Counterfactual Energy Equilibrium Reasoning

Status: one bounded transition-mechanism pilot; no reasoning or novelty claim.

Hypothesis

PCSD, FCPT, CGSGR, and QVESR all manipulate evidence or state through learned additive proposals. Their modules are causally active, yet better local consistency does not become better composition. Counterfactual Energy Equilibrium Reasoning (CEER) changes the transition itself.

A complete latent state predicts every prompt-owned source consequence. Their masked negative log likelihood defines a scalar energy:

E(S; X) = mean_j -log p(y_j | S, probe_j)
g_t = dE / dS_t
S_(t+1) = S_t - D_theta(S_t, g_t) * normalized(g_t)

D_theta is a positive diagonal preconditioner, so it can change step size and geometry but cannot reverse the local energy gradient. The late query is absent from equilibrium inference. Reasoning is therefore inner optimization of one model-owned state against source evidence, not a sequence of arbitrary recurrent proposals.

Prior-art boundary

Energy-based models, predictive coding, active inference, learned optimizers, deep equilibrium networks, Hopfield networks, recurrent refinement, and gradient-based latent inference are established. CEER does not claim those ingredients as new. Its bounded question is whether differentiating a learned prompt-owned consequence energy supplies a materially better compositional transition than an ordinary recurrent updater under exact matched execution.

Matched control

Every arm instantiates and executes both candidate transitions in every round:

• ENERGY: positive-preconditioned descent of consequence energy;
• RECURRENT: dense cross-attention to all evidence followed by an ordinary gated recurrent update.

The selected state is the only arm-dependent line. Parameter count, module execution, recurrent rounds, examples, data, update count, and frozen cohorts are identical. Both arms receive all evidence every round, eliminating sparse selection as a confound.

The seed-37 pilot uses 1,000 updates, 256 examples/update, four inference rounds, training depths 2--4, and frozen depth-5/7 noncommuting, binding, and induction cohorts. ENERGY advances only if it:

1. beats RECURRENT by at least five absolute macro points;
2. improves the mean of both depths in every family;
3. reduces its own evidence energy across inference;
4. loses at least three macro points when evidence outcomes are shuffled; and
5. loses at least three macro points when its energy gradient is zeroed.

A miss closes this exact energy-transition mechanism. It does not authorize a step-size, duration, width, seed, preconditioner, energy, or recurrence sweep.

Result

The bounded seed-37 pilot is complete and CEER is closed.

Both arms have exactly 112,726 parameters, receive 256,000 training examples, execute both transition modules at every round, and differ only at the selected state transition. ENERGY reduces prompt-evidence energy by a mean 0.720 nats. Its mechanism is causally active: shuffling evidence outcomes reduces macro accuracy to 10.449% and zeroing the energy gradient reduces it to 10.661%. Nevertheless, the final capability gain is only 0.163 points, it is negative on three of six cohorts, and polynomial induction remains at chance. CEER therefore misses both the +5-point and every-family gates.

Report SHA-256 values are:

• ENERGY: 9eaf0bed993d3a662b971131a8e1505ead902b8a274faa7f882863f2696d4868
• RECURRENT: e96a49c86badef46dba930faa4ed8541437249f9910e7cd5a1b18605b1ef5f76

Read-only interface diagnostic

CEER learns evidence predictions with ConsequenceHead but answers the late query with a separate attention/readout head. A checkpoint-only diagnostic applied the learned consequence head directly to the held-out query without changing weights. This shared consequence readout reaches only 4.801% macro for ENERGY and 4.867% for RECURRENT, versus 21.891% and 21.729% through the separate readers. It scores 0% on both noncommuting cohorts and remains near chance on induction.

Diagnostic SHA-256: f03ae392464a406a09052459b8124b509c2f229191c4a5d20349dc27a8639c2b.

This rules out a post-hoc shared-head swap. The learned state/head pair can fit observed consequences but does not encode one law that extends to an unseen probe. The next bounded mechanism must make a single probe-conditioned law responsible for both source consequences and the final query during training. It must not add another selector, recurrence sweep, or unconstrained opaque state reader.