Prismix
arXiv — Machine Learning · · 4 min read

Training Under Challenge: Executable Certificates and Challenge-Closed Optimality for Neural Networks

#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:2608.12655 (cs)
[Submitted on 12 Aug 2026]

Title:Training Under Challenge: Executable Certificates and Challenge-Closed Optimality for Neural Networks

View a PDF of the paper titled Training Under Challenge: Executable Certificates and Challenge-Closed Optimality for Neural Networks, by Farhang Yeganegi and 2 other authors
View PDF HTML (experimental)
Abstract:A flat training curve does not reveal whether a neural network has reached a global optimum, is locally trapped, is representation-limited, or is mismatched to its trainer. We introduce Training Under Challenge, an executable-certificate framework in which predeclared, architecture-valid procedures construct complete alternatives in the same certified class and reevaluate the same objective. Any lower-valued candidate is a replayable witness that lower-bounds the checkpoint's empirical global-optimality gap. Passing a finite suite is only suite-relative; global-gap conclusions require a separately justified coverage mechanism. We define a resource-indexed challenge-power modulus that characterizes the largest gap compatible with passage. For squared loss, current block-decrease operators make coverage checkable and yield uniform and realized-residual bounds. We prove the converse frontier: without coverage, a first-order ReLU trainer can reach infinitely many exact conditional head optima while converging to a non-global point. On a channel-gated ResNet-18 distillation problem with known optimum, eight internal challenges cover all 240 audited output directions, and realized-residual bounds lie within factors of 1.74--3.02 of the true gap. Paired predictive certificates separate decoder under-use from representation insufficiency, while quantized-denoising studies demonstrate diagnosis, repair, and current-state recertification.
Comments: 82 pages, 24 figures, 10 tables. Ancillary reproducibility materials included
Subjects: Machine Learning (cs.LG); Machine Learning (stat.ML)
Cite as: arXiv:2608.12655 [cs.LG]
  (or arXiv:2608.12655v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2608.12655
arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Mojtaba Soltanalian [view email]
[v1] Wed, 12 Aug 2026 23:37:57 UTC (7,591 KB)
Full-text links:

Access Paper:

    View a PDF of the paper titled Training Under Challenge: Executable Certificates and Challenge-Closed Optimality for Neural Networks, by Farhang Yeganegi and 2 other authors
  • View PDF
  • HTML (experimental)
  • TeX Source
Ancillary-file links:

Ancillary files (details):

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