Related papers: Full normalization for transfinite stacks
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
There has been recent interest in improving performance of simple models for multiple reasons such as interpretability, robust learning from small data, deployment in memory constrained settings as well as environmental considerations. In…
Finite-state tree automata are a well studied formalism for representing term languages. This paper studies the problem of determining the regularity of the set of instances of a finite set of terms with variables, where each variable is…
Recombining trinomial trees are a workhorse for modeling discrete-event systems in option pricing, logistics, and feedback control. Because each node stores a state-dependent quantity, a depth-$D$ tree naively yields $\mathcal{O}(3^{D})$…
We advance the recently proposed neuro-symbolic Differentiable Tree Machine, which learns tree operations using a combination of transformers and Tensor Product Representations. We investigate the architecture and propose two key…
For a natural class of $r \times n$ integer matrices, we construct a non-convex polytope which periodically tiles $\mathbb R^n$. From this tiling, we provide a family of geometrically meaningful maps from a generalized sandpile group to a…
Let $M$ be a fine structural mouse and let $F\in M$ be such that $M\models$``$F$ is a total extender'' and $(M||\mathrm{lh}(F),F)$ is a premouse. We show that it follows that $F\in\mathbb{E}^M$, where $\mathbb{E}^M$ is the extender sequence…
Decision trees and diffusion models are ostensibly disparate model classes, one discrete and hierarchical, the other continuous and dynamic. This work unifies the two by establishing a crisp mathematical correspondence between hierarchical…
This paper presents simple, syntactic strong normalization proofs for the simply-typed lambda-calculus and the polymorphic lambda-calculus (system F) with the full set of logical connectives, and all the permutative reductions. The…
We identify a property of renormalizable SU(N)/U(1) gauge theories, the intrinsic Conformality ($iCF$), which underlies the scale invariance of physical observables and leads to a remarkably efficient method to solve the conventional…
Several sequences of free cumulants that count binary plane trees correspond to sequences of classical cumulants that count the decreasing versions of the same trees. Using two new operations on colored binary plane trees that we call…
We study the ridge method for min-max problems, and investigate its convergence without any convexity, differentiability or qualification assumption. The central issue is to determine whether the ''parametric optimality formula'' provides a…
To model complex real-world systems, such as traders in stock markets, or the dissemination of contagious diseases, graphon mean-field games (GMFG) have been proposed to model many agents. Despite the empirical success, our understanding of…
We study compositional generalization, viz., the problem of zero-shot generalization to novel compositions of concepts in a domain. Standard neural networks fail to a large extent on compositional learning. We propose Tree Stack Memory…
Many recent successful (deep) reinforcement learning algorithms make use of regularization, generally based on entropy or Kullback-Leibler divergence. We propose a general theory of regularized Markov Decision Processes that generalizes…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
The lack of interpretability remains a key barrier to the adoption of deep models in many applications. In this work, we explicitly regularize deep models so human users might step through the process behind their predictions in little…
An m-extracting procedure produces unbiased random bits from a loaded dice with m faces. A binarization takes inputs from an m-faced dice and produce bit sequences to be fed into a (binary) extracting procedure to obtain random bits. Thus,…
In this article we review how categorical equivalences are realized by renormalization group flow in physical realizations of stacks, derived categories, and derived schemes. We begin by reviewing the physical realization of sigma models on…
In this paper, we propose a simple yet effective method to stabilize extremely deep Transformers. Specifically, we introduce a new normalization function (DeepNorm) to modify the residual connection in Transformer, accompanying with…