# Revising P_target Dynamics: Implementing Gradual Adaptation (Mechanism 2) ## 1. Motivation: Addressing Run 3 Findings Simulation Run 3 [[releases/archive/Information Ontology 1/0110_IO_Simulation_Run3]] revealed that the simple "Reset/Reinforce" mechanism (Mechanism 1a from [[releases/archive/Information Ontology 1/0103_IO_P_target_Dynamics]]) for updating the Target Probability Vector `P_target` led to a rapid collapse of potentiality entropy, even in a highly dynamic regime. This suggests the rule is too aggressive in eliminating potential based solely on short-term stability. To foster more complex dynamics and allow the system's intrinsic potentials to adapt more realistically to persistent environmental/causal influences, this node specifies an implementation of **Mechanism 2 (Gradual Adaptation to Context)** combined with elements of Mechanism 1 and 3, as outlined in [[releases/archive/Information Ontology 1/0103_IO_P_target_Dynamics]]. ## 2. Core Idea of Mechanism 2 The intrinsic potential probabilities `P_target` should slowly drift towards a distribution favored by the persistent causal context, while still being influenced by immediate stability (Θ) and protected from complete fixation by Η. ## 3. Proposed Revised `P_target` Update Rule This rule replaces Step 5b/6c (Update Potential) and Step 7c/8c (Update Potential) in the consolidated algorithm [[releases/archive/Information Ontology 1/0104_IO_Formalism_v2_Summary]] and the implementations [[releases/archive/Information Ontology 1/0107_IO_Simulation_v2_1D_Implementation]]. **Inputs at Step S for node `i`:** * `P_target(i, S)`: Current target probability vector. * `ε(i, S)`: Current actual state. * `ε(i, S+1)`: The *just determined* next actual state. * `Θ_val(i, S+1)`: The *just updated* stability value for the *next* step (either `Θ_base` if changed, or incremented if maintained). * `Influence_k(i, S)`: Weighted causal input favoring state `k` (calculated in Phase 1). * `Total_Causal_Weight(i, S)`: Total causal input weight. **Parameters:** * `Δp_inc`: Base learning rate for stability reinforcement. * `λ_adapt`: Adaptation rate towards contextual target (small value, e.g., 0.01). * `p_min`: Η-driven minimum probability floor. * `N_states`: Number of possible ε states. **Update Logic for `P_target(i, S+1)`:** 1. **Determine Intermediate Target based on Stability/Change:** * **If `ε` Changed (`ε(i, S+1) ≠ ε(i, S)`):** * Start with a baseline reset distribution `P_reset`. Options: * Uniform: `P_reset = [1/N_states] * N_states`. * Biased Uniform: Slightly increase probability for `ε(i, S+1)` in `P_reset`. (Let's use Uniform for now). * Set `P_intermediate = P_reset`. * **If `ε` Maintained (`ε(i, S+1) == ε(i, S)`):** * Reinforce the probability corresponding to the current state `k_current = ε(i, S)`. * `p_k_current_new = P_target[k_current](i, S) + Δp_inc` * For `k ≠ k_current`: `p_k_new = P_target[k](i, S) - Δp_inc / (N_states - 1)` * Set `P_intermediate = [p_0_new, p_1_new, ...]`. * Normalize `P_intermediate` (including applying `p_min` floor *before* normalization might be needed here or later). 2. **Calculate Contextual Target `P_context`:** * Based on weighted causal inputs `Influence_k`. * `p_{context, k} = Influence_k(i, S) / Total_Causal_Weight(i, S)` (Handle `Total_Causal_Weight=0` case, e.g., by setting `P_context` to uniform). * Ensure `P_context` is normalized. 3. **Apply Gradual Adaptation:** * `P_target(i, S+1) = (1 - λ_adapt) * P_intermediate + λ_adapt * P_context` 4. **Apply Η Floor and Normalize:** * `P_target(i, S+1) = np.maximum(P_target(i, S+1), p_min)` * Normalize `P_target(i, S+1)` so `Σ_k p_k = 1`. ## 4. Rationale and Expected Effects * **Separates Immediate vs. Slow Change:** The immediate effect of stability/change influences `P_intermediate`, while the persistent context slowly shapes the baseline potential via `λ_adapt`. * **Preserves Potentiality:** Resetting to uniform (or biased uniform) after a change prevents potential from being instantly quenched. Reinforcement is gradual. The `λ_adapt` term ensures potential doesn't get stuck if the context changes. * **Contextual Learning:** Allows the intrinsic potentials to reflect long-term statistical patterns in the causal input, representing a form of learning or adaptation within κ itself. * **Η Floor:** Maintains minimal exploratory potential. ## 5. Next Steps 1. **Implement:** Create a new code node (e.g., [[releases/archive/Information Ontology 1/0112_IO_Simulation_v2.1_Code]]) incorporating this revised `P_target` update logic into the simulation framework from [[releases/archive/Information Ontology 1/0107_IO_Simulation_v2_1D_Implementation]]. 2. **Test:** Run simulations (e.g., [[releases/archive/Information Ontology 1/0113_IO_Simulation_Run4]]) using parameters similar to Run 3 [[releases/archive/Information Ontology 1/0110_IO_Simulation_Run3]] (high H, low Θ/M) to see if this revised logic prevents the collapse of potentiality entropy and allows for more complex dynamics. 3. **Tune:** Explore the effect of the new parameter `λ_adapt`. ## 6. Conclusion: Towards Adaptive Potentiality This revised formalism for `P_target` dynamics attempts to address the shortcomings observed in previous simulations by implementing a more nuanced update rule. By combining immediate reinforcement/reset based on stability with a gradual adaptation to the causal context, and ensuring a minimum exploratory potential via an Η floor, this mechanism aims to allow for both historical influence (Θ) and adaptive learning within Potentiality (κ) itself. Its implementation and testing are the critical next steps in exploring the emergence of complex dynamics within the IO framework.