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In-Context Learning (ICL) allows Large Language Models (LLMs) to adapt to new tasks with just a few examples, but their predictions often suffer from systematic biases, leading to unstable performance in classification. While calibration…

Current LLM evaluations often rely on a single instruction template, overlooking models' sensitivity to instruction style-a critical aspect for real-world deployments. We present RCScore, a multi-dimensional framework quantifying how…

Cylindrical algebraic decomposition (CAD) is an important tool for the study of real algebraic geometry with many applications both within mathematics and elsewhere. It is known to have doubly exponential complexity in the number of…

This work undertakes a twofold investigation. In the first part, we examine the inequalities and uncertainty principles in the framework of offset linear canonical transform (OLCT), with particular attention to its scaling and shifting…

This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly…

Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations: (1) hallucination, (2) context compression, (3) reasoning degradation, (4) retrieval fragility, and (5)…

A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of…

Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with…

This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…

Deep learning models achieve state-of-the-art performance across domains but face scalability challenges in real-time or resource-constrained scenarios. To address this, we propose Loss Trajectory Correlation (LTC), a novel metric for…

Large Language Models (LLMs) have demonstrated the ability to solve complex tasks through In-Context Learning (ICL), where models learn from a few input-output pairs without explicit fine-tuning. In this paper, we explore the capacity of…

Many-shot in-context learning (ICL) has emerged as a unique setup to both utilize and test the ability of large language models to handle long context. This paper delves into long-context language model (LCLM) evaluation through many-shot…

Logically constrained rewrite systems (LCTRSs) are a versatile and efficient rewriting formalism that can be used to model programs from various programming paradigms, as well as simplification systems in compilers and SMT solvers. In this…

Hamiltonian Monte Carlo (HMC) is a widely deployed method to sample from high-dimensional distributions in Statistics and Machine learning. HMC is known to run very efficiently in practice and its popular second-order "leapfrog"…

We show that coefficients in unicellular LLT polynomials are evaluations of Hecke algebra traces at Kazhdan-Lusztig basis elements. We express these in terms of traditional trace bases, induction, and Kazhdan-Lusztig R-polynomials.

A new purely algebraic algorithm is presented for computation of invariants (generalized Casimir operators) of Lie algebras. It uses the Cartan's method of moving frames and the knowledge of the group of inner automorphisms of each Lie…

Chain-of-Thought (CoT) prompting has been widely recognized for its ability to enhance reasoning capabilities in large language models (LLMs). However, our study reveals a surprising contradiction to this prevailing perspective within the…

In-context learning (ICL) has emerged as a particularly remarkable characteristic of Large Language Models (LLM): given a pretrained LLM and an observed dataset, LLMs can make predictions for new data points from the same distribution…

Hyperproperties, which generalize trace properties by relating multiple traces, are widely studied in information-flow security. Recently, a number of logics for hyperproperties have been proposed, and there is a need to understand their…

Characterizing the Hamiltonians of continuous-variable (CV) quantum systems is a fundamental challenge laden with difficulties arising from infinite-dimensional Hilbert spaces and unbounded operators. Existing protocols for achieving the…