Generative modelling paradigms based on denoising diffusion processes have emerged as a leading candidate for conditional sampling in inverse problems. In many real-world applications, we often have access to large, expensively trained unconditional diffusion models, which we aim to exploit for improving conditional sampling. Most recent approaches are motivated heuristically and lack a unifying framework, obscuring connections between them. Further, they often suffer from issues such as being very sensitive to hyperparameters, being expensive to train or needing access to weights hidden behind a closed API. In this work, we unify conditional training and sampling using the mathematically well-understood Doob's h-transform. This new perspective allows us to unify many existing methods under a common umbrella. Under this framework, we propose DEFT (Doob's h-transform Efficient FineTuning), a new approach for conditional generation that simply fine-tunes a very small network to quickly learn the conditional $h$-transform, while keeping the larger unconditional network unchanged. DEFT is much faster than existing baselines while achieving state-of-the-art performance across a variety of linear and non-linear benchmarks. On image reconstruction tasks, we achieve speedups of up to 1.6$\times$, while having the best perceptual quality on natural images and reconstruction performance on medical images.

Epigraphs Stone inscriptions are important artifacts in the field of archaeology. Although several cultures follow different methods as primary forms of writing, for example, palm leaf manuscripts by Dravidians, papyrus manuscripts by Egyptians, and Animal Hide manuscripts by several European civilizations, stone inscriptions remained a robust secondary form of writing across all the civilizations that practiced writing. This is mainly due to the robustness associated with the medium, as it is impossible to manipulate, change the stone inscriptions and very difficult to mutilate them. Therefore, several historically important documents such as treaties, grants, and tombstones are engraved in stones.

Generative models on discrete state-spaces have a wide range of potential applications, particularly in the domain of natural sciences. In continuous state-spaces, controllable and flexible generation of samples with desired properties has been realized using guidance on diffusion and flow models. However, these guidance approaches are not readily amenable to discrete state-space models. Consequently, we introduce a general and principled method for applying guidance on such models. Our method depends on leveraging continuous-time Markov processes on discrete state-spaces, which unlocks computational tractability for sampling from a desired guided distribution. We demonstrate the utility of our approach, Discrete Guidance, on a range of applications including guided generation of images, small-molecules, DNA sequences and protein sequences.

In this paper, we seek to learn a robot policy guaranteed to satisfy state constraints. To encourage constraint satisfaction, existing RL algorithms typically rely on Constrained Markov Decision Processes and discourage constraint violations through reward shaping. However, such soft constraints cannot offer verifiable safety guarantees. To address this gap, we propose POLICEd RL, a novel RL algorithm explicitly designed to enforce affine hard constraints in closed-loop with a black-box environment. Our key insight is to force the learned policy to be affine around the unsafe set and use this affine region as a repulsive buffer to prevent trajectories from violating the constraint. We prove that such policies exist and guarantee constraint satisfaction. Our proposed framework is applicable to both systems with continuous and discrete state and action spaces and is agnostic to the choice of the RL training algorithm. Our results demonstrate the capacity of POLICEd RL to enforce hard constraints in robotic tasks while significantly outperforming existing methods.

Much work has been done to develop causal reasoning techniques across a number of domains, however the utilisation of causality within autonomous systems is still in its infancy. Autonomous systems would greatly benefit from the integration of causality through the use of representations such as structural causal models (SCMs). The system would be afforded a higher level of transparency, it would enable post-hoc explanations of outcomes, and assist in the online inference of exogenous variables. These qualities are either directly beneficial to the autonomous system or a valuable step in building public trust and informing regulation. To such an end we present a case study in which we describe a module-based autonomous driving system comprised of SCMs. Approaching this task requires considerations of a number of challenges when dealing with a system of great complexity and size, that must operate for extended periods of time by itself. Here we describe these challenges, and present solutions. The first of these is SCM contexts, with the remainder being three new variable categories -- two of which are based upon functional programming monads. Finally, we conclude by presenting an example application of the causal capabilities of the autonomous driving system. In this example, we aim to attribute culpability between vehicular agents in a hypothetical road collision incident.

We study the generalization behavior of Markov Logic Networks (MLNs) across relational structures of different sizes. Multiple works have noticed that MLNs learned on a given domain generalize poorly across domains of different sizes. This behavior emerges from a lack of internal consistency within an MLN when used across different domain sizes. In this paper, we quantify this inconsistency and bound it in terms of the variance of the MLN parameters. The parameter variance also bounds the KL divergence between an MLN's marginal distributions taken from different domain sizes. We use these bounds to show that maximizing the data log-likelihood while simultaneously minimizing the parameter variance corresponds to two natural notions of generalization across domain sizes. Our theoretical results apply to Exponential Random Graphs and other Markov network based relational models. Finally, we observe that solutions known to decrease the variance of the MLN parameters, like regularization and Domain-Size Aware MLNs, increase the internal consistency of the MLNs. We empirically verify our results on four different datasets, with different methods to control parameter variance, showing that controlling parameter variance leads to better generalization.

