Existing studies on preference optimization (PO) have been focused on constructing pairwise preference data following simple heuristics, such as maximizing the margin between chosen and rejected responses based on human (or AI) ratings. In this work, we develop a novel PO framework that provides theoretical guidance to effectively sample rejected responses. To achieve this, we formulate PO as minimizing the negative log-likelihood (NLL) of a probability model and propose a sampling-based solution to estimate its normalization constant via contrastive divergence. We show that these estimative samples can act as rejected responses in PO. Leveraging the connection established between PO and NLL estimation, we propose a novel PO algorithm, called Monte-Carlo-based PO (MC-PO), that applies a MC kernel to sample *hard negatives* w.r.t.~the log-likelihood of the target policy. Intuitively, these hard negatives represent the rejected samples that are most difficult for the current policy to differentiate. We show that MC-PO outperforms existing SOTA baselines on popular alignment benchmarks.

The unique capabilities of Large Language Models (LLMs), such as the natural language text generation ability, position them as strong candidates for providing explanation for recommendations. However, despite the size of the LLM, most existing models struggle to produce zero-shot explanations reliably. To address this issue, we propose a framework called Logic-Scaffolding, that combines the ideas of aspect-based explanation and chain-of-thought prompting to generate explanations through intermediate reasoning steps. In this paper, we share our experience in building the framework and present an interactive demonstration for exploring our results.

Despite the wide applications of neural networks, there have been increasing concerns about their vulnerability issue. While numerous attack and defense techniques have been developed, this work investigates the robustness issue from a new angle: can we design a self-healing neural network that can automatically detect and fix the vulnerability issue by itself? A typical self-healing mechanism is the immune system of a human body. This biology-inspired idea has been used in many engineering designs but has rarely been investigated in deep learning. This paper considers the post-training self-healing of a neural network, and proposes a closed-loop control formulation to automatically detect and fix the errors caused by various attacks or perturbations. We provide a margin-based analysis to explain how this formulation can improve the robustness of a classifier. To speed up the inference, we convert the optimal control problem to Pontryagon's Maximum Principle and solve it via the method of successive approximation. Lastly, we present an error estimation of the proposed framework for neural networks with nonlinear activation functions. We validate the performance of several network architectures against various perturbations. Since the self-healing method does not need a-priori information about data perturbations or attacks, it can handle a broad class of unforeseen perturbations.

We consider adversarial training of deep neural networks through the lens of Bayesian learning and present a principled framework for adversarial training of Bayesian Neural Networks (BNNs) with certifiable guarantees. We rely on techniques from constraint relaxation of non-convex optimisation problems and modify the standard cross-entropy error model to enforce posterior robustness to worst-case perturbations in $\epsilon-$balls around input points. We illustrate how the resulting framework can be combined with methods commonly employed for approximate inference of BNNs. In an empirical investigation, we demonstrate that the presented approach enables training of certifiably robust models on MNIST, FashionMNIST, and CIFAR-10 and can also be beneficial for uncertainty calibration. Our method is the first to directly train certifiable BNNs, thus facilitating their deployment in safety-critical applications.