Abstract: Neural Radiance Fields (NeRF) is a popular view synthesis technique that represents a scene as a continuous volumetric function, parameterized by multilayer perceptrons that provide the volume density and view-dependent emitted radiance at each location. While NeRF-based techniques excel at representing fine geometric structures with smoothly varying view-dependent appearance, they often fail to accurately capture and reproduce the appearance of glossy surfaces. We address this limitation by introducing Ref-NeRF, which replaces NeRF's parameterization of view-dependent outgoing radiance with a representation of reflected radiance and structures this function using a collection of spatially-varying scene properties. We show that together with a regularizer on normal vectors, our model significantly improves the realism and accuracy of specular reflections. Furthermore, we show that our model's internal representation of outgoing radiance is interpretable and useful for scene editing.

Abstract: Image-guided depth completion aims to generate dense depth maps with sparse depth measurements and corresponding RGB images. Currently, spatial propagation networks (SPNs) are the most popular affinity-based methods in depth completion, but they still suffer from the representation limitation of the fixed affinity and the over smoothing during iterations. Our solution is to estimate independent affinity matrices in each SPN iteration, but it is over-parameterized and heavy calculation.This paper introduces an efficient model that learns the affinity among neighboring pixels with an attention-based, dynamic approach. Specifically, the Dynamic Spatial Propagation Network (DySPN) we proposed makes use of a non-linear propagation model (NLPM). It decouples the neighborhood into parts regarding to different distances and recursively generates independent attention maps to refine these parts into adaptive affinity matrices. Furthermore, we adopt a diffusion suppression (DS) operation so that the model converges at an early stage to prevent over-smoothing of dense depth. Finally, in order to decrease the computational cost required, we also introduce three variations that reduce the amount of neighbors and attentions needed while still retaining similar accuracy. In practice, our method requires less iteration to match the performance of other SPNs and yields better results overall. DySPN outperforms other state-of-the-art (SoTA) methods on KITTI Depth Completion (DC) evaluation by the time of submission and is able to yield SoTA performance in NYU Depth v2 dataset as well.

Abstract: Electrophysiological power spectra typically consist of two components: An aperiodic part usually following an 1/f power law [Formula: see text] and periodic components appearing as spectral peaks. While the investigation of the periodic parts, commonly referred to as neural oscillations, has received considerable attention, the study of the aperiodic part has only recently gained more interest. The periodic part is usually quantified by center frequencies, powers, and bandwidths, while the aperiodic part is parameterized by the y-intercept and the 1/f exponent [Formula: see text]. For investigation of either part, however, it is essential to separate the two components. In this article, we scrutinize two frequently used methods, FOOOF (Fitting Oscillations & One-Over-F) and IRASA (Irregular Resampling Auto-Spectral Analysis), that are commonly used to separate the periodic from the aperiodic component. We evaluate these methods using diverse spectra obtained with electroencephalography (EEG), magnetoencephalography (MEG), and local field potential (LFP) recordings relating to three independent research datasets. Each method and each dataset poses distinct challenges for the extraction of both spectral parts. The specific spectral features hindering the periodic and aperiodic separation are highlighted by simulations of power spectra emphasizing these features. Through comparison with the simulation parameters defined a priori, the parameterization error of each method is quantified. Based on the real and simulated power spectra, we evaluate the advantages of both methods, discuss common challenges, note which spectral features impede the separation, assess the computational costs, and propose recommendations on how to use them.

Abstract: Parameterized quantum circuits serve as ans\"{a}tze for solving variational problems and provide a flexible paradigm for programming near-term quantum computers. Ideally, such ans\"{a}tze should be highly expressive so that a close approximation of the desired solution can be accessed. On the other hand, the ansatz must also have sufficiently large gradients to allow for training. Here, we derive a fundamental relationship between these two essential properties: expressibility and trainability. This is done by extending the well established barren plateau phenomenon, which holds for ans\"{a}tze that form exact 2-designs, to arbitrary ans\"{a}tze. Specifically, we calculate the variance in the cost gradient in terms of the expressibility of the ansatz, as measured by its distance from being a 2-design. Our resulting bounds indicate that highly expressive ans\"{a}tze exhibit flatter cost landscapes and therefore will be harder to train. Furthermore, we provide numerics illustrating the effect of expressiblity on gradient scalings, and we discuss the implications for designing strategies to avoid barren plateaus.

