Teaching a Minimalist Machine to Discover Recursive Programs for Arithmetic

Dominik Magiera; Christiane Wiebel-Herboth; Frank Jäkel

Home/Archive/arXiv

arXiv · 2610.06304

Teaching a Minimalist Machine to Discover Recursive Programs for Arithmetic

Dominik Magiera·Christiane Wiebel-Herboth·Frank Jäkel

View original source ↗Read source document ↗Export metadata ↓

Abstract

Humans can often acquire and synthesize complex, recursive concepts from minimal experience. Leveraging cognitive insights, we propose the Minimalist Machine, a framework for inductive program synthesis designed to model such conceptual learning. The system uses a compact relational subset of Prolog: Programs are searched within a fixed schema of body-free facts and two-body conjunctive Horn clauses. Recursion is not defined by a dedicated metarule. Instead, it emerges when a target predicate is reused inside the body of a learned clause. Inspired by a primary school curriculum, the model is taught through a human-curated, sequential introduction of new concepts in arithmetic. Starting from initially empty knowledge base, it first acquires simple structural predicates, then successor-based state transformations, and finally recursive programs for addition, subtraction, multiplication, and division. Ultimately, this approach yields the fully transparent, inductive reasoning trace necessary for human-like conceptual learning.

Explore related subjects

cs.AI

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Dominik Magiera, Christiane Wiebel-Herboth, Frank Jäkel. 2026-10-05. Teaching a Minimalist Machine to Discover Recursive Programs for Arithmetic. https://arxiv.org/abs/2610.06304

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Answer Set Networks: Casting Answer Set Programming into Deep Learning

Although Answer Set Programming (ASP) allows constraining neural-symbolic (NeSy) systems, its employment is hindered by the prohibitive costs of computing stable models and the CPU-bound nature of state-of-the-art solvers. To this end, we propose Answer Set Networks (ASN), a NeSy solver. Based on Graph Neural Networks (GNN), ASNs are a scalable approach to ASP-based Deep Probabilistic Logic Programming (DPPL). Specifically, we show how to translate ASPs into ASNs and demonstrate how ASNs can efficiently solve the encoded problem by leveraging GPU's batching and parallelization capabilities. Our experimental evaluations demonstrate that ASNs outperform state-of-the-art CPU-bound NeSy systems on multiple tasks. Simultaneously, we make the following two contributions based on the strengths of ASNs. Namely, we are the first to show the finetuning of Large Language Models (LLM) with DPPLs, employing ASNs to guide the training with logic. Further, we show the "constitutional navigation" of drones, i.e., encoding public aviation laws in an ASN for routing Unmanned Aerial Vehicles in uncertain environments.

cs.AI↗

arXiv2026

Towards LLM Agents for Earth Observation

Earth Observation (EO) provides critical planetary data for environmental monitoring, disaster management, climate science, and other scientific domains. In this work we ask: Are AI systems ready for reliable Earth Observation? To answer this, we introduce UnivEARTH, a coding benchmark of 408 yes/no questions from NASA Earth Observatory articles across 7 various topics and over 15 satellite instruments and sources. Using Google Earth Engine API as a tool in a zero-shot setup, LLM agents achieve an accuracy of 40.0% where the code fails to run over 44% of the time. To better understand LLM agent behavior, we also analyze the impact of using the JavaScript API versus Python and the effect of providing documentation. Furthermore, we find that using a Reflexion framework significantly reduces errors: Claude-4.5-Sonnet, Gemini-2.5-Pro, and GPT-5 accuracies rise to around 60%. However, these results remain only marginally above random chance. Taken together, our findings identify significant challenges to be solved before AI agents can automate earth observation, and suggest paths forward.

cs.AI↗

arXiv2026

OpenPhone: Mobile Agentic Foundation Models

With the advancement of multimodal large language models (MLLMs), building GUI agent systems has become an increasingly promising direction--especially for mobile platforms, given their rich app ecosystems and intuitive touch interactions. Yet mobile GUI agents face a critical dilemma: truly on-device models (4B or smaller) lack sufficient performance, while capable models (starting from 7B) are either too large for mobile deployment or prohibitively costly (e.g., cloud-only closed-source MLLMs). To resolve this, we propose OpenPhone, a mobile GUI agent system that leverages device-cloud collaboration to tap the cost-efficiency of on device models and the high capability of cloud models, while avoiding their drawbacks. Specifically, OpenPhone enhances Qwen2.5-VL-3B via two-stage SFT->GRPO training on synthetic GUI data for strong decision-making, integrates an efficient long-reasoning and memory management mechanism to utilize historical interactions under tight resources, and defaults to on-device execution--only escalating challenging subtasks to the cloud via real-time complexity assessment. Experiments on the online AndroidLab benchmark and diverse apps show OpenPhone matches or nears larger models, with a significant reduction in cloud costs.

cs.AI↗