# Limits of Reliability and Scaling in Language Models

arXiv: https://arxiv.org/abs/2607.14112 · HTML: https://mlsanity.com/paper/2607.14112/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 54 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 30 of 37)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Get To The Point: Summarization with Pointer-Generator Networks](https://mlsanity.com/paper/1704.04368/) (2017)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [Hallucination is Inevitable: An Innate Limitation of Large Language Models](https://mlsanity.com/paper/2401.11817/) (2024)
- [Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks](https://mlsanity.com/paper/2002.02561/) (2020)
- [Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks](https://mlsanity.com/paper/2006.13198/) (2020)
- [Tensor Programs II: Neural Tangent Kernel for Any Architecture](https://mlsanity.com/paper/2006.14548/) (2020)
- [On Exposure Bias, Hallucination and Domain Shift in Neural Machine Translation](https://mlsanity.com/paper/2005.03642/) (2020)
- [Broken Neural Scaling Laws](https://mlsanity.com/paper/2210.14891/) (2022)
- [WritingBench: A Comprehensive Benchmark for Generative Writing](https://mlsanity.com/paper/2503.05244/) (2025)
- [EQ-Bench: An Emotional Intelligence Benchmark for Large Language Models](https://mlsanity.com/paper/2312.06281/) (2023)
- [Chinchilla Scaling: A replication attempt](https://mlsanity.com/paper/2404.10102/) (2024)
- [When AI Benchmarks Plateau: A Systematic Study of Benchmark Saturation](https://mlsanity.com/paper/2602.16763/) (2026)
- [Understanding Scaling Laws with Statistical and Approximation Theory for Transformer Neural Networks on Intrinsically Low-dimensional Data](https://mlsanity.com/paper/2411.06646/) (2024)
- [Deriving Neural Scaling Laws from the statistics of natural language](https://mlsanity.com/paper/2602.07488/) (2026)
- [Bayesian scaling laws for in-context learning](https://mlsanity.com/paper/2410.16531/) (2024)
- [Revisiting LLM Reasoning via Information Bottleneck](https://mlsanity.com/paper/2507.18391/) (2025)
- [On the Fundamental Limits of LLMs at Scale](https://mlsanity.com/paper/2511.12869/) (2025)

## Abstract (arXiv)

Large language models (LLMs) are trained and evaluated as though perfect reliability is achievable for any task given sufficient scale. We show that this assumption is information-theoretically unjustified. Every generative task has a reliability ceiling that no model can exceed, determined by how much output uncertainty is resolvable from observable context. The gap decomposes into a resolvable component closable with additional context and a subjective component inherent to task ambiguity. Autoregressive generation further degrades this ceiling at a rate governed by the task's dependency kernel, which quantifies inter-token correlations in the output. From these two primitives, we derive a first-principles scaling law where LLM performance is bottlenecked by the scarcer resource: training data or model capacity. This law recovers the Chinchilla scaling law as a special case and provides a structural account of when scaling improves reliability. Beyond scaling, our framework unifies diverse practical phenomena, such as the benefits of retrieval-augmentation and the spectral mechanics of catastrophic forgetting. Our work formalizes the resource-complexity tradeoffs that govern model performance across domains, offering a unified theory of performance limits in generative language models.