Abstract: For the vast majority of local problems on graphs of small treewidth (where, by local we mean that a solution can be verified by checking separately the neighbourhood of each vertex), standard dynamic programming techniques give c tw | V | O(1) time algorithms, where tw is the treewidth of the input graph G = ( V,E ) and c is a constant. On the other hand, for problems with a global requirement (usually connectivity) the best–known algorithms were naive dynamic programming schemes running in at least tw tw time. We bridge this gap by introducing a technique we named Cut&Count that allows to produce c tw | V | O(1) time Monte-Carlo algorithms for most connectivity-type problems, including Hamiltonian Path , Steiner Tree , Feedback Vertex Set and Connected Dominating Set . These results have numerous consequences in various fields, like parameterized complexity, exact and approximate algorithms on planar and H -minor-free graphs and exact algorithms on graphs of bounded degree. The constant c in our algorithms is in all cases small, and in several cases we are able to show that improving those constants would cause the Strong Exponential Time Hypothesis to fail. In all these fields we are able to improve the best-known results for some problems. Also, looking from a more theoretical perspective, our results are surprising since the equivalence relation that partitions all partial solutions with respect to extendability to global solutions seems to consist of at least tw tw equivalence classes for all these problems. Our results answer an open problem raised by Lokshtanov, Marx and Saurabh [SODA’11]. In contrast to the problems aimed at minimizing the number of connected components that we solve using Cut&Count as mentioned above, we show that, assuming the Exponential Time Hypothesis, the aforementioned gap cannot be bridged for some problems that aim to maximize the number of connected components like Cycle Packing .

Abstract: Efficient methods for loading given classical data into quantum circuits are essential for various quantum algorithms. In this paper, we propose an algorithm called Approximate Amplitude Encoding that can effectively load all the components of a given real-valued data vector into the amplitude of quantum state, while the previous proposal can only load the absolute values of those components. The key of our algorithm is to variationally train a shallow parameterized quantum circuit, using the results of two types of measurement; the standard computational-basis measurement plus the measurement in the Hadamard-transformed basis, introduced in order to handle the sign of the data components. The variational algorithm changes the circuit parameters so as to minimize the sum of two costs corresponding to those two measurement basis, both of which are given by the efficiently-computable maximum mean discrepancy. We also consider the problem of constructing the singular value decomposition entropy via the stock market dataset to give a financial market indicator; a quantum algorithm (the variational singular value decomposition algorithm) is known to produce a solution faster than classical, which yet requires the sign-dependent amplitude encoding. We demonstrate, with an in-depth numerical analysis, that our algorithm realizes loading of time-series of real stock prices on quantum state with small approximation error, and thereby it enables constructing an indicator of the financial market based on the stock prices.

Abstract: Image denoising methods using deep neural networks have achieved a great progress in the image restoration. However, the recovered images restored by these deep denoising methods usually suffer from severe over-smoothness, artifacts, and detail loss. To improve the quality of restored images, we first propose Supplemental Priors (SP) method to adaptively predict depth-directed and sample-directed prior information for the reconstruction (decoder) networks. Furthermore, the over-parameterized deep neural networks and too precise supplemental prior information may cause an over-fitting, restricting the performance promotion. To improve the generalization of denoising networks, we further propose Regularization Priors (RP) method to flexibly learn depth-directed and dataset-directed regularization noise for the retrieving (encoder) networks. By respectively integrating the encoder and decoder with these plug-and-play RP block and SP block, we propose the final Adaptive Prior Denoising Networks, called APD-Nets. APD-Nets is the first attempt to simultaneously regularize and supplement denoising networks from the adaptive priors’ view with drawing learning-based mechanism into producing adaptive regularization noise and supplemental information. Extensive experiment results demonstrate our method significantly improves the generalization of denoising networks and the quality of restored images with greatly outperforming the traditional deep denoising methods both quantitatively and visually. The code will be released at https://github.com/JiangBoCS/APD-Nets.

Abstract: We have investigated the systematic differences introduced when performing a Bayesian-inference analysis of the equation of state (EOS) of neutron stars employing either variable- or constant-likelihood functions. The former has the advantage of retaining the full information on the distributions of the measurements, making exhaustive usage of the data. The latter, on the other hand, has the advantage of a much simpler implementation and reduced computational costs. In both approaches, the EOSs have identical priors and have been built using the sound speed parameterization method so as to satisfy the constraints from X-ray and gravitational waves observations, as well as those from chiral effective theory and perturbative quantum chromodynamics. In all cases, the two approaches lead to very similar results and the 90% confidence levels essentially overlap. Some differences do appear, but in regions where the probability density is extremely small and are mostly due to the sharp cutoff on the binary tidal deformability Λ˜≤720 set in the constant-likelihood approach. Our analysis has also produced two additional results. First, an inverse correlation between the normalized central number density, n c,TOV/n s , and the radius of a maximally massive star, R TOV. Second, and most importantly, it has confirmed the relation between the chirp mass and the binary tidal deformability. The importance of this result is that it relates chirp , which is measured very accurately, and Λ˜ , which contains important information on the EOS. Hence, when chirp is measured in future detections, our relation can be used to set tight constraints on Λ˜ .

