Related papers: Counterexample to majority optimality in NICD with…
The Index-Erasure problem is a quantum state generation problem that asks a quantum computer to prepare a uniform superposition over the image of an injective function given by an oracle. We prove a tight $\Omega(\sqrt{n})$ lower bound on…
Recent LLMs have significantly improved reasoning capabilities, primarily by including an explicit, lengthy Thinking process as part of generation. In this paper, we question whether this explicit thinking is necessary. Using the…
Modern digital electronics support remarkably reliable computing, especially given the challenge of controlling nanoscale logical components that interact in fluctuating environments. However, we demonstrate that the high-reliability limit…
Knowledge distillation (KD) is the de facto standard for compressing large-scale models into smaller ones. Prior works have explored ever more complex KD strategies involving different objective functions, teacher-ensembles, and weight…
The number partition problem is a well-known problem, which is one of 21 Karp's NP-complete problems \cite{karp}. The partition function is a boolean function that is equivalent to the number partition problem with number range restricted.…
Let $0 < \epsilon < 1/2$ be a noise parameter, and let $T_{\epsilon}$ be the noise operator acting on functions on the boolean cube $\{0,1\}^n$. Let $f$ be a nonnegative function on $\{0,1\}^n$. We upper bound the entropy of $T_{\epsilon}…
Floating-point non-associativity makes fundamental deep learning operations, such as matrix multiplication (matmul) on GPUs, inherently non-deterministic. Despite this, the statistical structure of the resulting numerical error remains…
Gaussian Boson Sampling (GBS), which can be realized with a photonic quantum computing model, perform some special kind of sampling tasks. In [4], we introduced algorithms that use GBS samples to approximate Gaussian expectation problems.…
We determine the exact freezing threshold, r^f, for a family of models of random boolean constraint satisfaction problems, including NAE-SAT and hypergraph 2-colouring, when the constraint size is sufficiently large. If the…
Despite the empirical success of knowledge distillation, current state-of-the-art methods are computationally expensive to train, which makes them difficult to adopt in practice. To address this problem, we introduce two distinct…
In this paper, we prove that with high probability, random Reed-Solomon codes approach the half-Singleton bound - the optimal rate versus error tradeoff for linear insdel codes - with linear-sized alphabets. More precisely, we prove that,…
A Gaussian boson sampler (GBS) is a special-purpose quantum computer that can be practically realized at large scale in optics. Here we report on experiments in which we used a frequency-multiplexed GBS with $>400$ modes as the reservoir in…
We propose an algorithm for answering conjunctive queries with negation, where the negated relations have bounded degree. Its data complexity matches that of the best known algorithms for the positive subquery of the input query and is…
The choice of negative examples is important in noise contrastive estimation. Recent works find that hard negatives -- highest-scoring incorrect examples under the model -- are effective in practice, but they are used without a formal…
We study the properties of error correcting codes for noise models in the presence of asymmetries and/or correlations by means of the entanglement fidelity and the code entropy. First, we consider a dephasing Markovian memory channel and…
This paper introduces a new algorithm for the fundamental problem of generating a random integer from a discrete probability distribution using a source of independent and unbiased random coin flips. We prove that this algorithm, which we…
In the number partitioning problem (NPP) one aims to partition a given set of $N$ real numbers into two subsets with approximately equal sum. The NPP is a well-studied optimization problem and is famous for possessing a…
Non-adaptive group testing refers to the problem of inferring a sparse set of defectives from a larger population using the minimum number of simultaneous pooled tests. Recent positive results for noiseless group testing have motivated the…
One of the most controversial problems in neural decoding is quantifying the information loss caused by ignoring noise correlations during optimal brain computations. For more than a decade, the measure here called $ \Delta I^{DL} $ has…
Large-scale nonsmooth optimization problems arise in many real-world applications, but obtaining exact function and subgradient values for these problems may be computationally expensive or even infeasible. In many practical settings, only…