# The Alignment Bottleneck

arXiv: https://arxiv.org/abs/2509.15932 · HTML: https://mlsanity.com/paper/2509.15932/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 62 of its 78 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 30 of 62)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [RLAIF vs. RLHF: Scaling Reinforcement Learning from Human Feedback with AI Feedback](https://mlsanity.com/paper/2309.00267/) (2023)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [AI safety via debate](https://mlsanity.com/paper/1805.00899/) (2018)
- [The Effects of Reward Misspecification: Mapping and Mitigating Misaligned Models](https://mlsanity.com/paper/2201.03544/) (2022)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [The Alignment Problem from a Deep Learning Perspective](https://mlsanity.com/paper/2209.00626/) (2022)
- [A Roadmap to Pluralistic Alignment](https://mlsanity.com/paper/2402.05070/) (2024)
- [Mitigating the Alignment Tax of RLHF](https://mlsanity.com/paper/2309.06256/) (2023)
- [Scaling Laws for Reward Model Overoptimization in Direct Alignment Algorithms](https://mlsanity.com/paper/2406.02900/) (2024)
- [Goal Misgeneralization in Deep Reinforcement Learning](https://mlsanity.com/paper/2105.14111/) (2021)
- [Reward Tampering Problems and Solutions in Reinforcement Learning: A Causal Influence Diagram Perspective](https://mlsanity.com/paper/1908.04734/) (2019)
- [Rule Based Rewards for Language Model Safety](https://mlsanity.com/paper/2411.01111/) (2024)
- [Controllable Preference Optimization: Toward Controllable Multi-Objective Alignment](https://mlsanity.com/paper/2402.19085/) (2024)

## Built on by (most cited first, 1 of 1)

- [Generative Models Erode Human Temporal Learning Through Market Selection](https://mlsanity.com/paper/2606.06572/) (2026)

## Abstract (arXiv)

Large language models improve with scale, yet feedback-based alignment still exhibits systematic deviations from intended behavior. Motivated by bounded rationality in economics and cognitive science, we view judgment as resource-limited and feedback as a constrained channel. On this basis, we model the loop as a two-stage cascade U → H → Y given S, with cognitive capacity Ccog|S and average total capacity barCtot|S. Our main result is a capacity-coupled Alignment Performance Interval. It pairs a data size-independent Fano lower bound proved on a separable codebook mixture with a PAC-Bayes upper bound whose KL term is controlled by the same channel via m , barCtot|S. The PAC-Bayes bound becomes an upper bound on the same true risk when the canonical observable loss is used and the dataset is drawn from the same mixture. Under these matched conditions, both limits are governed by a single capacity. Consequences include that, with value complexity and capacity fixed, adding labels alone cannot cross the bound; attaining lower risk on more complex targets requires capacity that grows with log M; and once useful signal saturates capacity, further optimization tends to fit channel regularities, consistent with reports of sycophancy and reward hacking. The analysis views alignment as interface engineering: measure and allocate limited capacity, manage task complexity, and decide where information is spent.