ActPC-Chem: Discrete Active Predictive Coding for Goal-Guided Algorithmic Chemistry as a Potential Cognitive Kernel for Hyperon & PRIMUS-Based AGI
Abstract: We explore a novel paradigm (labeled ActPC-Chem) for biologically inspired, goal-guided AI centered on a form of Discrete Active Predictive Coding (ActPC) operating within an algorithmic chemistry of rewrite rules. ActPC-Chem is envisioned as a foundational "cognitive kernel" for advanced cognitive architectures, such as the OpenCog Hyperon system, incorporating essential elements of the PRIMUS cognitive architecture. The central thesis is that general-intelligence-capable cognitive structures and dynamics can emerge in a system where both data and models are represented as evolving patterns of metagraph rewrite rules, and where prediction errors, intrinsic and extrinsic rewards, and semantic constraints guide the continual reorganization and refinement of these rules. Using a virtual "robot bug" thought experiment, we illustrate how such a system might self-organize to handle challenging tasks involving delayed and context-dependent rewards, integrating causal rule inference (AIRIS) and probabilistic logical abstraction (PLN) to discover and exploit conceptual patterns and causal constraints. Next, we describe how continuous predictive coding neural networks, which excel at handling noisy sensory data and motor control signals, can be coherently merged with the discrete ActPC substrate. Finally, we outline how these ideas might be extended to create a transformer-like architecture that foregoes traditional backpropagation in favor of rule-based transformations guided by ActPC. This layered architecture, supplemented with AIRIS and PLN, promises structured, multi-modal, and logically consistent next-token predictions and narrative sequences.
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Knowledge Gaps
Knowledge gaps, limitations, and open questions
Below is a single, concrete list of what the paper leaves missing, uncertain, or unexplored, phrased to guide follow‑up research.
- Formalization—Exact specification of the metagraph and rewrite rule syntax/semantics (e.g., in MeTTa/GSLT), including matching semantics, variable binding, scoping, higher‑order rules, and how rules encode/consume probabilistic weights.
- Termination/confluence—Criteria and mechanisms to ensure the generative operator Γ halts (or is resource‑bounded) and how confluence/critical‑pair conflicts are handled when multiple rules match, to avoid non‑deterministic or cyclic rewrites.
- Pattern space definition—What constitutes a “pattern” m for distributions p_t(m) and q_t(m) (e.g., subgraph isomorphism classes, motifs, tokens, typed atoms), and how pattern granularity affects bias, variance, and tractability.
- Probability estimation—Concrete algorithms to estimate p_t(m) from a stochastic rewrite process (e.g., sampling strategies, partition functions, normalization of overlapping matches), and to construct q_t(m) from observed outputs.
- Variance control—Methods to reduce high variance in Monte Carlo estimates of p_t(m)/q_t(m) in large combinatorial state spaces (e.g., importance sampling, control variates, Rao‑Blackwellization).
- Information measures—Empirical and theoretical comparison of candidate error metrics (KL, cross‑entropy, JS divergence, Wasserstein, compression‑based surrogates), including sensitivity to sparse counts and support mismatch.
- Algorithmic complexity surrogates—Operational definition and choice of compressors or model‑based estimators for “approximate Kolmogorov complexity,” including domain bias, normalization across pattern lengths, and compute costs.
- Credit assignment—A principled mechanism to attribute global prediction error to specific rules (and their substructures) in a large “rule soup” (e.g., counterfactuals, Shapley‑style attributions, eligibility traces for rules).
- Rule weights—How rule “weights” are represented, updated, normalized, and combined with structural rewrites; how weights interact with ECAN’s STI/activation and probabilistic firing.
- Update neighborhood N(r_i)—Systematic design of candidate rule modifications (operators for generalize/specialize/split/merge/refactor), and how to bias proposals for efficiency and diversity (e.g., EDA, MCMC, program synthesis priors).
- Search strategy—Replacement of the naive argmin local search with scalable strategies (e.g., beam search, MCTS over rewrite trajectories, Metropolis‑Hastings on rule spaces, MOSES/GP), with clear acceptance criteria.
- Discrete natural gradient—A concrete derivation and algorithm for “discrete natural gradients grounded in optimal transport” over rule distributions: choice of metric (e.g., Fisher–Rao on categorical families, OT distances), parameterization, and efficient computation.
