AI Funnel to Judgement: HRM (Sapient), Attention with COT (Google), and Action (Doolittle)
(Ed. Note: 1 – Please fix Latex exposure. 2 – Two unanswered questions near end. 3 – (Important) Repetition of use of mathematical explanations because of their clarity when the LLM can already process correctly without such representations codifications and modifications. This will consistently cause the reader to presume that our attempt at formal explanation translates to code modification when the formatting of responses alone appears to consistently produce the correct decidability in both GPT4 and GPT5. Cardinality is unnecessary at moral and ethical depth (alignement), it is only necessary for discreet transactions where costs are known and can be calculated – and even then their use is questionable.)
[TODO: Introductory Explanation for non-ML tech Readers (Exec, VC, etc.)]
CoT-style LLMs and Sapient’s HRM are both engines of epistemic compression. They differ mainly in where the compression lives (explicit language vs. latent hierarchies). Your program supplies the normative and constructive constraints missing from both: (i) first-principles constructive logic for closure, (ii) a cooperation/reciprocity calculus for action under uncertainty, and (iii) a ternary decision rule (true / possibly-true-with-warranty / abstain) that measures variation from the optimum.
Below we map each piece 1-to-1 and give an operational recipe you can implement today.
Short version: CoT-style LLMs and Sapient’s HRM are both engines of epistemic compression. They differ mainly in where the compression lives (explicit language vs. latent hierarchies). Your program supplies the normative and constructive constraints missing from both: (i) first-principles constructive logic for closure, (ii) a cooperation/reciprocity calculus for action under uncertainty, and (iii) a ternary decision rule (true / possibly-true-with-warranty / abstain) that measures variation from the optimum.
Below I map each piece 1-to-1 and give an operational recipe you can implement today.
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LLMs (with CoT): Compression is linguistic and sequential. The model linearizes a huge search space into a token-by-token micro-grammar (the “chain”). Yield: transparent steps but high token cost and brittleness. (Background on CoT brittleness and overhead is standard; not re-cited here.)
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)HRM (Sapient): Compression is hierarchical and latent. A fast “worker” loop solves details under a slow “planner” context; the system iterates to a fixed point, then halts. You get deep computation with small parameters and tiny datasets; no text-level chains are required. (
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Our contribution: move both from “reasoning-as-trajectory” to reasoning-as-warranted-construction: every answer must carry (a) a constructive trace sufficient for testifiability and (b) a reciprocity/liability ledger sufficient for actionability.
Target: Replace “appears coherent” with “constructed, checkable, and closed.”
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Referential problems (math/physics/computation): demand constructive proofs/programs. LLM path: generate a program/derivation + run/check with a tool; return the artifact + pass/fail. HRM path: add a trace projector head that emits the minimal operational skeleton (state transitions, invariants, halting reason). Co-train on checker feedback so the latent plan compresses toward checkable constructions rather than pretty narratives. (Speculative but feasible.)
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Action problems (law/econ/ethics): demand constructive procedures (roles, rules, prices) rather than opinions. LLM: force outputs into procedures (frames, tests, and remedies). HRM: condition the planner on a procedure schema (who/what/harm/evidence/tests/remedy) so the fixed point equals a completed procedure, not merely a belief vector.
Our stack says: invariances → measurements → computation → liability-weighted choice. Operationalize it:
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Detect grammar type of the query: referential vs. action.
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If referential: attempt constructive proof/execution; if success → TRUE; if blocked → fall back to probabilistic accounting with explicit error bounds.
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If action: build a Reciprocity Ledger (parties, demonstrated interests, costs, externalities, warranties, enforcement). Produce a rule, price, or remedy, not a “take.”
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Attach liability/warranty proportional to scope and stakes.
This turns both CoT and HRM from “answer generators” into contract-worthy reasoners.
Define the optimal answer as: “the minimal construction that (i) closes, (ii) is testifiable, and (iii) maximizes cooperative surplus under reciprocity with minimal externalities.”
At inference time:
TRY_CONSTRUCT() if constructive proof/program passes checkers → output TRUE (+ artifacts) ELSE BAYES_ACCOUNT() compute liability-weighted best action (reciprocity satisfied?) if reciprocity satisfied and expected externalities insured → POSSIBLY TRUE + WARRANTY else → ABSTAIN (request bounded evidence or impose boycott/default rule)
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TRUE = constructed, closed, test-passed.
