{"id":10395,"date":"2026-02-11T07:02:32","date_gmt":"2026-02-11T07:02:32","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2026\/02\/11\/2602-09394\/"},"modified":"2026-02-11T07:02:32","modified_gmt":"2026-02-11T07:02:32","slug":"2602-09394","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2026\/02\/11\/2602-09394\/","title":{"rendered":"The Critical Horizon: Inspection Design Principles for Multi-Stage Operations and Deep Reasoning"},"content":{"rendered":"

The Critical Horizon: Inspection Design Principles for Multi-Stage Operations and Deep Reasoning
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arXiv:2602.09394v1 Announce Type: new
\nAbstract: Manufacturing lines, service journeys, supply chains, and AI reasoning chains share a common challenge: attributing a terminal outcome to the intermediate stage that caused it. We establish an information-theoretic barrier to this credit assignment problem: the signal connecting early steps to final outcomes decays exponentially with depth, creating a critical horizon beyond which no algorithm can learn from endpoint data alone. We prove four results. First, a Signal Decay Bound: sample complexity for attributing outcomes to early stages grows exponentially in the number of intervening steps. Second, Width Limits: parallel rollouts provide only logarithmic relief, with correlation capping the effective number of independent samples. Third, an Objective Mismatch: additive reward aggregation optimizes the wrong quantity when sequential validity requires all steps to be correct. Fourth, Optimal Inspection Design: uniform checkpoint spacing is minimax-optimal under homogeneous signal attenuation, while a greedy algorithm yields optimal non-uniform schedules under heterogeneous attenuation. Together, these results provide a common analytical foundation for inspection design in operations and supervision design in AI.<\/div>\n

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\n Seyed Morteza Emadi
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The Critical Horizon: Inspection Design Principles for Multi-Stage Operations and Deep Reasoning arXiv:2602.09394v1 Announce Type: new Abstract: Manufacturing lines, service journeys, supply chains, and AI reasoning chains share a common challenge: attributing a terminal outcome to the intermediate stage that caused it. We establish an information-theoretic barrier to this credit assignment problem: the signal connecting […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,187,414,113,415,112],"tags":[1437,147,4754],"class_list":["post-10395","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-ai","category-cs-it","category-cs-lg","category-math-it","category-stat-ml","tag-critical","tag-design","tag-inspection"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10395"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=10395"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10395\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=10395"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=10395"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=10395"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}