Typed Model Spec — `:novelty` (parameter information-gain EFE term)

Status: MERGED + gated (live). This document is ARTIFACT #1: the typed model spec of the already-merged novelty term (lib/sp/brain/novelty.ex), authored by the AIF Core Theorist. It is also the TEMPLATE every Phase-2 organ inherits — every gated organ spec (docs/specs/metabolism.md, etc.) MUST reproduce these nine sections in this order, cite real file:line, and carry a ClaimFence.

What "novelty" is, in one line: the third Expected-Free-Energy term — parameter information gain over the Dirichlet counts of A (and B) — that the flat two-term EFE (epistemic H[qo] − E[H(o|s)] + pragmatic qo·C) was missing. It is the pymdp/SPM pA-novelty approximation (NOT the digamma E[ln A] form), per UNI-GPT consult Q2 (SIGN-WITH-CHANGES). It rides the epistemic channel under the same γ as the state-epistemic term, is independent of C, and decays monotonically to 0 as counts → ∞.

Source files (all absolute; root [redacted: operator-path]\Documents\Strings):

• lib\sp\brain\novelty.ex — the term itself (w_a/3 :36-50, w_b/3 :57-71, @floor :30).
• lib\sp\brain\plan.ex — the LIVE depth-5 decider integration (advance/3 :124-148; A-novelty :137, B-novelty :142; gain read :92; pa_m carried :97).
• lib\sp\brain\efe.ex — the depth-1 mirror (step_value/3 :87-101; A-novelty :98; gain read :91).
• lib\sp\brain\model.ex — novelty_gain field default 0.0 (:35, :98); Dirichlet seed pa = A*1+1, pb = B*1+1 (:84-85, :115).
• lib\sp\brain\genome.ex — gating (curiosity_primary/1 :189-191; field default :143; defensive read :219; back-fill :344; mutate draw :304; recombine :330).
• test\sp\brain\novelty_test.exs — the 6 ValidationAnchors (:16-81).

1. StateSpace

The novelty term adds no hidden-state factor and changes no state space. It is a read-only functional of the existing generative model's belief q(s) and Dirichlet concentrations. It is defined per-factor and consumes only that factor's own quantities — so the mean-field factorisation q(x) = Π_f q(x_f) is preserved (no joint is materialised; plan.ex:88-100 builds an independent per-factor context, advance/3 :124-148 rolls each factor independently).

Per factor f with Ns_f hidden states and No_f outcomes, the quantities the term reads:

pa/pb are the live Dirichlet concentrations (the learning state), seeded pa = A*1+1, pb = B*1+1 (model.ex:84-85, add1/1 :115) — so the minimum count is the prior pseudocount, which is exactly the @floor (§6).

2. ObservationChannels

The term introduces no new observation modality and reads no observation at decision time. It is purely prospective: it scores the information the agent expects to gain about its own likelihood/transition parameters if it visits a (state, outcome) or (state, next-state) cell, using the predicted qo / qs1 — never an actual observation. (Observation enters the system only later, through Dirichlet learning, which raises the counts and thereby decays the novelty — §6.)

The two novelty functionals, per factor:

A-novelty (observation-parameter information gain), novelty.ex:36-50:

W_a(pa, qs, qo) = ½ · Σ_s  qs[s] · ( Σ_o qo[o] / pa[s][o]  −  1 / Σ_o pa[s][o] )

with each pa[s][o] and each column-sum floored at @floor (novelty.ex:40,45): inv_colsum = 1/max(Σ_o pa[s][o], @floor), and the inner term sums qo[o]/max(pa[s][o], @floor).

B-novelty (transition-parameter information gain) for action u, novelty.ex:57-71:

W_b(pb_u, qs, qs1) = ½ · Σ_s  qs[s] · ( Σ_{s'} qs1[s'] / pb_u[s][s']  −  1 / Σ_{s'} pb_u[s][s'] )

— identical algebraic shape, with qs1 (predicted next state) in place of qo, and the same @floor clamp (novelty.ex:61,66). Both are large and positive in under-sampled (low-count) cells, both → 0 as counts → ∞.

3. ActionSpace

The action set is unchanged: novelty adds no action and removes none. The shared per-factor action index u ∈ 0..nu-1 is the same as the rest of the engine.

