arXiv Machine Learning

Objects Without Morphisms: What LLMs for Mathematics Do Not Represent

arXiv AI
1d ago

Knowing When Not to Answer: Cross-Domain and Multi-Turn Generalization of Latent Underspecification Signals

The paper presents a new multi‑turn benchmark of 423 conversations with 1,661 labeled turn‑states to study when language models should refrain from answering. It shows that probes for unanswerability transfer well across datasets that share the same underlying signal, but fail to generalise to other forms of epistemic uncertainty. While a calibrated probe can identify underspecified turns more accurately than chance, it does not consistently improve overall generation quality compared to standard methods.

By Jerzy Kami\'nski, Ilya Galyukshev, Artem Kuznetsov, Danil Fedorov, Kirill Redko, Sergey Chuprin, Aidar Shumbalov, Stanislav Chumakov, Anna Kalyuzhnaya
arXiv AI
Jun 16

The Faithfulness Gap: Certifying Semantic Equivalence Between Natural-Language and Formal Mathematical Statements

arXiv:2606. 16541v1 Announce Type: new Abstract: Autoformalization, translating natural-language mathematics into formal proof assistants, is bottlenecked not by translation fluency but by \emph{faithfulness}: a formal statement can typecheck and be provable, yet still encode a different theorem than the source intended.

By Noor Islam S. Mohammad, Tamim Sheikh
arXiv AI
Jul 10

Rethinking LLM-as-a-Judge: Representation-as-a-Judge with Small Language Models via Semantic Capacity Asymmetry

arXiv:2601. 22588v2 Announce Type: replace-cross Abstract: Large language models (LLMs) are widely used as reference-free evaluators via prompting, but this "LLM-as-a-Judge" paradigm is costly, opaque, and sensitive to prompt design.

By Zhuochun Li, Yong Zhang, Ming Li, Yuelyu Ji, Yiming Zeng, Ning Cheng, Yun Zhu, Yanmeng Wang, Shaojun Wang, Jing Xiao, Daqing He
arXiv Machine Learning
Aug 19

Thinking in a Low-Resource Language: What SFT Builds, What RL Fixes, What Accuracy Cannot See

The paper evaluates how three large mixture‑of‑experts models (Alibaba, OpenAI, NVIDIA) can be fine‑tuned to reason in a low‑resource language, specifically Greek. Accuracy metrics show little change, but the authors uncover significant qualitative improvements: after supervised fine‑tuning, models reason in Greek on ~98% of items, with better grammaticality and retained general ability. Reinforcement learning with pre‑registered rewards further eliminates reasoning‑channel leaks and format skips, while the Greek‑reasoning habit remains robust to an accuracy‑only gradient.

By Ayoub Kirouane, Christos Petrocheilos
arXiv Machine Learning
Sep 17

A Calibrated Instrument for Measuring How Inference Optimizations Affect Output Quality

The paper introduces a calibrated instrument for rigorously measuring how inference optimizations—such as quantization, early‑exit, and speculative decoding—affect the output quality of large language models. It uses a formally calibrated LLM judge that verifies no systematic bias between statistically equivalent outputs and includes a null condition to ensure measured differences are zero. Applying this method, the authors find that a 4‑bit model is indistinguishable from its 16‑bit counterpart, while 3‑bit quantization and early‑exit techniques incur measurable quality losses that vary by language and task, and that token‑certainty‑based acceptance rules cannot reliably identify impactful errors.

By Jerry Kaplan
arXiv Machine Learning
Sep 3

The Implications of Linguistic Illegibility for LLM Security

The paper introduces the concept of "linguistic illegibility," describing how a large language model’s (LLM) language outputs and extracted linguistic features may not accurately reflect its internal computations. It argues that because LLMs compute primarily in activation spaces, any reliance on linguistic self‑reporting for security—such as chain‑of‑thought monitoring or constitutional self‑critique—cannot be fully reliable. The authors propose taint tracking and other sandboxing techniques that do not depend on the model’s linguistic state as a more robust security foundation.

By James Mickens