发表机构
AIXI Labs; Google DeepMind; ANU; UBC; Amii（AIXI实验室; 谷歌DeepMind; 澳大利亚国立大学; 不列颠哥伦比亚大学; 阿尔伯塔机器智能研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文提出相对化所罗门诺夫归纳以应对元NFL定理，将归纳偏置转向信息可访问性，并指出算法信息论是解释AI泛化的唯一已知基础。
AI 中文摘要
经典统计理论不足以解释通用人工智能模型的成功，因为它依赖于无法证明其合理性的手工归纳偏置。无免费午餐（NFL）定理迫使任何在某些环境上优于随机的学习者在其他环境上表现不佳。我们可能希望过去的经验能告知我们预期哪些环境，但NFL同样适用于元学习。因此，任何做出有意义预测的方法都必须始于数据之外的归纳偏置。选择偏向于短程序会产生所罗门诺夫归纳（SI），其性能在所有可计算学习器中具有竞争力——尽管在与利用背景信息的专门方法比较时，“常数”会变得很大。因此，我们将SI相对于信息视角进行相对化，偏向于访问所有先前信息的短程序。这重新构建了归纳偏置：我们不再寻求某种绝对的简单性概念，而是倾向于相对于我们视角的可访问性。一个算法只能在代码包含关于数据的额外信息时才能超越相对化的SI，且没有算法能生成此类信息。虽然SI不可计算，因此不是实用算法，但它在无限计算极限下为推理提供了形式上的最优，并且有证据表明前沿AI系统大致近似于它。因此，对元NFL唯一已知的答案根植于算法信息论，我们应预期其在解释现代（及未来）AI系统的泛化行为中发挥基础作用。
英文摘要
Classical statistical theory is insufficient to explain the successes of general-purpose AI models, because it depends on handcrafted inductive biases that it cannot justify. No Free Lunch (NFL) theorems force any learner that beats chance on some environments to underperform on others. We might hope that past experience informs which environments to expect, but NFL applies equally to meta-learning. Thus, any method that makes meaningful predictions necessarily begins with an inductive bias external to the data. Choosing to bias toward short programs yields Solomonoff induction (SI), whose performance is competitive against all computable learners - albeit up to "constants" that become large when comparing against specialized methods that exploit background information. We therefore relativize SI to an information vantage point, biasing toward short programs with access to all preexisting information. This reframes the inductive bias: instead of seeking some absolute notion of simplicity, we favor accessibility with respect to our vantage point. An algorithm can only outpredict the relativized SI to the extent that its code contains additional information about the data, and no algorithm can generate such information. While SI is incomputable and hence not a practical algorithm, it provides a formal optimum for inference in the limit of infinite compute, and there is evidence to suggest that frontier AI systems roughly approximate it. Thus, the only known answer to meta-NFL is rooted in algorithmic information theory, which we should expect to play a fundamental role in explaining the generalization behavior of modern (and future) AI systems.
CommentsPublished at NeurIPS 2026 Position Paper Track
