Behaviour-Space Spectral Geometry

Read this as an audit method. The paper is about measuring what a fielded adapter fleet does, while keeping model weights, activations, and raw responses inside the boundary.

LoRA adapters are a common way to specialize large language models. But once an organization has many adapters, it becomes hard to know what behavioural differences the fleet actually contains.

The usual path starts from weights: decompose the adapter parameters, then try to predict behaviour. The paper inverts that. It starts from behaviour: run a fixed battery of synthetic probes, grade the responses, and decompose the resulting behaviour matrix.

The Method

Each adapter is evaluated on a fixed probe set. Responses are reduced to trinary grade vectors. Those vectors form a behaviour matrix. Singular value decomposition then identifies the principal axes of variation across the fleet.

Because the decomposition happens on measured behaviour, variance attribution is direct. The paper's phrase is that the two-stage decompose-then-predict pipeline collapses to a single stage.

The Reported Findings

On a fleet of 53 adapters, the record reports 18 distinct behavioural profiles. The first principal component captures 57.8% of variance, while all five components remain non-negligible, with the smallest at 3.9%.

On a controlled six-corpus sub-fleet, the geometry collapses to rank one. A single axis, the response to a null prompt, captures 100% of the variance. The paper interprets that as the geometric signature of a training objective that structurally precludes refusal.

The Attestation Boundary

The paper also describes a bounded verification surface. Only derived behavioural metadata, fixed-dimensional spectral coordinates, and a Merkle root over pinned artifacts cross to an external verifier. Weights, activations, and raw responses stay inside.

What Is Claimed

• Direct measurement: behaviour is measured before it is explained.
• Spectral map: SVD turns response grades into principal behavioural axes.
• Bounded attestation: third parties can verify derived structure without receiving the model or raw outputs.

Why This Matters

The result is useful when an adapter fleet is sensitive, air-gapped, or proprietary. It gives the outside verifier something structured to check without asking the operator to disclose the model itself.