arXiv subjects

Vibhu Dalal

Publications and source records attributed to Vibhu Dalal.

3 recordsLinked to original sources

arXiv2025

Formalising Propositional Information via Implication Hypergraphs

This work introduces a framework for quantifying the information content of logical propositions through the use of implication hypergraphs. We posit that a proposition's informativeness is primarily determined by its relationships with other propositions; specifically, the extent to which it implies or derives other propositions. To formalize this notion, we develop a framework based on implication hypergraphs, that seeks to capture these relationships. Within this framework, we define propositional information, derive some key properties, and illustrate the concept through examples. While the approach is broadly applicable, mathematical propositions emerge as an ideal domain for its application due to their inherently rich and interconnected structure. We provide several examples to illustrate this and subsequently discuss the limitations of the framework, along with suggestions for potential refinements.

math.LO↗

arXiv2025

Dataset Distillation via the Wasserstein Metric

Dataset Distillation (DD) aims to generate a compact synthetic dataset that enables models to achieve performance comparable to training on the full large dataset, significantly reducing computational costs. Drawing from optimal transport theory, we introduce WMDD (Wasserstein Metric-based Dataset Distillation), a straightforward yet powerful method that employs the Wasserstein metric to enhance distribution matching. We compute the Wasserstein barycenter of features from a pretrained classifier to capture essential characteristics of the original data distribution. By optimizing synthetic data to align with this barycenter in feature space and leveraging per-class BatchNorm statistics to preserve intra-class variations, WMDD maintains the efficiency of distribution matching approaches while achieving state-of-the-art results across various high-resolution datasets. Our extensive experiments demonstrate WMDD's effectiveness and adaptability, highlighting its potential for advancing machine learning applications at scale.

cs.CV↗

arXiv2024

Short-Time Fourier Transform for deblurring Variational Autoencoders

Variational Autoencoders (VAEs) are powerful generative models, however their generated samples are known to suffer from a characteristic blurriness, as compared to the outputs of alternative generating techniques. Extensive research efforts have been made to tackle this problem, and several works have focused on modifying the reconstruction term of the evidence lower bound (ELBO). In particular, many have experimented with augmenting the reconstruction loss with losses in the frequency domain. Such loss functions usually employ the Fourier transform to explicitly penalise the lack of higher frequency components in the generated samples, which are responsible for sharp visual features. In this paper, we explore the aspects of previous such approaches which aren't well understood, and we propose an augmentation to the reconstruction term in response to them. Our reasoning leads us to use the short-time Fourier transform and to emphasise on local phase coherence between the input and output samples. We illustrate the potential of our proposed loss on the MNIST dataset by providing both qualitative and quantitative results.

eess.IV↗