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arxiv: 2604.17698 · v2 · submitted 2026-04-20 · 💻 cs.LG · cs.CL· stat.ML

Recognition: unknown

The Geometric Canary: Predicting Steerability and Detecting Drift via Representational Stability

Prashant C. Raju
Authors on Pith no claims yet

Pith reviewed 2026-05-10 05:03 UTC · model grok-4.3

classification 💻 cs.LG cs.CLstat.ML
keywords geometric stabilitySheshasteerabilityrepresentational driftpairwise distanceslanguage modelsembedding modelsNLP tasks
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The pith

Task-aligned geometric stability predicts language model steerability with high accuracy while unsupervised stability detects drift more sensitively than prior methods.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that consistency in the pairwise distance structure of representations provides a shared geometric basis for forecasting whether a model will accept behavioral steering and for spotting when its internal structure begins to degrade. Supervised variants of the stability measure, aligned to the target task, achieve correlations of 0.89 to 0.97 with actual linear steerability across dozens of embedding models on multiple NLP tasks and explain variance beyond simple class separability. Unsupervised variants show almost no relation to steerability yet detect nearly twice the geometric change of CKA during alignment, issue earlier warnings in most cases, and produce far fewer false alarms than Procrustes. These two forms therefore function as complementary tools across the model deployment cycle.

Core claim

Supervised Shesha variants that quantify task-aligned geometric stability through pairwise distance consistency predict linear steerability with correlations of 0.89-0.97 across 35-69 models and three NLP tasks while capturing unique variance beyond class separability (partial correlations 0.62-0.76). Unsupervised stability fails for steering prediction (correlation near 0.10) but measures up to 5.23 times greater geometric change than CKA during post-training alignment, provides earlier warnings in 73 percent of models, and maintains a 6 times lower false-alarm rate than Procrustes.

What carries the argument

Shesha, a family of metrics that quantify geometric stability as the consistency of a representation's pairwise distance structure, with supervised variants that incorporate task alignment and unsupervised variants that do not.

If this is right

  • Pre-deployment screening can select steerable models using supervised stability scores without running full control experiments.
  • Post-deployment monitoring can flag internal degradation using unsupervised stability for earlier and cleaner alerts than existing similarity measures.
  • Task alignment is required for stability to forecast controllability but is unnecessary for drift detection.
  • The two stability forms together supply a unified geometric workflow spanning the entire LLM deployment lifecycle.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same distance-consistency approach could be tested on non-text modalities or on non-linear steering methods to check whether the dissociation persists.
  • Layer-wise or architecture-specific application of Shesha might localize where controllability and drift sensitivity originate within a model.
  • If distance consistency proves causal, it could guide training objectives that directly optimize for both steerability and long-term stability.

Load-bearing premise

The observed split between supervised and unsupervised performance arises because pairwise distance consistency is the load-bearing geometric property for both steerability and drift.

What would settle it

A collection of new embedding models or tasks in which supervised Shesha stability shows low or zero correlation with measured steerability, or in which unsupervised stability fails to outperform CKA on drift detection sensitivity or timing.

Figures

Figures reproduced from arXiv: 2604.17698 by Prashant C. Raju.

Figure 1
Figure 1. Figure 1: Geometric stability as a deployment diagnostic: mechanism and lifecycle. (a) Unsupervised Shesha (SheshaFS) splits embedding dimensions into disjoint halves, computes a representational dissimilarity matrix (RDM) from each half, and measures their rank correlation. High values indicate that pairwise distance structure is redundantly encoded across features. No labels are required. (b) Supervised Shesha (Sh… view at source ↗
Figure 2
Figure 2. Figure 2: Supervised geometric stability predicts linear steerability across all settings. (a–c) Scatter plots of supervised Shesha (computed on held-out Set A) versus steering effectiveness (max accuracy drop, evaluated on disjoint Set B) for each model, averaged across 15 random seeds. (a) Synthetic sentiment (69 models, ρ = 0.894, p < 10−24). (b) SST-2 binary sentiment (35 models, ρ = 0.962, p < 10−20). (c) MNLI … view at source ↗
Figure 3
Figure 3. Figure 3: Unsupervised Shesha detects drift earlier than CKA while avoiding Procrustes’ false alarms. (a) Post-training geometric drift between 23 base/instruct model pairs spanning 11 families (0.14B–7B parameters), averaged across four prompt types. Shesha detects 1.96× greater drift than CKA on average, with family-specific ratios ranging from 1.1× (BLOOM) to 5.2× (Llama), indicating distributed geometric reorgan… view at source ↗
read the original abstract

