The Active Discoverer Framework: Towards Autonomous Physics Reasoning through Neuro-Symbolic LaTeX Synthesis

TL;DR

The paper introduces the Active Discoverer Framework, a neuro-symbolic AI architecture that achieves cosmic-scale physics reasoning and discovery of universal constants through invariant, interpretable, and extrapolation-capable models.

Contribution

It presents a novel digit-native neuro-symbolic architecture with LaTeX synthesis, enabling autonomous physics reasoning and overcoming the Float Wall problem in AI extrapolation.

Findings

Achieves 0% precision loss with LSB encoding up to 10^{50}

Successfully deduces universal constants like G at cosmic scales

Outperforms traditional models that collapse at large scales

Abstract

Modern artificial intelligence excels at statistical interpolation within seen manifolds but fundamentally fails at the exact reasoning required for theoretical physics and mathematics. We identify the "Float Wall" -- a catastrophic collapse of neural extrapolation at scales beyond $10^{16}$ -- caused by standard floating-point representation and linguistic tokenization (BPE). To resolve this, we introduce the Active Discoverer Framework, a digit-native neuro-symbolic architecture designed for invariant discovery. At its core is NumberNet, a Siamese Arithmetic Transformer that utilizes least-significant-bit (LSB) sequence encoding to achieve 0% precision loss and cosmic-scale extrapolation up to $10^{50}$. To enforce physical grounding, we implement a Hamiltonian-based energy descent and Symmetry Grouping layer, ensuring the model respects Noether's theorem natively. The primary innovation is the Symbolic LaTeX Bottleneck: an active discovery loop where the model is forced to hypothesize unknown physical variables through an autoregressive LaTeX decoder. By reconciling numeric "hallucinations" with structurally valid mathematical expressions, the framework ensures that any discovered physics is parsimonious and human-interpretable. We evaluate this system against a 30-billion scale benchmark and the Universal Physics Pantheon, featuring 50 "Chaos Mode" systemic perturbations. Our results demonstrate that while traditional GBDT and LLM-based architectures collapse at cosmic scales, the Active Discoverer autonomously deduces universal constants such as the Gravitational Constant ($G$) with high fidelity. This framework establishes a path toward zero-hallucination artificial intelligence and truly autonomous scientific research agents.