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Trivium introduces a structural fix for agentic systems by treating temporal regret as a primary objective alongside outcome and epistemic regret, ensuring that causal miscalibrations are logged and corrected rather than recurring. Theoretical proofs and preliminary benchmarks demonstrate that this approach reduces probe complexity to logarithmic scales, effectively distinguishing causal from spurious structures where outcome-only methods fail. This framework offers a falsifiable path toward more robust, long-horizon AI agents capable of self-correction without relying solely on reward optimization.
Trivium: Temporal Regret as a First-Class Objective for Causal-Memory Controllers
arXiv:2606.04421v2 Announce Type: replace-cross Abstract: Many current agentic systems and LLM pipelines correct mistakes by optimizing outcome reward. This addresses only the what of failure: when an outcome diverges from prediction, the why and when of the mismatch are not systematically logged, reviewed, or corrected, so the same error can recur episode after episode. We argue that this is a structural problem, not merely a model-capacity one. We propose long-horizon temporal regret as a first-class objective alongside outcome regret and epistemic regret over the working causal model. Temporal regret captures when failure persists: how long a miscalibrated causal model is tolerated before correction. Epistemic regret captures why failure persists: residual uncertainty or error in the working causal model. Together, the three regrets give a falsifiable account of what, why, and when a long-lived agent can fail. Modeling the agent as a stream of E episodes, we prove three conditional results under explicit causal-probing, persistence, and detectability assumptions. First, under observationally equivalent confounding, outcome-only learning cannot distinguish causal from spurious structure without an intervention channel, so temporal miscalibration can persist linearly even after outcome regret is driven to zero. Second, with a persistent causal log and budgeted probes, total probe complexity is logarithmic in the episode horizon, inducing O(log E) temporal regret. Third, under K detectable change-points, the rate extends to O(K log E). We instantiate Trivium and pre-register five falsifiable predictions. On CausalBench-Seq, Trivium follows the predicted logarithmic envelope while outcome-only baselines grow linearly. A pilot real-LLM stream provides preliminary external-validity evidence across one full E = 500 run and three E = 100 frontier-model pilots. Self-learning here means revising an external causal model, not retraining LLM weights.
Abstract:Many current agentic systems and LLM pipelines correct mistakes by optimizing outcome reward. This addresses only the what of failure: when an outcome diverges from prediction, the why and when of the mismatch are not systematically logged, reviewed, or corrected, so the same error can recur episode after episode. We argue that this is a structural problem, not merely a model-capacity one. We propose long-horizon temporal regret as a first-class objective alongside outcome regret and epistemic regret over the working causal model. Temporal regret captures when failure persists: how long a miscalibrated causal model is tolerated before correction. Epistemic regret captures why failure persists: residual uncertainty or error in the working causal model. Together, the three regrets give a falsifiable account of what, why, and when a long-lived agent can fail. Modeling the agent as a stream of E episodes, we prove three conditional results under explicit causal-probing, persistence, and detectability assumptions. First, under observationally equivalent confounding, outcome-only learning cannot distinguish causal from spurious structure without an intervention channel, so temporal miscalibration can persist linearly even after outcome regret is driven to zero. Second, with a persistent causal log and budgeted probes, total probe complexity is logarithmic in the episode horizon, inducing O(log E) temporal regret. Third, under K detectable change-points, the rate extends to O(K log E). We instantiate Trivium and pre-register five falsifiable predictions. On CausalBench-Seq, Trivium follows the predicted logarithmic envelope while outcome-only baselines grow linearly. A pilot real-LLM stream provides preliminary external-validity evidence across one full E = 500 run and three E = 100 frontier-model pilots. Self-learning here means revising an external causal model, not retraining LLM weights.
Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
arXiv:2606.04421 [cs.AI]
(or arXiv:2606.04421v2 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2606.04421 Focus to learn more arXiv-issued DOI via DataCite
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