5 papers
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 work, we will establish that the Langevin Monte-Carlo algorithm can learn depth-2 neural nets of any size and for any data and we give non-asymptotic convergence rates for…
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…