5 papers · 1 filter
Convergent Stochastic Training of Multi-Headed Attention and Understanding LoRA
Zhengkai Sun, Dibyakanti Kumar, Alejandro F Frangi +2
Transformers have revolutionized machine learning and deploying attention layers in the model is increasingly standard across a myriad of applications. Further, for large models, i…
Generalization Bounds for Physics-Informed Neural Networks for the Incompressible Navier-Stokes Equations
Sebastien Andre-Sloan, Dibyakanti Kumar, Alejandro F Frangi +1
This work establishes rigorous first-of-its-kind upper bounds on the generalization error for the method of approximating solutions to the (d+1)-dimensional incompressible Navier-S…
Langevin Monte-Carlo Provably Learns Depth Two Neural Nets at Any Size and Data
Dibyakanti Kumar, Samyak Jha, Anirbit Mukherjee
In this note we prove that the Langevin Monte Carlo (LMC) algorithm can minimize the population risk of appropriately regularized depth-2 nets with no restrictions on the size of t…
Investigating the Ability of PINNs To Solve Burgers' PDE Near Finite-Time BlowUp
Dibyakanti Kumar, Anirbit Mukherjee
Physics Informed Neural Networks (PINNs) have been achieving ever newer feats of solving complicated PDEs numerically while offering an attractive trade-off between accuracy and sp…
Towards Size-Independent Generalization Bounds for Deep Operator Nets
Pulkit Gopalani, Sayar Karmakar, Dibyakanti Kumar +1
In recent times machine learning methods have made significant advances in becoming a useful tool for analyzing physical systems. A particularly active area in this theme has been…