The Gumbel-Softmax probability distribution allows learning discrete tokens in generative learning, while the Gumbel-Argmax probability distribution is useful in learning discrete structures in discriminative learning. Despite the efforts invested in optimizing these probability models, their statistical properties are under-explored. In this work, we investigate their representation properties and determine for which families of parameters these probability distributions are complete, i.e., can represent any probability distribution, and minimal, i.e., can represent a probability distribution uniquely. We rely on convexity and differentiability to determine these statistical conditions and extend this framework to general probability models, such as Gaussian-Softmax and Gaussian-Argmax. We experimentally validate the qualities of these extensions, which enjoy a faster convergence rate. We conclude the analysis by identifying two sets of parameters that satisfy these assumptions and thus admit a complete and minimal representation. Our contribution is theoretical with supporting practical evaluation.

Expectation propagation (EP) is a family of algorithms for performing approximate inference in probabilistic models. The updates of EP involve the evaluation of moments -- expectations of certain functions -- which can be estimated from Monte Carlo (MC) samples. However, the updates are not robust to MC noise when performed naively, and various prior works have attempted to address this issue in different ways. In this work, we provide a novel perspective on the moment-matching updates of EP; namely, that they perform natural-gradient-based optimisation of a variational objective. We use this insight to motivate two new EP variants, with updates that are particularly well-suited to MC estimation; they remain stable and are most sample-efficient when estimated with just a single sample. These new variants combine the benefits of their predecessors and address key weaknesses. In particular, they are easier to tune, offer an improved speed-accuracy trade-off, and do not rely on the use of debiasing estimators. We demonstrate their efficacy on a variety of probabilistic inference tasks.

We consider the task of active geo-localization (AGL) in which an agent uses a sequence of visual cues observed during aerial navigation to find a target specified through multiple possible modalities. This could emulate a UAV involved in a search-and-rescue operation navigating through an area, observing a stream of aerial images as it goes. The AGL task is associated with two important challenges. Firstly, an agent must deal with a goal specification in one of multiple modalities (e.g., through a natural language description) while the search cues are provided in other modalities (aerial imagery). The second challenge is limited localization time (e.g., limited battery life, urgency) so that the goal must be localized as efficiently as possible, i.e. the agent must effectively leverage its sequentially observed aerial views when searching for the goal. To address these challenges, we propose GOMAA-Geo - a goal modality agnostic active geo-localization agent - for zeroshot generalization between different goal modalities. Our approach combines cross-modality contrastive learning to align representations across modalities with supervised foundation model pretraining and reinforcement learning to obtain highly effective navigation and localization policies. Through extensive evaluations, we show that GOMAA-Geo outperforms alternative learnable approaches and that it generalizes across datasets - e.g., to disaster-hit areas without seeing a single disaster scenario during training - and goal modalities - e.g., to ground-level imagery or textual descriptions, despite only being trained with goals specified as aerial views. Code and models will be made publicly available at this link.

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}}