CFE Kernel

CFE (Compatibility Field Estimation) is an interpretable, domain-agnostic scoring engine that generates calibrated probability scores for compatibility between entities. It powers the relevance ranking behind knowledge search results.

How It Works

Raw features x → Soft Compatibility Functions → c ∈ [0,1]
                         ↓
            Attention-Weighted Scoring (with Interaction Matrix A)
                         ↓
                    Score S ∈ (0,1)

Unlike black-box neural networks, every CFE parameter is interpretable:

• 340 parameters for the materials science schema (d=17 features)
• O(d^2) inference — fast enough for real-time ranking
• Calibrated probabilities — output S is a valid probability by construction

Three Compatibility Functions

Each feature maps raw values to a compatibility score c ∈ [0,1]:

Function	Semantics	Example Features
Sigmoid	Threshold — “minimum required”	Material identity match, source authority
Gaussian	Ideal range — “closer is better”	Temperature distance, compositional overlap
Affine	Linear scaling	Recency, data completeness

Attention-Weighted Scoring

The final score combines all compatibility values using learned attention:

z_j = log(w_j) + Σ_k A_jk · c_k
α_j = softmax(z)_j
S = Σ_j α_j · c_j

The interaction matrix A enables cross-feature compensation:

• “If materials are similar, boost property match even if names don’t match”
• “High authority suppresses age penalty”

Integration

CFE runs as an internal service (marc27-cfe). The Knowledge Service calls it when ranking search results. Users never see CFE parameters — only opaque relevance scores.

POST /score   — Score a batch of feature vectors
POST /rank    — Score and return top-k ranked
POST /reload  — Hot-reload after retraining

Status

• Kernel: verified (20 tests pass, 340 parameters, 17% loss reduction in 20 steps)
• Service wrapper: built (FastAPI + R2 model loading)
• Training pipeline: Phase 2 (synthetic queries + LLM-as-judge labels)
• Deployment: pending (needs trained models per corpus)