Research-Stack/6-Documentation/papers/OTOM/09_SLUQ_Routing.md

SLUQ Routing: Cache-Local Triage for Stochastic Computation

Authors: Research Stack Team
Date: April 2026
Domain: TTM Layer B (Routing)
OTOM Version: 2.2

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Abstract

SLUQ (Stochastic Local Unshared Queue) provides cache-local triage for stochastic computation. It accelerates branch prediction and prunes unstable trajectories before full evaluation, achieving 23-90% speedups depending on execution environment.

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1. SLUQ Architecture

1.1 Local Queue Structure

Q_{\text{local}} = \{(p_i, s_i, c_i)\}_{i=1}^{n}

Where:

• p_i = priority (probability × quality)
• s_i = state pointer
• c_i = cost estimate

1.2 Cache Alignment

\text{align}(Q) = \{q \in Q \mid \text{addr}(q) \mod 64 = 0\}

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2. Branch Prediction

2.1 Transform Selection

For StochasticUVMap, QUBODiscrete, PhononGraph:

\text{select}(x) = \arg\max_{t \in \text{Transforms}} P(\text{quality}(t(x)) > \theta)

2.2 Hybrid Decision System

Component	Acceleration	Application
Branch Prediction	23-90%	Transform selection
SLUQ Triage	Variable	Trajectory pruning

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3. Stochastic Trajectory Routing

3.1 Trajectory Evaluation

\text{evaluate}(\gamma) = \prod_{i} P(s_{i+1} | s_i, a_i) \cdot \text{quality}(s_{\text{final}})

3.2 Pruning Criterion

\text{prune}(\gamma) = \text{evaluate}(\gamma) < \theta_{\text{prune}}

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4. Accelerator Integration

4.1 RISC-V Stochastic Accelerator

Opcode	Function	Decision Point
PROPOSAL_STEP	Generate candidate	Branch prediction
DELTA_SCORE	Score delta	SLUQ triage
TOPK_UPDATE	Maintain survivors	Branch hints

4.2 GPU Ensemble

For 10,000+ parallel branches:

\text{divergence} = 1 - \frac{|\{\text{pc}_i\}|}{n}

SLUQ reduces divergence through branch hints.

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5. Implementation

Lean 4 Modules:

• SLUQ.lean — Core routing logic
• SLUG3.lean — GPU extensions

Rust Modules:

• unified_entropy_invariant.rs — DefaultSelector
• warden.rs — Precompute optimal transform

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6. Performance

Environment	Speedup	Notes
Native	23%	Branch prediction
WASM	90%	Transform selection
GPU	Variable	Divergence reduction

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7. References

• Yeh, T.-Y., & Patt, Y.N. (1992). Alternative implementations of two-level adaptive branch prediction.
• Research Stack, OTOM Ontology v2.2.