Having an LLM that aligns with human preferences is essential for accommodating individual needs, such as maintaining writing style or generating specific topics of interest. The majority of current alignment methods rely on fine-tuning or prompting, which can be either costly or difficult to control. Model steering algorithms, which modify the model output by constructing specific steering directions, are typically easy to implement and optimization-free. However, their capabilities are typically limited to steering the model into one of the two directions (i.e., bidirectional steering), and there has been no theoretical understanding to guarantee their performance. In this work, we propose a theoretical framework to understand and quantify the model steering methods. Inspired by the framework, we propose a confident direction steering method (CONFST) that steers LLMs via modifying their activations at inference time. More specifically, CONFST builds a confident direction that is closely aligned with users' preferences, and this direction is then added to the activations of the LLMs to effectively steer the model output. Our approach offers three key advantages over popular bidirectional model steering methods: 1) It is more powerful, since multiple (i.e. more than two) users' preferences can be aligned simultaneously; 2) It is simple to implement, since there is no need to determine which layer to add the steering vector to; 3) No explicit user instruction is required. We validate our method on GPT-2 XL (1.5B), Mistral (7B) and Gemma-it (9B) models for tasks that require shifting the output of LLMs across various topics and styles, achieving superior performance over competing methods.

While the Transformer architecture has achieved remarkable success across various domains, a thorough theoretical foundation explaining its optimization dynamics is yet to be fully developed. In this study, we aim to bridge this understanding gap by answering the following two core questions: (1) Which types of Transformer architectures allow Gradient Descent (GD) to achieve guaranteed convergence? and (2) Under what initial conditions and architectural specifics does the Transformer achieve rapid convergence during training? By analyzing the loss landscape of a single Transformer layer using Softmax and Gaussian attention kernels, our work provides concrete answers to these questions. Our findings demonstrate that, with appropriate weight initialization, GD can train a Transformer model (with either kernel type) to achieve a global optimal solution, especially when the input embedding dimension is large. Nonetheless, certain scenarios highlight potential pitfalls: training a Transformer using the Softmax attention kernel may sometimes lead to suboptimal local solutions. In contrast, the Gaussian attention kernel exhibits a much favorable behavior. Our empirical study further validate the theoretical findings.