Related papers: Recognising the small Ree groups in their natural …
Computational problem certificates are additional data structures for each output, which can be used by a-possibly randomized-verification algorithm that proves the correctness of each output. In this paper, we give an algorithm that…
Retrieval-Augmented Generation (RAG) equips large language models (LLMs) with external evidence by retrieving documents at inference time, but it also turns the retrieval corpusinto a sensitive asset. Under a black-box setting, an adversary…
We compute the l-modular decomposition matrices of the simple Ree groups 2F4(q^2), where q^2=2^{2n+1} and n is a positive integer, for all primes l > 3 up to some entries in the unipotent characters. Using these matrices we determine the…
Given a black box group $\mathsf{Y}$ encrypting $\rm{PSL}_2(\mathbb{F})$ over an unknown field $\mathbb{F}$ of unknown odd characteristic $p$ and a global exponent $E$ for $\mathsf{Y}$ (that is, an integer $E$ such that $\mathsf{y}^E=1$ for…
We present several algorithms for evaluating point containment in constructive solid geometry (CSG) trees with unbounded primitives. Three algorithms are presented based on postfix, prefix, and infix notations of the CSG binary expression…
A structured variable selection problem is considered in which the covariates, divided into predefined groups, activate according to sparse patterns with few nonzero entries per group. Capitalizing on the concept of atomic norm, a composite…
We consider several subgroup-related algorithmic questions in groups, modeled after the classic computational lattice problems, and study their computational complexity. We find polynomial time solutions to problems like finding a subgroup…
We develop a systematic approach for surrogate model construction in reduced input parameter spaces. A sparse set of model evaluations in the original input space is used to approximate derivative based global sensitivity measures (DGSMs)…
We develop a statistical proxy framework for retrieval-augmented generation (RAG), designed to formalize how a language model (LM) should balance its own predictions with retrieved evidence. For each query x, the system combines a frozen…
As demonstrated by GPT-3 and T5, transformers grow in capability as parameter spaces become larger and larger. However, for tasks that require a large amount of knowledge, non-parametric memory allows models to grow dramatically with a…
We give an efficient algorithm for Lang's Theorem in split connected reductive groups defined over finite fields of characteristic greater than 3. This algorithm can be used to construct many important structures in finite groups of Lie…
Local robustness ensures that a model classifies all inputs within an $\ell_2$-ball consistently, which precludes various forms of adversarial inputs. In this paper, we present a fast procedure for checking local robustness in feed-forward…
Restricted Boltzmann Machines (RBMs) are widely used probabilistic undirected graphical models with visible and latent nodes, playing an important role in statistics and machine learning. The task of structure learning for RBMs involves…
Automated question-answering (QA) systems increasingly rely on retrieval-augmented generation (RAG) to ground large language models (LLMs) in authoritative medical knowledge, ensuring clinical accuracy and patient safety in Artificial…
Retrieval-augmented generation (RAG) systems expose numerous design choices spanning query rewriting, chunking, retrieval depth, reranking, and context compression. In practice, these choices are often configured through heuristics,…
This paper introduces the theory and practice of formal verification of self-assembling systems. We interpret a well-studied abstraction of nanomolecular self assembly, the Abstract Tile Assembly Model (aTAM), into Computation Tree Logic…
We study the class of 3-dimensional nonlinear 2-hessian equations mentioned in the text. We perform preliminary group classification on 2-hessian equation. In fact, we find additional equivalence transformation on the space (x,y,z,u,f),…
The problem of finding a nontrivial factor of a polynomial f(x) over a finite field F_q has many known efficient, but randomized, algorithms. The deterministic complexity of this problem is a famous open question even assuming the…
Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension…
We present RAG Playground, an open-source framework for systematic evaluation of Retrieval-Augmented Generation (RAG) systems. The framework implements and compares three retrieval approaches: naive vector search, reranking, and hybrid…