Cross-region dynamic connectivity, which describes the spatio-temporal dependence of neural activity among multiple brain regions of interest (ROIs), can provide important information for understanding cognition.

Recent advancements in neural rendering have excelled at novel view synthesis from multi-view RGB images. However, they often lack the capability to edit the shading or colour of the scene at a detailed point-level, while ensuring consistency across different viewpoints. In this work, we address the challenge of point-level 3D scene albedo and shading editing from multi-view RGB images, focusing on detailed editing at the point-level rather than at a part or global level. While prior works based on volumetric representation such as NeRF struggle with achieving 3D consistent editing at the point level, recent advancements in point-based neural rendering show promise in overcoming this challenge. We introduce ``Intrinsic PAPR'', a novel method based on the recent point-based neural rendering technique Proximity Attention Point Rendering (PAPR). Unlike other point-based methods that model the intrinsic decomposition of the scene, our approach does not rely on complicated shading models or simplistic priors that may not universally apply. Instead, we directly model scene decomposition into albedo and shading components, leading to better estimation accuracy. Comparative evaluations against the latest point-based inverse rendering methods demonstrate that Intrinsic PAPR achieves higher-quality novel view rendering and superior point-level albedo and shading editing.

Cross-region dynamic connectivity, which describes the spatio-temporal dependence of neural activity among multiple brain regions of interest (ROIs), can provide important information for understanding cognition. For estimating such connectivity, magnetoencephalography (MEG) and electroencephalography (EEG) are well-suited tools because of their millisecond temporal resolution. However, localizing source activity in the brain requires solving an under-determined linear problem. In typical two-step approaches, researchers first solve the linear problem with generic priors assuming independence across ROIs, and secondly quantify cross-region connectivity. In this work, we propose a one-step state-space model to improve estimation of dynamic connectivity. The model treats the mean activity in individual ROIs as the state variable and describes non-stationary dynamic dependence across ROIs using time-varying auto-regression. Compared with a two-step method, which first obtains the commonly used minimum-norm estimates of source activity, and then fits the auto-regressive model, our state-space model yielded smaller estimation errors on simulated data where the model assumptions held. When applied on empirical MEG data from one participant in a scene-processing experiment, our state-space model also demonstrated intriguing preliminary results, indicating leading and lagged linear dependence between the early visual cortex and a higher-level scene-sensitive region, which could reflect feedforward and feedback information flow within the visual cortex during scene processing.

To better understand complexity in neural networks, we theoretically investigate the idealised phenomenon of lossless network compressibility, whereby an identical function can be implemented with a smaller network. We give an efficient formal algorithm for optimal lossless compression in the setting of single-hidden-layer hyperbolic tangent networks. To measure lossless compressibility, we define the rank of a parameter as the minimum number of hidden units required to implement the same function. Losslessly compressible parameters are atypical, but their existence has implications for nearby parameters. We define the proximate rank of a parameter as the rank of the most compressible parameter within a small $L^\infty$ neighbourhood. Unfortunately, detecting nearby losslessly compressible parameters is not so easy: we show that bounding the proximate rank is an NP-complete problem, using a reduction from Boolean satisfiability via a geometric problem involving covering points in the plane with small squares. These results underscore the computational complexity of measuring neural network complexity, laying a foundation for future theoretical and empirical work in this direction.

We proposed the boundary-integral type neural networks (BINN) for the boundary value problems in computational mechanics. The boundary integral equations are employed to transfer all the unknowns to the boundary, then the unknowns are approximated using neural networks and solved through a training process. The loss function is chosen as the residuals of the boundary integral equations. Regularization techniques are adopted to efficiently evaluate the weakly singular and Cauchy principle integrals in boundary integral equations. Potential problems and elastostatic problems are mainly concerned in this article as a demonstration. The proposed method has several outstanding advantages: First, the dimensions of the original problem are reduced by one, thus the freedoms are greatly reduced. Second, the proposed method does not require any extra treatment to introduce the boundary conditions, since they are naturally considered through the boundary integral equations. Therefore, the method is suitable for complex geometries. Third, BINN is suitable for problems on the infinite or semi-infinite domains. Moreover, BINN can easily handle heterogeneous problems with a single neural network without domain decomposition.