Abstract: Compared to convolutional layers, fully-connected (FC) layers are better at modeling the long-range dependencies but worse at capturing the local patterns, hence usually less favored for image recognition. In this paper, we propose a methodology, Locality Injection, to incorporate local priors into an FC layer via merging the trained parameters of a parallel conv kernel into the FC kernel. Locality Injection can be viewed as a novel Structural Re-parameterization method since it equivalently converts the structures via transforming the parameters. Based on that, we propose a multi-layer-perceptron (MLP) block named RepMLP Block, which uses three FC layers to extract features, and a novel architecture named RepMLPNet. The hierarchical design distinguishes RepMLPNet from the other concurrently proposed vision MLPs. As it produces feature maps of different levels, it qualifies as a backbone model for downstream tasks like semantic segmentation. Our results reveal that 1) Locality Injection is a general methodology for MLP models; 2) RepMLPNet has favorable accuracy-efficiency trade-off compared to the other MLPs; 3) RepMLPNet is the first MLP that seamlessly transfer to Cityscapes semantic segmentation. The code and models are available at https://github.com/DingXiaoH/RepMLP.

Abstract: The existing results show the applicability of the Over-Parameterized Model based Hammerstein-Wiener model identification methods. However, it requires to estimate extra parameters and performer a low rank approximation step. Therefore, it may give rise to unnecessarily high variance in parameter estimates for highly nonlinear systems, especially using a small and noisy data set. To overcome this corruptive phenomenon. To overcome this corruptive phenomenon, in this paper, a robust Hammerstein-Wiener model identification method is developed for highly nonlinear systems when using a small and noisy data set, where two parsimonious parametrization models with fewer parameters are used, and an iteration method is then used to retrieve the true system parameters from the parametrization models. Such modification can improve the parameter estimation performance in terms of accuracy and variance compared with the over-parametrization model based identification methods. All the above-mentioned developments are analyzed with variance analysis, along with a simulation example to confirm the effectiveness.

Abstract: Buildings serve as the main places of human activities, and it is essential to automatically extract each building instance for a wide range of applications. Recently, automatic building segmentation approaches have made great progress in both detection and segmentation accuracy due to the rapid development of deep learning. However, these approaches struggle to delineate regular and accurate building boundaries due to the limitations in inferring overall structure of the building instance; this might lead to inconsistency in building geometry and difficulty in being applied directly to practical engineering. To tackle this challenge, this article presents an adaptive polygon generation algorithm (APGA), a novel method that aims at directly generating a polygonal output, parameterized as a sequence of building vertices, to outline each building instance. To achieve this, APGA predicts the candidate locations of building vertices and determines the arrangement of these vertices with the help of the position and orientation of the building boundary. Moreover, to introduce local context features and achieve improved performance of the predicted building polygon, APGA integrates finer structures around the candidate vertices to refine their positions. Experiments on several challenging building extraction datasets demonstrated that APGA outperformed state-of-the-art methods in terms of building coverage and geometric similarity.

Abstract: We describe a method to generate 3D architected materials based on mathematically parameterized human readable word input, offering a direct materialization of language. Our method uses a combination of a vector quantized generative adversarial network and contrastive language-image pre-training neural networks to generate images, which are translated into 3D architectures that are then 3D printed using fused deposition modeling into materials with varying rigidity. The novel materials are further analyzed in a metallic realization as an aluminum-based nano-architecture, using molecular dynamics modeling and thereby providing mechanistic insights into the physical behavior of the material under extreme compressive loading. This work offers a novel way to design, understand, and manufacture 3D architected materials designed from mathematically parameterized language input. Our work features, at its core, a generally applicable algorithm that transforms any 2D image data into hierarchical fully tileable, periodic architected materials. This method can have broader applications beyond language-based materials design and can render other avenues for the analysis and manufacturing of architected materials, including microstructure gradients through parametric modeling. As an emerging field, language-based design approaches can have a profound impact on end-to-end design environments and drive a new understanding of physical phenomena that intersect directly with human language and creativity. It may also be used to exploit information mined from diverse and complex databases and data sources.

