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

Prashant C. Raju

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

Prashant C. Raju

arXiv:2604.17698v2Apr 20, 2026cs.LGcs.CLstat.ML

TL;DR

Reliable language-model deployment needs controllability prediction before release and drift detection afterward, but these are usually treated separately. This paper uses supervised and unsupervised geometric stability to address both, finding complementary success across the deployment lifecycle.

Problem
Deployment requires predicting targeted behavioral control before release and detecting internal structural degradation afterward, questions typically addressed by separate literatures.
Method
The paper measures task-aligned geometry with supervised Shesha for steerability and task-agnostic geometric consistency with unsupervised Shesha for drift detection.
Results
ρ = 0.89–0.97 for supervised stability predicting linear steerability, while unsupervised stability detects 2× greater drift than CKA and has a 6× lower false-alarm rate than Procrustes.
Takeaways & Limitations
Supervised and unsupervised stability are complementary diagnostics for pre-deployment controllability assessment and post-deployment monitoring.
Takeaways & Limitations
The steering experiments use sentence-embedding models rather than decoder hidden states during generation, limiting the evaluated scope.

Abstract

from arXiv · show

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 ($ρ= 0.89$-$0.97$) across 35-69 embedding models and three NLP tasks, capturing unique variance beyond class separability (partial $ρ= 0.62$-$0.76$). A critical dissociation emerges: unsupervised stability fails entirely for steering on real-world tasks ($ρ\approx 0.10$), 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.

1 Introduction

The paper frames pre-deployment steerability and post-deployment drift detection as one problem: assessing the reliability of a model’s representational geometry. It introduces supervised and unsupervised Shesha variants as complementary measurements for these two stages.

Motivation: Safe deployment requires predicting targeted behavioral control before deployment and detecting internal structural degradation afterward.These questions are usually treated as separate problems, but the paper links them through representational geometry.
Monitoring gap: Post-training alignment reshapes internal representations, while CKA underestimates geometric change and Procrustes produces false alarms.Procrustes triggers false alarms in 44% of cases without functional degradation.
Our approach: Supervised Shesha measures task-aligned geometric stability, the property identified as relevant for predicting steering success.The metric quantifies self-consistency in a representation’s pairwise distance structure without requiring a trained probe.
Complementary diagnostics: Unsupervised stability reaches ρ = 0.77 in synthetic settings but fails on real-world steering at ρ ≈0.10 on SST-2, while detecting drift 2× more sensitively than CKA.For drift monitoring, it also maintains a 6× lower false alarm rate than Procrustes and provides earlier warning in 73% of models.
Controllability results: ρ = 0.89–0.97 supervised stability predicts linear steerability across 69 embedding models and three NLP tasks, beyond class separability at partial ρ = 0.62–0.76.The reported signal is unique beyond class separability and spans tasks of increasing complexity.

2 Supervised Geometric Stability

Supervised geometric stability measures whether a representation’s distance structure is aligned with task labels, rather than merely internally consistent. The section introduces four task-aware variants that assess alignment, class structure, or decision-boundary robustness.

Task-aligned variants: Supervised Shesha correlates a model’s representational dissimilarity matrix with an ideal label-derived matrix to measure task-relevant geometric alignment without training a probe.The ideal matrix encodes label dissimilarity using Hamming distance on one-hot labels.
Task-aligned variants: The four supervised variants are Sheshasup, Sheshavar, Sheshasep, and SheshaLDA, covering RDM alignment, variance attribution, distance-based class separation, and decision-boundary stability.Together they evaluate complementary geometric properties associated with task structure.
Task-aligned variants: Sheshavar provides a computationally efficient approximation based on the proportion of total variance attributable to class structure.Its variance ratio uses class centroids, the global mean, and class sample counts.
Task-aligned variants: Sheshasep measures class separation in pairwise-distance space by comparing mean between-class and within-class distances.It uses bootstrap subsampling with B=50 iterations and a 50% subsampling rate.
Task-aligned variants: SheshaLDA measures whether the optimal linear decision boundary remains consistent under resampling, with low values indicating sample-dependent separability.It compares the unit-normalized full-data LDA direction with directions fitted on bootstrap subsamples.
Task alignment versus internal consistency: Internal consistency and task alignment are logically independent: geometry can be internally rigid yet poorly organized for a task, or task-aligned yet fragile under feature perturbation.Unsupervised SheshaFS assesses internal consistency, whereas supervised variants assess alignment with a specific task.

