We introduce LAWS (Learning from Actual Workloads Symbolically), a self-certifying inference caching architecture that builds a growing library of certified expert functions from deployment observations. Each expert covers a region of input space defined by a node in the Probabilistic Language Trie (PLT) of the base model and carries a formal error bound holding uniformly over all inputs. The central result is a self-certification theorem: for any input x, the LAWS approximation error is bounded by epsilon_fit + 2*Lambda(W)*C_E, where Lambda(W) is the model Lipschitz constant, C_E is the maximum embedding diameter, and epsilon_fit is the expert training error -- all checkable at deployment time without ground truth. We prove that LAWS generalizes both Mixture-of-Experts and KV prefix caching as special cases and is strictly more expressive than any fixed-K MoE or finite cache. Further results include a monotone hit rate theorem (any-match routing ensures coverage only increases), an expert library growth rate of O(2^H log N) where H is workload entropy, a fleet learning convergence theorem with Omega(K) speedup for K-unit fleets, and an over-the-air update bandwidth bound. We conjecture that LAWS is acquisition-optimal among stationary online caching algorithms and that the effective Lipschitz constant on the training distribution grows polynomially rather than exponentially in depth. Applications are developed for LLM inference, robotic control, and multi-agent edge deployment.

翻译：我们提出LAWS（从实际工作负载中符号化学习），一种自验证推理缓存架构，它通过部署观测构建不断增长的经认证专家函数库。每个专家覆盖由基础模型概率语言词典树（PLT）中节点定义的输入空间区域，并携带对全体输入一致成立的正式误差界。核心结果是一条自验证定理：对于任意输入x，LAWS近似误差以epsilon_fit + 2*Lambda(W)*C_E为上界，其中Lambda(W)为模型Lipschitz常数，C_E为最大嵌入直径，epsilon_fit为专家训练误差——所有指标均可在无真实标签情况下的部署时直接验证。我们证明LAWS推广了混合专家模型（MoE）和KV前缀缓存作为特例，且其表达能力严格强于任意固定K的MoE或有限缓存。进一步结果包括：单调命中率定理（任意匹配路由确保覆盖范围单调增长）、专家库增长率O(2^H log N)（H为工作负载熵）、Omega(K)速度提升的K单元集群学习收敛定理，以及空中更新带宽界。我们猜想LAWS是固定规则在线缓存算法中获取最优的，且训练分布上的有效Lipschitz常数随深度呈多项式而非指数增长。该架构已发展出面向大语言模型推理、机器人控制及多智能体边缘部署的应用。