Statistical Mechanics of Semantic Compression

• URL: http://arxiv.org/abs/2503.00612v1
• Date: Sat, 01 Mar 2025 20:38:16 GMT
• Title: Statistical Mechanics of Semantic Compression
• Authors: Tankut Can,
• Abstract summary: We take inspiration from cognitive neuroscience and machine learning and model semantic space as a continuous Euclidean vector space.<n>We map the optimization problem of determining the minimal-length, meaning-preserving message to a spin glass Hamiltonian.<n>We 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Hierarchical Semantic Compression for Consistent Image Semantic Restoration [62.97519327310638]
  We propose a novel hierarchical semantic compression (HSC) framework that purely operates within intrinsic semantic spaces from generative models.<n> Experimental results demonstrate that the proposed HSC framework achieves the state-of-the-art performance on subjective quality and consistency for human vision.
  arXiv  Detail & Related papers  (2025-02-24T03:20:44Z)
• Problem-dependent convergence bounds for randomized linear gradient compression [4.656302602746228]
  In distributed optimization, the communication model updates can be a performance bottleneck.<n> gradient compression has been proposed as a means of increasing optimization.<n>We study how the impact of compression on throughput can be in terms of the norm of the Hessian objective.
  arXiv  Detail & Related papers  (2024-11-19T22:26:42Z)
• Compression of Structured Data with Autoencoders: Provable Benefit of Nonlinearities and Depth [83.15263499262824]
  We prove that gradient descent converges to a solution that completely disregards the sparse structure of the input. We show how to improve upon Gaussian performance for the compression of sparse data by adding a denoising function to a shallow architecture. We validate our findings on image datasets, such as CIFAR-10 and MNIST.
  arXiv  Detail & Related papers  (2024-02-07T16:32:29Z)
• Crossword: A Semantic Approach to Data Compression via Masking [38.107509264270924]
  This study places careful emphasis on English text and exploits its semantic aspect to enhance the compression efficiency further. The proposed masking-based strategy resembles the above game. In a nutshell, the encoder evaluates the semantic importance of each word according to the semantic loss and then masks the minor ones, while the decoder aims to recover the masked words from the semantic context by means of the Transformer.
  arXiv  Detail & Related papers  (2023-04-03T16:04:06Z)
• Lower Bounds and Nearly Optimal Algorithms in Distributed Learning with Communication Compression [33.217552987061474]
  Communication compression is one of the most effective means of reducing communication. Recent advances in distributed optimization and learning have shown that communication compression is one of the most effective means of reducing communication.
  arXiv  Detail & Related papers  (2022-06-08T03:36:34Z)
• Unified Multivariate Gaussian Mixture for Efficient Neural Image Compression [151.3826781154146]
  latent variables with priors and hyperpriors is an essential problem in variational image compression. We find inter-correlations and intra-correlations exist when observing latent variables in a vectorized perspective. Our model has better rate-distortion performance and an impressive $3.18times$ compression speed up.
  arXiv  Detail & Related papers  (2022-03-21T11:44:17Z)
• Partition and Code: learning how to compress graphs [50.29024357495154]
  "Partition and Code" framework entails three steps: first, a partitioning algorithm decomposes the graph into elementary structures, then these are mapped to the elements of a small dictionary on which we learn a probability distribution, and finally, an entropy encoder translates the representation into bits. Our algorithms are quantitatively evaluated on diverse real-world networks obtaining significant performance improvements with respect to different families of non-parametric and parametric graph compressor.
  arXiv  Detail & Related papers  (2021-07-05T11:41:16Z)
• Permute, Quantize, and Fine-tune: Efficient Compression of Neural Networks [70.0243910593064]
  Key to success of vector quantization is deciding which parameter groups should be compressed together. In this paper we make the observation that the weights of two adjacent layers can be permuted while expressing the same function. We then establish a connection to rate-distortion theory and search for permutations that result in networks that are easier to compress.
  arXiv  Detail & Related papers  (2020-10-29T15:47:26Z)
• Linear Convergent Decentralized Optimization with Compression [50.44269451541387]
  Existing decentralized algorithms with compression mainly focus on compressing DGD-type algorithms. Motivated by primal-dual algorithms, this paper proposes first underlineLinunderlineEAr convergent. underlineDecentralized with compression, LEAD.
  arXiv  Detail & Related papers  (2020-07-01T04:35:00Z)
• Uncertainty Principle for Communication Compression in Distributed and Federated Learning and the Search for an Optimal Compressor [5.09755285351264]
  We consider an unbiased compression method inspired by the Kashin representation of vectors, which we call em Kashin compression (KC). KC enjoys a em dimension independent variance bound for which we derive an explicit formula even in the regime when only a few bits need to be communicate per each vector entry.
  arXiv  Detail & Related papers  (2020-02-20T17:20:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.