Your Agentic Loop Will Drift. Here Is the KL Divergence Equation That Measures How Far It Has Wandered From Its Original Instruction.

Author(s): Dr Swarneendu AI Originally published on Towards AI. After 500 cycles, a long-running agent is not the same agent that started. Its goal has shifted. Its constraints have eroded. This is measurable, preventable, and nobody has built the instrument. Until now. Fareed Khan’s long-running agent survived a host reboot. It survived context overflow. It survived 31 items over-scoped to 14. No image found in the provided HTML.The article explains why representational drift is mathematically inevitable in long-running agents: repeated lossy compression (summarisation, decision-logging distillation, and abstraction/consolidation) erases recoverable information, so an agent’s output distribution diverges from its early-cycle behavior (quantified via KL divergence). It then proposes a practical, probe-based drift detector using lightweight multiple-choice questions with known correct answers and statistical hypothesis testing (chi-squared) to detect shifts in interpretation. When drift is detected, the recommended fix is to inject the original instruction as a targeted “drift correction” anchor into the active context, re-grounding the agent before the deviation compounds—keeping the KL divergence near zero. The piece closes by highlighting that this instrumentation can distinguish useful long-running agents from expensive near-misses and provides related references. Read the full blog for free on Medium. Join thousands of data leaders on the AI newsletter. Join over 80,000 subscribers and keep up to date with the latest developments in AI. From research to projects and ideas. If you are building an AI startup, an AI-related product, or a service, we invite you to consider becoming a sponsor. Published via Towards AI