Robust Probabilistic Model Checking with Continuous Reward Domains

Probabilistic model checking traditionally verifies properties on the expected value of a measure of interest. This restriction may fail to capture the quality of service of a significant proportion of a system's runs, especially when the probability distribution of the measure of interest is poorly represented by its expected value due to heavy-tail behaviors or multiple modalities. Recent works inspired by distributional reinforcement learning use discrete histograms to approximate integer reward distribution, but they struggle with continuous reward space and present challenges in balancing accuracy and scalability. We propose a novel method for handling both continuous and discrete reward distributions in Discrete Time Markov Chains using moment matching with Erlang mixtures. By analytically deriving higher-order moments through Moment Generating Functions, our method approximates the reward distribution with theoretically bounded error while preserving the statistical properties of the true distribution. This detailed distributional insight enables the formulation and robust model checking of quality properties based on the entire reward distribution function, rather than restricting to its expected value. We include a theoretical foundation ensuring bounded approximation errors, along with an experimental evaluation demonstrating our method's accuracy and scalability in practical model-checking problems.

Almost Surely Safe Alignment of Large Language Models at Inference-Time

Even highly capable large language models (LLMs) can produce biased or unsafe responses, and alignment techniques, such as RLHF, aimed at mitigating this issue, are expensive and prone to overfitting as they retrain the LLM. This paper introduces a novel inference-time alignment approach that ensures LLMs generate safe responses almost surely, i.e., with a probability approaching one. We achieve this by framing the safe generation of inference-time responses as a constrained Markov decision process within the LLM's latent space. Crucially, we augment a safety state that tracks the evolution of safety constraints and enables us to demonstrate formal safety guarantees upon solving the MDP in the latent space. Building on this foundation, we propose InferenceGuard, a practical implementation that safely aligns LLMs without modifying the model weights. Empirically, we demonstrate InferenceGuard effectively balances safety and task performance, outperforming existing inference-time alignment methods in generating safe and aligned responses.

Probabilistic Counterexample Guidance for Safer Reinforcement Learning (Extended Version)

Safe exploration aims at addressing the limitations of Reinforcement Learning (RL) in safety-critical scenarios, where failures during trial-and-error learning may incur high costs. Several methods exist to incorporate external knowledge or to use proximal sensor data to limit the exploration of unsafe states. However, reducing exploration risks in unknown environments, where an agent must discover safety threats during exploration, remains challenging. In this paper, we target the problem of safe exploration by guiding the training with counterexamples of the safety requirement. Our method abstracts both continuous and discrete state-space systems into compact abstract models representing the safety-relevant knowledge acquired by the agent during exploration. We then exploit probabilistic counterexample generation to construct minimal simulation submodels eliciting safety requirement violations, where the agent can efficiently train offline to refine its policy towards minimising the risk of safety violations during the subsequent online exploration. We demonstrate our method's effectiveness in reducing safety violations during online exploration in preliminary experiments by an average of 40.3% compared with QL and DQN standard algorithms and 29.1% compared with previous related work, while achieving comparable cumulative rewards with respect to unrestricted exploration and alternative approaches.

Revealing Reliable Signatures by Learning Top-Rank Pairs

Signature verification, as a crucial practical documentation analysis task, has been continuously studied by researchers in machine learning and pattern recognition fields. In specific scenarios like confirming financial documents and legal instruments, ensuring the absolute reliability of signatures is of top priority. In this work, we proposed a new method to learn "top-rank pairs" for writer-independent offline signature verification tasks. By this scheme, it is possible to maximize the number of absolutely reliable signatures. More precisely, our method to learn top-rank pairs aims at pushing positive samples beyond negative samples, after pairing each of them with a genuine reference signature. In the experiment, BHSig-B and BHSig-H datasets are used for evaluation, on which the proposed model achieves overwhelming better pos@top (the ratio of absolute top positive samples to all of the positive samples) while showing encouraging performance on both Area Under the Curve (AUC) and accuracy.

Optimal Rejection Function Meets Character Recognition Tasks

In this paper, we propose an optimal rejection method for rejecting ambiguous samples by a rejection function. This rejection function is trained together with a classification function under the framework of Learning-with-Rejection (LwR). The highlights of LwR are: (1) the rejection strategy is not heuristic but has a strong background from a machine learning theory, and (2) the rejection function can be trained on an arbitrary feature space which is different from the feature space for classification. The latter suggests we can choose a feature space that is more suitable for rejection. Although the past research on LwR focused only on its theoretical aspect, we propose to utilize LwR for practical pattern classification tasks. Moreover, we propose to use features from different CNN layers for classification and rejection. Our extensive experiments of notMNIST classification and character/non-character classification demonstrate that the proposed method achieves better performance than traditional rejection strategies.