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This research introduces "Trivium," a framework that elevates temporal and epistemic regret to first-class objectives for causal-memory controllers, addressing the limitations of outcome-only reward optimization in agentic systems. By proving logarithmic bounds on identification delay under specific probing assumptions, the work offers diagnostic tools to distinguish between spurious correlations and genuine causal structures before they persist across episodes. The study demonstrates that revising external causal models rather than retraining weights is essential for preventing recurring errors when observational confounding exists.
Trivium: Temporal Regret as a First-Class Objective for Causal-Memory Controllers
arXiv:2606.04421v3 Announce Type: replace-cross Abstract: Many agentic systems and LLM pipelines correct mistakes by optimizing outcome reward. This addresses only the what of failure; the why and when may go unlogged, allowing the same error to recur across episodes. We propose long-horizon temporal regret alongside outcome regret and epistemic regret. These are diagnostic quantities, not standard comparator-based online-learning regrets. Temporal regret captures how long an unresolved or incorrect causal model is tolerated; epistemic regret captures posterior error over that model. Over a stream of E episodes, we prove three conditional results under explicit probing, persistence, and detectability assumptions. First, under observationally equivalent confounding, outcome-only learning cannot separate causal from spurious structure, so miscalibration can persist after outcome regret reaches zero. Second, with a persistent causal log and budgeted probes, total probe complexity is logarithmic in E, inducing O(log E) delayed-identification temporal regret. The implemented clipped soft score adds a linear numerical floor, so this logarithmic claim applies only to identification delay. Third, under K detectable change-points, the rate extends to O(K log E). We instantiate Trivium and state five falsifiable predictions. On CausalBench-Seq, a hard structural readout records 7.8+-2.9 misidentified episodes per seed over 500 episodes and 20 seeds, with zero observed stationary errors, while outcome-only controllers remain misidentified throughout. Audit ablations show that continued posterior updating, not detector reopening or local repair, drives posterior recovery; local repair instead reduces committed-graph dispatch exposure. The prior logarithmic-envelope verdict based on a clipped soft score is withdrawn. A pilot real-LLM stream provides external evidence. Self-learning here means revising an external causal model, not retraining LLM weights.
Abstract:Many agentic systems and LLM pipelines correct mistakes by optimizing outcome reward. This addresses only the what of failure; the why and when may go unlogged, allowing the same error to recur across episodes. We propose long-horizon temporal regret alongside outcome regret and epistemic regret. These are diagnostic quantities, not standard comparator-based online-learning regrets. Temporal regret captures how long an unresolved or incorrect causal model is tolerated; epistemic regret captures posterior error over that model. Over a stream of E episodes, we prove three conditional results under explicit probing, persistence, and detectability assumptions. First, under observationally equivalent confounding, outcome-only learning cannot separate causal from spurious structure, so miscalibration can persist after outcome regret reaches zero. Second, with a persistent causal log and budgeted probes, total probe complexity is logarithmic in E, inducing O(log E) delayed-identification temporal regret. The implemented clipped soft score adds a linear numerical floor, so this logarithmic claim applies only to identification delay. Third, under K detectable change-points, the rate extends to O(K log E). We instantiate Trivium and state five falsifiable predictions. On CausalBench-Seq, a hard structural readout records 7.8+-2.9 misidentified episodes per seed over 500 episodes and 20 seeds, with zero observed stationary errors, while outcome-only controllers remain misidentified throughout. Audit ablations show that continued posterior updating, not detector reopening or local repair, drives posterior recovery; local repair instead reduces committed-graph dispatch exposure. The prior logarithmic-envelope verdict based on a clipped soft score is withdrawn. A pilot real-LLM stream provides external evidence. Self-learning here means revising an external causal model, not retraining LLM weights.
Note on version 2 (closure). This version corrects errors in v1. The use of the term "regret'' also caused confusion because the quantities defined here are not standard comparator-based online-learning regret. Subsequent work will use "liability'' or "debt'' to be clear
Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
arXiv:2606.04421 [cs.AI]
(or arXiv:2606.04421v3 [cs.AI] for this version)
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