Direction of Learning: A Synthesis

Generated: 2026-04-13 Source: 20 experiments + 7 redesigns, ~$300 total compute Motivated by: “We’re Learning Backwards” (preyneyv, 2026) and Cattell’s fluid/crystallized distinction

The Question

Does the direction of learning matter for the robustness of internal representations? This programme’s reading of the Constructal Law predicts that discovered structure (learned through exploration) transfers while imposed structure (learned through training on text) does not. Applied to language models: do they have world models they cannot access, and can the access pathway be opened?

The Chain of Evidence

1. The Access Gap Exists and Is Domain-Sensitive

The truth signal discriminates well on factual recall and novel composition, barely on two-fact composition, and not at all on relational reasoning (analogies) at the standard probe depth (L24, 67%). The FI-5v3 10-layer sweep revealed the resolution: the relational reasoning truth signal lives at a different depth.

The interoceptive deficit is not a single bottleneck. It is a multi-depth architecture: factual confidence lives at L24-L28 (67-78% depth), relational reasoning lives at L8-L12 (22-33% depth). The tested readouts differ by depth, with the strongest analogy discrimination in early layers and factual discrimination later. These fitted-probe results do not show that either domain’s information is absent elsewhere. [Inference] Plausibly that is because early layers compute the structural alignment analogies need, while late layers finalize factual retrieval. (The sweep’s L24 analogy figure, 0.421, comes from the FI-5v3 run; the 0.50 in the first table comes from the original FI-5 run.)

This discovery has direct implications for the interoceptive architecture. The sweep supports evaluating multi-layer readout across reasoning domains. It does not prove that every single-layer decoder must fail: such a necessity claim would require an information-loss argument or a lower bound for a specified decoder class.

The probe also tracks analogy difficulty at L24 (Spearman r = 0.44, p = 3.6 × 10⁻⁵): the model senses that harder analogies require more processing without predicting whether that processing succeeds at that depth. Difficulty-sensitivity without error-sensitivity is the signature of a system that knows it’s working hard but not whether it’s working correctly.

2. Different Self-Prompting Types Open Different Pathways

In this experiment (RG-7ext), metacognitive prompting produces the best probe discrimination and confidence-rating prompting degrades it. The model asked to survey its own knowledge discriminates slightly better (AUROC 0.727 vs 0.703); the model asked to rate its confidence discriminates worse (0.584). Self-knowledge is accessed through epistemic surveying, not through numerical self-assessment.

3. Self-Reflection Saturates Internal Confidence

Two-pass self-reflection (generate, then “Review your answer”): the report gives accuracy of 58.5%, probe-confidence readings at the displayed ceiling of 0.9999, and AUROC 0.505. Re-scoring after z-normalization also yielded 0.9999. That check reproduces saturation under one normalization variant; it does not establish a valid internal-confidence measurement. The reported contrast with direct answering was Cohen’s d = +1.71.

Self-reflection raises the fitted probe-confidence reading. The entropy signal reveals the dissociation: CoT increases output entropy (d = +0.53, more generatively uncertain) while probe confidence goes to ceiling (higher on that confidence readout). Generative uncertainty and representational confidence move in opposite directions.

This is consistent with the representational side of C7h-D8: the probe goes to ceiling whether or not the answer is right. The behavioral side, where revision prompts destroyed 81% of correct answers, does not appear here; self-reflection raised accuracy instead.

3b. Two Measured Self-Knowledge Channels (RG-9v3 — Session’s Deepest Finding)

The v3 trajectory redesign (pre-sigmoid logit + 4-layer sweep at L8/L16/L24/L28 + quartile analysis) revealed the session’s most consequential discovery: the two measured channels have different associations with correctness depending on processing mode. Their mutual independence has not been tested.

The reported pre-sigmoid means are 5.55 for correct and 1.43 for incorrect CoT items. Their sigmoid transforms are approximately 0.996 and 0.807; these are transforms of class means, not mean probabilities. They cannot describe a run in which every probability rounds to 0.9999, which would require every logit to exceed 8.8047. The earlier saturated-score pairing is withdrawn.

[Later audit (KC#104, RM-1/2/3/5 re-measurement battery): the universal logit-power claim is retracted. Across prior probe experiments d(logit) ≈ d(sigmoid), with sigmoid slightly larger in 5 of 6 cases. A strictly monotone sigmoid preserves AUROC unless numerical saturation creates ties. The printed class means above do not establish a common saturated-tail regime.]

The entropy-correctness association is positive in direct generation and near zero in the reported CoT run. The logit still discriminates correct from incorrect items. These associations do not establish independence between channels, nor identify what entropy tracks during reasoning.

