Idempotent generative networks (IGNs) are a new line of generative models based on idempotent mapping to a target manifold. IGNs support both single-and multi-step generation, allowing for a flexible trade-off between computational cost and sample quality. But similar to Generative Adversarial Networks (GANs), conventional IGNs require adversarial training and are prone to training instabilities and mode collapse. Diffusion and score-based models are popular approaches to generative modeling that iteratively transport samples from one distribution, usually a Gaussian, to a target data distribution. These models have gained popularity due to their stable training dynamics and high-fidelity generation quality. However, this stability and quality come at the cost of high computational cost, as the data must be transported incrementally along the entire trajectory. New sampling methods, model distillation, and consistency models have been developed to reduce the sampling cost and even perform one-shot sampling from diffusion models. In this work, we unite diffusion and IGNs by distilling idempotent models from diffusion model scores, called SIGN. Our proposed method is highly stable and does not require adversarial losses. We provide a theoretical analysis of our proposed score-based training methods and empirically show that IGNs can be effectively distilled from a pre-trained diffusion model, enabling faster inference than iterative score-based models. SIGNs can perform multi-step sampling, allowing users to trade off quality for efficiency. These models operate directly on the source domain; they can project corrupted or alternate distributions back onto the target manifold, enabling zero-shot editing of inputs. We validate our models on multiple image datasets, achieving state-of-the-art results for idempotent models on the CIFAR and CelebA datasets.

Genes, proteins and other biological entities influence one another via causal molecular networks. Causal relationships in such networks are mediated by complex and diverse mechanisms, through latent variables, and are often specific to cellular context. It remains challenging to characterise such networks in practice. Here, we present a novel framework to evaluate large language models (LLMs) for zero-shot inference of causal relationships in biology. In particular, we systematically evaluate causal claims obtained from an LLM using real-world interventional data. This is done over one hundred variables and thousands of causal hypotheses. Furthermore, we consider several prompting and retrieval-augmentation strategies, including large, and potentially conflicting, collections of scientific articles. Our results show that with tailored augmentation and prompting, even relatively small LLMs can capture meaningful aspects of causal structure in biological systems. This supports the notion that LLMs could act as orchestration tools in biological discovery, by helping to distil current knowledge in ways amenable to downstream analysis. Our approach to assessing LLMs with respect to experimental data is relevant for a broad range of problems at the intersection of causal learning, LLMs and scientific discovery.

Prompting has emerged as the dominant paradigm for adapting large, pre-trained transformer-based models to downstream tasks. The Prompting Decision Transformer (PDT) enables large-scale, multi-task offline reinforcement learning pre-training by leveraging stochastic trajectory prompts to identify the target task. However, these prompts are sampled uniformly from expert demonstrations, overlooking a critical limitation: Not all prompts are equally informative for differentiating between tasks. To address this, we propose an inference time bandit-based prompt-tuning framework that explores and optimizes trajectory prompt selection to enhance task performance. Our experiments indicate not only clear performance gains due to bandit-based prompt-tuning, but also better sample complexity, scalability, and prompt space exploration compared to prompt-tuning baselines.

The notion of generalization has moved away from the classical one defined in statistical learning theory towards an emphasis on out-of-domain generalization (OODG). Recently, there is a growing focus on inductive generalization, where a progression of difficulty implicitly governs the direction of domain shifts. In inductive generalization, it is often assumed that the training data lie in the easier side, while the testing data lie in the harder side. The challenge is that training data are always finite, but a learner is expected to infer an inductive principle that could be applied in an unbounded manner. This emerging regime has appeared in the literature under different names, such as length/logical/algorithmic extrapolation, but a formal definition is lacking. This work provides such a formalization that centers on the concept of model successors. Then we outline directions to adapt well-established techniques towards the learning of model successors. This work calls for restructuring of the research discussion around inductive generalization from fragmented task-centric communities to a more unified effort, focused on universal properties of learning and computation.

