We show that if the conditional distribution p(C | T) factors through a sufficient statistic ϕ(T), then the Information Bottleneck (IB) problem for (T, C) is exactly equivalent to the IB problem for (ϕ(T), C). The reduction is loss-free: it preserves the full IB curve, the Lagrangian optimum at every trade-off parameter \b{eta}, and the optimal representations up to pullback through ϕ. As a result, the computational complexity of solving the IB problem is governed by the dimension of the sufficient statistic rather than the ambient dimension of the source. This identifies an exact structural condition under which the generic IB problem becomes tractable, and gives a formal bridge between the discrete and linear-Gaussian regimes. We then show that the classical Gaussian IB solution of Chechik, Globerson, Tishby and Weiss is an immediate corollary of this reduction, and we state a nonlinear-Gaussian generalisation. A small numerical example illustrates the practical consequence: when a low-dimensional sufficient statistic is available, the exact IB curve can be computed on the reduced problem at a cost determined by the statistic rather than by the ambient source dimension.

We introduce Hyper Input Convex Neural Networks (HyCNNs), a novel neural network architecture designed for learning convex functions. HyCNNs combine the principles of Maxout networks with input convex neural networks (ICNNs) to create a neural network that is always convex in the input, theoretically capable of leveraging depth, and performs reliable when trained at scale compared to ICNNs. Concretely, we prove that HyCNNs require exponentially fewer parameters than ICNNs to approximate quadratic functions up to a given precision. Throughout a series of synthetic experiments, we demonstrate that HyCNNs outperform existing ICNNs and MLPs in terms of predictive performance for convex regression and interpolation tasks. We further apply HyCNNs to learn high-dimensional optimal transport maps for synthetic examples and for single-cell RNA sequencing data, where they oftentimes outperform ICNN-based neural optimal transport methods and other baselines across a wide range of settings.

Emerging neural reconstruction techniques based on tomography (e.g., NeRF, NeAT, and NeRP) have started showing unique capabilities in medical imaging. In this work, we present a novel Polychromatic neural representation (Polyner) to tackle the challenging problem of CT imaging when metallic implants exist within the human body. CT metal artifacts arise from the drastic variation of metal's attenuation coefficients at various energy levels of the X-ray spectrum, leading to a nonlinear metal effect in CT measurements. Recovering CT images from metal-affected measurements hence poses a complicated nonlinear inverse problem where empirical models adopted in previous metal artifact reduction (MAR) approaches lead to signal loss and strongly aliased reconstructions.

Automated seizure detection is of great importance to epilepsy diagnosis and treatment. An emerging method used in seizure detection, stereoelectroencephalography (SEEG), can provide detailed and stereoscopic brainwave information. However, modeling SEEG in clinical scenarios will face challenges like huge domain shift between different patients and dramatic pattern evolution among different brain areas. In this study, we propose a Pretraining-based model for Patient-independent seizure detection (PPi) to address these challenges. Firstly, we design two novel self-supervised tasks which can extract rich information from abundant SEEG data while preserving the unique characteristics between brain signals recorded from different brain areas. Then two techniques, channel background subtraction and brain region enhancement, are proposed to effectively tackle the domain shift problem. Extensive experiments show that PPi outperforms the SOTA baselines on two public datasets and a real-world clinical dataset collected by us, which demonstrates the effectiveness and practicability of PPi. Finally, visualization analysis illustrates the rationality of the two domain generalization techniques.

The introduction of neural radiance fields has greatly improved the effectiveness of view synthesis for monocular videos. However, existing algorithms face difficulties when dealing with uncontrolled or lengthy scenarios, and require extensive training time specific to each new scenario. To tackle these limitations, we propose DynPoint, an algorithm designed to facilitate the rapid synthesis of novel views for unconstrained monocular videos. Rather than encoding the entirety of the scenario information into a latent representation, DynPoint concentrates on predicting the explicit 3D correspondence between neighboring frames to realize information aggregation. Specifically, this correspondence prediction is achieved through the estimation of consistent depth and scene flow information across frames. Subsequently, the acquired correspondence is utilized to aggregate information from multiple reference frames to a target frame, by constructing hierarchical neural point clouds. The resulting framework enables swift and accurate view synthesis for desired views of target frames. The experimental results obtained demonstrate the considerable acceleration of training time achieved - typically an order of magnitude - by our proposed method while yielding comparable outcomes compared to prior approaches. Furthermore, our method exhibits strong robustness in handling long-duration videos without learning a canonical representation of video content.