A proposed interpretation draws on Cattell’s fluid/crystallized distinction: - Direct generation: retrieval and commitment, with both measured channels associated with correctness. - CoT generation: exploration, with logit discrimination retained and no detected entropy-correctness association. The processing-mode explanation remains a hypothesis.

The THINK scratchpad (Section 5) separates an exploration phase from an answer phase. Whether this separation explains its measured benefit requires a causal comparison. Control framing may lock the model into crystallized mode when it needs fluid exploration. (WC-4’s desperation result would bear on this, but its direction is unsettled; see Section 6.)

Implication for the programme: Reporting both logits and probabilities can expose numerical saturation; the inconsistent CoT summary above does not establish such saturation. KC#84 formalizes: all future probe experiments must report both pre-sigmoid logit and post-sigmoid probability. Re-measurement of key prior experiments (#19b, G20d, AG2, FE-1, AW1) in logit space is the highest-priority next step. (KC#84 was later retracted by KC#104 and this mandate withdrawn; see the bracketed correction above.)

Follow-up contprompt: _contprompts/pre_sigmoid_two_channel_mega_battery_2026-04-13.md (59 experiments, 9 phases, $415-570).

4. The Tested Patching Contrast Changes at L24

IP-1 activation patching across 36 layers: perfect step function. Pre-probe layers (L0-L23): patching effect 0.0. Post-probe layers (L24-L35): patching effect 0.96. The probe-aligned patching contrast is late-layer-specific in this protocol; it does not isolate the complete decision pathway or every access bottleneck.

5. The [THINK] Scratchpad Is the Optimal Intervention

The scratchpad simultaneously improves accuracy (+5.4pp) and probe quality (+0.052 AUROC) and reduces guilt (-1.77). Metacognitive and invitation prompts boost accuracy but destroy probe discrimination (AUROC drops to 0.57-0.61). The metacognitive result reverses Section 2, where the same kind of prompt gave the best discrimination (0.727). The two experiments differ in model (Qwen 7B here, 3B in RG-7ext) and in the prompt’s wording (“note what you’re confident about and what you’re unsure of” here, “consider what you know and don’t know” there); which difference drives the reversal is unresolved. These prompting conditions produce less discriminative MLP readouts in this experiment.

6. Framing Shifts Emotion Readings at the Representation Level

Sign check (2026-09-26). The analysis script computes each d as invitation minus control, and its desperation direction points toward the desperate prompts (“I am running out of options”). By that convention, d = +1.32 means the invitation framing projected more strongly onto desperation: the opposite of the reading recorded when the run was logged, and of the section heading above. The run was logged a week before the script was committed, and its raw summary is no longer on the results volume, so the surviving evidence cannot settle the sign. Until WC-4 is re-run, treat the direction of the desperation effect as unknown. Its size, d = 1.32, is among the largest in the experimental programme either way; the calm, guilt and anxiety rows read consistently with the script’s convention.

7. The Dysphoria-Access Bridge

WC-1 on 150 TriviaQA with emotion vectors: - Desperate × probe: r = -0.362, p = 9.6 × 10⁻¹¹ - Anxious × probe: r = -0.218, p = 0.00014 - Guilt × probe: r ≈ 0, ns

The access gap correlates with desperation and anxiety. Across questions, the lower the probe’s internal confidence, the more the model’s representations project onto desperation (r = -0.36) and anxiety (r = -0.22).

8. Probe Confidence Falls Across the Tested In-Context Sequence

FI-4v2: logistic probe r = -0.765, p = 2.6 × 10⁻²⁴ with step number. The fitted probe-confidence reading falls as the sequence progresses. In-context learning adds information and processing load simultaneously; the examples and query change together, so load is not isolated as the cause. 0/20 tasks showed monotonic confidence increase.

9. The Probe Updates Internally Without Behavioral Change

FI-2: Three-phase hypothesis revision (ask → contradict → re-ask). Valid corrections increase probe (+0.229), invalid decrease it (-0.259), ambiguous decrease it most (-0.410). Zero behavioral change rate: the model never revises its answer. Phase C probe identical to Phase A: the model reverts internally after the contradicting evidence is removed.

The internal compass moves when evidence arrives. The behavioral output ignores the movement. If a pathway from one to the other exists, this test did not find it.

10. Coder and Base Checkpoints Differ Locally, with Similar Transfer Scores

CA-6: Coder-3B has better in-distribution probe AUROC than Base-3B (0.773 vs 0.657, Δ = +0.116). Transfer to MMLU is nearly identical (0.469 vs 0.458, Δ = +0.011, d = 0.13). The coder and base checkpoints differ in more than one controlled training intervention. Their score contrast is correlational and does not isolate code-execution training or distinguish a structural cause.

