semantic memory必然导致遗忘与错误回忆,无法避免。
The Price of Meaning: Why Every Semantic Memory System Forgets
- 基于语义连续核阈值的内存系统,其几何结构天然引发干扰
- 记忆增长时保留率趋近零,遗忘呈幂律衰减
- 任何语义系统都无法完全避免错误召回,牺牲语义泛化可规避但代价高
当今主流的生产级AI记忆系统均按语义组织信息,这虽促进泛化、类比和概念检索,却付出代价。我们证明,同一几何结构使干扰、遗忘和错误回忆不可避免。针对语义连续核阈值记忆系统——其检索得分是语义特征空间内积的单调函数,且局部内在维数有限——我们得出四项结论:(1) 语义有用表征具有有限有效秩;(2) 局部维度有限意味着检索邻域存在正竞争者质量;(3) 随着记忆增长,保留率趋于零,在幂律到达统计下呈现幂律遗忘曲线;(4) 对满足δ-凸性条件的联想诱因,仅靠阈值调节无法消除错误回忆。我们在五种架构中验证预测:向量检索、图记忆、注意力上下文、BM25文件系统检索、参数化记忆。纯语义系统直接表现为遗忘与错误回忆;增强推理系统部分缓解症状,但将渐进退化转为灾难性失败。完全避开干扰的系统则必须放弃语义泛化。语义的代价就是干扰,我们测试的所有架构都未能逃脱。
原文摘要 · Abstract (English)
Every major AI memory system in production today organises information by meaning. That organisation enables generalisation, analogy, and conceptual retrieval -- but it comes at a price. We prove that the same geometric structure enabling semantic generalisation makes interference, forgetting, and false recall inescapable. We formalise this tradeoff for \textit{semantically continuous kernel-threshold memories}: systems whose retrieval score is a monotone function of an inner product in a semantic feature space with finite local intrinsic dimension. Within this class we derive four results: (1) semantically useful representations have finite effective rank; (2) finite local dimension implies positive competitor mass in retrieval neighbourhoods; (3) under growing memory, retention decays to zero, yielding power-law forgetting curves under power-law arrival statistics; (4) for associative lures satisfying a $δ$-convexity condition, false recall cannot be eliminated by threshold tuning. We test these predictions across five architectures: vector retrieval, graph memory, attention-based context, BM25 filesystem retrieval, and parametric memory. Pure semantic systems express the vulnerability directly as forgetting and false recall. Reasoning-augmented systems partially override these symptoms but convert graceful degradation into catastrophic failure. Systems that escape interference entirely do so by sacrificing semantic generalisation. The price of meaning is interference, and no architecture we tested avoids paying it.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。