- Geometry/constraints—How to incorporate constraints (sparsity, safety, logical invariants) into the discrete natural gradient updates without breaking probabilistic semantics or causing mode collapse.
- ECAN coupling—Exact equations linking ECAN’s attention/importance dynamics with ActPC’s prediction error and rewards, and whether natural‑gradient acceleration for ECAN carries over to rule selection in ActPC‑Chem.
- Reward shaping—Procedures to set and adapt α_int and α_ep, prevent “surprise‑seeking” pathologies (maximizing epistemic reward by injecting noise), and balance exploration/exploitation under sparse/ delayed rewards.
- Temporal credit—Mechanisms for handling delayed and context‑dependent rewards in a discrete setting (e.g., value estimation, predictive state representations, temporal abstraction/options), beyond the “robot bug” thought experiment.
- Planning/control—Mapping from predicted output subgraphs to real‑time actions (latency budgets, control frequencies), and whether on‑policy/off‑policy evaluation is feasible in a rule‑rewriting loop.
- Stability and convergence—Any theoretical guarantees (or empirical diagnostics) for stability of the self‑modifying rule soup under the combined epistemic/instrumental signals, and conditions for convergence vs. oscillation/divergence.
- Catastrophic interference—For non‑stationary environments, strategies for retention/forgetting in rule populations (e.g., replay buffers for rules, elastic weight consolidation analogues for discrete rules, gated modules).
- Safety of self‑modification—Constraints preventing meta‑rules from disabling reward/error computation, corrupting grounding, or engaging in wireheading; auditing and rollback mechanisms for deleterious self‑edits.
- Grounding across modalities—A concrete interface for mapping continuous PC errors to discrete rule updates (and back), including quantization schemes, symbol grounding, and stability of cross‑level error propagation.
- Alignment with AIRIS/PLN—Operational pipelines for injecting causal constraints (AIRIS) and probabilistic logical abstractions (PLN) into the rewrite process: where they read/write, how they influence p_t(m), and conflict resolution.
- Causal credit—How interventions/causal discovery (AIRIS) inform which rewrites improve counterfactual predictions, not just observational fit; benchmarks for causal generalization in ActPC‑Chem.
- Expressivity vs. tractability—Guidelines for selecting rule abstraction levels (simple patterns vs. GSLT‑level constructs) balancing expressivity, interpretability, and match cost (e.g., subgraph isomorphism complexity).
- Matching/indexing—Data structures and approximate matching methods (e.g., graph fingerprints, LSH) to make frequent subgraph matching feasible at scale; error impacts of approximate matches.
- Γ scheduling—Policies for rule application order, conflict resolution, and depth limits; effects on the induced probability distribution and reproducibility.
- Normalization and duplication—How to normalize probabilities when multiple rules produce identical outputs or overlapping derivations, avoiding double counting and ensuring proper likelihoods.
- Benchmarking—A concrete experimental plan beyond the thought experiment: domains, datasets, metrics (predictive accuracy, compression ratio, reward, causal generalization), and ablations (with/without AIRIS/PLN/ECAN).
- Comparative baselines—Systematic comparisons to AERA, GP/MOSES, program‑synthesis RL, and continuous ActPC on shared tasks, to validate claimed advantages in reasoning, scalability, and biological plausibility.
- Sample efficiency—Techniques to improve data efficiency (e.g., meta‑learning of rule priors, unsupervised pretraining via compression, curriculum learning of patterns).
- Regularization—Controls to prevent overfitting/memorization by rule proliferation (minimum description length penalties, Bayesian priors over rule complexity, sparsity constraints).
- Multimodal integration—How multimodal inputs (vision, language, proprioception) are represented in the metagraph and jointly modeled by rules without exploding the pattern vocabulary.
- Transformer‑like extension—An explicit design for the proposed backprop‑free, rule‑based “transformer‑like” architecture: tokenization to rewrite rules, attention analogues, training loop, and next‑token evaluation pipeline.
- Engineering/runtime—Parallelism and scheduling in Hyperon/MeTTa for large rule soups, memory management for metagraphs, and profiling results on realistic hardware budgets.
- Reproducibility—Plans for releasing reference implementations, rule corpora, and evaluation harnesses to enable independent verification and progress tracking.
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