Technical

Series: Building Auditable LLM Systems · Part 6 of 11 In an LLM–algorithm system, evidence tools form a read-only interface to environment state, algorithm outputs, and mechanism evidence. These tools retrieve information and perform deterministic computation. They do not generate natural-language conclusions, recommend actions, or execute state changes. The model combines structured evidence into an interpretation and a bounded proposal; a verifier and deterministic backend retain authority over legality and execution. ...

Series: Stochastic Approximation from First Principles · Part 6 of 22 Step sizes above one can amplify noise and overshoot the target. But what about $\alpha=1$? Without noise, it reaches the target in one step. Under persistent noise, the same choice becomes a memoryless update. The Argument in One Chain The logic is: With no noise, $\alpha=1$ reaches $w^*$ immediately. With noise, it becomes $w_{k+1}=w^*+\eta_k$ and discards all history. With $\alpha<1$, the new position retains weight from the previous position as well as the new judgment. Both updates can be unbiased, but the history-preserving update can have lower variance. That advantage depends on assumptions about the noise: zero mean, finite variance, independence, and identical distribution in the simplified analysis. If $\alpha$ must remain one, convergence requires the noise itself to vanish. What Changes When Alpha Equals One The traveler executes $w_{k+1}=(1-\alpha)w_k+\alpha\text{target}_k$. After the analyst substitutes $\text{target}_k=w^*+\eta_k$, this becomes: ...

Series: Stochastic Approximation from First Principles · Part 7 of 22 The choice between $\alpha=1$ and $\alpha<1$ changes meaning as soon as the target contains noise. Without Noise Step size Update Meaning $\alpha=1$ $w_{k+1}=w^*$ The current observation is the exact target $0<\alpha<1$ $w_{k+1}=(1-\alpha)w_k+\alpha w^*$ Moves partway from the current position to the target If the target judgment is exact and the model allows direct movement, $\alpha=1$ is the fastest choice: a riverbank at 100 meters and a target of 100 meters produce immediate arrival. ...

Series: Building Auditable LLM Systems · Part 7 of 11 Begin the design of an LLM decision system with its action space. Before designing prompts, tools, memory, or workflow logic, answer a simpler question: What is the model actually allowed to change? Once that boundary is fixed, the rest of the architecture can be derived from it: What may the model change? -> What must it know to choose that action? -> How can the system verify that the action follows from that evidence? -> How is the model prevented from taking other actions? -> Who validates and executes the proposal? -> How are consequences returned as feedback? Schemas, prompts, tools, workflows, and memory all serve this chain from information to action and consequence. ...

Series: Stochastic Approximation from First Principles · Part 8 of 22 When $\alpha=1$, the update $$ w_{k+1}=w^*+\eta_k $$looks memoryless. That resemblance can be confused with the Markov property, but the two ideas are not equivalent. A Memoryless Update Fully Trusts the Current Observation At $\alpha_k=1$: $$ w_{k+1}=\text{target}_k=w^*+\eta_k. $$The update: ignores the previous state $w_k$; gives the previous position zero weight in the new position; depends only on the current noisy target. In the river analogy, you completely trust the latest sound and move directly to the location it suggests. The difficulty is that $\text{target}_k$ is not the river. It is an estimate contaminated by location error. ...

Series: Building Auditable LLM Systems · Part 8 of 11 Every fact, interpretation, and decision in an LLM system needs a clear owner. An artifact records what happened. A model may interpret evidence but cannot overwrite it. A validator determines whether derived content is suitable for a versioned asset. A controller proposes an action; a verifier and backend determine what is actually executed. Any derived information must preserve the lineage from source facts to final use. Being summarized by a model, stored in memory, or inserted into a prompt does not grant information greater factual authority. ...

Series: Stochastic Approximation from First Principles · Part 9 of 22 Suppose the statistical properties of $\eta_k$ are known, while the behavior of $w_k$ is what we want to determine. We can use the former to compare two update mechanisms: $\alpha=1$ and $0<\alpha<1$. The goal is a traveler whose position is centered on the true riverbank $w^*$ and whose individual journeys do not fluctuate excessively. The Memoryless Update With $\alpha=1$: $$ w_{k+1}=w^*+\eta_k. $$Therefore: ...

Series: Building Auditable LLM Systems · Part 9 of 11 Several LLM methods can share infrastructure. Share only the components whose meaning, timing, and tests remain unchanged. Sending model requests, validating output structure, recording traces, and executing legal actions are often generic. The meaning of evidence, the semantics of an action, the way experience is learned, and the definition of success are usually method-specific. Do not decide the boundary from code duplication alone. Ask whether sharing changes or conceals the meaning of the method. ...

Series: Building Auditable LLM Systems · Part 10 of 11 An online evaluation is valid only when every decision point begins from a shared boundary on visible information. An LLM, a deterministic rule, and an online planner may use different data formats and computations. They must still base their decisions on semantically equivalent current state, observed history, and future-information boundaries. A method that sees more information may remain useful as a hindsight upper bound. It is no longer a fair online comparison and cannot by itself prove that the LLM made the wrong decision. ...

Series: Stochastic Approximation from First Principles · Part 10 of 22 Preserving history helps only when the history contains enough signal to average out the noise. The usual noise assumptions explain when that hope is justified. In the river analogy, $\eta_k$ is not the wind or the echo itself. It is the location error produced after those physical disturbances affect your judgment: $$ \eta_k=\text{target}_k-w^*. $$The assumptions describe the errors in the inferred target. ...