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Where Cognition Lives: Dissecting Emergent from Computed Function in a Minimal Complete Cognitive Architecture
Francisco M. Arrabal-Campos, Francisco G. Montoya, Alfredo Alcayde, Ignacio Fernández
TL;DR
The paper asks which functions in a minimal complete cognitive architecture emerge from training and which must be computed explicitly. It tests this with controlled reasoning tasks, adaptive halting, homeostatic control, and value allocation, then audits apparent gains and extends the instruments to a frozen language-model actuator. Competence emerges, but the apparent value of posterior self-observation is a readout artifact, while value-shaped decisions are captured by explicit computation under the tested conditions.
Problem
The paper examines whether cognitive functions emerge from gradient descent or require dedicated computational machinery.
Method
The study evaluates a minimal complete architecture and frozen solver checkpoints using matched-compute allocation arms, certification tests, audits, and a frozen language-model actuator.
Results
At matched readout and budget, posterior self-observation contributes only +0.0011 [+0.0003, +0.0019], while explicit allocation captures the ex-ante ceiling and trained value coupling captures none.
Takeaways & Limitations
Under the tested construction, competence and stopping can emerge, but value-shaped second-order decisions must be computed explicitly when value is orthogonal to content.
Takeaways & Limitations
Replication across actuators was not run, and the conclusion that value must be computed was not tested when value correlates with content.
Abstract
from arXiv · showhide
A cognitive architecture is more than the module that reasons: it must also decide how long to think and what deserves the effort. We built a minimal but complete system - a recurrent reasoner with adaptive halting, a homeostatic control field, and a value module - and asked of each part: does this function emerge from gradient descent, or must it be computed? Competence emerges. Stopping appears to emerge too, and to be worth more than everything decidable in advance, but that appearance is instrumentation: payoff at matched mean compute climbs from 0.467 (uniform) through 0.546 (difficulty) to 0.698 (ex-ante value), and the further climb to 0.921 (posterior self-observation) does not survive audit. PonderNet-style halting returns a halting-weighted mixture of hidden states while forced-depth baselines return one, and the language head is trained on the mixture alone; equalizing the readout annihilates the apparent advantage of native execution (residual +0.000 [0.000, 0.000]). Value does not emerge: trained couplings capture zero of a payoff an explicit allocator captures completely (+0.151, routing correlation +0.79), so the second-order decisions that pay must be computed, at least where value is orthogonal to content, as here by construction. On a frozen LLM actuator the same instruments show self-consistency voting to be a measured bound (+0.0236 [+0.0150, +0.0326]) and inter-sample agreement nearly worthless as a stopping signal, its mass concentrating on wrong answers. Every null we assert carries a mechanism and a positive control, and the protocol is part of the contribution. Executing our own falsifiable prediction, value under commitment pays +0.1312 [+0.1124, +0.1502] in a cliff-cost family, some seven times the smooth-family estimate - not because the cliff shifts information ex ante, but because it multiplies the attainable range fivefold (5.1x [3.4, 8.2]).
1 Introduction
The paper tests whether cognition’s functions emerge through training or require explicit machinery, using a deliberately modest but structurally complete architecture and controlled algorithmic tasks. It finds competence and stopping in the reasoner, while value-shaped decisions require explicit computation.
- The paper experimentally tests which functions of a complete cognitive architecture emerge from training and which require explicit machinery.
- The testbed combines a decoder-only transformer, recurrent adaptive-halting reasoner, homeostatic compute field, explicit slot memory, and value module.
- Algorithmic S5 composition tasks provide controllable difficulty and information structure for evaluating serial reasoning and length generalization.
- 0.467 < 0.546 < 0.698 is the matched-compute hierarchy from uniform allocation through difficulty information to ex-ante value.
- A solver is a frozen trained checkpoint, and allocation arms map instances to reasoner iterations under a shared budget at matched mean compute.
- The study measures computation value at matched resource use, connecting its hierarchy to rational metareasoning and resource-rational analysis.
2 The substrate and its certification
The substrate is certified as a reasoning regime through seriality, memory, informed halting, and depth extrapolation, while the homeostatic field is shown to modulate compute without carrying task content. Its apparent accuracy cost and evidence-accumulation role do not survive the reported audits.
- Certification: State swaps transfer answers in 0.83–0.92 of cases, never revert to the recipient answer, and readout fidelity rises from 0.5 to 0.85–0.89 across ticks.These measurements support the trajectory-memory and serial-computation criteria of the T-M-I-P certification battery.
