Exact Learning of Arithmetic with Differentiable Agents

• URL: http://arxiv.org/abs/2511.22751v1
• Date: Thu, 27 Nov 2025 20:51:16 GMT
• Title: Exact Learning of Arithmetic with Differentiable Agents
• Authors: Hristo Papazov, Francesco D'Angelo, Nicolas Flammarion,
• Abstract summary: Differentiable Finite-State Transducers (DFSTs) are a Turing-complete model family that avoids the pitfalls of prior architectures.<n>We train DFSTs to perform binary and decimal addition and multiplication.<n>Remarkably, models trained on tiny datasets generalize without error to inputs thousands of times longer than the training examples.
• Score: 33.08873643449408
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We explore the possibility of exact algorithmic learning with gradient-based methods and introduce a differentiable framework capable of strong length generalization on arithmetic tasks. Our approach centers on Differentiable Finite-State Transducers (DFSTs), a Turing-complete model family that avoids the pitfalls of prior architectures by enabling constant-precision, constant-time generation, and end-to-end log-parallel differentiable training. Leveraging policy-trajectory observations from expert agents, we train DFSTs to perform binary and decimal addition and multiplication. Remarkably, models trained on tiny datasets generalize without error to inputs thousands of times longer than the training examples. These results show that training differentiable agents on structured intermediate supervision could pave the way towards exact gradient-based learning of algorithmic skills. Code available at \href{https://github.com/dngfra/differentiable-exact-algorithmic-learner.git}{https://github.com/dngfra/differentiable-exact-algorithmic-learner.git}.

Related papers

• Informative regularization for a multi-layer perceptron RR Lyrae classifier under data shift [3.303002683812084]
  We propose a scalable and easily adaptable approach based on an informative regularization and an ad-hoc training procedure to mitigate the shift problem. Our method provides a new path to incorporate knowledge from characteristic features into artificial neural networks to manage the underlying data shift problem.
  arXiv  Detail & Related papers  (2023-03-12T02:49:19Z)
• Generalized Differentiable RANSAC [95.95627475224231]
  $nabla$-RANSAC is a differentiable RANSAC that allows learning the entire randomized robust estimation pipeline. $nabla$-RANSAC is superior to the state-of-the-art in terms of accuracy while running at a similar speed to its less accurate alternatives.
  arXiv  Detail & Related papers  (2022-12-26T15:13:13Z)
• Learning with Differentiable Algorithms [6.47243430672461]
  This thesis explores combining classic algorithms and machine learning systems like neural networks. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable sorting gates, and differentiable logic gate networks.
  arXiv  Detail & Related papers  (2022-09-01T17:30:00Z)
• Towards Diverse Evaluation of Class Incremental Learning: A Representation Learning Perspective [67.45111837188685]
  Class incremental learning (CIL) algorithms aim to continually learn new object classes from incrementally arriving data. We experimentally analyze neural network models trained by CIL algorithms using various evaluation protocols in representation learning.
  arXiv  Detail & Related papers  (2022-06-16T11:44:11Z)
• Stabilizing Q-learning with Linear Architectures for Provably Efficient Learning [53.17258888552998]
  This work proposes an exploration variant of the basic $Q$-learning protocol with linear function approximation. We show that the performance of the algorithm degrades very gracefully under a novel and more permissive notion of approximation error.
  arXiv  Detail & Related papers  (2022-06-01T23:26:51Z)
• Scaling Structured Inference with Randomization [64.18063627155128]
  We propose a family of dynamic programming (RDP) randomized for scaling structured models to tens of thousands of latent states. Our method is widely applicable to classical DP-based inference. It is also compatible with automatic differentiation so can be integrated with neural networks seamlessly.
  arXiv  Detail & Related papers  (2021-12-07T11:26:41Z)
• Simple Stochastic and Online Gradient DescentAlgorithms for Pairwise Learning [65.54757265434465]
  Pairwise learning refers to learning tasks where the loss function depends on a pair instances. Online descent (OGD) is a popular approach to handle streaming data in pairwise learning. In this paper, we propose simple and online descent to methods for pairwise learning.
  arXiv  Detail & Related papers  (2021-11-23T18:10:48Z)
• Evolving Reinforcement Learning Algorithms [186.62294652057062]
  We propose a method for meta-learning reinforcement learning algorithms. The learned algorithms are domain-agnostic and can generalize to new environments not seen during training. We highlight two learned algorithms which obtain good generalization performance over other classical control tasks, gridworld type tasks, and Atari games.
  arXiv  Detail & Related papers  (2021-01-08T18:55:07Z)
• Bridging the Gap: Unifying the Training and Evaluation of Neural Network Binary Classifiers [0.4893345190925178]
  We propose a unifying approach to training neural network binary classifiers that combines a differentiable approximation of the Heaviside function with a probabilistic view of the typical confusion matrix values using soft sets. Our theoretical analysis shows the benefit of using our method to optimize for a given evaluation metric, such as $F_$-Score, with soft sets.
  arXiv  Detail & Related papers  (2020-09-02T22:13:26Z)
• Convergence of Online Adaptive and Recurrent Optimization Algorithms [0.0]
  We prove local convergence of several notable descent algorithms used in machine learning. We adopt an "ergodic" rather than probabilistic viewpoint, working with empirical time averages instead of probability distributions.
  arXiv  Detail & Related papers  (2020-05-12T09:48:52Z)
• Learning with Differentiable Perturbed Optimizers [54.351317101356614]
  We propose a systematic method to transform operations into operations that are differentiable and never locally constant. Our approach relies on perturbeds, and can be used readily together with existing solvers. We show how this framework can be connected to a family of losses developed in structured prediction, and give theoretical guarantees for their use in learning tasks.
  arXiv  Detail & Related papers  (2020-02-20T11:11:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.