Miracle-dz/UniFAR-FTUs huggingface dataset:
The Sierpinski Carpet as a Final Coalgebra

We advance the program of connections between ﬁnal coalgebras as sources of circularity in mathematics and fractal sets of real numbers. In particular, we are interested in the Sierpinski carpet, taking it as a fractal subset of the unit square. We construct a category of square sets and an endofunctor on it which corresponds to the operation of gluing copies of a square set along segments. We show that the initial algebra and ﬁnal coalgebra exist for our functor, and that the ﬁnal coalgebra is bi-Lipschitz equivalent to the Sierpinski carpet. Along the way, we make connections to topics such as the itera-tive construction of initial algebras as ω -colimits, corecursive algebras, and the classic treatment of fractal sets due to Hutchinson [8].
A Primer on Near-Field Beamforming for Arrays and Reconfigurable Intelligent Surfaces

Wireless communication systems have almost exclusively operated in the far-field of antennas and antenna arrays, which is conventionally characterized by having propagation distances beyond the Fraunhofer distance. This is natural since the Fraunhofer distance is normally only a few wavelengths. With the advent of active arrays and passive reconfigurable intelligent surfaces (RIS) that are physically large, it is plausible that the transmitter or receiver is located in between the Fraunhofer distance of the individual array/surface elements and the Fraunhofer distance of the entire array. An RIS then can be configured to reflect the incident waveform towards a point in the radiative near-field of the surface, resulting in a beam with finite depth, or as a conventional angular beam with infinity focus, which only results in amplification in the far-field. To understand when these different options are viable, an accurate characterization of the near-field behaviors is necessary. In this paper, we revisit the motivation and approximations behind the Fraunhofer distance and show that it is not the right metric for determining when near-field focusing is possible. We obtain the distance range where finite-depth beamforming is possible and the distance where the beamforming gain tapers off.
Coronal Magnetic Field Measurements along a Partially Erupting Filament in a Solar Flare

Magnetic flux ropes are the centerpiece of solar eruptions. Direct measurements for the magnetic field of flux ropes are crucial for understanding the triggering and energy release processes, yet they remain heretofore elusive. Here we report microwave imaging spectroscopy observations of an M1.4-class solar flare that occurred on 2017 September 6, using data obtained by the Expanded Owens Valley Solar Array. This flare event is associated with a partial eruption of a twisted filament observed in Hα by the Goode Solar Telescope at the Big Bear Solar Observatory. The extreme ultraviolet (EUV) and X-ray signatures of the event are generally consistent with the standard scenario of eruptive flares, with the presence of double flare ribbons connected by a bright flare arcade. Intriguingly, this partial eruption event features a microwave counterpart, whose spatial and temporal evolution closely follow the filament seen in Hα and EUV. The spectral properties of the microwave source are consistent with nonthermal gyrosynchrotron radiation. Using spatially resolved microwave spectral analysis, we derive the magnetic field strength along the filament spine, which ranges from 600 to 1400 Gauss from its apex to the legs. The results agree well with the nonlinear force-free magnetic model extrapolated from the preflare photospheric magnetogram. We conclude that the microwave counterpart of the erupting filament is likely due to flare-accelerated electrons injected into the filament-hosting magnetic flux rope cavity following the newly reconnected magnetic field lines.
Logic Constraints to Feature Importances

In recent years, Artificial Intelligence (AI) algorithms have been proven to outperform traditional statistical methods in terms of predictivity, especially when a large amount of data was available. Nevertheless, the ”black box” nature of AI models is often a limit for a reliable application in high-stakes fields like diagnostic techniques, autonomous guide, etc. Recent works have shown that an adequate level of interpretability could enforce the more general concept of model trustworthiness [1]. The basic idea of this paper is to exploit the human prior knowledge of the features’ importance for a specific task, in order to coherently aid the phase of the model’s fitting. This sort of ”weighted” AI is obtained by extending the empirical loss with a regularization term encouraging the importance of the features to follow predetermined constraints. This procedure relies on local methods for the feature importance computation, e.g. LRP, LIME, etc. that are the link between the model weights to be optimized and the user-defined constraints on feature importance. In the fairness area, promising experimental results have been obtained for the Adult dataset. Many other possible applications of this model agnostic theoretical framework are described.
Witnessing objectivity on a quantum computer

Understanding the emergence of objectivity from the quantum realm has been a long standing issue strongly related to the quantum to classical crossover. Quantum Darwinism (QD) provides an answer, interpreting objectivity as consensus between independent observers. Quantum computers provide an interesting platform for such experimental investigation of QD, fulfiling their initial intended purpose as quantum simulators. Here we assess to what degree current Noisy intermediate-scale quantum devices can be used as experimental platforms in the field of QD. We do this by simulating an exactly solvable stochastic collision model, taking advantage of the analytical solution to benchmark the experimental results.
SDR — Medium Rare with Fast Computations