- Certification: Informed stopping reaches AUC 0.79–0.90 after preregistered remedies and re-certification, following an initial failure against all preregistered thresholds.
- Audit: The replicated accuracy cost was −0.011 [−0.068, +0.045], so the original −0.055 effect was retired as insufficiently reliable.The program consequently requires at least two independent runs per cell for effects below approximately 0.05.
- Homeostatic governor: The homeostatic field modulates compute but does not carry content, and a learned governor with the same interface performs similarly.
- Homeostatic governor: Field physics does not determine accuracy: making the field the computation source is catastrophic, while stateful modulation—not physical superiority—survives.The reported mechanism is that training coarse-grains temporal demands into a quasi-static set-point.
- Homeostatic governor: The evidence-accumulator kill-gate found ΔAUC = +0.0007 [−0.0065, +0.0079], because the recurrent state already integrates history and the last tick is sufficient.
4 Second-order decisions do not emerge; they are computed
The paper tests whether second-order decisions about compute and value emerge from gradient training. In smooth environments, anticipation and trained value couplings fail, whereas an explicit allocator over learned self-models captures the ex-ante payoff ceiling.
- Motivation: Second-order decisions concern what matters and how much computation to spend, and the design routes capability through the environment rather than the loss.
- Smooth-family anticipation: Anticipation provides at most +0.001 payoff in the scanned smooth-family environments, including comparisons with a perfect-history Bayes-filter oracle.
- Trained coupling: Routing correlation was −0.01 in every trained value-coupling arm, while stake information weakened from 1.00 in raw embeddings to 0.79 in the trained state.Stake-weighted cross-entropy also reduced performance to 0.786 versus 0.931 for the stake-blind control, with effective sample size 0.40.
- Explicit allocation: +0.151 is the allocator’s gain over the difficulty-only baseline, using n* = arg max_n ŝ · p̂(success | n) − λn.Removing the learned success self-model leaves +0.06 on the table.
- Conclusion: In this construction, value is orthogonal to content, so second-order decisions are computed from learned self-models rather than emerging from gradients.Whether this verdict holds when value correlates with content remains untested.
5 The information hierarchy
At matched compute, ex-ante value allocation reaches the honest ceiling, while posterior self-observation’s apparent advantage disappears when adaptive and forced executions share the same readout. The remaining benefit reflects a learned population-level mixture shape rather than instance-specific allocation.
- Matched-compute hierarchy: 0.467 uniform allocation rises to 0.546 with task difficulty and 0.698 with ex-ante value, while native self-observation appears to reach 0.921 through a different readout.The ex-ante value result equals the class-oracle ceiling; native execution uses emergent mean depth 5.47 versus exact e=5 for ex-ante arms.
- Audit: +0.430 native advantage over uniform falls to +0.047 when execution is forced at native per-instance depths, leaving +0.383 initially attributed to elastic execution.The remaining advantage is later identified as a readout artifact rather than the value of on-policy execution.
- Readout audit: PonderNet-style halting returns a halting-weighted mixture, whereas forced execution returns one hidden state, and the language head was trained only on the mixture.Post-hoc reconstruction from the same native trajectory reproduces the native arm and separates readout from execution.
- Posterior allocation: +0.0011 [+0.0003, +0.0019] is the matched-readout, matched-budget value of knowing which instance needs how much compute.A derangement of halting distributions produces the same small-scale effect, while a second derangement straddles zero.
- Interpretation: The ex-ante rung is the honest ceiling because self-observation adds essentially nothing beyond the mixture-readout artifact in this architecture.The scope is limited to PonderNet-style mixture readouts and does not establish the same result for other adaptive-depth designs.
6 The precondition of governance: a frozen LLM actuator
On a frozen language-model actuator, test-time compute has a measurable but limited value range. Self-consistency can improve outcomes, but agreement is a weak stopping signal and remains below the preregistered relevance threshold.
- Dynamic range: Across seventeen cells, the test-time compute lever is real but bounded well below practical relevance, spanning task families and base accuracies from 0.13 to 0.96.The chapter frames dynamic range as a prerequisite for governance of test-time compute.
- Value allocation: +0.0236 [+0.0150, +0.0326] is the value-allocation ceiling at T=1.3, below the preregistered relevance threshold of 0.04.The ceiling is computed from the measured vote curve with an unbiased without-replacement estimator and paired bootstrap.
- Benchmark anchor: On GSM8K, accuracy rises from acc1 = 0.905 to a vote-curve peak of 0.941 at n=7–9, while modal-error mass is 0.066.About 70% of the remaining error is systematic, and ε = +0.029 in the reported anchor cell.
