6 papers
Approximate Uniformity in Finite Convolution Models
Nilava Metya, Satyaki Mukherjee
The problem of the uniform law being a sum of two independent distributions has been well studied. Here, we study the approximation of the uniform law to a sum of two distributions…
Beyond Linear and Overcomplete Regimes: A Mean-Field Analysis of Bottleneck Autoencoders
Santanu Das, Ramyak Bilas, Pascal Esser +1
Autoencoders (AEs) learn low-dimensional representations by mapping data into a latent space while minimizing reconstruction error. Despite their empirical success, theoretical und…
Approximate FKG inequalities for phase-bound spin systems, with applications to central limit theorems for exponential random graphs
Satyaki Mukherjee, Vilas Winstein
The Fortuin-Kasteleyn-Ginibre (FKG) inequality is an invaluable tool in monotone spin systems satisfying the FKG lattice condition, which provides positive correlations for all coo…
Recovering Imbalanced Clusters via Gradient-Based Projection Pursuit
Martin Eppert, Satyaki Mukherjee, Debarghya Ghoshdastidar
Projection Pursuit is a classic exploratory technique for finding interesting projections of a dataset. We propose a method for recovering projections containing either Imbalanced…
Representation Learning Dynamics of Self-Supervised Models
Pascal Esser, Satyaki Mukherjee, Debarghya Ghoshdastidar
Self-Supervised Learning (SSL) is an important paradigm for learning representations from unlabelled data, and SSL with neural networks has been highly successful in practice. Howe…
Improved Representation Learning Through Tensorized Autoencoders
Pascal Mattia Esser, Satyaki Mukherjee, Mahalakshmi Sabanayagam +1
The central question in representation learning is what constitutes a good or meaningful representation. In this work we argue that if we consider data with inherent cluster struct…