Since the debut of DPO, it has been shown that aligning a target LLM with human preferences via the KL-constrained RLHF loss is mathematically equivalent to a special kind of reward modeling task. Concretely, the task requires: 1) using the target LLM to parameterize the reward model, and 2) tuning the reward model so that it has a 1:1 linear relationship with the true reward. However, we identify a significant issue: the DPO loss might have multiple minimizers, of which only one satisfies the required linearity condition. The problem arises from a well-known issue of the underlying Bradley-Terry preference model: it does not always have a unique maximum likelihood estimator (MLE). Consequently,the minimizer of the RLHF loss might be unattainable because it is merely one among many minimizers of the DPO loss. As a better alternative, we propose an energy-based model (EBM) that always has a unique MLE, inherently satisfying the linearity requirement. To approximate the MLE in practice, we propose a contrastive loss named Energy Preference Alignment (EPA), wherein each positive sample is contrasted against one or more strong negatives as well as many free weak negatives. Theoretical properties of our EBM enable the approximation error of EPA to almost surely vanish when a sufficient number of negatives are used. Empirically, we demonstrate that EPA consistently delivers better performance on open benchmarks compared to DPO, thereby showing the superiority of our EBM.

Alignment, endowing a pre-trained Large language model (LLM) with the ability to follow instructions, is crucial for its real-world applications. Conventional supervised fine-tuning (SFT) methods formalize it as causal language modeling typically with a cross-entropy objective, requiring a large amount of high-quality instruction-response pairs. However, the quality of widely used SFT datasets can not be guaranteed due to the high cost and intensive labor for the creation and maintenance in practice. To overcome the limitations associated with the quality of SFT datasets, we introduce a novel \textbf{p}reference-\textbf{o}riented supervised \textbf{f}ine-\textbf{t}uning approach, namely PoFT. The intuition is to boost SFT by imposing a particular preference: \textit{favoring the target model over aligned LLMs on the same SFT data.} This preference encourages the target model to predict a higher likelihood than that predicted by the aligned LLMs, incorporating assessment information on data quality (i.e., predicted likelihood by the aligned LLMs) into the training process. Extensive experiments are conducted, and the results validate the effectiveness of the proposed method. PoFT achieves stable and consistent improvements over the SFT baselines across different training datasets and base models. Moreover, we prove that PoFT can be integrated with existing SFT data filtering methods to achieve better performance, and further improved by following preference optimization procedures, such as DPO.

In recent years, Parameter-Efficient Fine-Tuning (PEFT) methods like Low-Rank Adaptation (LoRA) have significantly enhanced the adaptability of large-scale pre-trained models. Weight-Decomposed Low-Rank Adaptation (DoRA) improves upon LoRA by separating the magnitude and direction components of the weight matrix, leading to superior performance. However, DoRA's improvements are limited to the vertical dimension, resulting in an asymmetrical pattern between horizontal and vertical dimensions. This paper introduces BoRA, an innovative extension of LoRA and DoRA, characterized by symmetrical properties across horizontal and vertical dimensions. Our approach optimizes the weight matrix symmetrically Figure 1: Structure of BoRA: blue indicates frozen parameters, by adjusting both column-wise and green indicates trainable parameters.