Liquid democracy with ranked delegations is a novel voting scheme that unites the practicability of representative democracy with the idealistic appeal of direct democracy: Every voter decides between casting their vote on a question at hand or delegating their voting weight to some other, trusted agent. Delegations are transitive, and since voters may end up in a delegation cycle, they are encouraged to indicate not only a single delegate, but a set of potential delegates and a ranking among them. Based on the delegation preferences of all voters, a delegation rule selects one representative per voter. Previous work has revealed a trade-off between two properties of delegation rules called anonymity and copy-robustness. To overcome this issue we study two fractional delegation rules: MIXEDBORDA BRANCHING, which generalizes a rule satisfying copy-robustness, and the RANDOMWALKRULE, which satisfies anonymity. Using the Markov chain tree theorem, we show that the two rules are in fact equivalent, and simultaneously satisfy generalized versions of the two properties. Combining the same theorem with Fulkerson's algorithm, we develop a polynomial-time algorithm for computing the outcome of the studied delegation rule. This algorithm is of independent interest, having applications in semi-supervised learning and graph theory.

Binary Balanced Tree Recursive Neural Networks (BBT-RvNNs) enforce sequence composition according to a preset balanced binary tree structure. Thus, their nonlinear recursion depth (which is the tree depth) is just log2 n(nbeing the sequence length). Such logarithmic scaling makes BBT-RvNNs efficient and scalable on long sequence tasks such as Long Range Arena (LRA). However, such computational efficiency comes at a cost because BBT-RvNNs cannot solve simple arithmetic tasks like ListOps. On the flip side, RvNN models (e.g., Beam Tree RvNN) that do succeed on ListOps (and other structure-sensitive tasks like formal logical inference) are generally several times more expensive (in time and space) than even Recurrent Neural Networks.

Traditional federated learning (FL) algorithms operate under the assumption that the data distributions at training (source domains) and testing (target domain) are the same. The fact that domain shifts often occur in practice necessitates equipping FL methods with a domain generalization (DG) capability. However, existing DG algorithms face fundamental challenges in FL setups due to the lack of samples/domains in each client's local dataset. In this paper, we propose StableFDG, a style and attention based learning strategy for accomplishing federated domain generalization, introducing two key contributions. The first is style-based learning, which enables each client to explore novel styles beyond the original source domains in its local dataset, improving domain diversity based on the proposed style sharing, shifting, and exploration strategies. Our second contribution is an attention-based feature highlighter, which captures the similarities between the features of data samples in the same class, and emphasizes the important/common characteristics to better learn the domain-invariant characteristics of each class in data-poor FL scenarios. Experimental results show that StableFDG outperforms existing baselines on various DG benchmark datasets, demonstrating its efficacy.

We introduce a data-driven learning framework that assimilates two powerful ideas: ideal large eddy simulation (LES) from turbulence closure modeling and neural stochastic differential equations (SDE) for stochastic modeling. The ideal LES models the LES flow by treating each full-order trajectory as a random realization of the underlying dynamics, as such, the effect of small-scales is marginalized to obtain the deterministic evolution of the LES state. However, ideal LES is analytically intractable. In our work, we use a latent neural SDE to model the evolution of the stochastic process and an encoder-decoder pair for transforming between the latent space and the desired ideal flow field. This stands in sharp contrast to other types of neural parameterization of closure models where each trajectory is treated as a deterministic realization of the dynamics. We show the effectiveness of our approach (niLES - neural ideal LES) on two challenging chaotic dynamical systems: Kolmogorov flow at a Reynolds number of 20,000 and flow past a cylinder at Reynolds number 500. Compared to competing methods, our method can handle non-uniform geometries using unstructured meshes seamlessly. In particular, niLES leads to trajectories with more accurate statistics and enhances stability, particularly for long-horizon rollouts.