3 Supervised Stability Predicts Steering Performance

Supervised geometric stability strongly predicts linear steering performance across synthetic and real-world NLP tasks, including variance beyond class separability. Unsupervised stability does not generalize to real-world steering, establishing task alignment as essential for controllability prediction.

Cross-task prediction: ρ = 0.894, 0.962, and 0.974 link supervised Shesha to steering effectiveness on Synthetic, SST-2, and MNLI, respectively.These results span 69 models in Synthetic and 35 models each in SST-2 and MNLI.
Unique signal beyond separability: ρpartial = 0.665, 0.764, and 0.620 show supervised Shesha retains substantial signal after controlling for Fisher discriminant and silhouette score.All partial correlations are significant at p < 0.001, indicating stability captures information beyond class separation.
Supervised–unsupervised dissociation: ρ = 0.10 on SST-2 and ρ = 0.35 on MNLI show unsupervised feature-split Shesha fails to predict steering on real-world tasks.Unsupervised stability correlates with steering only in Synthetic, where the data manifold aligns with sentiment polarity; residual correlations fall below ρpartial = 0.10.
Training objectives and steerability: Supervised contrastive models are most steerable, whereas unsupervised and retrieval-specialized models are least steerable.The results attribute reliable linear intervention to the combination of class separation and geometric rigidity produced by supervised contrastive training.
Practical diagnostic: Sheshasup can predict controllability from a labeled calibration set before steering experiments, with held-out metric computation and disjoint steering evaluation preventing information leakage.Steering effectiveness is measured as the maximum accuracy drop after interventions along learned task directions.

4 Stability Detects Representational Drift

Unsupervised Shesha provides a practical post-deployment drift monitor, detecting substantially more geometric change than CKA while warning earlier and producing far fewer false alarms than Procrustes. Canary experiments show that this sensitivity tracks functional degradation comparably to competing metrics.

Motivation: Unsupervised stability is suited to continuous production monitoring because supervised stability requires labeled data and a known task.The unsupervised variant failed for steering prediction but serves post-deployment surveillance by detecting degradation without task labels.
Post-training drift: 1.96× greater drift: Shesha measured 25.1% geometric change versus 12.9% for CKA across 23 base/instruct model pairs.The gap reached 5.23× for Llama, with 34.0% Shesha drift versus 6.5% CKA drift; BLOOM showed near-parity at 1.14×.
Structured perturbations: 1.7× more drift: at Gaussian noise σ = 0.5, Shesha captured 71% drift versus 43% for CKA, while all metrics increased monotonically with perturbation magnitude.Structured perturbations included Gaussian noise, INT8 and INT4 quantization, and LoRA modifications across 16 causal language models.
Canary validation: 73% of models: Shesha warned earlier than CKA in 19/26 canary models, triggering at σ = 0.123 versus σ = 0.136 for CKA.All three metrics correlated similarly with SST-2 accuracy drop: Shesha ρ = 0.927, CKA ρ = 0.937, and Procrustes ρ = 0.935.
Metric specificity: 44% false alarms: Procrustes triggered in stable cases versus 7.3% for both Shesha and CKA, a 6× difference.At minimal perturbation with unchanged functional performance, Procrustes reported 1.50% drift versus 0.04% for Shesha.
Practical recommendation: Shesha is recommended as the primary production-monitoring metric, with CKA as conservative confirmation and Procrustes reserved for settings accepting false alarms.The recommendation reflects Shesha's sensitivity to geometric fracturing before functional failure while avoiding alarm fatigue.

5 Discussion · Appendix · A Related Work

The paper presents supervised and unsupervised Shesha as complementary geometric diagnostics: supervised stability assesses pre-deployment steering potential, while unsupervised stability monitors post-deployment geometric drift. It situates this framework within representation engineering and related work, while noting limitations and extensions for decoder models and localized monitoring.

