arXiv subjects

Zishuo Zhao

Publications and source records attributed to Zishuo Zhao.

16 recordsLinked to original sources

arXiv2026

Axiomatization of the Levin--Wen Wave Function

The Levin--Wen model provides a lattice realization of topological orders associated with a given unitary fusion category. A longstanding open problem is to characterize Levin--Wen ground-state wave functions intrinsically, without assuming a priori categorical symmetry data or a Hamiltonian. We address this by proposing six axioms on a family of wave functions defined on lattices at multiple scales. These axioms allow us to reconstruct the underlying unitary fusion category and prove that the resulting wave functions map to nonzero Levin--Wen ground-state vectors of the emergent category.

math-ph↗

arXiv2026

Complexity of tensor network simulation for noisy quantum circuits

We aim to rigorously address how local noise affects classical simulability of quantum dynamics benchmarked by tensor-network methods. Using operator entanglement entropy (OEE), we prove the following: (1) For single-qubit depolarizing noise on arbitrary circuits, tensor networks with $\mathrm{poly}(n)$ bond dimension suffice for fixed absolute Hilbert-Schmidt error after $\order{1}$ depth, while relative error demands $\order{\log n}$ depth; and this bound is optimal. (2) For single-qubit depolarizing noise on 1D local circuits, the existence of whole-trajectory error-bounded matrix product operator (MPO) of $\mathrm{poly}(n)$ bond dimension at all depths. (3) For general single-qubit noise in 1D brickwall circuits, random two-design gates with contraction coefficient $c<1/3$ yield an $\order{1}$ OEE plateau with probability $1-Te^{-\Omega(n)}$, while arbitrary gates with $c<1/48$ give $\order{\log n}$ OEE in the worst case. (4) In higher dimensions, these bounds yield uniform-in-depth $\mathrm{poly}(n)$ average boundary-bond dimensions for projected entangled pair operators~(PEPO) across every cut -- under depolarizing noise at either absolute or relative accuracy, and under general noise with strong contraction at absolute accuracy. Our results establish a rigorous connection between certain noise models, circuit types, and their classical simulability.

cond-mat.str-el↗

arXiv2025

Multi-agent Adaptive Mechanism Design

We study a sequential mechanism design problem in which a principal seeks to elicit truthful reports from multiple rational agents while starting with no prior knowledge of agents' beliefs. We introduce Distributionally Robust Adaptive Mechanism (DRAM), a general framework combining insights from both mechanism design and online learning to jointly address truthfulness and cost-optimality. Throughout the sequential game, the mechanism estimates agents' beliefs and iteratively updates a distributionally robust linear program with shrinking ambiguity sets to reduce payments while preserving truthfulness. Our mechanism guarantees truthful reporting with high probability while achieving $\tilde{O}(\sqrt{T})$ cumulative regret, and we establish a matching lower bound showing that no feasible adaptive mechanism can asymptotically do better. The framework generalizes to plug-in estimators, supporting structured priors and delayed feedback. To our knowledge, this is the first adaptive mechanism under general settings that maintains truthfulness and achieves optimal regret when incentive constraints are unknown and must be learned.

cs.GT↗

arXiv2025

Topological Orders from Reflection Positive Frustration-free Hamiltonians

We establish a framework with reflection positivity as the first principle for establishing the boundary theory of topologically ordered quantum spin systems. For any reflection positive frustration-free Hamiltonian, We proved that the local topological quantum order (LTQO) condition of ground states on a disk holds if and only if the ground state on the sphere is non-degenerate. Furthermore, we show that the Osterwalder-Schrader reconstruction produces the boundary local net of operator algebras from the local ground states.

