arXiv subjects

Romie Banerjee

Publications and source records attributed to Romie Banerjee.

7 recordsLinked to original sources

arXiv2026

CAS I: A Geometric Coding Theorem

This paper establishes a direct analogue of the classical Coding Theorem in the setting of symmetry groups. We consider computable bijections on the set of binary strings, called symmetries and define the symmetry prior of a string as the probability that a randomly chosen symmetry from a given group has the string as its unique fixed point. We show that for any fix-retractable symmetry group, a group admitting a computable section that selects an isolating symmetry for every string, the symmetry prior is a universal lower semi-computable semi-measure. In this case, the Geometric Coding Theorem holds. We also develop a Galois connection between subgroups of G and subsets of binary strings, characterizing closed points and maximal closed subgroups, and explore the join-semilattice of dense subgroups. Our results unify algorithmic information theory with group theory and provide a framework for studying symmetry-induced complexity measures. This paper is the first in a series on Computational Algorithmic Statistics (CAS).

cs.IT↗

arXiv2026

A Short Review of Estimators for the GLM predictive of Laplace Bayesian Neural Networks

This short review examines the primary approaches for estimating the predictive distribution of Laplace-approximated Bayesian neural networks, with particular focus on the Generalized Linear Model (GLM) formulation. We survey the landscape of estimation strategies, from exact GLM computations requiring full Jacobian evaluations to Monte Carlo approximations that trade computational cost for statistical efficiency. The review covers the theoretical foundations of the Laplace approximation, the Kronecker-factored approximate curvature (KFAC) method for scalable posterior inference, and the various predictive estimation techniques developed in the literature. We provide a unified presentation that clarifies the relationships between methods and highlights their respective computational and statistical trade-offs.

math.ST↗

arXiv2017

Tannakization of quasi-categories and monadic descent

Given a symmetric monoidal stable $\infty$-category $\mathcal{C}$ and a left adjoint symmetric monoidal fiber functor to $\operatorname{Mod}_A^{\otimes}$ for some $\mathbb{E}_{\infty}$-ring $A$, one can construct a derived group scheme $G$ of monoidal automorphisms of this functor. The left adjoint fiber functor also induces a monad on $\mathcal{C}$. Under some finiteness hypothesis on the fiber functor, we show there is a comparison functor from the category of representations of $G$ to the descent category of the induced monad on $\mathcal{C}$.

math.CT↗

arXiv2015

Galois Descent for Real Spectra

We prove analogs of faithfully flat descent and Galois descent for categories of modules over $E_{\infty}$-ring spectra using the $\infty$-categorical Barr-Beck theorem proved by Lurie. In particular, faithful $G$-Galois extensions are shown to be of effective descent for modules. Using this we study the category of $ER(n)$-modules, where $ER(n)$ is the $\mathbb{Z}/2$-fixed points under complex conjugation of a generalized Johnson-Wilson spectrum $E(n)$. In particular, we show that $ER(n)$-modules is equivalent to $\mathbb{Z}$/2-equivariant $E(n)$-modules as stable $\infty$-categories.

math.AT↗

arXiv2014

A modular description of ER(2)

We give a description of the maximally unramified extension of completed second Real Johnson-Wilson theory using supersingular elliptic curves with $Γ_0(3)$-level structures.

math.AT↗

arXiv2013

On the ER(2) cohomology of some odd dimensional projective spaces

Kitchloo and Wilson have used the homotopy fixed points spectrum ER(2) of the classical complex-oriented Johnson-Wilson spectrum E(2) to deduce certain non-immmersion results for real projective spaces. ER(n) is a $2^{n+2}(2^n-1)$-periodic spectrum. The key result to use is the existence of a stable cofibration $Σ^{λ(n)}ER(n) \rightarrow ER(n) \rightarrow E(n)$ connecting the real Johnson-Wilson spectrum with the classical one. The value of $λ(n)$ is $2^{2n+1}-2^{n+2}+1$. We extend Kitchloo-Wilson's results on non-immersions of real projective spaces by computing the second real Johnson-Wilson cohomology ER(2) of the odd-dimensional real projective spaces $RP^{16K+9}$. This enables us to solve certain non-immersion problems of projective spaces using obstructions in ER(2)-cohomology.

math.AT↗

arXiv2012

Categories of modules and their deformations

Using Quillen-Lurie deformation theory formalism we develop an obstruction theory for studying the stable $\infty$-category of modules over a given geometric $\infty$-stack. The obstruction theory studies the problem of lifting compact objects to the stable $\infty$-category of quasi-coherent modules over a derived geometric stack from the category of modules over its underlying classical stack. The obstructions live in Andre-Quillen cohomology. An explicit description of the space of realizations of a given module over X as a colimit of perfect modules can be given in terms of the k-invariants of a postnikov tower of X and the cotangent complex of the moduli functor of perfect modules.

math.AG↗