Related papers: Universality, optimality, and randomness deficienc…
Today's pursuit of a single Large Language Model (LMM) for all software engineering tasks is resource-intensive and overlooks the potential benefits of complementarity, where different models contribute unique strengths. However, the degree…
We identify a universal structural principle underlying the smoothing of classical divergences: the optimizer of the smoothing problem is a clipped probability vector, independently of the specific divergence. This yields a…
In this paper, we investigate the potential of open-source Large Language Models (LLMs) for grading Unified Modeling Language (UML) class diagrams. In contrast to existing work, which primarily evaluates proprietary LLMs, we focus on…
Maximum mean discrepancy (MMD) has enjoyed a lot of success in many machine learning and statistical applications, including non-parametric hypothesis testing, because of its ability to handle non-Euclidean data. Recently, it has been…
Self-consistency with chain-of-thought prompting (CoT) has demonstrated remarkable performance gains on various challenging tasks, by utilizing multiple reasoning paths sampled from large language models (LLMs). However, self-consistency…
The statistics of transmission through random 1D media are generally presumed to be universal and to depend only upon a single dimensionless parameter-the ratio of the sample length and the mean free path, s = L/l. Here, we show in…
The seminal result of Johnson and Lindenstrauss on random embeddings has been intensively studied in applied and theoretical computer science. Despite that vast body of literature, we still lack of complete understanding of statistical…
We have discussed earlier the correlation functions of the random variables $\det(\la-X)$ in which $X$ is a random matrix. In particular the moments of the distribution of these random variables are universal functions, when measured in the…
A number of recent experimental measurements suggest the possibility of a breakdown of lepton ($\ell$) universality in exclusive $b \to c \ell \nu_\ell$ semileptonic meson decays. We analyze the full differential decay rates for several…
The paper contains two main parts: in the first part, we analyze the general case of $p\geq 2$ matrices coupled in a chain subject to Cauchy interaction. Similarly to the Itzykson-Zuber interaction model, the eigenvalues of the Cauchy chain…
We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the…
Solomonoff unified Occam's razor and Epicurus' principle of multiple explanations to one elegant, formal, universal theory of inductive inference, which initiated the field of algorithmic information theory. His central result is that the…
Representation learning has been widely studied in the context of meta-learning, enabling rapid learning of new tasks through shared representations. Recent works such as MAML have explored using fine-tuning-based metrics, which measure the…
Nies and Scholz introduced the notion of a state to describe an infinite sequence of qubits and defined quantum-Martin-Lof randomness for states, analogously to the well known concept of Martin-L\"of randomness for elements of Cantor space…
Many works in statistics aim at designing a universal estimation procedure, that is, an estimator that would converge to the best approximation of the (unknown) data generating distribution in a model, without any assumption on this…
This paper extends standard results from learning theory with independent data to sequences of dependent data. Contrary to most of the literature, we do not rely on mixing arguments or sequential measures of complexity and derive uniform…
The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…
When analyzing modern machine learning algorithms, we may need to handle kernel density estimation (KDE) with intricate kernels that are not designed by the user and might even be irregular and asymmetric. To handle this emerging challenge,…
We provide two results concerning the optimality of the maximum mutual information (MMI) decoder. First, we prove that the error exponents of the typical random codes under the optimal maximum likelihood (ML) decoder and the MMI decoder are…
The design and implementation of unit tests is a complex task many programmers neglect. This research evaluates the potential of Large Language Models (LLMs) in automatically generating test cases, comparing them with manual tests. An…