We revisit the widely used bss_eval metrics for source separation with an eye out for performance. We propose a fast algorithm fixing shortcomings of publicly available implementations. First, we show that the metrics are fully specified by the squared cosine of just two angles between estimate and reference subspaces. Second, large linear systems are involved. However, they are structured, and we apply a fast iterative method based on conjugate gradient descent. The complexity of this step is thus reduced by a factor quadratic in the distortion filter size used in bss_eval, usually 512. In experiments, we assess speed and numerical accuracy. Not only is the loss of accuracy due to the approximate solver acceptable for most applications, but the speed-up is up to two orders of magnitude in some, not so extreme, cases. We confirm that our implementation can train neural networks, and find that longer distortion filters may be beneficial.
Reducing the Covariate Shift by Mirror Samples in Cross Domain Alignment

Eliminating the covariate shift cross domains is one of the common methods to deal with the issue of domain shift in visual unsupervised domain adaptation. However, current alignment methods, especially the prototype based or sample-level based methods neglect the structural properties of the underlying distribution and even break the condition of covariate shift. To relieve the limitations and conflicts, we introduce a novel concept named (virtual) mirror, which represents the equivalent sample in another domain. The equivalent sample pairs, named mirror pairs reflect the natural correspondence of the empirical distributions. Then a mirror loss, which aligns the mirror pairs cross domains, is constructed to enhance the alignment of the domains. The proposed method does not distort the internal structure of the underlying distribution. We also provide theoretical proof that the mirror samples and mirror loss have better asymptotic properties in reducing the domain shift. By applying the virtual mirror and mirror loss to the generic unsupervised domain adaptation model, we achieved consistent superior performance on several mainstream benchmarks. Code is available at https://github.com/CTI-VISION/Mirror-Sample
Dropout Prediction Variation Estimation Using Neuron Activation Strength

It is well-known DNNs would generate different prediction results even given the same model configuration and training dataset. As a result, it becomes more and more important to study prediction variation, i.e. the variation of the predictions on a given input example, in neural network models. Dropout has been commonly used in various applications to quantify prediction variations. However, using dropout in practice can be expensive as it requires running dropout inference many times to estimate prediction variation. In this paper, we study how to estimate dropout prediction variation in a resource-efficient manner. In particular, we demonstrate that we can use neuron activation strength to estimate dropout prediction variation under different dropout settings and on a variety of tasks using three large datasets, MovieLens, Criteo, and EMNIST. Our approach provides an inference-once alternative to estimate dropout prediction variation as an auxiliary task when the main prediction model is served. Moreover, we show that using activation strength features from a subset of neural network layers can be sufficient to achieve similar variation estimation performance compared to using activation features from all layers. This can provide further resource reduction for variation estimation.
REGULARIZED STEP DIRECTIONS IN CONJUGATE GRADIENT MINIMIZATION FOR MACHINE LEARNING

Conjugate gradient minimization methods (CGM) and their accelerated variants are widely used in machine learning applications. We focus on the use of cubic regularization to improve the CGM direction independent of the steplength (learning rate) computation. Using Shanno’s reformulation of CGM as a memoryless BFGS method, we derive new formulas for the regularized step direction, which can be evaluated without additional computational eﬀort. The new step directions are shown to improve iteration counts and runtimes and reduce the need to restart the CGM.
Leveraging Automated Unit Tests for Unsupervised Code Translation

With little to no parallel data available for programming languages, unsupervised methods are well-suited to source code translation. However, the majority of unsupervised machine translation approaches rely on back-translation, a method developed in the context of natural language translation and one that inherently involves training on noisy inputs. Unfortunately, source code is highly sensitive to small changes; a single token can result in compilation failures or erroneous programs, unlike natural languages where small inaccuracies may not change the meaning of a sentence. To address this issue, we propose to leverage an automated unit-testing system to filter out invalid translations, thereby creating a fully tested parallel corpus. We found that fine-tuning an unsupervised model with this filtered data set significantly reduces the noise in the translations so-generated, comfortably outperforming the state-of-the-art for all language pairs studied. In particular, for Java $\to$ Python and Python $\to$ C++ we outperform the best previous methods by more than 16% and 24% respectively, reducing the error rate by more than 35%.
EditVAE: Unsupervised Part-Aware Controllable 3D Point Cloud Shape Generation

