Related papers: On Reversible Transducers
We answer an open question in the theory of transducer degrees initially posed in [1] on the existence of a diamond structure in the transducer hierarchy. Transducer degrees are the equivalence classes formed by word transformations which…
Our purpose in this paper is to study when a planar differential system polynomial in one variable linearizes in the sense that it has an inverse integrating factor which can be constructed by means of the solutions of linear differential…
To solve a new task from minimal experience, it is essential to effectively reuse knowledge from previous tasks, a problem known as meta-learning. Compositional solutions, where common elements of computation are flexibly recombined into…
Transducers generalise automata by producing output word(s) for each input word, thereby defining a relation over words. A transducer is said to be finite-valued if, for every input word, it produces at most $k$ output words, for some…
This paper concerns the twice epi-differentiability and parabolic regularity of a class of non-amenable functions, the composition of a piecewise twice differentiable (PWTD) function and a parabolically semidifferentiable mapping. Such…
High dimensional data can have a surprising property: pairs of data points may be easily separated from each other, or even from arbitrary subsets, with high probability using just simple linear classifiers. However, this is more of a rule…
Diffusion models are a remarkably effective way of learning and sampling from a distribution $p(x)$. In posterior sampling, one is also given a measurement model $p(y \mid x)$ and a measurement $y$, and would like to sample from $p(x \mid…
Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its scalability (unlike Damas-Milner type inference, bidirectional typing remains decidable even for very…
Reversible systems feature both forward computations and backward computations, where the latter undo the effects of the former in a causally consistent manner. The compositionality properties and equational characterizations of strong and…
The purpose of this paper is to present an algorithm for inferring nondeterministic functional transducers. It has a lot in common with other well known algorithms such has RPNI and OSTIA. Indeed we will argue that this algorithm is a…
We study a nonlinear decomposition of a positive definite matrix into two components: the inverse of another positive definite matrix and a symmetric matrix constrained to lie in a prescribed linear subspace. Equivalently, the inverse…
In this paper, we construct two classes of permutation polynomials over $\mathbb{F}_{q^2}$ with odd characteristic from rational R\'{e}dei functions. A complete characterization of their compositional inverses is also given. These…
We consider a stack sorting algorithm where only the appropriate output values are popped from the stack and then any remaining entries in the stack are run through the stack in reverse order. We identify the basis for the $2$-reverse pass…
In this note we give a simple unifying proof of the undecidability of several diagrammatic properties of term rewriting systems that include: local confluence, strong confluence, diamond property, subcommutative property, and the existence…
Effective conductivity of a 2D random composite is expressed in the form of long series in the volume fraction of ideally conducting disks. The problem of a {\it direct} reconstruction of the critical index for superconductivity from the…
The question of the state-size cost for simulation of two-way nondeterministic automata (2NFAs) by two-way deterministic automata (2DFAs) was raised in 1978 and, despite many attempts, it is still open. Subsequently, the problem was…
World models have been recently proposed as sandbox environments in which AI agents can be trained and evaluated before deployment. While realistic world models often have high computational demands, this can often be alleviated by…
A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally…
Mechanistic interpretability of transformers requires identifying not just which components matter but how they compose into the computational route that produced a prediction. Both attention and MLP follow a shared key-value template…
A deep learning system typically suffers from a lack of reproducibility that is partially rooted in hardware or software implementation details. The irreproducibility leads to skepticism in deep learning technologies and it can hinder them…