相关论文: A Tight Parallel Repetition Theorem for Partially …

Using proof-theoretical techniques, we analyze a proof by H.-K. Xu regarding a result of strong convergence for the Halpern type proximal point algorithm. We obtain a rate of metastability (in the sense of T. Tao) and also a rate of…

We introduce a variant of PCPs, that we refer to as rectangular PCPs, wherein proofs are thought of as square matrices, and the random coins used by the verifier can be partitioned into two disjoint sets, one determining the row of each…

We show that any language in nondeterministic time $\exp(\exp(\cdots \exp(n)))$, where the number of iterated exponentials is an arbitrary function $R(n)$, can be decided by a multiprover interactive proof system with a classical…

We study channel simulation under common randomness assistance in the finite-blocklength regime and identify the smooth channel max-information as a linear program one-shot converse on the minimal simulation cost for fixed error tolerance.…

We consider distributed plurality consensus in a complete graph of size $n$ with $k$ initial opinions. We design an efficient and simple protocol in the asynchronous communication model that ensures that all nodes eventually agree on the…

In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…

In this paper, we extend the protocol of classical verification of quantum computations (CVQC) recently proposed by Mahadev to make the verification efficient. Our result is obtained in the following three steps: $\bullet$ We show that…

Quantum crosstalk which stems from unwanted interference of quantum operations with nearby qubits is a major source of noise or errors in a quantum processor. In the context of shared quantum computing, it is challenging to mitigate the…

We consider the problem of implementing distributed protocols, despite adversarial channel errors, on synchronous-messaging networks with arbitrary topology. In our first result we show that any $n$-party $T$-round protocol on an undirected…

We study the maximum $k$-set coverage problem in the following distributed setting. A collection of sets $S_1,\ldots,S_m$ over a universe $[n]$ is partitioned across $p$ machines and the goal is to find $k$ sets whose union covers the most…

It is imperative to ensure the stability of every prediction made by a language model; that is, a language's prediction should remain consistent despite minor input variations, like word substitutions. In this paper, we investigate the…

We propose an analytical framework for studying parallel repetition, a basic product operation for one-round two-player games. In this framework, we consider a relaxation of the value of a game, $\mathrm{val}_+$, and prove that for…

We study linear contextual bandits under adversarial corruption and heavy-tailed noise with finite $(1+\epsilon)$-th moments for some $\epsilon \in (0,1]$. Existing work that addresses both adversarial corruption and heavy-tailed noise…

Improving reasoning abilities of Large Language Models (LLMs), especially under parameter constraints, is crucial for real-world applications. Looped transformers address this by performing multiple latent iterations to refine each token…

We study the consensus problem in a synchronous distributed system of $n$ nodes under an adaptive adversary that has a slightly outdated view of the system and can block all incoming and outgoing communication of a constant fraction of the…

This paper proves that the computational power of quantum interactive proof systems, with a double-exponentially small gap in acceptance probability between the completeness and soundness cases, is precisely characterized by EXP, the class…

In near-term quantum computations that do not employ error correction, noise can proliferate rapidly, corrupting the quantum state and making results unreliable. These errors originate from both decoherence and control imprecision. The…

Latent reasoning offers a more efficient alternative to explicit reasoning by compressing intermediate reasoning into continuous representations and substantially shortening reasoning chains. However, existing latent reasoning methods…

When two agents of different computational capacities interact with the same environment, they need not compress a common semantic alphabet differently; they can induce different semantic alphabets altogether. We show that the quotient…

We study the convergence of a random iterative sequence of a family of operators on infinite dimensional Hilbert spaces, inspired by the Stochastic Gradient Descent (SGD) algorithm in the case of the noiseless regression, as studied in [1].…