https://www.eigenform.ai/continuous-learning-tool-tips/tags/g%C3%B6del-machine/Recent content in Gödel Machine on Eigenform Continuous Learning Tool TipsHugoen-USTue, 10 Nov 2026 09:00:00 +0800https://www.eigenform.ai/continuous-learning-tool-tips/agent-self-improvement-proofs/Tue, 10 Nov 2026 09:00:00 +0800https://www.eigenform.ai/continuous-learning-tool-tips/agent-self-improvement-proofs/<figure class="article-image"> <picture> <source type="image/webp" srcset="https://www.eigenform.ai/continuous-learning-tool-tips/agent-self-improvement-proofs/cover-agent-self-improvement_hu_d6d6806bd8bb42c1.webp 480w, https://www.eigenform.ai/continuous-learning-tool-tips/agent-self-improvement-proofs/cover-agent-self-improvement_hu_d886fcc34444cf75.webp 800w, https://www.eigenform.ai/continuous-learning-tool-tips/agent-self-improvement-proofs/cover-agent-self-improvement_hu_15069e0ae1a1a2a4.webp 1200w" sizes="(min-width: 900px) 800px, 100vw"> <source type="image/webp" srcset="https://www.eigenform.ai/continuous-learning-tool-tips/agent-self-improvement-proofs/cover-agent-self-improvement_hu_b4ec7960b090c46f.webp 480w, https://www.eigenform.ai/continuous-learning-tool-tips/agent-self-improvement-proofs/cover-agent-self-improvement_hu_2d43475a3a917f76.webp 800w, https://www.eigenform.ai/continuous-learning-tool-tips/agent-self-improvement-proofs/cover-agent-self-improvement_hu_4264ca768acceea5.webp 1200w" sizes="(min-width: 900px) 800px, 100vw"> <img src="https://www.eigenform.ai/continuous-learning-tool-tips/agent-self-improvement-proofs/cover-agent-self-improvement_hu_2d43475a3a917f76.webp" alt="Agent self-improvement without formal proofs: an etched parchment engraving with a heavy brass door sealed by a padlock at the top of a crumbling staircase on the left, standing for a proof gate that never opens, and on the right a balance scale testing small clockwork agents, with the ones that pass walking under a stone arch to a shelf archive of varied specimens, one carrying an amber adapter" title="A proof gate never opens in a real environment, so the agent keeps what an empirical test accepts" width="1376" height="768" loading="eager" fetchpriority="high" decoding="async" class="zoomable" data-full-url="https://www.eigenform.ai/continuous-learning-tool-tips/agent-self-improvement-proofs/cover-agent-self-improvement.webp"> </picture><figcaption>A proof gate never opens in a real environment, so the agent keeps what an empirical test accepts</figcaption></figure><p><strong>TL;DR:</strong> Schmidhuber&rsquo;s Gödel machine is the formal ideal of agent self-improvement: a solver that modifies itself only when it can prove the modification pays. Real environments do not supply the axioms such a proof needs, so every working system since has swapped the theorem prover for an empirical test and bounded what the agent may change. The systems differ in where the test lives: a benchmark, a held-out metric, or the environment the agent has to keep operating in.</p>