Yuchen Du

Separate Schemas, Prompts, Tools, Workflows, and Memory in an LLM System

Fri, 17 Jul 2026 00:00:00 +0000

Why an LLM decision system needs five separable layers rather than one increasingly large prompt.

Where Stochastic Approximation Begins: Learning from a Noisy Target

Fri, 17 Jul 2026 00:00:00 +0000

Stochastic approximation begins when the true target is hidden and each update can use only a noisy estimate of it.

Model Error as Distance to the True Target

Fri, 17 Jul 2026 00:00:00 +0000

Why convergence should track distance to the true target rather than the size of the latest update.

Separate Offline Memory Extraction from Online Action Execution

Fri, 17 Jul 2026 00:00:00 +0000

A clean LLM architecture separates the production of reusable experience from its read-only use during online decisions.

Separate Facts from Model Judgment in LLM Schemas

Fri, 17 Jul 2026 00:00:00 +0000

A schema preserves the boundary between computed facts, model judgments, explicit rationale, and external feedback.

What a Noisy Iteration Needs in Order to Converge

Fri, 17 Jul 2026 00:00:00 +0000

A compact map of the step-size and noise assumptions behind stochastic-approximation convergence.

Separate Plausible Environments from LLM Task Distributions

Fri, 17 Jul 2026 00:00:00 +0000

Reliable evaluation separates plausible executable environments from meaningful LLM task distributions.

What the Step Size Really Means

Fri, 17 Jul 2026 00:00:00 +0000

The step size is simultaneously a movement ratio, a trust coefficient, and a weight on new information.

Treat the Prompt as a Decision Interface, Not a State Dump

Fri, 17 Jul 2026 00:00:00 +0000

A prompt follows the order of an actual decision and keeps facts, memory, tools, actions, and runtime logic in separate layers.

Why the Step Size Must Stay Below One under Noise

Fri, 17 Jul 2026 00:00:00 +0000

Step sizes between zero and one are the only range that combines monotone error contraction with attenuation of new noise.

Treat LLM Evidence Tools as Read-Only Interfaces

Fri, 17 Jul 2026 00:00:00 +0000

Evidence tools expose structured facts and deterministic calculations without making decisions on the model's behalf.

Why Alpha Cannot Equal One Under Persistent Noise

Fri, 17 Jul 2026 00:00:00 +0000

With alpha equal to one, every update discards history and inherits the full error of the latest noisy target.

The Same Step Size Behaves Differently with and without Noise

Fri, 17 Jul 2026 00:00:00 +0000

Alpha equal to one is optimal for an exact target but accepts the full disturbance when the target is noisy.

Use the Action Space to Anchor LLM System Design

Fri, 17 Jul 2026 00:00:00 +0000

Define what an LLM is allowed to change before designing its schemas, prompts, tools, workflows, and memory.

A Memoryless Update Is Not the Same as Markov Sufficiency

Fri, 17 Jul 2026 00:00:00 +0000

An update can erase the previous iterate without becoming Markov; Markov sufficiency is a property of the chosen state.

Establish Fact Ownership and Evidence Provenance in LLM Systems

Fri, 17 Jul 2026 00:00:00 +0000

Every fact, interpretation, proposal, and outcome in an LLM system needs a clear owner and a traceable evidence lineage.

Expectation and Variance Explain Why History Stabilizes an Update

Fri, 17 Jul 2026 00:00:00 +0000

A direct derivation compares memoryless and history-preserving updates under zero-mean finite-variance noise.

Share Only Modules Whose Meaning Survives a Method Change

Fri, 17 Jul 2026 00:00:00 +0000

Share code across LLM methods only when its meaning, lifecycle, failure handling, and tests remain unchanged.

Give Every Decision Point a Shared Information Boundary

Fri, 17 Jul 2026 00:00:00 +0000

Fair online comparison requires every method to decide from the same semantic snapshot and the same boundary on future information.

What the Noise Assumptions Actually Buy Us

Fri, 17 Jul 2026 00:00:00 +0000

Zero mean, finite variance, independence, and identical distribution each support a different part of noise averaging.

Alpha Equal to One Requires the Noise to Vanish

Fri, 17 Jul 2026 00:00:00 +0000

If every update fully replaces the current position, convergence requires the river-location judgment error itself to disappear.

Use Only Observable and Executable Training Targets

Fri, 17 Jul 2026 00:00:00 +0000

A strong teacher result is a valid target only when the model can observe its basis and execute the same action.

The Robbins–Monro Conditions Balance Learning and Noise

Fri, 17 Jul 2026 00:00:00 +0000

The step sizes must remain large enough to keep correcting error and become small enough to suppress accumulated noise.

Why the Step Sizes Must Sum to Infinity

Fri, 17 Jul 2026 00:00:00 +0000

A finite total step size can make an iteration stop moving before its error has disappeared.

Why the Squared Step Sizes Must Be Summable

Fri, 17 Jul 2026 00:00:00 +0000

For a changing step-size sequence, square summability bounds the total variance injected by noisy observations.

Dvoretzky's Theorem Turns Noisy Contraction into Pathwise Convergence

Fri, 17 Jul 2026 00:00:00 +0000

Dvoretzky generalizes the stochastic-approximation error recursion and gives conditions for almost-sure convergence.