5.1 Two phases, one principle: Before deployment, supervised Shesha uses task-relevant held-out data to assess whether representational geometry supports linear steering; after deployment, unsupervised Shesha monitors geometric reorganization.The paper frames these as complementary phases rather than competing diagnostics.
5.2 Why the distinction explains steering vs. drift: ρ ≈0.10 on SST-2 for steering contrasts with 2× greater sensitivity than CKA for drift detection, establishing a dissociation between the two uses.The distinction follows from what each stability variant measures.
5.2 Why the distinction explains steering vs. drift: Unsupervised Shesha can miss task-relevant semantic organization because it measures generic feature-split consistency across the embedding space rather than alignment with a steering axis.A representation may retain rigid overall geometry while its task-relevant subspace is fragile or disorganized.
5.2 Why the distinction explains steering vs. drift: Unsupervised stability is suited to drift detection because it tests whether pairwise distances have changed, an intrinsic and task-agnostic property of the data manifold.The same intrinsic criterion can also apply to biological perturbation analysis and compression detection.
5.3 Implications for representation engineering: The Linear Representation Hypothesis treats concepts as linear directions in activation space, and supervised Shesha makes the associated geometric-stability assumption testable and quantitative.Supervised contrastive models including BGE, E5, and GTE exhibit both the class s…
5.4 Implications for safety monitoring: 5.23× discrepancy between Shesha and CKA in Llama indicates substantial manifold reorganization from instruction tuning and supports geometric monitoring as an earlier signal than behavioral failure.Behavioral probes primarily identify failure after downstream accuracy, toxicity, or calibration symptoms appear.
5.5 Limitations and future work: The experiments use sentence embedding models rather than decoder hidden states, analyze held-out prompts, require labeled data for supervised metric computation, and estimate stability through multiple forward passes.The metric also operates globally rather than isolating localized geometric damage.
A Related Work: Related work covers representation-similarity metrics, static geometric properties, activation steering, representational drift, robustness, and alignment-induced capability tradeoffs, but lacks a unified framework for geometric stability.Cited methods include CKA, SVCCA, PWCCA, RSA, Procrustes distance, and approaches based on the Linear Representation Hypothesis.

B Steering: Extended Methods and Results … B.3 Split-half protocol

The extended steering experiments span diverse sentence-embedding models and tasks, use combinatorially generated synthetic data for broad geometric coverage, and enforce strict split-half separation across 15 random seeds. These design choices support evaluation of metric computation independently from steering assessment.

B.1 Model lists: 69 sentence embedding models in Experiment 1 span 11 architecture families, three parameter-size tiers, and supervised or unsupervised objectives.The models include families such as MiniLM, DistilBERT, MPNet, BERT, RoBERTa, DeBERTa, E5, BGE, GTE, UAE, and SimCSE.
B.1 Model lists: 35 sentence embedding models in Experiments 2–3 cover seven model families and use mean-pooled outputs from the base encoder.These experiments evaluate SST-2 and MNLI.
B.2 Synthetic data generation: 1,000 sentiment-laden sentences were generated with a combinatorial grammar produced by Claude Sonnet to ensure broad geometric coverage.The grammar combines contexts, nouns, and positive or negative adjectives.
B.2 Synthetic data generation: 256 unique positive and 256 unique negative sentences per polarity were generated from 4 × 8 × 8 combinations, with resampling to reach 1,000 total.The combinatorial structure is intended to avoid lexical memorization effects while maintaining broad geometric coverage.
B.3 Split-half protocol: Set A contained n = 500 synthetic or n = 400 SST-2/MNLI examples for metric computation, while disjoint Set B supported steering evaluation.Set B was further divided into equal training and testing subsets.
B.3 Split-half protocol: The split-half protocol prevents Shesha computed on Set A from trivially predicting steering on Set B through shared samples.This separation directly isolates metric computation from steering evaluation.

B.4 Full metric correlation tables

This section presents complete metric-correlation tables for steering across synthetic, SST-2, and MNLI experiments. The synthetic analysis aggregates correlations across 69 models and reports partial correlations controlling for Fisher discriminant and silhouette scores.

Experiment 1: Synthetic: Table 1 reports all geometric-metric correlations with steering effectiveness in the synthetic experiment.The correlations use Spearman ρ between geometric metrics and max drop, aggregated by model.
Experiment 1: Synthetic: 69 models contribute to the synthetic experiment’s aggregated metric correlations.Table 1 specifies n = 69 and reports correlations by model.
Experiment 1: Synthetic: Partial correlations in the synthetic experiment control for Fisher discriminant and silhouette score.These controls are specified in the Table 1 caption.
Experiment 2: SST-2: Table 2 reports metric correlations with steering for SST-2 across 35 models.The table is labeled as Experiment 2 and specifies n = 35 models.
Experiment 3: MNLI: Table 3 reports metric correlations with steering for MNLI across 35 models.The table is labeled as Experiment 3 and specifies n = 35 models.
Summary: Table 4 summarizes supervised Shesha’s steering predictions across all settings.The table is explicitly titled as a summary of supervised Shesha across all settings.

