KernelWeave

A kernel routing and verification system for language models.

What this actually is

A caching layer for verified reasoning patterns.

When a language model solves a task successfully, KernelWeave:

• Stores the reasoning pattern as a typed kernel
• Verifies future outputs against postconditions before caching
• Routes similar prompts to cached kernels
• Accumulates verified competence over time

What works now

• Semantic routing — Embedding-based similarity + calibration scoring
• Postcondition verification — Checks outputs against kernel constraints
• Feedback accumulation — Records success/failure for each kernel
• Auto-promotion — High-confidence repeated successes become candidate kernels
• Model-agnostic — Works with any OpenAI/Anthropic/openai-compatible backend

What doesn't work yet

Real self-compilation

Kernels are extracted from prompts + response text, not from observed reasoning traces. The model's actual chain-of-thought, tool calls, and intermediate states aren't captured. That requires structured generation or a separate observation layer.

Kernel composition

If you have a "structured comparison" kernel and an "evidence extraction" kernel, there's no mechanism to combine them. Composition over a kernel algebra is an open research problem.

Constrained generation

The kernel informs the model via system prompt, but doesn't constrain the output space during generation. The model can still output anything — verification happens after the fact. A frontier system would use kernels as structured decoding constraints during token generation.

Real contribution

"Postcondition verification as a routing signal."

The novel part isn't the routing (that's retrieval) or the kernels (that's program synthesis). It's using verification against formal postconditions to decide whether to trust cached reasoning for future prompts.

Testable claim: For repeated task families, routing + verification beats vanilla RAG on output quality and cost.

What's needed for a paper

1. Benchmark — Run on ToolBench, AgentBench, or a custom benchmark with repeatable tasks
2. Baselines — Compare against vanilla RAG, BM25 retrieval, no verification
3. Metrics — Routing precision/recall, output quality, cost per query
4. Ablations — Does verification actually improve routing decisions?

Without numbers, it's a prototype. With numbers, it's a 4-page workshop paper with a clear contribution.

Usage

# Initialize kernel store
python -m kernelweave.cli init ./store
python -m kernelweave.cli add-sample ./store

# Run with model backend
python -m kernelweave.cli model run qwen0_5 "compare two artifacts" \
  --kernel-store ./store \
  --auto-compile

# Verify routing
python -m kernelweave.cli plan ./store "summarize differences between files"

Architecture

prompt → embed → kernel match → execute kernel OR generate
                                          ↓
                                    verify output
                                          ↓
                                    record feedback
                                          ↓
                              auto-promote if high confidence

Components

• kernelweave/runtime.py — Routing + verification
• kernelweave/kernel.py — Kernel store + feedback accumulation
• kernelweave/calibration.py — Logistic regression confidence model
• kernelweave/llm/model.py — Model wrapper with kernel-aware prompts

When kernels are worth it

High repetition — Customer support, data pipelines, routine analysis
Low repetition — Creative writing, one-off research, exploratory chat

The overhead of compilation, matching, and verification only pays off when the same task family appears many times.

Status

Working prototype. Not frontier. Not a trained model. A useful piece of infrastructure for LLM-based systems with repeated tasks.