A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on fi…
New bounds on generalization error for distributed learning using rate-distortion theory.
problem Establishing upper bounds on generalization error for distributed learning algorithms.
method Using rate-distortion theory, the paper introduces new bounds that depend on the compressibility of each client's algorithm.
result The bounds suggest that the generalization error of the distributed setting decays faster than that of the centralized one with a factor of O(log(K)/K).
A distinctive property of human and animal intelligence is the ability to form abstractions by neglecting irrelevant information which allows to separate structure from noise. From an information theoretic point of view abstractions are desirable because they allow for very efficient information processing. In artifici…
This paper explores the problem of learning transforms for image compression via autoencoders. Usually, the rate-distortion performances of image compression are tuned by varying the quantization step size. In the case of autoen-coders, this in principle would require learning one transform per rate-distortion point at…
This paper studies communication efficiency in federated learning by optimizing the sum-rate-distortion function for indirect multiterminal source coding.
problem Indirect multiterminal source coding in federated learning where edge devices send noisy gradients to the server.
method Analyzes the rate region for the quadratic vector Gaussian CEO problem under unbiased estimator and derives an explicit formula for the sum-rate-distortion function.
result Derives an explicit formula for the sum-rate-distortion function in the special case of identical gradients over edge devices.
Feature Learning aims to extract relevant information contained in data sets in an automated fashion. It is driving force behind the current deep learning trend, a set of methods that have had widespread empirical success. What is lacking is a theoretical understanding of different feature learning schemes. This work p…
This work evaluates deep generative models using RD curves, providing a more comprehensive quality assessment.
problem Quantitative evaluation of deep generative models is challenging, especially for implicit models.
method Proposes using rate distortion (RD) curves to evaluate and compare deep generative models, approximating the entire curve with similar computations to log-likelihood estimation.
result Approximating the entire RD curve provides a more comprehensive quality assessment than scalar-valued metrics.
We present new intuitions and theoretical assessments of the emergence of disentangled representation in variational autoencoders. Taking a rate-distortion theory perspective, we show the circumstances under which representations aligned with the underlying generative factors of variation of data emerge when optimising…
This paper proposes a new method for efficient data compression using Bayesian neural networks.
problem Efficient compression of data represented as functions mapping coordinates to signal values.
method Overfitting variational Bayesian neural networks to the data and compressing an approximate posterior weight sample using relative entropy coding.
result Our method achieves strong performance on image and audio compression while retaining simplicity.
We present an information-theoretic framework for bounding the number of labeled samples needed to train a classifier in a parametric Bayesian setting. We derive bounds on the average Lp distance between the learned classifier and the true maximum a posteriori classifier, which are well-established surrogates for th…
The paper proposes a principle for dynamically adjusting the granularity of reinforcement learning abstractions.
problem Lack of general principles for dynamically adjusting the granularity of reinforcement learning abstractions.
method The paper proposes a principle based on rate-distortion theory, formalized through a performance certificate decomposing value error into learning and abstraction error bounds.
result Soft state-action abstractions can achieve near-optimal performance under substantial lossy compression of state and action information.