Large Language Models (LLMs) demonstrate the ability to solve reasoning and mathematical problems using the Chain-of-Thought (CoT) technique. Expanding CoT length, as seen in models such as DeepSeek-R1, significantly enhances this reasoning for complex problems, but requires costly and high-quality long CoT data and fine-tuning. This work, inspired by the deep thinking paradigm of DeepSeek-R1, utilizes a steering technique to enhance the reasoning ability of an LLM without external datasets. Our method first employs Sparse Autoencoders (SAEs) to extract interpretable features from vanilla CoT. These features are then used to steer the LLM’s internal states during generation. Recognizing that many LLMs do not have corresponding pre-trained SAEs, we further introduce a novel SAE-free steering algorithm, which directly computes steering directions from the residual activations of an LLM, obviating the need for an explicit SAE. Experimental results demonstrate that both our SAE-based and subsequent SAE-free steering algorithms significantly enhance the reasoning capabilities of LLMs.

Large language models (LLMs) store vast amounts of information, making them powerful yet raising privacy and safety concerns when selective knowledge removal is required. Existing unlearning strategies, ranging from gradient-based fine-tuning and model editing to sparse autoencoder (SAE) steering, either lack interpretability or fail to provide a robust defense against adversarial prompts. We propose **S**AE–Guided **S**ubspace **P**rojection **U**nlearning (**SSPU**), a novel framework that leverages SAE features to drive targeted updates in the model’s parameter space, enabling precise, interpretable, and robust unlearning. SSPU’s three-stage pipeline performs data-driven layer and feature selection, subspace construction via QR decomposition, and constrained optimization that controls activations into an “irrelevant” subspace while preserving retained knowledge. Overall, we use SAE features to construct a subspace that supervises unlearning, refining the loss and adding a regularization term to guide interpretable parameter updates. In experiments on the WMDP–Cyber forget set and three utility benchmarks (MMLU, TruthfulQA, GSM8K), SSPU reduces harmful knowledge accuracy by 3.22% compared to the strongest baseline. It also improves adversarial robustness, lowering malicious accuracy under jailbreak prompts compared to baselines. Our findings expose the limitations of prior unlearning methods and demonstrate how interpretable subspace-guided optimization can achieve robust, controllable model behavior.