Related papers: Internalizing Representation Independence with Uni…

The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded…

We propose an information-theoretic quantifier for the advantage gained from cooperation that captures the degree of dependency between subsystems of a global system. The quantifier is distinct from measures of multipartite correlations…

A new seemingly weak axiomatic formulation of information algebras is given. It is shown how such information algebras can be embedded into set (information) algebras. In set algebras there is a natural relation of conditional independence…

We explore a quantitative interpretation of 2-dimensional intuitionistic type theory (ITT) in which the identity type is interpreted as a "type of differences". We show that a fragment of ITT, that we call difference type theory (dTT),…

Search-based dialog models typically re-encode the dialog history at every turn, incurring high cost. Curved Contrastive Learning, a representation learning method that encodes relative distances between utterances into the embedding space…

The internal representations learned by deep networks are often sensitive to architecture-specific choices, raising questions about the stability, alignment, and transferability of learned structure across models. In this paper, we…

Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the…

In his article "Transcending Classical Invariant Theory" (J.A.M.S., 1989, Vol 2), Roger Howe established a correspondence between representations of a dual pair of reductive groups. This correspondence is known as Howe's correspondence or…

The i.i.d. assumption is a useful idealization that underpins many successful approaches to supervised machine learning. However, its violation can lead to models that learn to exploit spurious correlations in the training data, rendering…

In this paper, we examine how various notions of independence in non-commutative probability theory arise in bi-free probability. We exhibit how Boolean and monotone independence occur from bi-free pairs of faces and establish a Kac/Loeve…

We study the coherence and conservativity of extensions of dependent type theories by additional strict equalities. By considering notions of congruences and quotients of models of type theory, we reconstruct Hofmann's proof of the…

Python's dynamic typing mechanism, while promoting flexibility, is a significant source of runtime type errors that plague large-scale software, which inspires the automatic type inference techniques. Existing type inference tools have…

We establish the following input independence principle. If a quantum circuit $\mathcal C$ computes a unitary transformation $U_\mu$ along a computation path $\mu$, then the probability that computation of $\mathcal C$ follows path $\mu$ is…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field, and ${\Bbb S}$ a finite sequence of simple left $\Lambda$-modules. In [6, 9], quasiprojective algebraic varieties with accessible affine open covers were…

Analyzing the similarity of internal representations has been an important technique for understanding the behavior of deep neural networks. Most existing methods for analyzing the similarity between representations of high dimensions, such…

Dependent types allow us to express precisely what a function is intended to do. Recent work on Quantitative Type Theory (QTT) extends dependent type systems with linearity, also allowing precision in expressing when a function can run.…

Software development depends on the use of libraries whose public specifications inform client code and impose obligations on private implementations; it follows that verification at scale must also be modular, preserving such abstraction.…

Invariant inference algorithms such as interpolation-based inference and IC3/PDR show that it is feasible, in practice, to find inductive invariants for many interesting systems, but non-trivial upper bounds on the computational complexity…

Multi-view (or -modality) representation learning aims to understand the relationships between different view representations. Existing methods disentangle multi-view representations into consistent and view-specific representations by…

Representation learning plays a central role in structuring internal embeddings to capture the statistical properties of language, influencing the coherence and contextual consistency of generated text. Statistical Coherence Alignment is…