- Agreement as a signal: Stopping on inter-sample agreement buys at most +0.017 in point estimate, with an upper confidence limit of +0.025 over ex-ante allocation.The analogous posterior channel is nearly worthless, aligning the frozen-actuator result with the audited trained-substrate result.
7 Negative space as a map
The paper maps negative results to mechanisms rather than treating them as bare nulls. This boundary clarifies which functions do not arise from the tested substrates or signals and where positive results remain possible.
- Negative space: The field does not think, gradient coupling does not route, the loss does not teach values, self-observation does not allocate, and LLM agreement does not verify.Each negative result is paired with a measurement that explains it, defining the boundary around the positive results.
8 Method as a result
The paper treats experimental process as part of the result: preregistration, adversarial review, replication, and positive controls were used to expose and correct misleading measurements. The resulting protocol constrains how the reported nulls and effects should be interpreted.
- Preregistration and review: Every confirmatory experiment was preregistered with complete verdict branches, and adversarial review panels challenged designs before GPU expenditure.The process is reported as a contribution intended to reduce self-deception in the experimental program.
- Reporting structure: Table 1 organizes negative results as mechanism-backed measurements, while marking the integration non-replication, exploratory branch, and post-hoc audits separately.The table distinguishes preregistered confirmatory rows from the exceptional exploratory and reviewer-requested analyses.
- Replication: p = 0.011 was not confirmed on replication, whose interval covered both zero and the original effect, establishing two runs per cell for small effects.The non-replication is treated as unresolved rather than as a confirmed effect or confirmed null.
- Positive controls: Replacing sampling with replacement and a design-cap budget corrected the LLM vote-curve estimate from a false structural null to a measurable but sub-threshold lever.The correction demonstrates why positive controls are needed for interpreting negative measurements.
- Instrument validation: Three cliff-experiment instrument designs were blocked by a preregistered known-zero sanity check before conclusions could be contaminated.The third failure exposed a structural fact about the known zero and led to redesign of the final experiment.
9 The cliff: executing our own prediction
The cliff experiment tests whether ex-ante value matters when task cost is invisible before execution. On a frozen LLM actuator, value helps substantially, while normalized capture fractions do not show a detected family difference and key comparators remain limited.
- Act one: the family resists construction on the small substrate: The cliff family failed the small-substrate learnability gate because the recurrent loop blocked formation of the in-context retrieval component it required.The backbone learned retrieval under the same data regime, whereas the reasoner remained at prior through thirty thousand steps.
- Act two: the family’s natural home: The frozen LLM actuator genuinely walks: generation length costs tokens proportionally, while visible cycle length predicts cost poorly in the cliff family.Measured token-cost correlation was 1.00; visible-cost R2 was 0.26 for cliffs versus 0.75 for smooth arithmetic.
- Act three: the result: +0.1312 [+0.1124, +0.1502] value-minus-difficulty payoff in the cliff family exceeded the smooth-family estimate of +0.019.The cliff result was 3.4× its preregistered threshold.
- Act three: the result: Payoff rose from 0.674 under uniform allocation through 0.754 under difficulty allocation to 0.885 under ex-ante value allocation.Knowing who would arrive added exactly nothing, while exact-cost knowledge reached 0.952.
- Act three: the result: The best ex-ante policy captured 0.759 [0.703, 0.825] of cliff range and 0.763 [0.522, 0.899] of smooth range, with difference −0.004 [−0.150, +0.241].This post-hoc comparison is compatible with equality but too imprecise to establish invariance.
- Honesty requires two demotions: The exact-cost oracle exceeded the arrival oracle by +0.067, but the comparator was clairvoyant rather than realizable; strict muteness remains unadjudicated.The paper specifies a redesigned mid-flight comparator for future work and withholds the muteness claim because its positive control failed.
10 Discussion
The surviving architecture assigns different functions to learned competence, native stopping, explicit value computation, and homeostatic control. Its conclusions are bounded by task design, substrate scale, actuator coverage, and the orthogonality assumption for stake.
- The architecture that remains: Stopping is native and posterior, but readout auditing reduces its matched-budget value to +0.0011 after an apparent advantage from mixture readout.The explicit allocator reaches the ex-ante ceiling, while value is computed over learned self-models for commitment decisions.
- The architecture that remains: The homeostatic field survives as a certifiable compute governor rather than as the source of task computation.The paper characterizes its role as brainstem, not cortex.
- One law, met three times: The program repeatedly measures lever range, signal learnability, and cost visibility before interpreting governance results.The authors present this as a recurring methodological pattern rather than an established universal law.