Square the Error to Turn Convergence into Energy Dissipation

Fri, 17 Jul 2026 00:00:00 +0000

The Dvoretzky proof tracks squared error, shows that its positive drift is summable, and rules out a positive limiting energy.

A Second Proof Route Starts from Expectation and Variance

Fri, 17 Jul 2026 00:00:00 +0000

Expanding the recursion explains how initial error and historical noise decay, but usually yields convergence in probability rather than almost-sure convergence.

Expand the Error into Initial Bias and Historical Noise

Fri, 17 Jul 2026 00:00:00 +0000

The explicit error formula separates the residual initial condition from the weighted sum of all past disturbances.

How the Initial Error Disappears in Expectation

Fri, 17 Jul 2026 00:00:00 +0000

Zero-mean noise removes the disturbance terms from the expectation, leaving a product that vanishes when the step sizes sum to infinity.

How Historical Noise Is Attenuated

Fri, 17 Jul 2026 00:00:00 +0000

Each disturbance is controlled twice: by its entry coefficient and by every contraction that follows it.

Why Mean-Square Analysis Stops at Convergence in Probability

Fri, 17 Jul 2026 00:00:00 +0000

Vanishing expectation and variance control each time slice, but they do not directly control the shape of an infinite sample path.

Two Proof Routes Explain Different Levels of Convergence

Fri, 17 Jul 2026 00:00:00 +0000

Expectation and variance explain distributional concentration; the energy and martingale route proves almost-sure convergence.

sdr-sidewalk-sim: Pedestrian-Aware Sidewalk Delivery Robot Simulator

Wed, 10 Jun 2026 00:00:00 +0000

A research simulator for studying how pedestrian-aware sidewalk conditions affect delivery robot routing, dispatch, replay, and validation.

A Generative Model Is Like a Database: Decomposition Defines Its Schema

Mon, 08 Jun 2026 00:00:00 +0000

A database analogy reveals why generative models need data decomposition and why unit granularity determines what they can learn and generate.

Yellowstone

Sat, 23 May 2026 00:00:00 +0000

A small Yellowstone photo set.

Arches

Fri, 22 May 2026 00:00:00 +0000

A small Arches photo set.

California Highway 1

Fri, 22 May 2026 00:00:00 +0000

A small California Highway 1 photo set.

Canyonlands

Fri, 22 May 2026 00:00:00 +0000

A small Canyonlands photo set.

Monument Valley

Fri, 22 May 2026 00:00:00 +0000

A small Monument Valley photo set.

Sequoia

Fri, 22 May 2026 00:00:00 +0000

A small Sequoia photo set.

Washington, DC

Fri, 22 May 2026 00:00:00 +0000

A small Washington, DC photo set.

Zion

Fri, 22 May 2026 00:00:00 +0000

A small Zion National Park photo set.

Bryce Canyon

Thu, 21 May 2026 00:00:00 +0000

A small Bryce Canyon photo set.

CV

Thu, 21 May 2026 00:00:00 +0000

My current resume highlights LLM agents, machine learning, optimization, and simulation, including my Applied Scientist internship at Amazon and research on tool-using agents for dynamic fleet assignment.

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Glacier

Thu, 21 May 2026 00:00:00 +0000

A small Glacier National Park photo set.

Great Smoky

Thu, 21 May 2026 00:00:00 +0000

A small Great Smoky Mountains photo set.

Yosemite

Thu, 21 May 2026 00:00:00 +0000

A small Yosemite photo set.

We Understand the World by Building Maps

Mon, 30 Mar 2026 00:00:00 +0000

Why the same event becomes different internal inputs — and why scientific theories are maps of observable phenomena rather than reality itself.

Reviewing the Reviewer: Graph-Enhanced LLMs for E-commerce Appeal Adjudication

Thu, 26 Feb 2026 20:00:00 -0500

A two-stage LLM agent that uses RAG with graph-based memory to ground fraud-related seller-appeal recommendations in evidence, verification actions, and historical human corrections.

Designing Sidewalk Delivery Robot Fleets Under Uncertainty

Mon, 12 Jan 2026 10:00:00 -0500

A two-stage stochastic optimization framework for fleet and battery sizing of sidewalk delivery robots under uncertain demand.

Understanding Social Perceptions of Sidewalk Delivery Robots via YouTube Sentiment Analysis

Thu, 08 Jan 2026 10:00:00 -0500

A data-driven study leveraging YouTube comments to uncover public perceptions, safety concerns, and social acceptance of sidewalk delivery robots.

About

Sun, 28 Dec 2025 19:34:39 -0500

I’m a Ph.D. candidate in Industrial Engineering Technology at Purdue University, expecting to graduate in December 2026. I build reliable LLM agents and decision systems at the intersection of machine learning, optimization, and simulation.

My current research studies tool-using LLM agents for dynamic fleet assignment. At each decision point, an agent examines real-time request and fleet information, then assigns requests to vehicles while balancing service quality and operating efficiency across different spatial and temporal demand patterns. My broader research covers stochastic fleet and battery sizing, routing, large-scale system design, NLP-based social perception, and mobility simulation.