# PCA-guided Activation Scaling for Monotonic Bidirectional Control over LLM Sycophancy

arXiv: https://arxiv.org/abs/2608.16650 · HTML: https://mlsanity.com/paper/2608.16650/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 37 references that are in the map.
- First posted on arXiv 17 Aug 2026.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Discovering Language Model Behaviors with Model-Written Evaluations](https://mlsanity.com/paper/2212.09251/) (2022)
- [Whose Opinions Do Language Models Reflect?](https://mlsanity.com/paper/2303.17548/) (2023)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Rewarded soups: towards Pareto-optimal alignment by interpolating weights fine-tuned on diverse rewards](https://mlsanity.com/paper/2306.04488/) (2023)
- [Extracting Latent Steering Vectors from Pretrained Language Models](https://mlsanity.com/paper/2205.05124/) (2022)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (2024)
- [Simple synthetic data reduces sycophancy in large language models](https://mlsanity.com/paper/2308.03958/) (2023)
- [Analyzing the Generalization and Reliability of Steering Vectors](https://mlsanity.com/paper/2407.12404/) (2024)
- [SycEval: Evaluating LLM Sycophancy](https://mlsanity.com/paper/2502.08177/) (2025)
- [Calibrating Large Language Models with Sample Consistency](https://mlsanity.com/paper/2402.13904/) (2024)
- [Improving Activation Steering in Language Models with Mean-Centring](https://mlsanity.com/paper/2312.03813/) (2023)
- [From Yes-Men to Truth-Tellers: Addressing Sycophancy in Large Language Models with Pinpoint Tuning](https://mlsanity.com/paper/2409.01658/) (2024)
- [Angular Steering: Behavior Control via Rotation in Activation Space](https://mlsanity.com/paper/2510.26243/) (2025)
- [Steering Large Language Models using Conceptors: Improving Addition-Based Activation Engineering](https://mlsanity.com/paper/2410.16314/) (2024)
- [Sycophancy Is Not One Thing: Causal Separation of Sycophantic Behaviors in LLMs](https://mlsanity.com/paper/2509.21305/) (2025)
- [Activation Scaling for Steering and Interpreting Language Models](https://mlsanity.com/paper/2410.04962/) (2024)
- [Controlling Recurrent Neural Networks by Conceptors](https://mlsanity.com/paper/1403.3369/) (2014)

## Abstract (arXiv)

Large language models (LLMs) exhibit sycophancy, a tendency to agree with user beliefs regardless of factual accuracy. This can reinforce misconceptions, but eliminating it entirely risks over-correction against valid opinions. Effective control must therefore both reduce and increase sycophancy with predictable and gradual effect. Yet, existing methods fail to ensure a bidirectional and monotonic relationship between steering strength and behavioral outcome across models and datasets. We introduce PCA-guided Activation Scaling (PAS), an activation steering framework that decomposes residual stream activations into a PCA-identified sycophancy-honesty subspace and an orthogonal residual, then applies distinct scaling exponents to achieve monotonic, bidirectional control. Across three LLMs and three datasets, PAS achieves strong monotonicity (Spearman ρ = +0.92) and an average shift of 15.4% per direction, compared with 8.7% for the baselines. Ablation studies confirm that the decomposition, asymmetric exponents, and layer selection are each essential for maintaining monotonic control. The data and code are available at https://github.com/Bellafc/PCS.