serves as an extended road map for our long-term project "Mixed Random-quasiperiodic Cocycles" [arXiv:2201.04745, arXiv:2109.09544, arXiv:2210.16908, 6, 7] with Pedro Duarte and Silvius Klein. Despite exhibiting totally different natures, the random world and the quasi-periodic one may still have potential relations that we are keen to reveal. This was inspired by Jiangong You's intriguing question on the stability of the Lyapunov exponent of quasi-periodic Schr\"odinger operators under random noise in 2018.

math.DS

H\"older continuity of the Lyapunov exponent for Markov cocycles via Furstenberg's Formula

This paper is concerned with the study of linear cocycles over uniformly ergodic Markov shifts on a compact space of symbols. We establish the joint H\"older continuity of the maximal Lyapunov exponent as a function of the cocycle and the transition kernel in the vicinity of any irreducible cocycle with simple maximal Lyapunov exponent. Our approach, via Furstenberg's formula, shows the H\"older continuous dependence on the data of the stationary measure of the projective cocycle and in particular provides a more computable H\"older exponent.

math.DS

Statistical properties for mixing Markov chains with applications to dynamical systems

We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product encoding a random torus translation, a model we call a mixed random-quasiperiodic dynamical system. This abstract scheme is applicable to many other types of skew product dynamics, including systems for which the spectral gap property for the transition or the transfer operator does not hold.

math.DS

A dynamical Thouless formula

In this paper we establish an abstract, dynamical Thouless-type formula for affine families of $\mathrm{GL} (2,\mathbb{R})$ cocycles. This result extends the classical formula relating, via the Hilbert transform, the maximal Lyapunov exponent and the integrated density of states of a Schr\"odinger operator. Here, the role of the integrated density of states will be played by a more geometrical quantity, the fibered rotation number. As an application of this formula we present limitations on the modulus of continuity of random linear cocycles. Moreover, we derive H\"older-type continuity properties of the fibered rotation number for linear cocycles over various base dynamics.

math.DS

Furstenberg Theory of Mixed Random-Quasiperiodic Cocycles

We derive a criterion for the positivity of the maximal Lyapunov exponent of generic mixed random-quasiperiodic linear cocycles, a model introduced in a previous work. This result is applicable to cocycles corresponding to Schr\"odinger operators with randomly perturbed quasiperiodic potentials. Moreover, we establish an average uniform convergence to the Lyapunov exponent in the Oseledets theorem.

math.DS

Mixed Random-Quasiperiodic Cocycles

We introduce the concept of mixed random-quasiperiodic linear cocycles. We characterize the ergodicity of the base dynamics and establish a large deviations type estimate for certain types of observables. For the fiber dynamics we prove the uniform upper semicontinuity of the maximal Lyapunov exponent. This paper is meant to introduce a model to be studied in depth in further projects.

math.DS

The absolutely continuous spectrum of finitely differentiable quasi-periodic Schrödinger operators

We prove that the quasi-periodic Schrödinger operator with a finitely differentiable potential has purely absolutely continuous spectrum for all phases if the frequency is Diophantine and the potential is sufficiently small in the corresponding $C^k$ topology. This is based on a refined quantitative $C^{k,k_0}$ almost reducibility theorem which only requires a quite low initial regularity ``$k>14τ+2$'' and much of the regularity ``$k_0\leq k-2τ-2$'' is conserved in the end, where $τ$ is the Diophantine constant of the frequency.

math.DS

Reducibility of finitely differentiable quasi-periodic cocycles and its spectral applications

In this paper, we prove the generic version of Cantor spectrum for quasi-periodic Schrödinger operators with finitely smooth and small potentials, and we also show pure point spectrum for a class of multi-frequency $C^k$ long-range operators on $\ell^2(\Z^d)$. These results are based on reducibility properties of finitely differentiable quasi-periodic $SL(2,\R)$ cocycles. More precisely, we prove that if the base frequency is Diophantine, then a $C^k$ $SL(2,\R)$-valued cocycle is reducible if it is close to a constant cocycle, sufficiently smooth and the rotation number of it is Diophantine or rational with respect to the frequency.

math.DS

Polynomial decay of the gap length for C^k quasi-periodic Schrodinger operators and spectral application

For the quasi-periodic Schrödinger operators in the local perturbative regime where the frequency is Diophantine and the potential is $C^k$ sufficiently small depending on the Diophantine constants, we prove that the length of the corresponding spectral gap has a polynomial decay upper bound with respect to its label. This is based on a refined quantitative reducibility theorem for $C^k$ quasi-periodic ${\rm SL}(2,\mathbb{R})$ cocycles, and also based on the Moser-Pöschel argument for the related Schrödinger cocycles. As an application, we are able to show the homogeneity of the spectrum.

math.DS

Sharp Holder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles

We show that if the base frequency is Diophantine, then the Lyapunov exponent of a $C^{k}$ quasi-periodic $SL(2,\mathbb{R})$ cocycle is $1/2$-Hölder continuous in the almost reducible regime, if $k$ is large enough. As a consequence, we show that if the frequency is Diophantine, $k$ is large enough, and the potential is $C^k$ small, then the integrated density of states of the corresponding quasi-periodic Schrödinger operator is $1/2$-Hölder continuous.

math.DS