Graph Out-of-Distribution (OOD), requiring that models trained on biased data generalize to the unseen test data, has a massive of real-world applications. One of the most mainstream methods is to extract the invariant subgraph by aligning the original and augmented data with the help of environment augmentation. However, these solutions might lead to the loss or redundancy of semantic subgraph and further result in suboptimal generalization. To address this challenge, we propose a unified framework to exploit the Probability of Necessity and Sufficiency to extract the Invariant Substructure (PNSIS). Beyond that, this framework further leverages the spurious subgraph to boost the generalization performance in an ensemble manner to enhance the robustness on the noise data. Specificially, we first consider the data generation process for graph data. Under mild conditions, we show that the invariant subgraph can be extracted by minimizing an upper bound, which is built on the theoretical advance of probability of necessity and sufficiency. To further bridge the theory and algorithm, we devise the PNSIS model, which involves an invariant subgraph extractor for invariant graph learning as well invariant and spurious subgraph classifiers for generalization enhancement. Experimental results demonstrate that our \textbf{PNSIS} model outperforms the state-of-the-art techniques on graph OOD on several benchmarks, highlighting the effectiveness in real-world scenarios.

In this study, we aim to enhance the arithmetic reasoning ability of Large Language Models (LLMs) through zero-shot prompt optimization. We identify a previously overlooked objective of query dependency in such optimization and elucidate two ensuing challenges that impede the successful and economical design of prompt optimization techniques. One primary issue is the absence of an effective method to evaluate prompts during inference when the golden answer is unavailable. Concurrently, learning via interactions with the LLMs to navigate the expansive natural language prompting space proves to be resource-intensive. To address this, we introduce Prompt-OIRL, which harnesses offline inverse reinforcement learning to draw insights from offline prompting demonstration data. Such data exists as by-products when diverse prompts are benchmarked on open-accessible datasets. With Prompt-OIRL, the query-dependent prompt optimization objective is achieved by first learning an offline reward model. This model can evaluate any query-prompt pairs without accessing LLMs. Subsequently, a best-of-N strategy is deployed to recommend the optimal prompt. Our experimental evaluations across various LLM scales and arithmetic reasoning datasets underscore both the efficacy and economic viability of the proposed approach.

Transferring knowledge across domains is one of the most fundamental problems in machine learning, but doing so effectively in the context of reinforcement learning remains largely an open problem. Current methods make strong assumptions on the specifics of the task, often lack principled objectives, and -- crucially -- modify individual policies, which might be sub-optimal when the domains differ due to a drift in the state space, i.e., it is intrinsic to the environment and therefore affects every agent interacting with it. To address these drawbacks, we propose TvD: transfer via distribution matching, a framework to transfer knowledge across interactive domains. We approach the problem from a data-centric perspective, characterizing the discrepancy in environments by means of (potentially complex) transformation between their state spaces, and thus posing the problem of transfer as learning to undo this transformation. To accomplish this, we introduce a novel optimization objective based on an optimal transport distance between two distributions over trajectories -- those generated by an already-learned policy in the source domain and a learnable pushforward policy in the target domain. We show this objective leads to a policy update scheme reminiscent of imitation learning, and derive an efficient algorithm to implement it. Our experiments in simple gridworlds show that this method yields successful transfer learning across a wide range of environment transformations.

Learning the cumulative distribution function (CDF) of an outcome variable conditional on a set of features remains challenging, especially in high-dimensional settings. Conditional transformation models provide a semi-parametric approach that allows to model a large class of conditional CDFs without an explicit parametric distribution assumption and with only a few parameters. Existing estimation approaches within the class of transformation models are, however, either limited in their complexity and applicability to unstructured data sources such as images or text, or can incorporate complex effects of different features but lack interpretability. We close this gap by introducing the class of deep conditional transformation models which unify existing approaches and allow to learn both interpretable (non-)linear model terms and more complex predictors in one holistic neural network. To this end we propose a novel network architecture, provide details on different model definitions and derive suitable constraints and derive suitable network regularization terms. We demonstrate the efficacy of our approach through numerical experiments and applications.

This work-in-progress provides a preliminary cognitive investigation of how the external visualization of the Ternary diagram (TD) might be used as an underlying model for exploring the representation of simple 3D cuboids according to the theory of Conceptual Spaces. Gärdenfors introduced geometrical entities, known as conceptual spaces, for modeling concepts. He considered multidimensional spaces equipped with a range of similarity measures (such as metrics) and guided by criteria and mechanisms as a geometrical model for concept formation and management. Our work is inspired by the conceptual spaces approach and takes ternary diagrams as its underlying conceptual model. The main motivation for our work is twofold. First, Ternary Diagrams are powerful conceptual representations that have a solid historical and mathematical foundation. Second, the notion of overlaying an Information- Entropy function on a ternary diagram can lead to new insights into applications of reasoning about shape and other cognitive processes.