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The two-hand interaction is one of the most challenging signals to analyze due to the self-similarity, complicated articulations, and occlusions of hands. Although several datasets have been proposed for the two-hand interaction analysis, all of them do not achieve 1) diverse and realistic image appearances and 2) diverse and large-scale groundtruth (GT) 3D poses at the same time. In this work, we propose Re:InterHand, a dataset of relighted 3D interacting hands that achieve the two goals. To this end, we employ a state-of-the-art hand relighting network with our accurately tracked two-hand 3D poses. We compare our Re:InterHand with existing 3D interacting hands datasets and show the benefit of it. Our Re:InterHand is available in //mks0601.github.io/ReInterHand/.

Obtaining the solutions of partial differential equations based on various machine learning methods has drawn more and more attention in the fields of scientific computation and engineering applications. In this work, we first propose a coupled Extreme Learning Machine (called CELM) method incorporated with the physical laws to solve a class of fourth-order biharmonic equations by reformulating it into two well-posed Poisson problems. In addition, some activation functions including tangent, gauss, sine, and trigonometric (sin+cos) functions are introduced to assess our CELM method. Notably, the sine and trigonometric functions demonstrate a remarkable ability to effectively minimize the approximation error of the CELM model. In the end, several numerical experiments are performed to study the initializing approaches for both the weights and biases of the hidden units in our CELM model and explore the required number of hidden units. Numerical results show the proposed CELM algorithm is high-precision and efficient to address the biharmonic equation in both regular and irregular domains.

A number of engineering and scientific problems require representing and manipulating probability distributions over large alphabets, which we may think of as long vectors of reals summing to $1$. In some cases it is required to represent such a vector with only $b$ bits per entry. A natural choice is to partition the interval $[0,1]$ into $2^b$ uniform bins and quantize entries to each bin independently. We show that a minor modification of this procedure -- applying an entrywise non-linear function (compander) $f(x)$ prior to quantization -- yields an extremely effective quantization method. For example, for $b=8 (16)$ and $10^5$-sized alphabets, the quality of representation improves from a loss (under KL divergence) of $0.5 (0.1)$ bits/entry to $10^{-4} (10^{-9})$ bits/entry. Compared to floating point representations, our compander method improves the loss from $10^{-1}(10^{-6})$ to $10^{-4}(10^{-9})$ bits/entry. These numbers hold for both real-world data (word frequencies in books and DNA $k$-mer counts) and for synthetic randomly generated distributions. Theoretically, we set up a minimax optimality criterion and show that the compander $f(x) ~\propto~ \mathrm{ArcSinh}(\sqrt{(1/2) (K \log K) x})$ achieves near-optimal performance, attaining a KL-quantization loss of $\asymp 2^{-2b} \log^2 K$ for a $K$-letter alphabet and $b\to \infty$. Interestingly, a similar minimax criterion for the quadratic loss on the hypercube shows optimality of the standard uniform quantizer. This suggests that the $\mathrm{ArcSinh}$ quantizer is as fundamental for KL-distortion as the uniform quantizer for quadratic distortion.

We discuss a vulnerability involving a category of attribution methods used to provide explanations for the outputs of convolutional neural networks working as classifiers. It is known that this type of networks are vulnerable to adversarial attacks, in which imperceptible perturbations of the input may alter the outputs of the model. In contrast, here we focus on effects that small modifications in the model may cause on the attribution method without altering the model outputs.

We developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a pioneering inference method has been developed for logistic regression, which is a specific instance of GLMs, it is not feasible to apply this method directly to other GLMs because of unknown hyper-parameters. In this study, we addressed this limitation by developing a new inference method designed for a certain class of GLMs. Our method is based on the adjustment of asymptotic normality in high dimensions and is feasible in the sense that it is possible even with unknown hyper-parameters. Specifically, we introduce a novel convex loss-based estimator and its associated system, which are essential components of inference. Next, we devise a methodology for identifying the system parameters required by the method. Consequently, we construct confidence intervals for GLMs in a high-dimensional regime. We prove that our proposed method has desirable theoretical properties, such as strong consistency and exact coverage probability. Finally, we experimentally confirmed its validity.

The presence of symmetries imposes a stringent set of constraints on a system. This constrained structure allows intelligent agents interacting with such a system to drastically improve the efficiency of learning and generalization, through the internalisation of the system's symmetries into their information-processing. In parallel, principled models of complexity-constrained learning and behaviour make increasing use of information-theoretic methods. Here, we wish to marry these two perspectives and understand whether and in which form the information-theoretic lens can "see" the effect of symmetries of a system. For this purpose, we propose a novel variant of the Information Bottleneck principle, which has served as a productive basis for many principled studies of learning and information-constrained adaptive behaviour. We show (in the discrete case) that our approach formalises a certain duality between symmetry and information parsimony: namely, channel equivariances can be characterised by the optimal mutual information-preserving joint compression of the channel's input and output. This information-theoretic treatment furthermore suggests a principled notion of "soft" equivariance, whose "coarseness" is measured by the amount of input-output mutual information preserved by the corresponding optimal compression. This new notion offers a bridge between the field of bounded rationality and the study of symmetries in neural representations. The framework may also allow (exact and soft) equivariances to be automatically discovered.

While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this paper, we present GraphSplineNets, a novel deep-learning method to speed up the forecasting of physical systems by reducing the grid size and number of iteration steps of deep surrogate models. Our method uses two differentiable orthogonal spline collocation methods to efficiently predict response at any location in time and space. Additionally, we introduce an adaptive collocation strategy in space to prioritize sampling from the most important regions. GraphSplineNets improve the accuracy-speedup tradeoff in forecasting various dynamical systems with increasing complexity, including the heat equation, damped wave propagation, Navier-Stokes equations, and real-world ocean currents in both regular and irregular domains.

We provide several new results on the sample complexity of vector-valued linear predictors (parameterized by a matrix), and more generally neural networks. Focusing on size-independent bounds, where only the Frobenius norm distance of the parameters from some fixed reference matrix $W_0$ is controlled, we show that the sample complexity behavior can be surprisingly different than what we may expect considering the well-studied setting of scalar-valued linear predictors. This also leads to new sample complexity bounds for feed-forward neural networks, tackling some open questions in the literature, and establishing a new convex linear prediction problem that is provably learnable without uniform convergence.

Ising machines are a form of quantum-inspired processing-in-memory computer which has shown great promise for overcoming the limitations of traditional computing paradigms while operating at a fraction of the energy use. The process of designing Ising machines is known as the reverse Ising problem. Unfortunately, this problem is in general computationally intractable: it is a nonconvex mixed-integer linear programming problem which cannot be naively brute-forced except in the simplest cases due to exponential scaling of runtime with number of spins. We prove new theoretical results which allow us to reduce the search space to one with quadratic scaling. We utilize this theory to develop general purpose algorithmic solutions to the reverse Ising problem. In particular, we demonstrate Ising formulations of 3-bit and 4-bit integer multiplication which use fewer total spins than previously known methods by a factor of more than three. Our results increase the practicality of implementing such circuits on modern Ising hardware, where spins are at a premium.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.