- Limitations: The trained substrate is small and algorithmic, so absolute hierarchy values belong to the chosen task families despite stable ex-ante ordering across twelve solvers.The measured variants contain 4.2–5.6M parameters; the ordering held across six seeds and two runs.
- Limitations: The LLM evidence uses one frozen actuator, and replication across actuators was never run.Governance arms were evaluated offline over cached pools, while the cliff chapter used one recorded greedy generation per instance.
- Limitations: The computed-decision verdict depends on stake being orthogonal to content; correlated value was not tested and could produce a different result.The paper identifies training’s shedding of task-irrelevant information as the measured mechanism.
11 Conclusion
The paper concludes that cognition is located less in a fixed stack of faculties than in measured distinctions between learned competence, observed stopping, computed value, and environmental preconditions. Its evidence and artifacts are archived, but several scope boundaries remain explicit.
- Conclusion: The paper’s cross-scale conclusion is that competence emerges, while unobservable value-relevant decisions must be computed explicitly from learned self-models.The conclusion frames this as the recurring answer across the minimal architecture and frozen-LLM probes.
- Conclusion: Forced execution reproduces the posterior halting trajectory exactly, and equalized readout leaves per-instance choices worth only +0.0011 [+0.0003, +0.0019].The apparent native advantage was instead attributed to mixture readout, measured at +0.383 [+0.341, +0.424].
- Reproducibility: The repository contains preregistrations, findings documents, adjudications, checkpoints, caches, and analysis code, with reported macros checked against archived results.The reproducibility materials include declared exceptions hard-coded from the same files.
- Conclusion: The models are 4–6M-parameter decoder-only transformers solving length-K S5 composition problems on a frozen 16k-instance evaluation set.The twelve solvers comprise six seeds × two independent runs.
B Hierarchy arms and estimators
The hierarchy compares allocation policies at matched mean compute, including simple baselines, an explicit stake-aware allocator, and native halting. LLM governance uses cached sampled chains and deterministic policies evaluated through unbiased voting and dynamic-programming stopping analyses.
- Hierarchy arms: At exact matching of e=5 mean ticks, uniform, difficulty, rule, explicit allocator, class oracle, and native arms define the hierarchy’s allocation comparisons.The explicit allocator maximizes estimated stake-weighted success minus compute cost under the shared budget.
- Hierarchy arms: The explicit allocator chooses n* = arg max_n ŝ p̂(success | n) − λn using a stake head and a budget-set compute price.The stake-aware rule and class oracle provide simpler comparison points.
- LLM governance cells: For the frozen Qwen2.5-14B-Instruct actuator, each instance has 16–24 sampled chains across temperatures 0.7, 1.0, and 1.3 with top-p=0.9.Policies are deterministic functions of cached pools; the GSM8K anchor cell uses 256 official test items.
- LLM governance cells: The vote curve uses an unbiased without-replacement estimator, with uniform tie splitting and non-parses excluded from voting.Exchangeability makes sampled subsets i.i.d. draws for the estimator.
- LLM governance cells: Agreement-stopping policies use dynamic programming over recorded sample-walk states and are fitted and evaluated on disjoint halves.A paired bootstrap with B=200 resamples instances and repeats the full frontier-construction pipeline.
D Cliff recording, truncation, and arms
The experiments record cycle-walk and arithmetic instances with explicit structural properties, then define answer-arrival and budget accounting for matched allocation arms. Pre-hypothesis gates test cost relationships, answer validity, and censoring.
- Recording: Cycle-walk instances use random single-cycle permutations with visible cycle length L ∈{6, 10, 14} and hidden distance d ∼U[1, L−1].Arithmetic contrast instances instead use chained integer operations with visible operation count; one greedy generation per instance is retained as full token IDs.
- Recording: The arrival index c_i is the minimal token prefix containing a completed answer line, found by binary search over decoded prefixes.The passage also states that budgets are accounted as tokens spent, although its final wording is truncated.
- Arms: Allocations are solved exactly by multi-choice knapsack dynamic programming over a cap grid, with analytically marginalized stake payoffs and cross-fitted caps.The allocation rule uses i min(t_i, cap_i), with matching across arms and A↔B cross-fitting.
- Gates: Pre-hypothesis gates establish cost–distance correlation 1.00, visible-class cost predictability R2 0.26 vs 0.75, complete valid hop chains in 100% of correct answers, and censoring of 0.4%, 0.4%, and 0.0%.These checks are reported for the R, S, and censoring gates, respectively, across L=6, 10, 14 for the censoring rates.