Statistical Mechanics of Semantic Compression
This work addresses the fundamental challenge of compressing information based on meaning rather than bits, which could impact fields like natural language processing and data storage, though it appears incremental by applying statistical mechanics to an existing concept.
The paper tackles the problem of semantic compression, which aims to minimize message length while preserving meaning in a semantic space modeled as Euclidean vectors, and maps this optimization to a spin glass Hamiltonian solved using replica theory, identifying phase transitions between lossy/lossless and extractive/abstractive compression, with numerical simulations showing efficient near-optimal algorithms in typical cases.
The basic problem of semantic compression is to minimize the length of a message while preserving its meaning. This differs from classical notions of compression in that the distortion is not measured directly at the level of bits, but rather in an abstract semantic space. In order to make this precise, we take inspiration from cognitive neuroscience and machine learning and model semantic space as a continuous Euclidean vector space. In such a space, stimuli like speech, images, or even ideas, are mapped to high-dimensional real vectors, and the location of these embeddings determines their meaning relative to other embeddings. This suggests that a natural metric for semantic similarity is just the Euclidean distance, which is what we use in this work. We map the optimization problem of determining the minimal-length, meaning-preserving message to a spin glass Hamiltonian and solve the resulting statistical mechanics problem using replica theory. We map out the replica symmetric phase diagram, identifying distinct phases of semantic compression: a first-order transition occurs between lossy and lossless compression, whereas a continuous crossover is seen from extractive to abstractive compression. We conclude by showing numerical simulations of compressions obtained by simulated annealing and greedy algorithms, and argue that while the problem of finding a meaning-preserving compression is computationally hard in the worst case, there exist efficient algorithms which achieve near optimal performance in the typical case.