提出可衡量洞察的决策框架,用价值判断取舍信息并设计动态遗忘机制。
A Calculus of Discernment: Decision-Relevant Insight, Sequence Value, and Forgetting as Higher-Order Learning

- 以信息预期价值衡量洞察决策相关性,取代单纯追求新颖性。
- 发现动作顺序影响结果,存在序列溢价;遗忘是学习的核心机制而非知识丢弃。
- 在肥胖治疗决策任务中验证,有选择性遗忘使累计决策后悔降低24%-32%。
在生成式AI时代,候选见解虽多,但辨别其重要性、合理行动时机与顺序、以及适时遗忘的能力却稀缺。本文提出一个统一框架,将这些稀缺性归因于同一核心对象。定义洞察为对目标具有明确可测影响的杠杆,并通过信息预期价值而非新颖性来排序。我们证明行动具有顺序性:在现实信念动态下,内容“触碰”是非交换算子,固定计划按不同顺序执行产生不同结果,形成序列溢价。任何杠杆的价值是影子价格,统一了制药营销、股票选择与制造优化问题。最富推测性的是提出APOHA理论:遗忘不是知识清除,而是价值学习的运算符——保留项的价值等于遗忘的反事实成本;学习系统是最大遗忘后仍保持价值的残余,高阶价值是经反复遗忘后仍存留的结构(重整化相关的不变量),巩固为其共轭。提出核心开放问题(非平凡吸引子带谱隙),并在30个种子上测试遗忘理论:将APOHA实现为非平稳肥胖治疗决策代理,自适应遗忘使累计决策后悔降低24%-32%,内存规模缩小约6倍且更清洁,稳定收敛;值得注意的是盲目遗忘反而劣于从不遗忘,表明收益来自价值感知的遗忘。
原文摘要 · Abstract (English)
In a world of generative AI, candidate insights are abundant; what is scarce is the capacity to discern which matter, to act on them in the right amount and order, and to forget the rest so the system can adapt. We argue these scarcities are governed by one object and build a framework around it. We define an insight strictly as a lever with an identified, measurable effect on an objective, and rank candidates by decision-relevance via the expected value of information rather than novelty. We show action carries an order, not only a size: under realistic belief dynamics, content "touches" are non-commuting operators, so a fixed plan delivered in different orders yields different outcomes, defining a sequence premium. We observe that the value of any lever is a shadow price, unifying pharmaceutical marketing, equity selection, and manufacturing as one leverage-discovery problem. Most speculatively, we propose APOHA, a theory in which forgetting is not the disposal of knowledge but the operator by which value is learned: the value of a retained item is the counterfactual cost of forgetting it, a learning system is the residue of maximal forgetting subject to preserved value, and higher-order value is the structure that survives repeated forgetting (a renormalisation-relevant invariant), with consolidation as its conjugate. We state the central open problem (a non-trivial attractor with a spectral gap) and test the forgetting theory: operationalising APOHA as an agent on a non-stationary obesity-treatment decision world over 30 seeds, adaptive forgetting cut cumulative decision-regret by 24-32% against never-forget and a fixed half-life, kept a ~6x smaller, cleaner memory, and converged stably; notably, blind forgetting was worse than never forgetting, so the benefit is specific to value-aware forgetting. A multi-disciplinary critique stress-tests the whole.
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