Related papers: Algorithmically Expressive, Always-Terminating Mod…
In this paper, we investigate finite representations of DatalogMTL models. First, we discuss sufficient conditions for detecting programs that have finite models. Then, we study infinite models that eventually become constant and introduce…
Robots and autonomous agents often complete goal-based tasks with limited resources, relying on imperfect models and sensor measurements. In particular, reinforcement learning (RL) and feedback control can be used to help a robot achieve a…
Recurrent neural networks (RNNs) provide state-of-the-art performance in processing sequential data but are memory intensive to train, limiting the flexibility of RNN models which can be trained. Reversible RNNs---RNNs for which the…
This paper proposes the automatic Doubly Robust Random Forest (DRRF) algorithm for estimating the conditional expectation of a moment functional in the presence of high-dimensional nuisance functions. DRRF extends the automatic debiasing…
The Process Reward Model (PRM) plays a crucial role in mathematical reasoning tasks, requiring high-quality supervised process data. However, we observe that reasoning steps generated by Large Language Models (LLMs) often fail to exhibit…
Recent computational experiments have demonstrated the spontaneous emergence of self-replicating programs across universal automata, artificial chemistries, and self-modifying code systems. Remarkably, these results arise without explicit…
Large language models (LLMs) inevitably make mistakes when performing step-by-step mathematical reasoning. Process Reward Models (PRMs) have emerged as a promising solution by evaluating each reasoning step. However, existing PRMs typically…
We give a new characterization of the class of rational string functions from formal language theory using order-preserving interpretations with respect to a very weak monadic programming language. This refines the known characterization of…
Mathematical formulas are the crystallization of human wisdom in exploring the laws of nature for thousands of years. Describing the complex laws of nature with a concise mathematical formula is a constant pursuit of scientists and a great…
Tiny Recursive Models (TRM) solve complex reasoning tasks with a fraction of the parameters of modern large language models (LLMs) by iteratively refining a latent state and final answer. While powerful, their deterministic recursion can…
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…
Modern Reinforcement Learning (RL) is commonly applied to practical problems with an enormous number of states, where function approximation must be deployed to approximate either the value function or the policy. The introduction of…
Tail recursive functions allow for a wider range of optimisations than general recursive functions. For this reason, much research has gone into the transformation and optimisation of this family of functions, in particular those written in…
To effectively perform the task of next-word prediction, long short-term memory networks (LSTMs) must keep track of many types of information. Some information is directly related to the next word's identity, but some is more secondary…
We introduce algebraic machine reasoning, a new reasoning framework that is well-suited for abstract reasoning. Effectively, algebraic machine reasoning reduces the difficult process of novel problem-solving to routine algebraic…
Encodings, that is, injective functions from words to words, have been studied extensively in several settings. In computability theory the notion of encoding is crucial for defining computability on arbitrary domains, as well as for…
Neural reasoners such as Tiny Recursive Models (TRMs) solve complex problems by combining neural backbones with specialized inference schemes. Such inference schemes have been a central component of stochastic reasoning systems, where…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…
e use Prolog as a flexible meta-language to provide executable specifications of some fundamental mathematical objects and their transformations. In the process, isomorphisms are unraveled between natural numbers and combinatorial objects…