Related papers: Spectral Superposition: A Theory of Feature Geomet…
Comparing the internal representations of neural networks is a central goal in both neuroscience and machine learning. Standard alignment metrics operate on raw neural activations, implicitly assuming that similar representations produce…
Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of…
Interpreting graph neural networks (GNNs) is difficult because message passing mixes signals and internal channels rarely align with human concepts. We study superposition, the sharing of directions by multiple features, directly in the…
The representations of neural networks are often compared to those of biological systems by performing regression between the neural network responses and those measured from biological systems. Many different state-of-the-art deep neural…
A central idea in mechanistic interpretability is that neural networks represent more features than they have dimensions, arranging them in superposition to form an over-complete basis. This framing has been influential, motivating…
Motivated by the human way of memorizing images we introduce their functional representation, where an image is represented by a neural network. For this purpose, we construct a hypernetwork which takes an image and returns weights to the…
The superposition hypothesis states that single neurons may participate in representing multiple features in order for the neural network to represent more features than it has neurons. In neuroscience and AI, representational alignment…
Deep learning has been widely used for hyperspectral pixel classification due to its ability of generating deep feature representation. However, how to construct an efficient and powerful network suitable for hyperspectral data is still…
Model merging enables powerful capabilities in neural networks without requiring additional training. In this paper, we introduce a novel perspective on model merging by leveraging the fundamental mechanisms of neural network…
Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
Superposition refers to encoding representations of multiple features within a single neuron, which is common in deep neural networks. This property allows neurons to combine and represent multiple features, enabling the model to capture…
There is a large variety of machine learning methodologies that are based on the extraction of spectral geometric information from data. However, the implementations of many of these methods often depend on traditional eigensolvers, which…
Neural models learn data representations that lie on low-dimensional manifolds, yet modeling the relation between these representational spaces is an ongoing challenge. By integrating spectral geometry principles into neural modeling, we…
Neural networks achieve remarkable performance through superposition: encoding multiple features as overlapping directions in activation space rather than dedicating individual neurons to each feature. This challenges interpretability, yet…
Intermediate feature representations represent the backbone for the expressivity and adaptability of deep neural networks. However, their geometric structure remains poorly understood. In this submission, we provide indirect insights into…
One of the most prominent attributes of Neural Networks (NNs) constitutes their capability of learning to extract robust and descriptive features from high dimensional data, like images. Hence, such an ability renders their exploitation as…
We propose a metric, Layer Saturation, defined as the proportion of the number of eigenvalues needed to explain 99% of the variance of the latent representations, for analyzing the learned representations of neural network layers.…
Alignment, the tendency of adjacent weight matrices in deep networks to develop compatible subspace orientations, underlies gradient flow, Neural Collapse, and representation similarity across architectures. Despite extensive empirical…
The push to train ever larger neural networks has motivated the study of initialization and training at large network width. A key challenge is to scale training so that a network's internal representations evolve nontrivially at all…