Related papers: Composing Linear Layers from Irreducibles
In this paper we show that it is possible to retrieve structural information about complex block-oriented nonlinear systems, starting from linear approximations of the nonlinear system around different setpoints.The key idea is to monitor…
Human ability to recognize complex visual patterns arises through transformations performed by successive areas in the ventral visual cortex. Deep neural networks trained end-to-end for object recognition approach human capabilities, and…
Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…
We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
Deep neural networks used for image classification often use convolutional filters to extract distinguishing features before passing them to a linear classifier. Most interpretability literature focuses on providing semantic meaning to…
Processing spatial data is a key component in many learning tasks for autonomous driving such as motion forecasting, multi-agent simulation, and planning. Prior works have demonstrated the value in using SE(2) invariant network…
Recent work has proposed that language models perform computation by manipulating one-dimensional representations of concepts ("features") in activation space. In contrast, we explore whether some language model representations may be…
This work attempts to interpret modern deep (convolutional) networks from the principles of rate reduction and (shift) invariant classification. We show that the basic iterative gradient ascent scheme for optimizing the rate reduction of…
We present different methods for symbolic computer algebra computations in higher dimensional (\ge9) Clifford algebras using the \Clifford\ and \Bigebra\ packages for \Maple(R). This is achieved using graded tensor decompositions,…
Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind:…
Input-output maps are prevalent throughout science and technology. They are empirically observed to be biased towards simple outputs, but we don't understand why. To address this puzzle, we study the archetypal input-output map: a…
Large language models (LLMs) have demonstrated broad utility across molecular domains, spanning drug discovery and materials design. Analyzing LLMs' latent representations is crucial for elucidating their underlying mechanisms, improving…
We explore two differentiable deep declarative layers, namely least squares on sphere (LESS) and implicit eigen decomposition (IED), for learning the principal matrix features (PMaF). It can be used to represent data features with a…
Large language models (LLMs) have shown an impressive ability to perform tasks believed to require thought processes. When the model does not document an explicit thought process, it becomes difficult to understand the processes occurring…
We use a tensor unfolding technique to prove a new identifiability result for discrete bipartite graphical models, which have a bipartite graph between an observed and a latent layer. This model family includes popular models such as…
Task vector composition has emerged as a promising paradigm for editing pre-trained models, enabling model merging through addition and unlearning through subtraction. Fine-tuning in the tangent space of a pre-trained model (linear…
We construct an L^2-model of "very small" irreducible unitary representations of simple Lie groups G which, up to finite covering, occur as conformal groups Co(V) of simple Jordan algebras V. If $V$ is split and G is not of type A_n, then…
Geometric analyses of large language model (LLM) representations reveal structured variation across depth but remain fundamentally correlational with respect to token prediction formation. Meanwhile, causal interventions expose…
A number of applications, such as mobile robots or automated vehicles, use LiDAR sensors to obtain detailed information about their three-dimensional surroundings. Many methods use image-like projections to efficiently process these LiDAR…