This paper tackles the problem of parts-aware point cloud generation. Unlike existing works which require the point cloud to be segmented into parts a priori, our parts-aware editing and generation are performed in an unsupervised manner. We achieve this with a simple modification of the Variational Auto-Encoder which yields a joint model of the point cloud itself along with a schematic representation of it as a combination of shape primitives. In particular, we introduce a latent representation of the point cloud which can be decomposed into a disentangled representation for each part of the shape. These parts are in turn disentangled into both a shape primitive and a point cloud representation, along with a standardising transformation to a canonical coordinate system. The dependencies between our standardising transformations preserve the spatial dependencies between the parts in a manner that allows meaningful parts-aware point cloud generation and shape editing. In addition to the flexibility afforded by our disentangled representation, the inductive bias introduced by our joint modeling approach yields state-of-the-art experimental results on the ShapeNet dataset.
Possible Modification of the Standard Cosmological Model to Resolve a Tension with Hubble Constant Values

The tensions concerning the values of Hubble constant obtained from the early and the late Universe data pose a significant challenge to modern cosmology. Possible modifications of the flat homogeneous isotropic cosmological ΛCDM model are considered, in which the Universe contains the dark energy, cold baryonic matter, and dark matter. They are based on general relativity and satisfy two requirements: (1) the value of the Hubble constant calculated from the value of the Hubble parameter at the recombination by formulas of the flat ΛCDM model, should be equal to 92% of the one based on low-redshift observations; (2) deviations from the ΛCDM model should not lead to effects that contradict astronomical observations and estimations obtained thereof. The analysis showed that there are few opportunities for the choice. Either we should consider DM with negative pressure −pdmc2 ≪ pdm < 0, which weakly affects the evolution of the Universe and the observed manifestations of DM, or we should admit the mechanism of generation of new matter, for example, by the dark energy decay.
NeurIPS 2021 Competition IGLU: Interactive Grounded Language Understanding in a Collaborative Environment

Human intelligence has the remarkable ability to adapt to new tasks and environments quickly. Starting from a very young age, humans acquire new skills and learn how to solve new tasks either by imitating the behavior of others or by following provided natural language instructions. To facilitate research in this direction, we propose IGLU: Interactive Grounded Language Understanding in a Collaborative Environment. The primary goal of the competition is to approach the problem of how to build interactive agents that learn to solve a task while provided with grounded natural language instructions in a collaborative environment. Understanding the complexity of the challenge, we split it into sub-tasks to make it feasible for participants. This research challenge is naturally related, but not limited, to two fields of study that are highly relevant to the NeurIPS community: Natural Language Understanding and Generation (NLU/G) and Reinforcement Learning (RL). Therefore, the suggested challenge can bring two communities together to approach one of the important challenges in AI. Another important aspect of the challenge is the dedication to perform a human-in-the-loop evaluation as a final evaluation for the agents developed by contestants.
A scale-wise analysis of intermittent momentum transport in dense canopy flows

Abstract We investigate the intermittent dynamics of momentum transport and its underlying time scales in the near-wall region of the neutrally stratified atmospheric boundary layer in the presence of a vegetation canopy. This is achieved through an empirical analysis of the persistence time scales (periods between successive zero-crossings) of momentum flux events, and their connection to the ejection–sweep cycle. Using high-frequency measurements from the GoAmazon campaign, spanning multiple heights within and above a dense canopy, the analysis suggests that, when the persistence time scales ($t_p$) of momentum flux events from four different quadrants are separately normalized by $\varGamma _{w}$ (integral time scale of the vertical velocity), their distributions $P(t_p/\varGamma _{w})$ remain height-invariant. This result points to a persistent memory imposed by canopy-induced coherent structures, and to their role as an efficient momentum-transporting mechanism between the canopy airspace and the region immediately above. Moreover, $P(t_p/\varGamma _{w})$ exhibits a power-law scaling at times $t_{p}<\varGamma _{w}$, with an exponential tail appearing for $t_{p} \geq \varGamma _{w}$. By separating the flux events based on $t_p$, we discover that around 80 % of the momentum is transported through the long-lived events ($t_{p} \geq \varGamma _{w}$) at heights immediately above the canopy, while the short-lived ones ($t_{p} < \varGamma _{w}$) only contribute marginally ($\approx 20\,\%$). To explain the role of instantaneous flux amplitudes in momentum transport, we compare the measurements with newly developed surrogate data and establish that the range of time scales involved with amplitude variations in the fluxes tends to increase as one transitions from within to above the canopy.
The deep generative decoder: Using MAP estimates of representations

A deep generative model is characterized by a representation space, its distribution, and a neural network mapping the representation to a distribution over vectors in feature space. