https://dudusoar.github.io/categories/technical/Recent content in Technical on Yuchen DuHugo -- 0.164.0en-usFri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/llm-system-architecture/01-five-layer-llm-system/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/llm-system-architecture/01-five-layer-llm-system/Why an LLM decision system needs five separable layers rather than one increasingly large prompt.https://dudusoar.github.io/posts/stochastic-approximation/01-learning-from-a-noisy-target/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/01-learning-from-a-noisy-target/Stochastic approximation begins when the true target is hidden and each update can use only a noisy estimate of it.https://dudusoar.github.io/posts/stochastic-approximation/02-model-error-as-distance-to-target/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/02-model-error-as-distance-to-target/Why convergence should track distance to the true target rather than the size of the latest update.https://dudusoar.github.io/posts/llm-system-architecture/02-offline-memory-online-action/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/llm-system-architecture/02-offline-memory-online-action/A clean LLM architecture separates the production of reusable experience from its read-only use during online decisions.https://dudusoar.github.io/posts/llm-system-architecture/03-schema-design-facts-and-judgment/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/llm-system-architecture/03-schema-design-facts-and-judgment/A schema preserves the boundary between computed facts, model judgments, explicit rationale, and external feedback.https://dudusoar.github.io/posts/stochastic-approximation/03-what-convergence-requires/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/03-what-convergence-requires/A compact map of the step-size and noise assumptions behind stochastic-approximation convergence.https://dudusoar.github.io/posts/llm-system-architecture/04-environments-and-task-distributions/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/llm-system-architecture/04-environments-and-task-distributions/Reliable evaluation separates plausible executable environments from meaningful LLM task distributions.https://dudusoar.github.io/posts/stochastic-approximation/04-what-the-step-size-means/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/04-what-the-step-size-means/The step size is simultaneously a movement ratio, a trust coefficient, and a weight on new information.https://dudusoar.github.io/posts/llm-system-architecture/05-prompt-as-decision-interface/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/llm-system-architecture/05-prompt-as-decision-interface/A prompt follows the order of an actual decision and keeps facts, memory, tools, actions, and runtime logic in separate layers.https://dudusoar.github.io/posts/stochastic-approximation/05-why-the-step-size-stays-below-one/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/05-why-the-step-size-stays-below-one/Step sizes between zero and one are the only range that combines monotone error contraction with attenuation of new noise.https://dudusoar.github.io/posts/llm-system-architecture/06-tools-as-read-only-evidence-interfaces/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/llm-system-architecture/06-tools-as-read-only-evidence-interfaces/Evidence tools expose structured facts and deterministic calculations without making decisions on the model's behalf.https://dudusoar.github.io/posts/stochastic-approximation/06-why-alpha-cannot-equal-one/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/06-why-alpha-cannot-equal-one/With alpha equal to one, every update discards history and inherits the full error of the latest noisy target.https://dudusoar.github.io/posts/stochastic-approximation/07-noiseless-versus-noisy-updates/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/07-noiseless-versus-noisy-updates/Alpha equal to one is optimal for an exact target but accepts the full disturbance when the target is noisy.https://dudusoar.github.io/posts/llm-system-architecture/07-action-space-as-design-anchor/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/llm-system-architecture/07-action-space-as-design-anchor/Define what an LLM is allowed to change before designing its schemas, prompts, tools, workflows, and memory.https://dudusoar.github.io/posts/stochastic-approximation/08-memoryless-updates-and-markov-sufficiency/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/08-memoryless-updates-and-markov-sufficiency/An update can erase the previous iterate without becoming Markov; Markov sufficiency is a property of the chosen state.https://dudusoar.github.io/posts/llm-system-architecture/08-fact-ownership-and-provenance/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/llm-system-architecture/08-fact-ownership-and-provenance/Every fact, interpretation, proposal, and outcome in an LLM system needs a clear owner and a traceable evidence lineage.https://dudusoar.github.io/posts/stochastic-approximation/09-expectation-and-variance-of-two-updates/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/09-expectation-and-variance-of-two-updates/A direct derivation compares memoryless and history-preserving updates under zero-mean finite-variance noise.https://dudusoar.github.io/posts/llm-system-architecture/09-share-only-stable-meaning/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/llm-system-architecture/09-share-only-stable-meaning/Share code across LLM methods only when its meaning, lifecycle, failure handling, and tests remain unchanged.https://dudusoar.github.io/posts/llm-system-architecture/10-shared-information-boundary/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/llm-system-architecture/10-shared-information-boundary/Fair online comparison requires every method to decide from the same semantic snapshot and the same boundary on future information.https://dudusoar.github.io/posts/stochastic-approximation/10-what-noise-assumptions-buy-us/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/10-what-noise-assumptions-buy-us/Zero mean, finite variance, independence, and identical distribution each support a different part of noise averaging.https://dudusoar.github.io/posts/stochastic-approximation/11-alpha-one-requires-vanishing-noise/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/11-alpha-one-requires-vanishing-noise/If every update fully replaces the current position, convergence requires the river-location judgment error itself to disappear.https://dudusoar.github.io/posts/llm-system-architecture/11-observable-and-executable-training-targets/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/llm-system-architecture/11-observable-and-executable-training-targets/A strong teacher result is a valid target only when the model can observe its basis and execute the same action.https://dudusoar.github.io/posts/stochastic-approximation/12-robbins-monro-conditions/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/12-robbins-monro-conditions/The step sizes must remain large enough to keep correcting error and become small enough to suppress accumulated noise.https://dudusoar.github.io/posts/stochastic-approximation/13-why-step-sizes-must-sum-to-infinity/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/13-why-step-sizes-must-sum-to-infinity/A finite total step size can make an iteration stop moving before its error has disappeared.https://dudusoar.github.io/posts/stochastic-approximation/14-why-squared-step-sizes-must-be-summable/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/14-why-squared-step-sizes-must-be-summable/For a changing step-size sequence, square summability bounds the total variance injected by noisy observations.https://dudusoar.github.io/posts/stochastic-approximation/15-dvoretzky-convergence-theorem/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/15-dvoretzky-convergence-theorem/Dvoretzky generalizes the stochastic-approximation error recursion and gives conditions for almost-sure convergence.https://dudusoar.github.io/posts/stochastic-approximation/16-square-error-as-energy/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/16-square-error-as-energy/The Dvoretzky proof tracks squared error, shows that its positive drift is summable, and rules out a positive limiting energy.https://dudusoar.github.io/posts/stochastic-approximation/17-expectation-variance-proof-route/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/17-expectation-variance-proof-route/Expanding the recursion explains how initial error and historical noise decay, but usually yields convergence in probability rather than almost-sure convergence.https://dudusoar.github.io/posts/stochastic-approximation/18-expanding-the-error-recursion/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/18-expanding-the-error-recursion/The explicit error formula separates the residual initial condition from the weighted sum of all past disturbances.https://dudusoar.github.io/posts/stochastic-approximation/19-how-initial-error-disappears-in-expectation/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/19-how-initial-error-disappears-in-expectation/Zero-mean noise removes the disturbance terms from the expectation, leaving a product that vanishes when the step sizes sum to infinity.https://dudusoar.github.io/posts/stochastic-approximation/20-how-noise-variance-decays/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/20-how-noise-variance-decays/Each disturbance is controlled twice: by its entry coefficient and by every contraction that follows it.https://dudusoar.github.io/posts/stochastic-approximation/21-why-mean-square-analysis-stops-at-probability/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/21-why-mean-square-analysis-stops-at-probability/Vanishing expectation and variance control each time slice, but they do not directly control the shape of an infinite sample path.https://dudusoar.github.io/posts/stochastic-approximation/22-two-proof-routes-to-dvoretzky-convergence/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/22-two-proof-routes-to-dvoretzky-convergence/Expectation and variance explain distributional concentration; the energy and martingale route proves almost-sure convergence.