B.5 Model ranking analysis … C.6 Canary validation: predictive validity

Model rankings show that task-aligned geometric rigidity predicts steerability, while canary validation shows that geometric drift predicts downstream accuracy degradation across perturbed causal language models. The extended analysis specifies the evaluated models, prompt sets, extraction procedure, drift metrics, prompt-type effects, and predictive validity.

B.5 Model ranking analysis: Supervised contrastive embeddings—including BGE-large, GTE-large, E5-large, and UAE-large—consistently ranked in the top steerability quartile through pairwise supervision producing class separation and geometric rigidity.These models were the most steerable across all three settings.
B.5 Model ranking analysis: Unsupervised and retrieval-specialized models were least steerable because they lacked task-aligned or class-level geometric organization, despite retrieval models often achieving competitive classification accuracy.The result confirms that separability alone is insufficient for steering.
C.1 Model Lists: The drift study evaluated base/instruct model pairs, 16 causal language models for structured perturbations, 15 for extended canary validation, and 26 sentence embedding models.Extended validation excluded SmolLM2-1.7B because of SST-2 evaluation constraints; perturbations included Gaussian noise, quantization, and LoRA.
C.2 Prompt sets: Each model pair used 200 prompts across four coherent categories: factual, descriptive, instructions, and conversational.The categories contained 50 prompts each, generated synthetically with Claude Sonnet, Gemini, and ChatGPT.
C.3 Embedding extraction: Hidden states came from the final layer, mean-pooled over non-padding tokens, L2-normalized, and processed with available chat templates at a 256-token maximum.Generation prompts were disabled with add_generation_prompt=False to avoid assistant-prefix bias.
C.4 Drift metrics: Drift metrics were reported as dissimilarity, with higher values indicating more drift, using Procrustes and sliced Wasserstein alongside Shesha and CKA.Procrustes used optimal orthogonal alignment, while Wasserstein used 100 random projections.
C.5 Drift by prompt type: Shesha/CKA ratios were 2.37× for factual, 2.28× for descriptive, 1.82× for conversational, and 1.44× for instructions.The lower instruction ratio suggests instruction tuning produces less distributed reorganization for in-distribution inputs and greater reorganization for out-of-distribution prompts.
C.6 Canary validation: predictive validity: In 15 causal language models under Gaussian noise (σ ∈[0.00, 0.50]), Shesha (ρ = 0.915), CKA (ρ = 0.912), and Procrustes (ρ = 0.903) strongly predicted downstream accuracy degradation.The metrics differed in when and how reliably they detected degradation, not in what they predicted.

C.7 ROC analysis · C.8 False alarm mechanism

Shesha, Procrustes, and CKA all perform strongly on subtle LoRA drift, but Shesha detects more true positives at the operational threshold. Procrustes’ spectral-tail sensitivity produces inflated drift scores even when accuracy is essentially unchanged.

C.7 ROC analysis: Shesha achieved AUC = 0.990 on the LoRA perturbation benchmark.The benchmark targets subtle structural drift where detection is most challenging.
C.7 ROC analysis: Procrustes achieved AUC = 0.988 on the same benchmark.Its overall performance remained close to Shesha’s despite lower operational sensitivity.
C.7 ROC analysis: CKA achieved AUC = 0.987 on the same benchmark.All three metrics therefore had high overall performance for subtle LoRA drift.
C.7 ROC analysis: At a 5% false positive rate, Shesha reached 90.2% sensitivity versus 85.4% for Procrustes.This supports Shesha’s earlier detection as genuine signal rather than a threshold artifact.
C.8 False alarm mechanism: Procrustes minimizes the Frobenius residual over the full spectrum after optimal rotation.Its spectral objective attempts to align the entire representation spectrum.
C.8 False alarm mechanism: In high-dimensional representations, perturbations accumulate in the spectral tail as noise that Procrustes cannot align, inflating its drift score.This mechanism explains Procrustes’ oversensitivity.
C.8 False alarm mechanism: At LoRA init scale = 0.001, accuracy was essentially unchanged with ∆Acc ≈0.08%.This is the minimal-perturbation condition used to expose false-alarm behavior.
C.8 False alarm mechanism: At LoRA init scale = 0.001, Procrustes registered 37× more drift than Shesha.The supplied passage reports the comparison as evidence of Procrustes’ oversensitivity under minimal perturbation.