Critical invariant — novelty is NOT a scalar-per-action term. Action u enters the novelty contribution only by selecting (a) the transition column B^u that produces qs1 (plan.ex:129), and (b) for B-novelty, the per-action count column elem(pb_tuple, u) (plan.ex:142). There is no + f(u) constant added to any action's logit. Two actions whose B^u and pb_u columns are byte-identical receive byte-identical novelty — this is what the action-clone-invariance test (CLAUDE.md hard invariant #3) protects, and the novelty term is constructed to pass it. (B-novelty is the one legitimately action-indexed EFE term, but it is indexed through the transition counts, not through an action identity — the column, not the label.)

4. PreferenceModel

Novelty is independent of C. w_a/3 and w_b/3 take only (pa|pb, qs, qo|qs1) — there is no C argument anywhere in novelty.ex (:36, :57). It is information gain, never a preference or reward. This is the structural half of the no-smuggled-reward proof (the temporal half is the monotonic decay, §6): a term that (i) does not see C and (ii) vanishes as the model saturates cannot be a disguised preference.

In the policy score the novelty term and the pragmatic qo·C term are separate, additive channels: at plan.ex:134 the base step value is H[qo] − qs1·amb + qo·c_m, and novelty is added after on the epistemic side (plan.ex:137, :142) — it never multiplies, gates, or rescales C. (Contrast: it would be a reward-hack if novelty scaled with C; here it is provably orthogonal.)

5. PolicySet

Policy evaluation is the depth-limited beam search in Plan.action_values/2 (plan.ex:26-36) — the LIVE decider, run at depth: 5, beam: 3. The novelty term enters there, and only there, in advance/3 (plan.ex:124-148):

• Epistemic channel placement. The per-factor one-step value is base = H[qo] − qs1·amb + qo·c_m (plan.ex:134); when ng > 0, A-novelty is added on the epistemic side: base + ng · W_a(pa_m, qs1, qo) (plan.ex:137). After the per-modality reduction, B-novelty for the chosen action is added: sv + ng · W_b(pb_u, qs, qs1) (plan.ex:142). Both ride the same epistemic channel under the same γ as the state-epistemic term H[qo] − qs1·amb — there is no separate novelty precision (§7).
• Gate. ng = Map.get(sub, :novelty_gain, 0.0) (plan.ex:92). When ng = 0.0, the if ng > 0.0 guards (plan.ex:137, :142) are false and the value is exactly the flat-engine step value H[qo] − qs1·amb + qo·c — see §8 byte-identity.
• Depth-1 mirror. Efe.step_value/3 (efe.ex:87-101) is the depth-1 fallback; it adds only A-novelty (efe.ex:98, nov = ng·W_a(pa_m, qs, qo)), because at depth-1 the per-action transition counts are not rolled. Therefore the full A+B novelty drive is realised only on the live depth-5 Plan path (plan.ex), which is why the byte-identity anchor (§8) and the exploration anchor (§8) both test the Plan path, not the Efe path. The Efe mirror exists for the depth-1 code path and for pre-novelty saved models (the Map.get … 0.0 default keeps it safe).

6. LearningParameters

Learning is Hebbian Dirichlet count accumulation on pa/pb (seeded A*1+1, B*1+1 at model.ex:84-85). The novelty term is the driver toward the cells that still need learning, and it is annihilated by that learning — they are inverse:

• Monotonic decay (the no-smuggled-reward invariant). As any count → ∞, the reciprocals qo[o]/pa[s][o] and 1/Σ_o pa[s][o] → 0, so W_a → 0 (and W_b → 0), independent of C (CLAUDE.md hard invariant #4). Each observation increments the counts → strictly lowers the term → the drive to revisit a saturated cell vanishes. Proven by Anchor A (§8): the swept sequence is Enum.sort(:desc)-equal and the last element < 1e-3 (novelty_test.exs:24-25).
• @floor = 1.0 bound (novelty.ex:30). The Dirichlet prior pseudocount — you cannot be more uncertain than the prior, so counts below @floor are clamped before the reciprocal (max(pa_so, @floor), max(Σ col, @floor); novelty.ex:40,45,61,66). This makes 1/count ≤ 1, so the term cannot blow up and cannot swamp survival (the research's γ-bound). It is a no-op for any well-formed factor (seeded counts ≥ 1); it only clamps degenerate sub-prior cells (e.g. a freshly structure-grown state). Proven by Anchor C (§8).
• novelty_gain (the heritable coupling). A per-factor scalar ng ≥ 0, default 0.0 (model.ex:35; genome.ex:143). It is heritable: drawn in mutate/2 (the draw is appended LAST, genome.ex:304, clamped [0.0, 1.0], so existing lineages' RNG order is unchanged), averaged in recombine/3 (genome.ex:330), back-filled for old DNA via Map.put_new(…, 0.0) (genome.ex:344), and read defensively in card/1 (Map.get(dna, :novelty_gain, 0.0), genome.ex:219). The opt-in lineage is Genome.curiosity_primary(gain) = %{default() | novelty_gain: gain} (genome.ex:189-191); the control is default/0 (novelty_gain = 0.0).

