Prismix
arXiv — Machine Learning · · 7 min read

An Accuracy--Information Tradeoff for Loss-Difference Conditional Mutual Information

#paper

Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.

Like Read original ↗

Computer Science > Machine Learning

arXiv:2610.09206 (cs)
[Submitted on 6 Oct 2026]

Title:An Accuracy--Information Tradeoff for Loss-Difference Conditional Mutual Information

View a PDF of the paper titled An Accuracy--Information Tradeoff for Loss-Difference Conditional Mutual Information, by Hazar Yueksel
View PDF HTML (experimental)
Abstract:Loss-difference conditional mutual information (ld-CMI) uses the smallest of the standard observations in the supersample hierarchy of generalization bounds: it measures what a learner's loss differences reveal about which candidate of each pair it was trained on. Accuracy is known to force information into the model; data processing does not carry such lower bounds to losses. We show, by bounding three moments of the loss differences, that accuracy also forces ld-CMI. For linear predictors with a smooth convex loss of nonzero slope at zero, such as the logistic loss, plus a regularizer whose curvature and growth are both of power $r\ge2$, on product distributions over a scaled sign cube in dimension at least linear in $n$, every proper learner with expected excess risk at most $\varepsilon$ on these distributions at the optimal sample size $n\asymp\varepsilon^{-2+2/r}$ has worst-case ld-CMI of order $n$ bits, and $\Theta(n/(1+(\tau/\varepsilon)^2))$ bits under Gaussian noise of standard deviation $\tau$ on the loss differences. The same holds without a regularizer, at $n\asymp\varepsilon^{-2}$. Consequently, range-scaled ld-CMI bounds cannot vanish on these distributions, although every proper learner's generalization gap is $O(n^{-1/2})$. We also show that model-level information does not determine noisy loss-difference information, and that the growth, slope and dimension conditions are needed, the last up to a logarithm.
Comments: 61 pages, of which 8 pages main text. Code, data and the Lean 4 formalization are in the ancillary files
Subjects: Machine Learning (cs.LG); Information Theory (cs.IT); Machine Learning (stat.ML)
Cite as: arXiv:2610.09206 [cs.LG]
  (or arXiv:2610.09206v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2610.09206
arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Hazar Yueksel [view email]
[v1] Tue, 6 Oct 2026 23:07:16 UTC (3,308 KB)
Full-text links:

Access Paper:

Ancillary-file links:

Ancillary files (details):

Additional Features

Current browse context:

cs.LG
< prev   |   next >
Change to browse by:

References & Citations

Loading...

BibTeX formatted citation

loading...
Data provided by:

Bookmark

BibSonomy Reddit
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?)
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.

Discussion (0)

Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.

Sign in →

No comments yet. Sign in and be the first to say something.

More from arXiv — Machine Learning