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We introduce differentiable indirection -- a novel learned primitive that employs differentiable multi-scale lookup tables as an effective substitute for traditional compute and data operations across the graphics pipeline. We demonstrate…

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

The TTE computability notion in effective metric spaces is usually defined by using Cauchy representations. Under some weak assumptions, we characterize this notion in a way which avoids using the representations.

The intrinsic dimensionality refers to the ``true'' dimensionality of the data, as opposed to the dimensionality of the data representation. For example, when attributes are highly correlated, the intrinsic dimensionality can be much lower…

Using an iterative tree construction we show that for simple computable subsets of the Cantor space Hausdorff, constructive and computable dimensions might be incomputable.

We call a system super-linearizable if it admits finite-dimensional embedding as a linear system -- known as a finite-dimensional Koopman embedding; said otherwise, if its dynamics can be linearized by adding a finite set of observables. We…

In this paper, we build an interpreter by reusing host language functions instead of recoding mechanisms of function application that are already available in the host language (the language which is used to build the interpreter). In order…

Formal Concept Analysis and its associated conceptual structures have been used to support exploratory search through conceptual navigation. Relational Concept Analysis (RCA) is an extension of Formal Concept Analysis to process relational…

Addressing machines have been introduced as a formalism to construct models of the pure, untyped lambda-calculus. We extend the syntax of their programs by adding instructions for executing arithmetic operations on natural numbers, and…

Classification may not be reliable for several reasons: noise in the data, insufficient input information, overlapping distributions and sharp definition of classes. Faced with several possibilities neural network may in such cases still be…

Near-vector spaces extend linear algebra tools to non-linear algebraic structures, enabling the study of non-linear problems. However, explicit constructions remain rare. This paper introduces a broad computable family of near-vector…

We consider the problem of identifying significant predictors in large data bases, where the response variable depends on the linear combination of explanatory variables through an unknown link function, corrupted with the noise from the…

We prove in ZFC the existence of a definable, countably saturated elementary extension of the reals. It seems that it has been taken for granted that there is no distinguished, definable nonstandard model of the reals. (This means a…

We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…

We propose a new constructive model of the real continuum based on the notion of fractal definability. Rather than assuming the continuum as a completed uncountable totality, we view it as the cumulative result of a vast space of stratified…

We give an uncountability proof of the reals which relies on their order completeness instead of their sequential completeness. We use neither a form of the axiom of choice nor the law of excluded middle, therefore the proof applies to the…

Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…

The architectural blueprint of today's leading text-to-image models contains a fundamental flaw: an inability to handle logical composition. This survey investigates this breakdown across three core primitives-negation, counting, and…

In this paper, we use a simple discrete dynamical model to study partitions of integers into powers of another integer. We extend and generalize some known results about their enumeration and counting, and we give new structural results. In…

We construct a denotational model of linear logic, whose objects are all the locally convex and separated topological vector spaces endowed with their weak topology. The negation is interpreted as the dual, linear proofs are interpreted as…