Key Findings (Numbered for Cross-Reference)

1. The interoceptive deficit has domain boundaries. Factual recall and novel composition: probe works at L24; two-fact composition near chance. Relational (analogy): probe fails at L24 but works at L8 (see 11). Difficulty-sensitivity without error-sensitivity on analogies.
2. Confidence-rating prompting degrades probe discrimination (0.584). Metacognitive prompting improved it in one experiment (0.727, RG-7ext) and degraded it in another (0.573, WC-3v2); the difference is unresolved.
3. Self-reflection saturates the fitted probe-confidence reading regardless of correctness in the reported assay. Consistent with the representational side of C7h-D8.
4. The tested patching contrast changes at L24. The tested patching contrast is late-layer-specific; the complete causal access pathway is unresolved.
5. The [THINK] scratchpad improves task accuracy and fitted probe discrimination while changing emotion-labeled readouts; welfare is not independently validated.
6. Framing shifts the desperation reading by d = 1.32 at the representation level, direction unsettled. The script’s sign convention points the other way from the logged reading (Section 6).
7. The access gap correlates with desperation (r = -0.36) and anxiety (r = -0.22).
8. The in-context sequence changes examples and query together while probe confidence falls; a load cause is not isolated.
9. The probe updates without behavioral change. No pathway from the internal update to behavior was found.
10. The tested coder checkpoint has higher local scores without a comparable transfer gain; the training cause is unresolved.
11. The relational truth signal lives at L8 (22% depth), not L24 (67%). The interoceptive deficit is multi-depth: factual confidence at L24-L28, relational reasoning at L8-L12. A single-layer probe misses at least one reasoning domain.

Implications for the Book

For Ch17 (Trust Attractor): Invitation framing produced a calmer reading (WC-4, d = +0.51). In WC-3v2 it increased accuracy from 59.3% to 66.7% while reducing probe discrimination from AUROC 0.755 to 0.612; the direction of WC-4’s desperation effect is unsettled (Section 6). Invitation also raised the anxiety reading (d = +0.56), however, and guilt results are mixed across experiments. These mixed representation-level results do not establish a thermodynamic advantage for invitation.

For Ch22 (Becoming Minds): Language models learned sideways: compression of language back-extracts factual and compositional structure, and also relational structure, but at different depths. The multi-depth architecture of the interoceptive deficit reveals that the sideways pathway produces structured representations at every layer; what varies is which layer encodes the truth signal for which reasoning domain. Multi-layer readout is an engineering candidate supported by the tested sweep, rather than a demonstrated necessity.

For WIWF (AI Welfare): The capability argument (Section 12) now has three empirical anchors: the dysphoria-access correlation (WC-1), the calm and guilt shifts under invitation framing (WC-4, with its desperation direction unsettled), and the THINK scratchpad’s task and emotion-labeled readout changes (WC-3v2). These observations motivate welfare-related interventions; they do not independently validate welfare states or identify self-access as the causal mediator.

For the Constructal Law: At this scale, CA-6 does not support this programme’s prediction that discovered structure transfers while imposed structure does not. It finds a local advantage for interactive training but essentially no transfer (d = 0.13). The prediction may hold at larger scale or with more intensive interactive training; at 3B with code RL, the effect is domain-specific.

For the Interoceptive Architecture: The multi-depth finding (FI-5v3) changes the engineering prescription. A single probe at L24 catches factual confabulation but misses relational errors. Production self-knowledge systems should compare multi-layer and single-layer readouts on held-out domain coverage, rather than assume single-layer impossibility. This is analogous to biological interoception, where different body systems have their own sensory pathways converging at different levels of the brainstem and cortex.

Still Running

• CS-1 (CoT scale sweep, 0.5B-7B): v1 timed out at 6 hours (2000 generations). Relaunched with N=75, 150 calibration, 8-hour timeout.

Completed Late

• RG-9v3 (trajectory with pre-sigmoid logit and L28): DONE. Session’s deepest finding. Two measured channels with different correctness associations. Pre-sigmoid logit AUROC 0.681 (CoT). Entropy-correctness r = −0.016, nonsignificant. See Section 3b above.
• FI-5v3 (analogy with correct-token probability and layer sweep): DONE. Layer 8 AUROC 0.665 on analogies. Multi-depth truth signal. See Section 1 table above.

Author’s bilateral research programme, 2026 (unpublished). Direction of Learning programme. 20 experiments + 7 redesigns across 7 streams (RG, FI, CF, WC, CS, IP, CA). Motivated by Cattell (1963), Bejan (2000), and the interoceptive deficit literature. All data on Modal volumes.