srf-similarity-representation-factorization

name	srf-similarity-representation-factorization
description	Similarity-Based Representation Factorization (SRF) methodology for recovering low-dimensional, non-negative, interpretable embeddings from similarity matrices
version	1.0.0
author	Hermes Agent
created	2026-05-28T00:00:00.000Z
arxiv_id	2605.26921
tags	["representation-learning","dimensionality-reduction","similarity-matrix","interpretability","neuroscience","brain-representation","ai-alignment"]
activation_keywords	["srf","similarity-based representation","representation factorization","interpretable embeddings","brain representation","neural representation","similarity matrix","representation dimensions"]

Similarity-Based Representation Factorization (SRF)

Overview

SRF (Similarity-Based Representation Factorization) is a general computational method for recovering low-dimensional, non-negative, interpretable embeddings from similarity matrices derived from measured data. It addresses the fundamental challenge of understanding the dimensions that shape representations across neuroscience, psychology, and artificial intelligence.

Key Innovation

From Similarity Matrices to Interpretable Dimensions

• Recovers low-dimensional embeddings directly from similarity data
• Non-negative factorization for interpretability
• Works with sparsely sampled, incomplete data
• General-purpose method across diverse data types

Core Problem Addressed

Current representation analysis methods:

• Study representations through similarities between stimuli
• Provide limited access to underlying dimensions
• Often lack interpretability
• Cannot handle sparse/incomplete data well

SRF solution:

• Direct dimension recovery from similarity matrices
• Interpretable non-negative embeddings
• Robust to sparse sampling
• Higher power for hypothesis testing

Technical Framework

Mathematical Foundation

SRF Factorization:

Given similarity matrix S ∈ ℝⁿˣⁿ
Find: S ≈ F · Fᵀ
Where: F ∈ ℝⁿˣᵏ (k dimensions)
Constraint: F ≥ 0 (non-negative)

Key Properties:

• Low-dimensional representation (k << n)
• Non-negative factors for interpretability
• Interprets each dimension as a distinct representation feature
• Preserves similarity structure in factorized form

Algorithm Steps

1. Similarity Matrix Construction

   • Compute pairwise similarities from neural/behavioral/AI data
   • Handle sparse/incomplete sampling
   • Normalize similarity structure

2. Dimension Selection

   • Determine optimal number of dimensions k
   • Use cross-validation or information criteria
   • Balance interpretability vs accuracy

3. Non-Negative Factorization

   • Apply NMF-like optimization
   • Constrain factors to be non-negative
   • Ensure each dimension interpretable