C.9 Results · D Negative Control Details

Negative-control experiments show that representational drift responds systematically to quantization, LoRA configuration, and Gaussian noise, while remaining sensitive to functional degradation. Quantization produces modest drift, whereas LoRA scale and rank can induce substantial geometric reorganization.

C.9 Results: Drift metrics were averaged across four prompt types, while Gaussian-noise results were averaged across 16 models and four prompt types.The prompt types were factual, descriptive, instructions, and conversational.
C.9 Results: INT8 quantization caused minimal drift: Shesha 2.1%, CKA 1.4%, and Procrustes 5.3%.Procrustes showed the highest sensitivity to quantization effects.
C.9 Results: INT4 quantization induced approximately 3× more drift: Shesha 6.2%, CKA 4.2%, and Procrustes 9.7%.The heightened Procrustes sensitivity may largely reflect rigid geometric rotation given minimal functional degradation under quantization.
C.9 Results: r = 64 produced substantial LoRA reorganization: Shesha 15.3%, CKA 8.8%, and Procrustes 13.9%, compared with near-zero drift at r = 1.Drift increased monotonically with LoRA rank at fixed initialization scale 0.01.
C.9 Results: 0.001 to 0.1 initialization-scale growth increased Shesha drift from 0.06% to 44.2% at fixed rank r = 8.The result demonstrates that LoRA perturbation magnitude strongly controls representational reorganization.
D Negative Control Details: ρ > 0.92 linked Gaussian-noise drift to accuracy drop for Shesha, CKA, and Procrustes on STS-B sentence-embedding models.The correlation held across all three drift metrics and 26 models.

D.1 Shuffled label controls

Shuffled-label controls show that supervised Shesha depends on genuine task-relevant structure rather than spurious geometric patterns. Its metric collapses to −0.001 across synthetic, SST-2, and MNLI settings when labels are permuted.

Shuffled label controls: Supervised Shesha collapsed to −0.001 across all three settings under random label permutation.This collapse supports the metric’s sensitivity to genuine task structure rather than spurious geometry.
Shuffled label controls: 0.60 →−0.001 for Synthetic, 0.23 →−0.001 for SST-2, and 0.02 →−0.001 for MNLI, each with p < 10−10.These results quantify the collapse separately for each setting.
Shuffled label controls: The decreasing baseline values, 0.60, 0.23, and 0.02, reflect increasing geometric complexity across Synthetic, SST-2, and MNLI.Synthetic manifolds are strongly organized by sentiment, whereas MNLI’s ternary structure is more diffuse.

D.2 Random direction controls · D.3 Early warning: per-model breakdown

Random-direction controls show that true steering effects exceed noise most strongly on simpler tasks, while Shesha remains informative as intervention margins narrow. In validation, Shesha generally detected drift earlier than CKA, with no model favoring CKA.

D.2 Random direction controls: 10.8× larger effect: synthetic-task accuracy drops from the true probe direction than from random unit vectors.The comparison used the maximum drop from the true probe direction against the average drop from 20 random unit vectors per split.
D.2 Random direction controls: 1.3× larger effect: MNLI accuracy drops from the true probe direction than from random unit vectors.The smaller ratio reflects narrower steering margins for the more complex ternary-classification task.
D.2 Random direction controls: Shesha identifies steerable models even when intervention margins are slim by measuring the reliability of existing class structure rather than its magnitude.MNLI’s ternary classification distributes class structure more diffusely across the manifold, reducing large directional effects.
D.3 Early warning: per-model breakdown: 73%: Shesha detected drift before CKA in 19 of 26 sentence embedding models.The seven tied cases occurred when both metrics crossed the 5% threshold at σ = 0.10 or σ = 0.15.
D.3 Early warning: per-model breakdown: No case: CKA detected drift earlier than Shesha, whose mean detection threshold was σ = 0.123 versus CKA’s σ = 0.136.Tied models typically had 384–768 dimensions and small spectral gaps between dominant and tail components.