Related papers: Unguarded Recursion on Coinductive Resumptions
Resetting, as a protocol that restarts the evolution of a system, can significantly influence stochastic dynamics. One notable effect is the emergence of stationary states in unbounded potentials, where such states would otherwise be absent…
The algebraic properties of the combination of probabilistic choice and nondeterministic choice have long been a research topic in program semantics. This paper explains a formalization in the Coq proof assistant of a monad equipped with…
We elaborate on the recently introduced concept of reentrant Kondo effect in quantum impurities/dots coupled to hybrid metal-semiconductor contacts [G.~Diniz {\em et al.}, Phys. Rev. B {\bf 101}, 125115 (2020)]. By noticing the equivalence…
In this work, we study 'reduction monads', which are essentially the same as monads relative to the free functor from sets into multigraphs. Reduction monads account for two aspects of the lambda calculus: on the one hand, in the monadic…
We study implicit reasoning, i.e. the ability to combine knowledge or rules within a single forward pass. While transformer-based large language models store substantial factual knowledge and rules, they often fail to compose this knowledge…
There has been a lot of recent interest in designing neural network models to estimate a distribution from a set of examples. We introduce a simple modification for autoencoder neural networks that yields powerful generative models. Our…
Monotonic neural networks have recently been proposed as a way to define invertible transformations. These transformations can be combined into powerful autoregressive flows that have been shown to be universal approximators of continuous…
Chain-of-Thought (CoT) is an efficient prompting method that enables the reasoning ability of large language models by augmenting the query using multiple examples with multiple intermediate steps. Despite the empirical success, the…
The free algebra adjunction, between the category of algebras of a monad and the underlying category, induces a comonad on the category of algebras. The coalgebras of this comonad are the topic of study in this paper (following earlier…
We argue that all building blocks of transformer models can be expressed with a single concept: combinatorial Hopf algebra. Transformer learning emerges as a result of the subtle interplay between the algebraic and coalgebraic operations of…
Single-ended circuit topologies, and a theorem for the development thereof, are presented with which one may realize constant-resistance (or reflectionless) filters, having ideally zero reflection coefficient at all frequencies and from all…
A new class of modified gravity theories, made possible by subtle features of the canonical formulation of general covariance, naturally allows MOND-like behavior (MOdified Newtonian Dynamics) in effective space-time solutions without…
In the first part of the paper we recall the coalgebraic approach to handling the so-called invisible transitions that appear in different state-based systems semantics. We claim that these transitions are always part of the unit of a…
The generation of quadrilateral-dominant meshes is a cornerstone of professional 3D content creation. However, existing generative models generate quad meshes by first generating triangle meshes and then merging triangles into…
We introduce the abstract notions of "monadic operational semantics", a small-step semantics where computational effects are modularly modeled by a monad, and "type-and-effect system", including "effect types" whose interpretation lifts…
Chain of Thought (CoT) prompting has been shown to significantly improve the performance of large language models (LLMs), particularly in arithmetic and reasoning tasks, by instructing the model to produce intermediate reasoning steps.…
We prove a conjecture about the constructibility of coinductive types - in the principled form of indexed M-types - in Homotopy Type Theory. The conjecture says that in the presence of inductive types, coinductive types are derivable.…
Autoregressive models excel in modeling sequential dependencies by enforcing causal constraints, yet they struggle to capture complex bidirectional patterns due to their unidirectional nature. In contrast, mask-based models leverage…
The article aims at describing all covers of any finitely generated variety of cBCK-algebras. It is known that subdirectly irreducible cBCK-algebras are rooted trees (concerning their order). Also, all subdirectly irreducible members of…
We present the Insertion Transformer, an iterative, partially autoregressive model for sequence generation based on insertion operations. Unlike typical autoregressive models which rely on a fixed, often left-to-right ordering of the…