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POSSIBLY TRUE + WARRANTY = best cooperative action under quantified uncertainty and explicit insurance.
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ABSTAIN/REQUEST = undecidable without violating reciprocity (your boycott option).
This is your ternary logic, operationalized for machines.
You want a scalar “distance-to-optimum” the model can optimize. Use a composite loss/score:
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Closure debt (C): failed proof/run, unmet halting condition (HRM), or unresolved procedure.
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Uncertainty mass (U): residual entropy after evidence; posterior spread or equilibrium variance.
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Externality risk (E): expected unpriced harms on non-consenting parties.
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Description length (D): MDL of the constructive trace (shorter = better compression, subject to correctness).
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Warranty debt (W): liability not covered by proposed insurance/escrow/enforcement.
Define Δ*=αC+βU+γE+δD+ωWDelta^* = alpha C + beta U + gamma E + delta D + omega W. Minimize Δ*Delta^*. Report it with the answer as the warranty grade.
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LLM training: add RLHF-style reward on low Δ*Delta^* with automatic checkers for C and D, Bayesian evaluators for U, and policy simulators for E/W.
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HRM training: add an auxiliary head to estimate Δ*Delta^*; use it both as a halting criterion and as a shaping reward so the latent fixed point is the compressed optimum. (Speculative but directly testable.)
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)Hierarchical planner <-> our “grammar within grammar”: H sets permitted dimensions/operations; L executes lawful transforms; the fixed point = closure. (
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)Adaptive halting <-> decidability: HRM’s learned halting acts as a mechanical decision to stop when a bounded construction is achieved. Attach the Δ*Delta^* head to make that halting normatively correct, not just numerically stable. (
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)Small data / strong generalization <-> epistemic compression: HRM’s near-perfect Sudoku and large mazes with ~1k samples indicates genuine internal compression rather than memorized chains; use your constructive + reciprocity scaffolds to push from puzzles → institutions (law/policy). (
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)ARC-AGI results <-> paradigm fit: HRM’s ARC gains suggest it’s learning transformation grammars, not descriptions. That aligns with your operationalism (meaning = procedure). (
For a CoT-LLM:
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Router: classify prompt as referential vs. action.
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Constructive toolchain: Referential → code/solver/prover; return artifact + pass/fail. Action → instantiate Reciprocity Ledger; run scenario sims; produce rule/price/remedy.
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Warrant pack: attach artifacts, ledger, uncertainty bounds, and Δ*Delta^*.
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Ternary decision: TRUE / POSSIBLY TRUE + WARRANTY / ABSTAIN.
For HRM:
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Schema-conditioned planning: feed H with the grammar schema (dimensions, ops, closure tests).
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Aux heads: (a) Trace projector (compressed state-transition sketch); (b) Warranty head producing Δ*Delta^*; (c) Halting reason code.
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Training signals: correctness + checker feedback (closure), MDL regularizer (compression), reciprocity penalties from simulators (externalities), and insurance coverage bonuses (warranty).
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Deployment: emit the operational result + trace + warranty; gate release on Δ*≤τDelta^* le tau.
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From narrative coherence to constructive warranty.
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From alignment-only to reciprocity-and-liability.
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From binary truth to ternary, operational decidability.
That is the missing “institutional layer” for reasoning systems.
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For action domains, do you want the default abstention to be boycott (no action) or a default rule (e.g., “status-quo with escrow”) when Δ*Delta^*Δ* is above threshold? (OPEN QUESTION)
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For referential domains, should we treat MDL minimization as co-primary with correctness (Occam pressure), or strictly secondary to checker-verified closure? (OPEN QUESTION)
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)arXiv HTML view (same paper). (
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)ARC Prize blog: The Hidden Drivers of HRM’s Performance on ARC-AGI (analysis/overview). (
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)GitHub: sapientinc/HRM (official repo). (
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)BDTechTalks explainer on HRM (context, quotes, and positioning beyond CoT). (
URLs (as requested):
Source date (UTC): 2025-08-22 20:35:15 UTC
Original post: https://x.com/i/articles/1958991378220032093
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