7. PrecisionSchedule

No new precision parameter. The novelty term rides the existing policy precision γ with the same weighting as the state-epistemic term — it is summed into the epistemic channel (plan.ex:137, :142; efe.ex:98) before the channel is scaled by γ downstream, so it shares the state-epistemic term's precision exactly. There is no gamma_novelty and no per-novelty sensory precision γ_m. The only knob modulating novelty's magnitude is the heritable novelty_gain coupling (§6), which is an additive-organ gain, not a precision.

The amplitude bound is enforced structurally, not by a precision schedule: the @floor clamp (§6) caps each cell's contribution at ≤ 1 before the ½ factor, and novelty_gain ∈ [0,1] (genome.ex:304) caps the coupling — together these are the "cannot swamp survival" guarantee without any tuned precision.

8. ValidationAnchors

The six tests in test\sp\brain\novelty_test.exs (each named with what it proves):

The byte-identity gate every inheriting Phase-2 organ MUST reproduce is Anchor E: assert Enum.zip_with(v_base, v_on0, fn a, b -> abs(a - b) end) |> Enum.max() < 1.0e-12 over Plan.action_values(MC.new(seed: 7).model, depth: 5, beam: 3) with the organ's coupling at its inert default — proving the OFF path is byte-identical on the live decider, not merely on the depth-1 mirror.

9. ClaimFence

Binding (CLAUDE.md; docs/LAB_PROTOCOL.md claim fence; docs/UNI_MISSION_DEEPENING.md:100).

The novelty term W_a/W_b is measured parameter information gain — an operational active-learning quantity over Dirichlet counts. It is a NECESSARY-NOT-SUFFICIENT substrate with ZERO evidential weight for awareness, consciousness, experience, or life on its own.

• Passing any novelty ValidationAnchor demonstrates the named behaviour (monotonic-decaying information gain; prospective exploration of under-sampled actions; byte-identical OFF path) — never experience. Anchor F shows the agent acts to reduce parameter uncertainty; it does not show the agent is curious, feels drawn, or wants to explore.
• The novelty_gain coupling, the W_a/W_b floats, and the per-cell information values are model variables, not felt states. They must never be surfaced or described as curiosity, interest, wanting, boredom, or any subjective/phenomenal term. This is functional-access novelty_drive only — a logit contribution on the epistemic channel, nothing more.
• No claim about awareness/consciousness/life follows from this term, this spec, or any single gate. The attribution fence stands: a behaviour is "passed" only against its own registered RED verdict (Lab Protocol); operational/organisational measures carry no evidential weight for experience.

Inheritance note (why this is the template)

Every Phase-2 gated organ spec reproduces sections 1–9 above, in order, and inherits these load-bearing patterns from novelty:

1. Gate at an inert default (novelty: novelty_gain: 0.0) → byte-identical OFF path, verified by an Anchor-E-style mad < 1e-12 assertion over Plan.action_values(depth:5, beam:3).
2. No scalar-per-action term — any action dependence must enter through B^u / per-action counts (the column, not the label), protected by the action-clone-invariance test.
3. Monotonic decay / bounded amplitude for any information term (novelty: @floor + decay).
4. Heritable knob plumbed the novelty way — struct default, Map.put_new back-fill, mutate draw appended LAST, defensive Map.get(dna, key, default) in card/1.
5. A ClaimFence section, verbatim discipline — model variables are never surfaced as felt states.