Abstract: In the engineering practice, lacking of data especially labeled data typically hinders the wide application of deep learning in mechanical fault diagnosis. However, collecting and labeling data is often expensive and time-consuming. To address this problem, a kind of semi-supervised meta-learning networks (SSMN) with squeeze-and-excitation attention is proposed for few-shot fault diagnosis in this paper. SSMN consists of a parameterized encoder, a non-parameterized prototype refinement process and a distance function. Based on attention mechanism, the encoder is able to extract distinct features to generate prototypes and enhance the identification accuracy. With semi-supervised few-shot learning, SSMN utilizes unlabeled data to refine original prototypes for better fault recognition. A combinatorial learning optimizer is designed to optimize SSMN efficiently. The effectiveness of the proposed method is demonstrated through three bearing vibration datasets and the results indicate the outstanding adaptability in different situations. Comparison with other approaches is also made under the same setup and the experimental results prove the superiority of the proposed method for few-shot fault diagnosis.

Abstract: The field of model order reduction (MOR) is growing in importance due to its ability to extract the key insights from complex simulations while discarding computationally burdensome and superfluous information. We provide an overview of MOR methods for the creation of fast & accurate emulators of memory- and compute-intensive nuclear systems, focusing on eigen-emulators and variational emulators. As an example, we describe how "eigenvector continuation'' is a special case of a much more general and well-studied MOR formalism for parameterized systems. We continue with an introduction to the Ritz and Galerkin projection methods that underpin many such emulators, while pointing to the relevant MOR theory and its successful applications along the way. We believe that this will open the door to broader applications in nuclear physics and facilitate communication with practitioners in other fields.

Abstract: Intuitionistic fuzzy sets (IFSs) can effectively represent and simulate the uncertainty and diversity of judgment information offered by decision-makers (DMs). In comparison to fuzzy sets (FSs), IFSs are highly beneficial for expressing vagueness and uncertainty more accurately. As a result, in this research work, we offer an approach for solving group decision-making problems (GDMPs) with fuzzy parameterized intuitionistic multi fuzzy N-soft set (briefly, FPIMFNSS) of dimension q by introducing its induced fuzzy parameterized hesitant N-soft set (FPHNSS) as an extension of the multi-fuzzy N-soft set (MFNSS) based group decision-making method (GDMM). In this study, we use the proposed GDMM to solve a real-life GDMP involving candidate eligibility for a single vacant position advertised by an IT firm and compare the ranking performances of the proposed GDMM with the Fatimah-Alcantud method.

Abstract: The hypothesis that the anomalous behavior of liquid water is related to the existence of a second critical point in deeply supercooled states has long been the subject of intense debate. Recent, sophisticated experiments designed to observe the transformation between the two subcritical liquids on nano- and microsecond time scales, along with demanding numerical simulations based on classical (rigid) models parameterized to reproduce thermodynamic properties of water, have provided support to this hypothesis. A stronger numerical proof requires demonstrating that the critical point, which occurs at temperatures and pressures far from those at which the models were optimized, is robust with respect to model parameterization, specifically with respect to incorporating additional physical effects. Here, we show that a liquid-liquid critical point can be rigorously located also in the WAIL model of water [Pinnick et al., J. Chem. Phys. 137, 014510 (2012)], a model parameterized using ab initio calculations only. The model incorporates two features not present in many previously studied water models: It is both flexible and polarizable, properties which can significantly influence the phase behavior of water. The observation of the critical point in a model in which the water-water interaction is estimated using only quantum ab initio calculations provides strong support to the viewpoint according to which the existence of two distinct liquids is a robust feature in the free energy landscape of supercooled water.

Abstract: Abstract Self-supervised pretraining on protein sequences has led to state-of-the art performance on protein function and fitness prediction. However, sequence-only methods ignore the rich information contained in experimental and predicted protein structures. Meanwhile, inverse folding methods reconstruct a protein’s amino-acid sequence given its structure, but do not take advantage of sequences that do not have known structures. In this study, we train a masked inverse folding protein masked language model parameterized as a structured graph neural network. During pretraining, this model learns to reconstruct corrupted sequences conditioned on the backbone structure. We then show that using the outputs from a pretrained sequence-only protein masked language model as input to the inverse folding model further improves pretraining perplexity. We evaluate both of these models on downstream protein engineering tasks and analyze the effect of using information from experimental or predicted structures on performance.

