3 citations · 4 across the 9 of their papers we have counts for
11 papers
Machine-learnable Sets
Veit Elser, Manish Krishan Lal
In this study we present a formal definition of large discrete sets having, informally, three properties: their elements are easily recognized, easily generated, and the latter tas…
Learning with Boolean threshold functions
Veit Elser, Manish Krishan Lal
We develop a method for training neural networks on Boolean data in which the values at all nodes are strictly , and the resulting models are typically equivalent to network…
The Flow-Limit of Reflect-Reflect-Relax: Existence, Stability, and Discrete-Time Behavior
Manish Krishan Lal
We study the Reflect-Reflect-Relax (RRR) algorithm in its small-step (flow-limit) regime. In the smooth transversal setting, we show that the transverse dynamics form a hyperbolic…
Backpropagation from KL Projections: Differential and Exact I-Projection Correspondences
Manish Krishan Lal
We establish two correspondences between reverse-mode automatic differentiation (backpropagation at a given forward-pass point) and compositions of projection maps in Kullback--Lei…
Cross-fluctuation phase transitions reveal sampling dynamics in diffusion models
Sai Niranjan Ramachandran, Manish Krishan Lal, Suvrit Sra
We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using cross-fluctuations, a centered-moment statistic from statistical physics. Specifi…
A projection-based framework for gradient-free and parallel learning
Andreas Bergmeister, Manish Krishan Lal, Stefanie Jegelka +1
We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and us…
Real roots of real cubics and optimization
Heinz H. Bauschke, Manish Krishan Lal, Xianfu Wang
The solution of the cubic equation has a century-long history; however, the usual presentation is geared towards applications in algebra and is somewhat inconvenient to use in opti…
Projecting onto rectangular hyperbolic paraboloids in Hilbert space
Heinz H. Bauschke, Manish Krishan Lal, Xianfu Wang
In , a hyperbolic paraboloid is a classical saddle-shaped quadric surface. Recently, Elser has modeled problems arising in Deep Learning using rectangular hyperbolic…
Projections onto hyperbolas or bilinear constraint sets in Hilbert spaces
Heinz H. Bauschke, Manish Krishan Lal, Xianfu Wang
Sets of bilinear constraints are important in various machine learning models. Mathematically, they are hyperbolas in a product space. In this paper, we give a complete formula for…
The projection onto the cross
Heinz H. Bauschke, Manish Krishan Lal, Xianfu Wang
We consider the set of pairs of orthogonal vectors in Hilbert space, which is also called the cross because it is the union of the horizontal and vertical axes in the Euclidean pla…
Directional asymptotics of Fejér monotone sequences
Heinz H. Bauschke, Manish Krishan Lal, Xianfu Wang
The notion of Fejér monotonicity is instrumental in unifying the convergence proofs of many iterative methods, such as the Krasnoselskii-Mann iteration, the proximal point method,…