arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 2603.21272cs.AIcs.CLcs.DScs.LG
收藏

图书馆定理:外部组织如何支配代理推理能力

The Library Theorem: How External Organization Governs Agentic Reasoning Capacity

Champalimaud Foundation(Champalimaud基金会)

Zachary F. Mainen

AI总结:

本文探讨了外部组织对代理推理能力的影响,通过实验验证了索引外部记忆的代理在检索效率上的优势,并指出语言模型在索引构建与导航协议执行中的分离需求。

摘要:

外部化推理已通过链式思维被转换器代理所利用,但结构化检索——对自身推理状态的索引——仍被低估。我们正式将转换器上下文窗口视为I/O页面,并证明具有索引外部内存的工具增强代理的检索成本显著低于仅限于顺序扫描的代理:每查询O(log_b N)与Ω(N)页面读取,以及O(T log_b T)与Θ(T²)累计成本,随着深入思考而扩大。我们在受控查找基准上测试这些预测,跨三种内容类型——随机哈希、有序整数和百科条目,变化存储大小从50到5000项,并在两个模型版本(GPT-4o-mini和GPT-5.4)中复制关键条件。在抽象内容上,索引代理实现中位数1页读取,无论存储大小,确认O(1)预测。无索引的排序页面无法缩小差距:较弱的模型无法维持大规模二分查找,而较强的模型接近最优log₂N搜索,但仍输给索引5倍。在熟悉内容(百科条目)中,出现竞争失败模式:模型识别领域,绕过检索协议,从参数记忆生成答案,即使索引正确,仍导致灾难性token消耗。这种参数记忆竞争分离了索引结合的两种认知操作:理解内容(语言模型擅长)和遵循导航协议(语言模型在理解诱惑时失败)。结果表明应分离关注:使用语言模型构建索引(语义理解有助于),并使用确定性算法遍历索引(语义理解有害)。

英文摘要:

Externalized reasoning is already exploited by transformer-based agents through chain-of-thought, but structured retrieval -- indexing over one's own reasoning state -- remains underexplored. We formalize the transformer context window as an I/O page and prove that tool-augmented agents with indexed external memory achieve exponentially lower retrieval cost than agents restricted to sequential scanning: $O(\log_b N)$ versus $Ω(N)$ page reads per query, and $O(T \log_b T)$ versus $Θ(T^2)$ cumulative cost over $T$ reasoning steps -- a gap that widens as deliberation deepens. We test these predictions on a controlled lookup benchmark across three content types -- random hashes, ordered integers, and encyclopedia entries -- varying store size from 50 to 5,000 items, and replicate key conditions across two model generations (GPT-4o-mini and GPT-5.4). On abstract content, the indexed agent achieves median 1 page read regardless of store size, confirming the $O(1)$ prediction. Sorted pages without an index fail to close the gap: the weaker model cannot sustain binary search at scale, and the stronger model achieves near-optimal $\log_2 N$ search but still loses to the index by $5\times$. On familiar content (encyclopedia entries), a competing failure mode emerges: the model recognizes the domain, bypasses the retrieval protocol, and generates answers from parametric memory, producing catastrophic token expenditure even when the index is sound. This parametric memory competition dissociates the two cognitive operations that indexing combines: understanding content (where language models excel) and following navigational protocols (where they fail when understanding tempts them to shortcut). The result argues for a separation of concerns: use language models for index construction, where semantic understanding helps, and deterministic algorithms for index traversal, where it hurts.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