Related papers: A neuro-mathematical model for size and context re…
Large Language Models (LLMs) are powerful linguistic engines but remain susceptible to hallucinations: plausible-sounding outputs that are factually incorrect or unsupported. In this work, we present a mathematically grounded framework to…
Understanding sensory-induced cortical patterns in the primary visual cortex V1 is an important challenge both for physiological motivations and for improving our understanding of human perception and visual organisation. In this work, we…
Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their…
Previous work has shown correlations between the hidden states of large language models and fMRI brain responses, on language tasks. These correlations have been taken as evidence of the representational similarity of these models and brain…
We give a bird's-eye view of the plastic deformation of crystals aimed at the statistical physics community, and a broad introduction into the statistical theories of forced rigid systems aimed at the plasticity community. Memory effects in…
Large Language Models (LLMs) often hallucinate, producing unfaithful or factually incorrect outputs by misrepresenting the provided context or incorrectly recalling internal knowledge. Recent studies have identified specific attention heads…
On a slice of AdS_5, despite having a dimensionful coupling, gauge theories can exhibit logarithmic dependence on scale. In this paper, we utilize deconstruction to analyze the scaling behavior of the theory, both above and below the AdS…
The scaling of correlations as a function of system size provides important hints to understand critical phenomena on a variety of systems. Its study in biological systems offers two challenges: usually they are not of infinite size, and in…
Interest is growing in social learning models where users share opinions and adjust their beliefs in response to others. This paper introduces generalized-bias opinion models, an extension of the DeGroot model, that captures a broader range…
We quantify the degree of nonlinearity and stochasticity of the clustering of biased objects, using cosmological N-body simulations. Adopting the peaks and the halos as representative biasing models, we focus on the two-point correlation of…
We study obstructed deformation problems for two-dimensional residual Galois representations arising from weight~$2$ newforms of level~$N$. Using Poitou-Tate duality, we isolate local and global sources of obstructions and give concrete…
Given time series data, how can we answer questions like "what will happen in the future?" and "how did we get here?" These sorts of probabilistic inference questions are challenging when observations are high-dimensional. In this paper, we…
Scaling up language models has led to unprecedented performance gains, but little is understood about how the training dynamics change as models get larger. How do language models of different sizes learn during pre-training? Why do larger…
Recent advancements in text-to-image generative models have demonstrated a remarkable ability to capture a deep semantic understanding of images. In this work, we leverage this semantic knowledge to transfer the visual appearance between…
Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the FCA monograph, still has room for improvement. As it stands, even some of the basic…
We present a novel method to generate accurate and realistic clothing deformation from real data capture. Previous methods for realistic cloth modeling mainly rely on intensive computation of physics-based simulation (with numerous…
We study the matter bispectrum of large-scale structure by comparing the predictions of different perturbative and phenomenological models with the full three-dimensional bispectrum from $N$-body simulations estimated using modal methods.…
High-dimensional representations for words, text, images, knowledge graphs and other structured data are commonly used in different paradigms of machine learning and data mining. These representations have different degrees of…
We investigate the effect of a non-uniform deformation applied to one-dimensional (1D) quantum systems, where the local energy scale is proportional to $g_j = [\sin (j \pi / N)]^m$ determined by a positive integer $m$, site index $1 \leq j…
In recent years, promising mathematical models have been suggested which aim to describe conscious experience and its relation to the physical domain. Whereas the axioms and metaphysical ideas of these theories have been carefully…