GRADE detects LLM knowledge gaps by comparing gradient-subspace rank against hidden-state-subspace rank across layers

GRADE's diagnostic: what a model has activated (hidden states) may not match what a query requires — and the gap is measurable as "the proportion of effective required updates against activated knowledge." Per MLP layer, the gradient g = ∂L/∂W is projected into the hidden-state subspace; stable ranks of gradient and hidden state are compared as a per-layer rank ratio (srank(g)/srank(h)), and the cross-layer ratio vector feeds a small supervised gap detector. Across six benchmarks the method outperforms verbalized-confidence, probabilistic, and hidden-state baselines, with the largest gains on math reasoning, and is more robust to prompt paraphrase than hidden-state probes.

Two placement notes. First, this is the internalist branch of the gap-detection taxonomy — it reads the model's weights-versus-activations mismatch, where claim-llm-explicit-implicit-gap-detection reads corpora and claim-query-failure-clustering-as-gap-signal reads behavior; for a markdown vault it applies only "if SeekVault ever uses an embedded model as an index" (the promotion judgment of 2026-07-03 stands). Second, there is a pleasing symmetry the sources don't remark on: the gradient — training's own signal (claim-training-inference-compute-asymmetry-mechanism) — is here repurposed at inference time as a probe, a backward pass run not to learn but to ask what learning WOULD be required. Deployment cost of that backward pass is a queued open question. See moc-machine-self-knowledge.