Structured state-space models (SSMs) are gaining popularity as effective foundational architectures for sequential data, demonstrating outstanding performance across a diverse set of domains alongside desirable scalability properties. Recent developments show that if the linear recurrence powering SSMs allows for a selectivity mechanism leveraging multiplicative interactions between inputs and hidden states (e.g. Mamba, GLA, Hawk/Griffin, HGRN2), then the resulting architecture can surpass attention-powered foundation models trained on text in both accuracy and efficiency, at scales of billion parameters. In this paper, we give theoretical grounding to the selectivity mechanism, often linked to in-context learning, using tools from Rough Path Theory. We provide a framework for the theoretical analysis of generalized selective SSMs, fully characterizing their expressive power and identifying the gating mechanism as the crucial architectural choice. Our analysis provides a closed-form description of the expressive powers of modern SSMs, such as Mamba, quantifying theoretically the drastic improvement in performance from the previous generation of models, such as S4. Our theory not only motivates the success of modern selective state-space models, but also provides a solid framework to understand the expressive power of future SSM variants. In particular, it suggests cross-channel interactions could play a vital role in future improvements.

AI-empowered drug recommendation has become an important task in healthcare research areas, which offers an additional perspective to assist human doctors with more accurate and more efficient drug prescriptions. Generally, drug recommendation is based on patients' diagnosis results in the electronic health records. We assume that there are three key factors to be addressed in drug recommendation: 1) elimination of recommendation bias due to limitations of observable information, 2) better utilization of historical health condition and 3) coordination of multiple drugs to control safety. To this end, we propose DrugRec, a causal inference based drug recommendation model. The causal graphical model can identify and deconfound the recommendation bias with front-door adjustment. Meanwhile, we model the multi-visit in the causal graph to characterize a patient's historical health conditions. Finally, we model the drug-drug interactions (DDIs) as the propositional satisfiability (SAT) problem, and solving the SAT problem can help better coordinate the recommendation. Comprehensive experiment results show that our proposed model achieves state-of-the-art performance on the widely used datasets MIMIC-III and MIMIC-IV, demonstrating the effectiveness and safety of our method.

The field of novel view synthesis from images has seen rapid advancements with the introduction of Neural Radiance Fields (NeRF) and more recently with 3D Gaussian Splatting. Gaussian Splatting became widely adopted due to its efficiency and ability to render novel views accurately. While Gaussian Splatting performs well when a sufficient amount of training images are available, its unstructured explicit representation tends to overfit in scenarios with sparse input images, resulting in poor rendering performance. To address this, we present a 3D Gaussian-based novel view synthesis method using sparse input images that can accurately render the scene from the viewpoints not covered by the training images. We propose a multi-stage training scheme with matching-based consistency constraints imposed on the novel views without relying on pre-trained depth estimation or diffusion models. This is achieved by using the matches of the available training images to supervise the generation of the novel views sampled between the training frames with color, geometry, and semantic losses. In addition, we introduce a locality preserving regularization for 3D Gaussians which removes rendering artifacts by preserving the local color structure of the scene. Evaluation on synthetic and realworld datasets demonstrates competitive or superior performance of our method in few-shot novel view synthesis compared to existing state-of-the-art methods.

We argue that hedging is an activity that human and machine agents should engage in more broadly, even when the agent's value is not necessarily in monetary units. In this paper, we propose a decision-theoretic view of hedging based on augmenting a probabilistic graphical model - specifically a Bayesian network or an influence diagram - with a reward. Hedging is therefore posed as a particular kind of graph manipulation, and can be viewed as analogous to control/intervention and information gathering related analysis. Effective hedging occurs when a risk-averse agent finds opportunity to balance uncertain rewards in their current situation. We illustrate the concepts with examples and counter-examples, and conduct experiments to demonstrate the properties and applicability of the proposed computational tools that enable agents to proactively identify potential hedging opportunities in real-world situations.

Nucleic acid-based drugs like aptamers have recently demonstrated great therapeutic potential. However, experimental platforms for aptamer screening are costly, and the scarcity of labeled data presents a challenge for supervised methods to learn protein-aptamer binding. To this end, we develop an unsupervised learning approach based on the predicted pairwise contact map between a protein and a nucleic acid and demonstrate its effectiveness in protein-aptamer binding prediction.

Coupled oscillators are being increasingly used as the basis of machine learning (ML) architectures, for instance in sequence modeling, graph representation learning and in physical neural networks that are used in analog ML devices. We introduce an abstract class of neural oscillators that encompasses these architectures and prove that neural oscillators are universal, i.e, they can approximate any continuous and casual operator mapping between time-varying functions, to desired accuracy. This universality result provides theoretical justification for the use of oscillator based ML systems. The proof builds on a fundamental result of independent interest, which shows that a combination of forced harmonic oscillators with a nonlinear read-out suffices to approximate the underlying operators.