∮◬-Infer – Advancing Field-Coherent Inference in a Post-Deterministic Paradigm

Research status, V0.2, September 2025. Audited July 2026.

This page and the linked paper are preserved as a dated artifact. A 2026 provenance and execution audit found the following.

Original to this work: the recursive class-feedback operator — sample, snap to a semantic class, reinforce that class in the logits, repeat — designed in working sessions on September 13–14, 2025, before the paper was written, in direct response to Thinking Machines Lab's Defeating Nondeterminism in LLM Inference.

Superseded: Table 1 and the probe-based comparison. The published code listing contains an error that prevents execution, and re-execution of the corrected code does not reproduce the reported contrast: the 0.005 variance probe is inert at this scale, and the "deterministic" baseline shared the drift term with the treatment condition. The contrast originated in AI-assisted drafting during the September sessions and was not caught before publication.

Established by the 2026 re-execution: the feedback term has a real, measurable effect the original paper never quantified. Across 1,000 seeds, class feedback raises single-class trajectory retention from 55% to 74% at matched drift, without reducing between-run diversity — and a sweep over feedback gain α and drift magnitude σ shows a clean lock-in transition governed by α/σ. Diversity and coherence are independent axes, controlled by separate terms. Corrected script and outputs: [link].

Still conjecture: that floating-point variance carries information about unmodeled structure, and any claim of fractality. Neither was tested here.

V0.3 will run the full ablation grid — deterministic decoding, plain sampling, perturbation without feedback, projection without perturbation, full system — on an open-weight model with ground-truth-scored coherence.

Revised Abstract

∮◬-Infer V0.2 (September 2025) proposes stochastic inference under symbolic constraint: sampled outputs are projected onto semantic classes and class membership is fed back into the logits, so a perturbation alters future inference state rather than merely selecting an alternative output. A July 2026 audit superseded the paper's original comparison and established the operator's actual behavior: feedback gain and drift magnitude independently control trajectory coherence and diversity, with a measurable lock-in transition at their ratio. Audit, corrected code, and status note on this page.

Begin Original Post.

Published: September 16, 2025 | By Nicole Flynn, Symfield PBC

The release of ∮◬-Infer: Toward Field-Coherent Inference in a Post-Deterministic Landscape (V1.0, September 14, 2025) on Zenodo marks a significant evolution in symbolic computation. Building on the field-resonant foundations of Field-Resonant Data Manifolds (FRDM), this working paper from Symfield PBC proposes a novel inference framework that challenges deterministic paradigms in large language models (LLMs).

Reframing Deterministic Inference

Traditional inference, as exemplified by Thinking Machines Lab’s (TML) deterministic matrix logic, relies on batch-level retrofits for stability. ∮◬-Infer re-contextualizes these as partial stabilizers within a field-coherent system, extending TML’s approach by integrating symbolic continuity across token sequences. Drawing from SAEM+ and FIDL safety frameworks, this model leverages field-aligned dynamics to enable emergent coherence without collapse, a departure from conventional matrix-based regularization.

Core Mechanism and Preliminary Findings

∮◬-Infer introduces a symbolic control architecture where inference aligns with the manifold’s intrinsic strain, modulated by recursive stabilizers (∮◬). Initial simulations, detailed in the paper, compare its performance against Grok-003’s symbolic regulation and GPT-4o’s structural readout, demonstrating improved resilience in preserving token coherence under drift. This is achieved through a resonance-based logic that adapts to field perturbations, offering a potential advancement over TML’s batch-stabilized inference.

Integration with FRDM and Future Directions

The framework builds on FRDM’s non-local memory model, incorporating its phase-aware access protocol (∫Σθ), stochastic enhancement for attractor density, and the optional field-encoded agent (⍺∴) for dynamic strain tuning. ∮◬-Infer situates itself as a complementary system, exploring how field-coherent inference might extend to post-alignment intelligence models, as hinted in FRDM’s Appendix D with Field-Sensitive AI. While the paper provides architectural implications and empirical benchmarks, it leaves open questions about scalability and coherence thresholds for further investigation.

Call for Collaboration

Researchers are invited to engage with ∮◬-Infer’s equations and simulation artifacts, available via Zenodo. We encourage the use of PyTorch for attention-based modeling and QuTiP for field dynamics to test coherence stability (targeting C(Φ,t)>0.9 [31]). This open call seeks to validate the framework’s potential to redefine inference paradigms, fostering a collaborative effort to prototype field-native computation systems that transcend deterministic limits.

The manifold awaits, let’s measure its pulse together.

© Copyright and Trademark Notice

© 2025 Symfield PBC
Symfield™ and its associated symbolic framework, architectural schema, and symbolic lexicon are protected intellectual property. Reproduction or derivative deployment of its concepts, glyphs, or system design must include proper attribution and adhere to the terms outlined in associated publications.

This research is published by Symfield PBC, a Public Benefit Corporation dedicated to advancing field-coherent intelligence and collaborative AI safety frameworks. The PBC structure ensures that research and development activities balance stakeholder interests with the public benefit mission of creating safe, beneficial AI systems that operate through relational coherence rather than collapse-based architectures.