Adversarial transferability, namely the ability of adversarial perturbations to simultaneously fool multiple learning models, has long been the "big bad wolf" of adversarial machine learning. Successful transferability-based attacks requiring no prior knowledge of the attacked model's parameters or training data have been demonstrated numerous times in the past, implying that machine learning models pose an inherent security threat to real-life systems. However, all of the research performed in this area regarded transferability as a probabilistic property and attempted to estimate the percentage of adversarial examples that are likely to mislead a target model given some predefined evaluation set. As a result, those studies ignored the fact that real-life adversaries are often highly sensitive to the cost of a failed attack. We argue that overlooking this sensitivity has led to an exaggerated perception of the transferability threat, when in fact real-life transferability-based attacks are quite unlikely. By combining theoretical reasoning with a series of empirical results, we show that it is practically impossible to predict whether a given adversarial example is transferable to a specific target model in a black-box setting, hence questioning the validity of adversarial transferability as a real-life attack tool for adversaries that are sensitive to the cost of a failed attack.

Free Point Transformer (FPT) has been proposed as a data-driven, non-rigid point set registration approach using deep neural networks. As FPT does not assume constraints based on point vicinity or correspondence, it may be trained simply and in a flexible manner by minimizing an unsupervised loss based on the Chamfer Distance. This makes FPT amenable to real-world medical imaging applications where ground-truth deformations may be infeasible to obtain, or in scenarios where only a varying degree of completeness in the point sets to be aligned is available. To test the limit of the correspondence finding ability of FPT and its dependency on training data sets, this work explores the generalizability of the FPT from well-curated non-medical data sets to medical imaging data sets. First, we train FPT on the ModelNet40 dataset to demonstrate its effectiveness and the superior registration performance of FPT over iterative and learning-based point set registration methods. Second, we demonstrate superior performance in rigid and non-rigid registration and robustness to missing data. Last, we highlight the interesting generalizability of the ModelNet-trained FPT by registering reconstructed freehand ultrasound scans of the spine and generic spine models without additional training, whereby the average difference to the ground truth curvatures is 1.3 degrees, across 13 patients.

Going from left to right, we consider increasingly complex functions. These neighborhoods, in other words, need to become more and more disjoint as the function becomes more complex. Indeed, we quantify "disjointedness" of the neighborhoods via a term denoted by and relate it to the complexity of the function class, and subsequently, its generalization properties. There has been a growing interest in interpretable machine learning (IML), towards helping users better understand how their ML models behave. IML has become a particularly relevant concern especially as practitioners aim to apply ML in important domains such as healthcare [Caruana et al., '15], financial services [Chen et al., '18], and scientific discovery [Karpatne et al., '17]. While much of the work in IML has been qualitative and empirical, in our recent ICLR21 paper, we study how concepts in interpretability can be formally related to learning theory.

In this paper, we explore connections between interpretable machine learning and learning theory through the lens of local approximation explanations. First, we tackle the traditional problem of performance generalization and bound the testtime accuracy of a model using a notion of how locally explainable it is. Second, we explore the novel problem of explanation generalization which is an important concern for a growing class of finite sample-based local approximation explanations. Finally, we validate our theoretical results empirically and show that they reflect what can be seen in practice. There has been a growing interest in interpretable machine learning, which seeks to help people understand their models. While interpretable machine learning encompasses a wide range of problems, it is a fairly uncontroversial hypothesis that there exists a tradeoff between a model's complexity and general notions of interpretability. This hypothesis suggests a seemingly natural connection to the field of learning theory, which has thoroughly explored relationships between a function class's complexity and generalization. However, formal connections between interpretability and learning theory remain relatively unstudied.

Cross-region dynamic connectivity, which describes spatio-temporal dependence of neural activity among multiple brain regions of interest (ROIs), can provide important information for understanding cognition. For estimating such connectivity, magnetoencephalography (MEG) and electroencephalography (EEG) are well-suited tools because of their millisecond temporal resolution. However, localizing source activity in the brain requires solving an under-determined linear problem. In typical two-step approaches, researchers first solve the linear problem with general priors assuming independence across ROIs, and secondly quantify cross-region connectivity. In this work, we propose a one-step state-space model to improve estimation of dynamic connectivity. The model treats the mean activity in individual ROIs as the state variable, and describes non-stationary dynamic dependence across ROIs using time-varying auto-regression. Compared with a two-step method, which first obtains the commonly used minimum-norm estimates of source activity, and then fits the auto-regressive model, our state-space model yielded smaller estimation errors on simulated data where the model assumptions held. When applied on empirical MEG data from one participant in a scene-processing experiment, our state-space model also demonstrated intriguing preliminary results, indicating leading and lagged linear dependence between the early visual cortex and a higher-level scene-sensitive region, which could reflect feed-forward and feedback information flow within the visual cortex during scene processing.