通过符号化学习真实工作负载，实现神经推理的自认证缓存，提升边缘部署可靠性。
LAWS: Learning from Actual Workloads Symbolically -- A Self-Certifying Parametrized Cache Architecture for Neural Inference, Robotics, and Edge Deployment
- 基于概率语言树构建可证伪的专家函数库，覆盖输入空间不同区域。
- 自认证定理确保推理误差在部署时可验证，误差上限由训练误差和模型性质决定。
- 适用于大模型推理、机器人控制与多智能体边缘部署，支持空中更新与动态扩展。
我们提出LAWS（从实际工作负载中符号化学习），一种自认证的推理缓存架构，通过部署观察构建不断增长的经验证的专家函数库。每个专家覆盖基础模型概率语言树（PLT）节点定义的输入空间区域，并携带在整个输入范围内成立的形式化误差界。核心结果为自认证定理：对任意输入x，LAWS近似误差被限定在epsilon_fit + 2*Lambda(W)*C_E内，其中Lambda(W)为模型利普希茨常数，C_E为最大嵌入直径，epsilon_fit为专家训练误差——所有项均可在部署时检查而无需真值。证明显示LAWS广义了混合专家（MoE）与键值前缀缓存，且表达能力严格强于固定K的MoE或有限缓存。进一步结果包括单调命中率定理（任意匹配路由保证覆盖率仅增不减）、专家库增长速率为O(2^H log N)，H为工作负载熵；舰队学习收敛定理，具有Omega(K)加速效果的K单元舰队；以及空中更新带宽约束。我们猜想，LAWS在平稳在线缓存算法中具有最优采集性能，且训练分布上的有效利普希茨常数随深度呈多项式增长而非指数增长。应用场景涵盖大语言模型推理、机器人控制与多智能体边缘部署。
原文摘要 · Abstract (English)
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.
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