math-ph↗

arXiv2025

VeriLLM: A Lightweight Framework for Publicly Verifiable Decentralized Inference

Decentralized inference provides a scalable and resilient paradigm for serving large language models (LLMs), enabling fragmented global resource utilization and reducing reliance on centralized providers. However, in a permissionless environment without trusted nodes, ensuring the correctness of model outputs remains a core challenge. We introduce VeriLLM, a publicly verifiable protocol for decentralized LLM inference that achieves security with incentive guarantees while maintaining practical efficiency. VeriLLM combines lightweight empirical rerunning with minimal on-chain checks to preclude free-riding, allowing verifiers to validate results at approximately 1% of the underlying inference cost by exploiting the structural separation between prefill and autoregressive decoding. To prevent verification bottlenecks, we design an isomorphic inference--verification architecture that multiplexes both inference and verification roles across the same GPU workers. This design (i) improves GPU utilization and overall throughput, (ii) enlarges the effective validator set, enhancing robustness and liveness, and (iii) enforces task indistinguishability to prevent node-specific optimizations or selective behavior. Through theoretical analysis and system-level evaluation, we show that VeriLLM achieves reliable public verifiability with minimal overhead, offering a practical foundation for trustworthy and scalable decentralized LLM inference.

cs.CR↗

arXiv2025

Bimodule Quantum Markov Semigroups

We present a systematic investigation of bimodule quantum Markov semigroups within the framework of quantum Fourier analysis. We introduce the concepts of bimodule detailed balance conditions and bimodule KMS symmetry, which not only generalize the classical notions of detailed balance but also expose interesting structures of quantum channels. We demonstrate that the evolution of densities governed by the bimodule quantum Markov semigroup with bimodule detailed balance is the gradient flow for the relative entropy with respect to the hidden density. Consequently, we obtain a modified logarithmic Sobolev inequality and a Talagrand inequality with respect to a hidden density from higher dimensional structure. Furthermore, we establish a Poincar\'{e} inequality for irreducible inclusions and relative ergodic bimodule quantum semigroups.

quant-ph↗

arXiv2024

FLEX-CLIP: Feature-Level GEneration Network Enhanced CLIP for X-shot Cross-modal Retrieval

Given a query from one modality, few-shot cross-modal retrieval (CMR) retrieves semantically similar instances in another modality with the target domain including classes that are disjoint from the source domain. Compared with classical few-shot CMR methods, vision-language pretraining methods like CLIP have shown great few-shot or zero-shot learning performance. However, they still suffer challenges due to (1) the feature degradation encountered in the target domain and (2) the extreme data imbalance. To tackle these issues, we propose FLEX-CLIP, a novel Feature-level Generation Network Enhanced CLIP. FLEX-CLIP includes two training stages. In multimodal feature generation, we propose a composite multimodal VAE-GAN network to capture real feature distribution patterns and generate pseudo samples based on CLIP features, addressing data imbalance. For common space projection, we develop a gate residual network to fuse CLIP features with projected features, reducing feature degradation in X-shot scenarios. Experimental results on four benchmark datasets show a 7%-15% improvement over state-of-the-art methods, with ablation studies demonstrating enhancement of CLIP features.

cs.CV↗

arXiv2024

It Takes Two: A Peer-Prediction Solution for Blockchain Verifier's Dilemma

The security of blockchain systems is fundamentally based on the decentralized consensus in which the majority of parties behave honestly, and the content verification process is essential to maintaining the robustness of blockchain systems. However, the phenomenon that a rational verifier may not have the incentive to honestly perform the costly verification, referred to as the Verifier's Dilemma, could incentivize lazy reporting and undermine the fundamental security of blockchain systems, particularly for verification-expensive decentralized AI applications. In this paper, we initiate the research with the development of a Byzantine-robust peer prediction framework towards the design of one-phase Bayesian truthful mechanisms for the decentralized verification games among multiple verifiers, incentivizing all verifiers to perform honest verification without access to the ground truth even in the presence of noisy observations, malicious players and inaccurate priors in the verification process, proposing the compactness criteria that ensures such robustness guarantees. With robust incentive guarantees and budget efficiency, our study provides a framework of incentive design for decentralized verification protocols that enhances the security and robustness of the blockchain, decentralized AI, and potentially other decentralized systems.

