Related papers: Multivariate growth and cogrowth
This paper empirically investigates the relationship between subword vocabulary size and the performance of large language models (LLMs) to provide insights on how to define the vocabulary size. Experimental results show that larger…
In this paper we propose a class of randomized primal-dual methods to contend with large-scale saddle point problems defined by a convex-concave function $\mathcal{L}(\mathbf{x},y)\triangleq\sum_{i=1}^m f_i(x_i)+\Phi(\mathbf{x},y)-h(y)$. We…
The observed accelerated expansion of the Universe may be explained by dark energy or the breakdown of general relativity (GR) on cosmological scales. When the latter case, a modified gravity scenario, is considered, it is often assumed…
We study sampling from a target distribution ${\nu_* = e^{-f}}$ using the unadjusted Langevin Monte Carlo (LMC) algorithm. For any potential function $f$ whose tails behave like ${\|x\|^\alpha}$ for ${\alpha \in [1,2]}$, and has…
In this paper we further study the relationship between convexity and additive growth, building on the work of Schoen and Shkredov (\cite{SS}) to get some improvements to earlier results of Elekes, Nathanson and Ruzsa (\cite{ENR}). In…
We study the evolution of scalar cosmological perturbations in the (1+3)- covariant gauge-invariant formalism for generic $f(R)$ theories of gravity. Extending previous works, we give a complete set of equations describing the evolution of…
With the ascent of large language models (LLM), natural language processing has witnessed enhancements, such as LLM-based data augmentation. Nonetheless, prior research harbors two primary concerns: firstly, a lack of contemplation…
Large Language Models are increasingly used by students to explore advanced material in computer science, including graph theory. As these tools become integrated into undergraduate and graduate coursework, it is important to understand how…
Grammar-based test case generation has proven effective for competitive programming problems, but generating valid and general grammars from natural language specifications remains a key challenge, especially under limited supervision.…
We investigate quantitative aspects of the LEF property for subgroups of the topological full group $[[ \sigma ]]$ of a two-sided minimal subshift over a finite alphabet, measured via the LEF growth function. We show that the LEF growth of…
We present an improved framework for estimating the growth rate of large-scale structure, using measurements of the galaxy-velocity cross-correlation in configuration space. We consider standard estimators of the velocity auto-correlation…
The dominant approach to generating from language models subject to some constraint is locally constrained decoding (LCD), incrementally sampling tokens at each time step such that the constraint is never violated. Typically, this is…
Large language models (LLMs) are becoming increasingly better at a wide range of Natural Language Processing tasks (NLP), such as text generation and understanding. Recently, these models have extended their capabilities to coding tasks,…
Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the…
Large Language Models (LLMs) have demonstrated strong performance across a wide range of tasks, yet they still struggle with complex mathematical reasoning, a challenge fundamentally rooted in deep structural dependencies. To address this…
We define the Cayley graph and its growth function for multivalued groups. We prove that if we change a finite set of generators of multivalued group, or change the starting point, we get an equivalent growth function. We prove that if we…
The growth-fragmentation equation models systems of particles that grow and split as time proceeds. An important question concerns the large time asymptotic of its solutions. Doumic and Escobedo ($2016$) observed that when growth is a…
Current cosmological tensions show that it is crucial to test the predictions from the canonical $\Lambda$CDM paradigm at different cosmic times. One very appealing test of structure formation in the universe is the growth rate of structure…
Large Language Models (LLMs) have demonstrated the capability to refine their generated answers through self-correction, enabling continuous performance improvement over multiple rounds. However, the mechanisms underlying how and why…
This essay proposes an interpretive analogy between large language models (LLMs) and quasicrystals, systems that exhibit global coherence without periodic repetition, generated through local constraints. While LLMs are typically evaluated…