Specification for Latent Logic Topology & Soundness-Aware Calibration

The RLVR Convergence Paradox

The current paradigm for building "Large Reasoning Models" relies on a compute-intensive phase: Reinforcement Learning with Verifiable Rewards (RLVR). While effective, this process is non-deterministic. Empirical auditing reveals an "RLVR Lottery": identical alignment pipelines applied to different base models yield vastly different results.

We posit that this divergence is not a failure of alignment, but a topological feature of the pre-trained latent space. High-potential models possess an Intrinsic Soundness Topology—a physical separation in high-dimensional space where valid logical deductions are disentangled from probabilistic hallucinations.

The Metanthropic Protocol

To quantify this potential, we operationalize the model not as a token predictor, but as a probabilistic engine of Latent Causal Chains.

Phase 1: Holographic Feature Extraction

We utilize Cross-Layer Sparse Autoencoders (SAEs) to demultiplex the opaque residual stream into discrete, mono-semantic feature vectors. This gives us the atomic units of reasoning $(\alpha_c)$.

Phase 2: Latent Causal Chaining (Horn Clauses)

We formalize internal reasoning as chains of Horn Clauses $(P \rightarrow C)$. A latent rule implies that if a bundle of Premise features $(P)$ activates, a Conclusion feature $(C)$ follows with probability $p$.

Logic Rule: Premise_1 AND Premise_2 $\rightarrow$ Conclusion

For example, a stable reasoning circuit might encode: occur("sqrt") AND occur("4") $\rightarrow$ occur("2") (High Probability)

Phase 3: Soundness-Aware Calibration (SAL)

We categorize these discovered rules into semantic tiers using an automated Oracle:

• Strict: Axiomatic truths (Math, Code).
• Plausible: Heuristics.
• Noisy: Spurious correlations.

The Soundness-Aware Level (SAL) is computed as the Jensen-Shannon Divergence (JSD) between the probability distributions of these categories. A high SAL indicates that the model physically separates sound logic from noise.

Experimental Validation: The Topological Signal

We validated this metric across a matrix of models ranging from 0.5B to 14B parameters (Qwen, Mistral, Llama, DeepSeek).

1. Phase Separation

Strong reasoners (like Qwen-2.5-7B) display a Disentangled Topology. The probability mass for "Strict" axioms is concentrated at high confidence $(p > 0.8)$, acting as an intrinsic high-pass filter for logic. Weaker models show "Entropic Collapse," where signal and noise share overlapping distributions.

2. The SAL Scaling Law

We derived a formal empirical law linking the microscopic SAL metric $(s)$ to the macroscopic post-RLVR error rate $(\epsilon)$:

With an R-squared of 0.87, this metric allows us to predict downstream reasoning performance with high precision before allocating expensive GPU hours to RLVR training.

Conclusion

The Intrinsic Soundness Topology proves that reasoning capability is not an emergent phantom but a quantifiable structure. SAL functions as a Computational Gatekeeper, allowing Metanthropic to strictly allocate compute to substrates that have demonstrated the intrinsic ability to disentangle signal from noise.