Abstract: Classical computing plays a critical role in the advancement of quantum frontiers in the NISQ era. In this spirit, this work uses classical simulation to bootstrap Variational Quantum Algorithms (VQAs). VQAs rely upon the iterative optimization of a parameterized unitary circuit (ansatz) with respect to an objective function. Since quantum machines are noisy and expensive resources, it is imperative to classically choose the VQA ansatz initial parameters to be as close to optimal as possible to improve VQA accuracy and accelerate their convergence on today’s devices. This work tackles the problem of finding a good ansatz initialization, by proposing CAFQA, a Clifford Ansatz For Quantum Accuracy. The CAFQA ansatz is a hardware-efficient circuit built with only Clifford gates. In this ansatz, the parameters for the tunable gates are chosen by searching efficiently through the Clifford parameter space via classical simulation. The resulting initial states always equal or outperform traditional classical initialization (e.g., Hartree-Fock), and enable high-accuracy VQA estimations. CAFQA is well-suited to classical computation because: a) Clifford-only quantum circuits can be exactly simulated classically in polynomial time, and b) the discrete Clifford space is searched efficiently via Bayesian Optimization. For the Variational Quantum Eigensolver (VQE) task of molecular ground state energy estimation (up to 18 qubits), CAFQA’s Clifford Ansatz achieves a mean accuracy of nearly 99% and recovers as much as 99.99% of the molecular correlation energy that is lost in Hartree-Fock initialization. CAFQA achieves mean accuracy improvements of 6.4x and 56.8x, over the state-of-the-art, on different metrics. The scalability of the approach allows for preliminary ground state energy estimation of the challenging chromium dimer (Cr2) molecule. With CAFQA’s high-accuracy initialization, the convergence of VQAs is shown to accelerate by 2.5x, even for small molecules. Furthermore, preliminary exploration of allowing a limited number of non-Clifford (T) gates in the CAFQA framework, shows that as much as 99.9% of the correlation energy can be recovered at bond lengths for which Clifford-only CAFQA accuracy is relatively limited, while remaining classically simulable.

Abstract: In this work, we blend machine learning and dictionary-based learning with numerical analysis tools to discover differential equations from noisy and sparsely sampled measurement data of time-dependent processes. We use the fact that given a dictionary containing large candidate nonlinear functions, dynamical models can often be described by a few appropriately chosen basis functions. As a result, we obtain parsimonious models that can be better interpreted by practitioners, and potentially generalize better beyond the sampling regime than black-box modelling. In this work, we integrate a numerical integration framework with dictionary learning that yields differential equations without requiring or approximating derivative information at any stage. Hence, it is utterly effective for corrupted and sparsely sampled data. We discuss its extension to governing equations, containing rational nonlinearities that typically appear in biological networks. Moreover, we generalized the method to governing equations subject to parameter variations and externally controlled inputs. We demonstrate the efficiency of the method to discover a number of diverse differential equations using noisy measurements, including a model describing neural dynamics, chaotic Lorenz model, Michaelis-Menten kinetics and a parameterized Hopf normal form.

Abstract: Symmetric quantum signal processing provides a parameterized representation of a real polynomial, which can be translated into an efficient quantum circuit for performing a wide range of computational tasks on quantum computers. For a given polynomial f, the parameters (called phase factors) can be obtained by solving an optimization problem. However, the cost function is non-convex, and has a very complex energy landscape with numerous global and local minima. It is therefore surprising that the solution can be robustly obtained in practice, starting from a fixed initial guess Φ0 that contains no information of the input polynomial. To investigate this phenomenon, we first explicitly characterize all the global minima of the cost function. We then prove that one particular global minimum (called the maximal solution) belongs to a neighborhood of Φ0, on which the cost function is strongly convex under the condition ‖f‖∞=O(d−1) with d=deg(f). Our result provides a partial explanation of the aforementioned success of optimization algorithms.

Abstract: Data mixing augmentation have proved to be effective for improving the generalization ability of deep neural networks. While early methods mix samples by hand-crafted policies (e.g., linear interpolation), recent methods utilize saliency information to match the mixed samples and labels via complex offline optimization. However, there arises a trade-off between precise mixing policies and optimization complexity. To address this challenge, we propose a novel automatic mixup (AutoMix) framework, where the mixup policy is parameterized and serves the ultimate classification goal directly. Specifically, AutoMix reformulates the mixup classification into two sub-tasks (i.e., mixed sample generation and mixup classification) with corresponding sub-networks and solves them in a bi-level optimization framework. For the generation, a learnable lightweight mixup generator, Mix Block, is designed to generate mixed samples by modeling patch-wise relationships under the direct supervision of the corresponding mixed labels. To prevent the degradation and instability of bi-level optimization, we further introduce a momentum pipeline to train AutoMix in an end-to-end manner. Extensive experiments on nine image benchmarks prove the superiority of AutoMix compared with state-of-the-arts in various classification scenarios and downstream tasks.