[Submitted on 12 Aug 2026]
Title:Cosine Similarity Is Not Evidence: Measuring the Noise Floor of Interpretability Transfer Under Quantization
View a PDF of the paper titled Cosine Similarity Is Not Evidence: Measuring the Noise Floor of Interpretability Transfer Under Quantization, by Pranav Varshney
View PDF HTML (experimental)
Abstract:A statistic reported without the quantity needed to interpret it is not evidence. We develop that thesis for a concrete practice in AI safety. Interpretability artifacts are calibrated on full-precision weights, deployed on quantized ones, and certified as surviving the change by scale-invariant statistics (cosine similarity, correlation, AUROC) that are reported without their noise floor. For the difference-in-means direction estimator, the split-half floor is governed by one dimensionless number, $\kappa = n\rho^2/d$. The closed form $\mathbb{E}[\cos] \approx (1+4/\kappa)^{-1}$ is classical; the missing input is the class separation $\rho$, which we measure on real activations; no compression-transfer study we know of reports it. On Qwen2.5-1.5B-Instruct, $\rho = 33$--$61$ across depth, so two independent runs of the estimator agree to $0.978$--$0.994$ by sampling alone. A published cosine of $0.996$ between full-precision and quantized refusal directions therefore cannot be read as preservation without the $n$ it was computed at, which is not reported. Where $n$ is known, we judge each low-bit cosine against the split-half null measured within that quantized model, because a full-precision null assumes the low-bit estimator has the same variance. That assumption is exactly what a null exists to test. The result is plain: at INT4 the direction rotated, and the deficit exceeds the estimator's own noise. At INT8 we detect no movement, which is not an equivalence claim. We also show that a scale-invariant statistic cannot distinguish translation from attenuation of a transferred decision variable, although the two call for opposite remedies. We close with reporting recommendations that cost one forward pass. Code, data, and a one-cell reproduction are released at this https URL
Comments: 10 pages (5-page main text, plus references and appendices), 1 figure, 3 tables. Code, data, and a one-cell reproduction: this https URL
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2609.30275 [cs.LG]
(or arXiv:2609.30275v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.30275
arXiv-issued DOI via DataCite
Submission history
From: Pranav Varshney [view email] [v1] Wed, 12 Aug 2026 03:14:00 UTC (51 KB)
Full-text links:
Access Paper:
View a PDF of the paper titled Cosine Similarity Is Not Evidence: Measuring the Noise Floor of Interpretability Transfer Under Quantization, by Pranav Varshney
View PDF
HTML (experimental)
TeX Source
view license
Current browse context:
cs.LG
new | recent | 2026-09
Change to browse by:
cs
References & Citations
NASA ADS
Google Scholar
Semantic Scholar
Loading...
Data provided by:
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data, Media
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Related Papers
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
IArxiv recommender toggle
IArxiv Recommender (What is IArxiv?)
Author
Venue
Institution
Topic
About arXivLabs
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)