Science · Research program

Neural Firmware

A four-phase research program testing whether exact deterministic computation can live inside a language model's forward path.

Compendium article 050 Revision 0.6 · July 2026
17% untouched model on Phase 4 prompts
90% internal deterministic architecture
100% oracle-routed exact execution
24,225 learned Phase 4 interface parameters

Language models are useful because they can generate, interpret, and improvise. Those same strengths make them an awkward place to entrust a transition that has exactly one correct answer. Neural Firmware explores a hybrid boundary: keep language flexible, but make selected computation exact by construction.

Four linked experiments that progress from a controlled 264K-parameter transformer to a frozen Qwen2.5-0.5B model, then move the deterministic unit inside the repeated transformer stack and finally invoke it from varied natural language. Its purpose is to test whether small learned interfaces can connect generative language models to locked deterministic processes without relegating exact computation to post-inference correction.

Architectural through-line · four-phase program

Generative interpretation surrounds an exact typed transition.

The implementation is an internal registered coprocessor, not one scalar neuron and not a post-generation answer replacement. Later phases moved the same principle deeper into the transformer and added semantic routing.

Source: Neural Firmware research program · July 2026

The question behind Neural Firmware

The research began with Josiah's proposal to add or repurpose something neuron-like inside a transformer as a calculator. The implemented version is more structured than one scalar neuron: a typed deterministic cell with learned interfaces that translate between residual states and discrete arithmetic registers. Each phase tightened the claim by moving from a toy model to a pretrained model, from the output edge into the repeated stack, and from a registered command to varied English. Researchers and builders working on small-model reliability, neuro-symbolic systems, mechanistic control, or verifiable AI may find the experiments useful. Readers are affected by how novelty and authorship are framed, so prior art, AI collaboration, failures, and untested boundaries remain prominent.

How Neural Firmware took shape

The work was organized as four linked experiments with frozen evaluation rules, held-out prompt families, matched learned controls, raw result archives, and causal interventions. Failures were not discarded: Phase 2's late routing defect motivated deterministic scope, and Phase 4's family-clustered routing misses separated exact execution from natural-language recall. Josiah originated the neural-firmware research direction, selected mathematics as the first test domain, shaped the successive architectural questions, and directed the program. OpenAI Codex materially performed literature research, experimental design, implementation, execution, analysis, validation, visualization, and manuscript drafting under Josiah's direction.

What the evidence supports

Phase 3 passed all eight frozen criteria: 1,575 of 1,575 evaluated arithmetic generations were exact, a same-depth equal-parameter learned control scored 0 of 900 across the two random extrapolation splits, and causal state interventions controlled output. In Phase 4, the base scored 68 of 400, the matched learned control 21 of 400, and the internal architecture 360 of 400; oracle routing was 400 of 400 and every one of 349 automatic activations was exact. The evidence supports a narrow but striking engineering result: a weak small model can gain a large exact capability from a locked internal process, and the gain disappears when that process is disabled. It does not establish broad mathematical reasoning or conceptual priority. IGC had already demonstrated the general integrated-calculator family on a larger model; this program contributes small-model, tiny-interface, matched-control, deep-insertion, and causal evidence.

The papers are not peer reviewed or independently replicated. The closest prior integrated-calculator work is Dietz and Klakow's IGC, so this program does not claim invention of the broad concept. The strongest experiments cover only two-operand nonnegative decimal addition; Phase 4 retains a fixed candidate-number boundary, uses one Qwen checkpoint, and missed its positive-routing threshold by 2.75 points. The next study will compare the typed firmware architecture directly with an IGC-style learned calculator on the same small model and identical prompts, across multiple interface seeds and fixed parameter budgets. The next architectural milestone is learned token-to-register extraction and expansion beyond addition.

Published research series

Four experiments, each tightening the last one's weakest boundary.

Phases 3 and 4 are the principal portfolio papers. Phases 1 and 2 preserve the foundational result and the routing failure that shaped the later architecture.

  1. 01

    Exact addition in a controlled transformer

    Foundation

    10,500 / 10,500 confirmatory examples exact

    A compact transformer trained on one- to six-digit addition received an immutable ripple-carry process through a learned latent interface. The generic model extrapolated to none of the longer examples; the firmware model answered every confirmatory example exactly.

  2. 02

    Move into a pretrained 0.5B language model

    Mixed

    100% primary arithmetic; preservation threshold missed

    The first pretrained-model integration solved its primary extrapolation set, but failed the complete preregistered rule when a quoted calculator command later triggered inside an instruction to ignore it. That failure made routing and preservation first-class research problems.