10 citations · 26 across the 14 of their papers we have counts for
14 papers
Weak mixing behavior for the projectivized derivative extension
Shilpak Banerjee, Divya Khurana, Philipp Kunde
In both smooth and analytic categories, we construct examples of diffeomorphisms of topological entropy zero with intricate ergodic properties. On any smooth compact connected mani…
Ergodic and mixing quantum channels: From two-qubit to many-body quantum systems
S. Aravinda, Shilpak Banerjee, Ranjan Modak
The development of classical ergodic theory has had a significant impact in the areas of mathematics, physics, and, in general, applied sciences. The quantum ergodic theory of Hami…
SMU: smooth activation function for deep networks using smoothing maximum technique
Koushik Biswas, Sandeep Kumar, Shilpak Banerjee +1
Deep learning researchers have a keen interest in proposing two new novel activation functions which can boost network performance. A good choice of activation function can have si…
SAU: Smooth activation function using convolution with approximate identities
Koushik Biswas, Sandeep Kumar, Shilpak Banerjee +1
Well-known activation functions like ReLU or Leaky ReLU are non-differentiable at the origin. Over the years, many smooth approximations of ReLU have been proposed using various sm…
Slow entropy for some Anosov-Katok diffeomorphisms
Shilpak Banerjee, Philipp Kunde, Daren Wei
The Anosov-Katok method is one of the most powerful tools of constructing smooth volume-preserving diffeomorphisms of entropy zero with prescribed ergodic or topological properties…
ErfAct and Pserf: Non-monotonic Smooth Trainable Activation Functions
Koushik Biswas, Sandeep Kumar, Shilpak Banerjee +1
An activation function is a crucial component of a neural network that introduces non-linearity in the network. The state-of-the-art performance of a neural network depends also on…
Orthogonal-Padé Activation Functions: Trainable Activation functions for smooth and faster convergence in deep networks
Koushik Biswas, Shilpak Banerjee, Ashish Kumar Pandey
We have proposed orthogonal-Padé activation functions, which are trainable activation functions and show that they have faster learning capability and improves the accuracy in stan…
EIS -- a family of activation functions combining Exponential, ISRU, and Softplus
Koushik Biswas, Sandeep Kumar, Shilpak Banerjee +1
Activation functions play a pivotal role in the function learning using neural networks. The non-linearity in the learned function is achieved by repeated use of the activation fun…
Slow entropy of some combinatorial constructions
Shilpak Banerjee, Philipp Kunde, Daren Wei
Measure-theoretic slow entropy is a more refined invariant than the classical measure-theoretic entropy to characterize the complexity of dynamical systems with subexponential grow…
TanhSoft -- a family of activation functions combining Tanh and Softplus
Koushik Biswas, Sandeep Kumar, Shilpak Banerjee +1
Deep learning at its core, contains functions that are composition of a linear transformation with a non-linear function known as activation function. In past few years, there is a…
Real-analytic diffeomorphisms with homogeneous spectrum and disjointness of convolutions
Shilpak Banerjee, Philipp Kunde
On any torus , , we prove the existence of a real-analytic diffeomorphism with a good approximation of type , a maximal spectral typ…
Real-analytic realization of Uniform Circular Systems and some applications
Shilpak Banerjee, Philipp Kunde
Recently Matthew Foreman and Benjamin Weiss showed in a series of papers that smooth ergodic diffeomorphisms of a compact manifold are unclassifiable up to measure-isomorphism. In…
Real-analytic AbC constructions on the torus
Shilpak Banerjee, Philipp Kunde
In this article we demonstrate a way to extend the AbC (approximation by conjugation) method invented by Anosov and Katok from the smooth category to the category of real-analytic…
Non-standard real-analytic realizations of some rotations of the circle
Shilpak Banerjee
We extend some aspects of the smooth approximation by conjugation method to the real-analytic set-up and create examples of zero entropy, uniquely ergodic real-analytic diffeomorph…