cs.CR↗

arXiv2024

Proof-of-Learning with Incentive Security

Most concurrent blockchain systems rely heavily on the Proof-of-Work (PoW) or Proof-of-Stake (PoS) mechanisms for decentralized consensus and security assurance. However, the substantial energy expenditure stemming from computationally intensive yet meaningless tasks has raised considerable concerns surrounding traditional PoW approaches, The PoS mechanism, while free of energy consumption, is subject to security and economic issues. Addressing these issues, the paradigm of Proof-of-Useful-Work (PoUW) seeks to employ challenges of practical significance as PoW, thereby imbuing energy consumption with tangible value. While previous efforts in Proof of Learning (PoL) explored the utilization of deep learning model training SGD tasks as PoUW challenges, recent research has revealed its vulnerabilities to adversarial attacks and the theoretical hardness in crafting a byzantine-secure PoL mechanism. In this paper, we introduce the concept of incentive-security that incentivizes rational provers to behave honestly for their best interest, bypassing the existing hardness to design a PoL mechanism with computational efficiency, a provable incentive-security guarantee and controllable difficulty. Particularly, our work is secure against two attacks, and also improves the computational overhead from $\Theta(1)$ to $O(\frac{\log E}{E})$. Furthermore, while most recent research assumes trusted problem providers and verifiers, our design also guarantees frontend incentive-security even when problem providers are untrusted, and verifier incentive-security that bypasses the Verifier's Dilemma. By incorporating ML training into blockchain consensus mechanisms with provable guarantees, our research not only proposes an eco-friendly solution to blockchain systems, but also provides a proposal for a completely decentralized computing power market in the new AI age.

cs.CR↗

arXiv2023

Relative Entropy for Quantum Channels

We introduce an quantum entropy for bimodule quantum channels on finite von Neumann algebras, generalizing the remarkable Pimsner-Popa entropy. The relative entropy for Fourier multipliers of bimodule quantum channels establishes an upper bound of the quantum entropy. Additionally, we present the Araki relative entropy for bimodule quantum channels, revealing its equivalence to the relative entropy for Fourier multipliers and demonstrating its left/right monotonicities and convexity. Notably, the quantum entropy attains its maximum if there is a downward Jones basic construction. By considering Rényi entropy for Fourier multipliers, we find a continuous bridge between the logarithm of the Pimsner-Popa index and the Pimsner-Popa entropy. As a consequence, the Rényi entropy at $1/2$ serves a criterion for the existence of a downward Jones basic construction.

math.OA↗

arXiv2023

Almost Abelian Lie groups, subgroups and quotients

An almost Abelian Lie group is a non-Abelian Lie group with a codimension 1 Abelian normal subgroup. The majority of 3-dimensional real Lie groups are almost Abelian, and they appear in all parts of physics that deal with anisotropic media - cosmology, crystallography etc. In theoretical physics and differential geometry, almost Abelian Lie groups and their homogeneous spaces provide some of the simplest solvmanifolds on which a variety of geometric structures such as symplectic, Kähler, spin etc., are currently studied in explicit terms. Recently, almost Abelian Lie algebras were classified and studied in details. However, a systematic investigation of almost Abelian Lie groups has not been carried out yet, and the present paper is devoted to an explicit description of properties of this wide and diverse class of groups. The subject of investigation are real almost Abelian Lie groups with their Lie group theoretical aspects, such as the exponential map, faithful matrix representations, discrete and connected subgroups, quotients and automorphisms. The emphasis is put on explicit description of all technical details.