ChatGPT is instruct-tuned to generate general and human-expected content to align with human preference through Reinforcement Learning from Human Feedback (RLHF), meanwhile resulting in generated responses not salient enough. Therefore, in this case, ChatGPT may fail to satisfy domain requirements in zero-shot settings, leading to poor ROUGE scores. Inspired by the In-Context Learning (ICL) and retelling ability of ChatGPT, this paper proposes PADS, a \textbf{P}ipeline for \textbf{A}ssisting ChatGPT in \textbf{D}omain \textbf{S}ummarization. PADS consists of a retriever to retrieve similar examples from corpora and a rank model to rerank the multiple candidate summaries generated by ChatGPT. Specifically, given an inference document, we first retrieve an in-context demonstration via the retriever. Then, we require ChatGPT to generate $k$ candidate summaries for the inference document at a time under the guidance of the retrieved demonstration. Finally, the rank model independently scores the $k$ candidate summaries according to their quality and selects the optimal one. We extensively explore dense and sparse retrieval methods to select effective demonstrations for reference and efficiently train the rank model to reflect the quality of candidate summaries for each given summarized document. Additionally, PADS contains merely 400M trainable parameters originating from the rank model and we merely collect 2.5k data to train it. We evaluate PADS on five datasets from different domains, and the result indicates that each module in PADS is committed to effectively guiding ChatGPT to generate salient summaries fitting different domain requirements. Specifically, in the popular summarization dataset Gigaword, PADS achieves over +8 gain on ROUGE-L, compared with the naive ChatGPT in the zero-shot setting. \footnote{Our code are available at \url{https://github.com/jungao1106/PADS}}

Modern neural networks are often massively overparameterized leading to high compute costs during training and at inference. One effective method to improve both the compute and energy efficiency of neural networks while maintaining good performance is structured pruning, where full network structures (e.g. neurons or convolutional filters) that have limited impact on the model output are removed. In this work, we propose Bayesian Model Reduction for Structured pruning (BMRS), a fully end-to-end Bayesian method of structured pruning. BMRS is based on two recent methods: Bayesian structured pruning with multiplicative noise, and Bayesian model reduction (BMR), a method which allows efficient comparison of Bayesian models under a change in prior. We present two realizations of BMRS derived from different priors which yield different structured pruning characteristics: 1) BMRS_N with the truncated log-normal prior, which offers reliable compression rates and accuracy without the need for tuning any thresholds and 2) BMRS_U with the truncated log-uniform prior that can achieve more aggressive compression based on the boundaries of truncation. Overall, we find that BMRS offers a theoretically grounded approach to structured pruning of neural networks yielding both high compression rates and accuracy. Experiments on multiple datasets and neural networks of varying complexity showed that the two BMRS methods offer a competitive performance-efficiency trade-off compared to other pruning methods.

A key task in actuarial modelling involves modelling the distributional properties of losses. Classic (distributional) regression approaches like Generalized Linear Models (GLMs; Nelder and Wedderburn, 1972) are commonly used, but challenges remain in developing models that can (i) allow covariates to flexibly impact different aspects of the conditional distribution, (ii) integrate developments in machine learning and AI to maximise the predictive power while considering (i), and, (iii) maintain a level of interpretability in the model to enhance trust in the model and its outputs, which is often compromised in efforts pursuing (i) and (ii). We tackle this problem by proposing a Distributional Refinement Network (DRN), which combines an inherently interpretable baseline model (such as GLMs) with a flexible neural network-a modified Deep Distribution Regression (DDR; Li et al., 2019) method. Inspired by the Combined Actuarial Neural Network (CANN; Schelldorfer and W{\''u}thrich, 2019), our approach flexibly refines the entire baseline distribution. As a result, the DRN captures varying effects of features across all quantiles, improving predictive performance while maintaining adequate interpretability. Using both synthetic and real-world data, we demonstrate the DRN's superior distributional forecasting capacity. The DRN has the potential to be a powerful distributional regression model in actuarial science and beyond.

Reward learning involves inferring and shaping the underlying reward function from observed human demonstrations and feedback. Inverse reinforcement learning (IRL) and reinforcement learning from human feedback (RLHF, also known as preference-based reinforcement learning) are key methodologies in reward learning, applied in various sequential decision-making tasks such as games [1-3], robotics [4-6], and language models [7-11]. Particularly in the recent drastic development of large language models (LLMs), RLHF has played a crucial role in fine-tuning models to better align with human preferences [10]. However, despite the notable empirical success of these algorithms, a significant gap remains in the theoretical analysis of IRL and RLHF, limiting us to guarantee their reliability. This work aims to bridge this gap by proposing a novel theoretical framework for offline IRL and RLHF. IRL aims to infer a reward function that aligns with an expert behavior from demonstrations [12, 13]. Typical IRL algorithms employ a bi-level optimization framework within the context of maximum likelihood estimation (MLE). In this framework, the inner optimization evaluates the policy based on the current reward parameters, while the outer optimization updates these parameters to better match observed expert behavior. These algorithms have been extensively explored in the literature [14-18], and their convergence is studied in both online settings [17] and offline settings [18].