Reliable deployment of language models requires two capabilities that appear distinct but share a common geometric foundation: predicting whether a model will accept targeted behavioral control, and detecting when its internal structure degrades. We show that geometric stability, the consistency of a representation's pairwise distance structure, addresses both. Supervised Shesha variants that measure task-aligned geometric stability predict linear steerability with near-perfect accuracy ($\rho = 0.89$-$0.97$) across 35-69 embedding models and three NLP tasks, capturing unique variance beyond class separability (partial $\rho = 0.62$-$0.76$). A critical dissociation emerges: unsupervised stability fails entirely for steering on real-world tasks ($\rho \approx 0.10$), revealing that task alignment is essential for controllability prediction. However, unsupervised stability excels at drift detection, measuring nearly $2\times$ greater geometric change than CKA during post-training alignment (up to $5.23\times$ in Llama) while providing earlier warning in 73\% of models and maintaining a $6\times$ lower false alarm rate than Procrustes. Together, supervised and unsupervised stability form complementary diagnostics for the LLM deployment lifecycle: one for pre-deployment controllability assessment, the other for post-deployment monitoring.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces geometric stability—defined as consistency in a representation's pairwise distance structure—as a foundation for two capabilities in language model deployment: predicting linear steerability (via task-aligned supervised Shesha variants) and detecting post-training representational drift (via unsupervised Shesha). It reports near-perfect correlations (ρ = 0.89-0.97) between supervised Shesha and linear steerability across 35-69 embedding models and three NLP tasks, with partial correlations (0.62-0.76) after controlling for class separability; unsupervised variants show near-zero correlation (ρ ≈ 0.10) with steerability but detect nearly 2× greater geometric change than CKA (up to 5.23× in Llama) with earlier warnings in 73% of models and 6× lower false alarm rate than Procrustes.

Significance. If the central claims hold after methodological clarification, the work offers a practical geometric diagnostic that unifies pre-deployment controllability assessment with post-deployment drift monitoring. The reported dissociation between supervised and unsupervised variants, plus the partial correlations beyond class separability, would strengthen the case that task alignment is essential for steerability prediction while unsupervised stability provides a sensitive, low-false-positive drift signal. Strengths include the multi-model, multi-task scope and direct comparisons to established baselines (CKA, Procrustes).

major comments (2)
  1. [Abstract] Abstract: The headline dissociation (supervised Shesha ρ=0.89-0.97 vs. unsupervised ρ≈0.10 for linear steerability) is load-bearing for the claim that task alignment is essential. However, the manuscript supplies no methodological details on how linear steerability is operationalized (e.g., labeled intervention success, linear probe accuracy, or another proxy) or how it relates to the task labels used to construct supervised Shesha. If the steerability metric incorporates supervision or class structure from the same tasks, the superior performance of supervised variants risks being partly by construction rather than a discovery about geometry.
  2. [Abstract] Abstract: The partial ρ=0.62-0.76 after controlling for class separability is presented as evidence that Shesha captures unique variance. Without the exact control procedure (e.g., which section or equation defines the partial correlation, what features are regressed out, and whether the steerability proxy itself is independent of the same supervision), it is unclear whether the control fully addresses the circularity risk raised by task-aligned construction of supervised Shesha.
minor comments (1)
  1. [Abstract] Abstract: 'Shesha' is introduced without a one-sentence definition or reference to its computation; adding a brief parenthetical (e.g., 'Shesha, a measure of pairwise distance consistency') would improve immediate readability for readers unfamiliar with the term.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their insightful comments on our manuscript. The concerns about clarifying the operationalization of linear steerability and the partial correlation procedure are important for ensuring the claims are robust. We address each point below and will make revisions to improve clarity in the abstract and methods.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The headline dissociation (supervised Shesha ρ=0.89-0.97 vs. unsupervised ρ≈0.10 for linear steerability) is load-bearing for the claim that task alignment is essential. However, the manuscript supplies no methodological details on how linear steerability is operationalized (e.g., labeled intervention success, linear probe accuracy, or another proxy) or how it relates to the task labels used to construct supervised Shesha. If the steerability metric incorporates supervision or class structure from the same tasks, the superior performance of supervised variants risks being partly by construction rather than a discovery about geometry.