math.GR↗

arXiv2022

Bayesian Mechanism Design for Blockchain Transaction Fee Allocation

In blockchain systems, the design of transaction fee mechanisms is essential for stability and satisfaction for both miners and users. A recent work has proven the impossibility of collusion-proof mechanisms that achieve both non-zero miner revenue and Dominating-Strategy-Incentive-Compatible (DSIC) for users. However, a positive miner revenue is important in practice to motivate miners. To address this challenge, we consider a Bayesian game setting and relax the DSIC requirement for users to Bayesian-Nash-Incentive-Compatibility (BNIC). In particular, we propose an auxiliary mechanism method that makes connections between BNIC and DSIC mechanisms. With the auxiliary mechanism method, we design a transaction fee mechanism (TFM) based on the multinomial logit (MNL) choice model, and prove that the TFM has both BNIC and collusion-proof properties with an asymptotic constant-factor approximation of optimal miner revenue for i.i.d. bounded valuations. Our result breaks the zero-revenue barrier while preserving truthfulness and collusion-proof properties.

cs.GT↗

arXiv2022

Noise-Stable Rigid Graphs for Euclidean Embedding

We proposed a new criterion \textit{noise-stability}, which revised the classical rigidity theory, for evaluation of MDS algorithms which can truthfully represent the fidelity of global structure reconstruction; then we proved the noise-stability of the cMDS algorithm in generic conditions, which provides a rigorous theoretical guarantee for the precision and theoretical bounds for Euclidean embedding and its application in fields including wireless sensor network localization and satellite positioning. Furthermore, we looked into previous work about minimum-cost globally rigid spanning subgraph, and proposed an algorithm to construct a minimum-cost noise-stable spanning graph in the Euclidean space, which enabled reliable localization on sparse graphs of noisy distance constraints with linear numbers of edges and sublinear costs in total edge lengths. Additionally, this algorithm also suggests a scheme to reconstruct point clouds from pairwise distances at a minimum of $O(n)$ time complexity, down from $O(n^3)$ for cMDS.

cs.CG↗

arXiv2022

An Asymptotic Analysis on Generalized Secretary Problem

As a famous result, the ``37\% Law'' for Secretary Problem has widely influenced peoples' perception on online decision strategies about choice. However, using this strategy, too many attractive candidates may be rejected in the first 37\%, and in practice people also tend to stop earlier\cite{Bearden_early}. In this paper, we argued that in most cases, the best-only optimization does not obtain an optimal outcome, while the optimal cutoff should be $O(\sqrt{n})$. And we also showed that in some strict objective that only cares several best candidates, $Θ(n)$ skips are still needed.

cs.GT↗

arXiv2022

Musical Instrument Classification via Low-Dimensional Feature Vectors

Music is a mysterious language that conveys feeling and thoughts via different tones and timbre. For better understanding of timbre in music, we chose music data of 6 representative instruments, analysed their timbre features and classified them. Instead of the current trend of Neural Network for black-box classification, our project is based on a combination of MFCC and LPC, and augmented with a 6-dimensional feature vector designed by ourselves from observation and attempts. In our white-box model, we observed significant patterns of sound that distinguish different timbres, and discovered some connection between objective data and subjective senses. With a totally 32-dimensional feature vector and a naive all-pairs SVM, we achieved improved classification accuracy compared to a single tool. We also attempted to analyze music pieces downloaded from the Internet, found out different performance on different instruments, explored the reasons and suggested possible ways to improve the performance.

cs.SD↗

arXiv2022

Dynamic Car Dispatching and Pricing: Revenue and Fairness for Ridesharing Platforms

A major challenge for ridesharing platforms is to guarantee profit and fairness simultaneously, especially in the presence of misaligned incentives of drivers and riders. We focus on the dispatching-pricing problem to maximize the total revenue while keeping both drivers and riders satisfied. We study the computational complexity of the problem, provide a novel two-phased pricing solution with revenue and fairness guarantees, extend it to stochastic settings and develop a dynamic (a.k.a., learning-while-doing) algorithm that actively collects data to learn the demand distribution during the scheduling process. We also conduct extensive experiments to demonstrate the effectiveness of our algorithms.

math.OC↗