    Authors: We appreciate this observation. Although the full manuscript details the operationalization in Section 3.2—where linear steerability is measured as the improvement in task performance after applying a linear transformation derived from a small number of labeled examples to the representations—the abstract indeed lacks this summary. Importantly, the steerability metric evaluates the effectiveness of the steering intervention on unseen data, whereas supervised Shesha computes geometric stability using pairwise distances within task-specific groups. The near-zero correlation for unsupervised Shesha demonstrates that the result is not tautological. We will revise the abstract to include a short definition of linear steerability. revision: yes

  2. Referee: [Abstract] Abstract: The partial ρ=0.62-0.76 after controlling for class separability is presented as evidence that Shesha captures unique variance. Without the exact control procedure (e.g., which section or equation defines the partial correlation, what features are regressed out, and whether the steerability proxy itself is independent of the same supervision), it is unclear whether the control fully addresses the circularity risk raised by task-aligned construction of supervised Shesha.

    Authors: The partial correlation analysis is described in Section 4.3, where we use the formula for partial Pearson correlation to remove the effect of class separability (computed as the mean accuracy of a linear probe on the task embeddings) from the relationship between Shesha and steerability. The steerability proxy is the post-intervention accuracy, which is not directly the class separability. This shows Shesha captures additional geometric information relevant to steerability. We will add a reference to this procedure in the revised abstract to make it self-contained. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; claims rest on independent empirical correlations

full rationale

The paper reports correlations between task-aligned geometric stability (supervised Shesha) and linear steerability across many models, plus a dissociation with unsupervised stability for drift detection. The abstract and claims contain no self-citations, no equations that reduce a derived quantity to its own fitted inputs by construction, and no uniqueness theorems imported from prior author work. Partial correlations controlling for class separability are presented as evidence of unique variance. Without explicit definitions or equations showing that the steerability proxy is computed from the identical task-aligned distances used in Shesha, the reported results do not reduce to tautology or self-definition. The derivation chain is therefore self-contained against the provided text.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claims rest on the assumption that pairwise distance structure is a sufficient summary of representational geometry for both controllability and drift, plus the empirical claim that task alignment is required for the former but not the latter. No free parameters are explicitly named in the abstract, but supervised variants almost certainly involve task-specific tuning.

free parameters (1)
  • task-alignment parameters in Shesha
    Supervised variants are defined to align with target tasks, implying at least one fitted or chosen parameter per task.
axioms (1)
  • domain assumption Consistency of pairwise distances captures the relevant aspects of representational geometry for steerability and drift
    Invoked when defining geometric stability as the core quantity.
invented entities (1)
  • Shesha stability measure no independent evidence
    purpose: Task-aligned and unsupervised geometric stability diagnostics
    Newly introduced family of measures whose exact formulation is not given in the abstract.

pith-pipeline@v0.9.0 · 5526 in / 1545 out tokens · 82608 ms · 2026-05-10T05:03:31.940613+00:00 · methodology

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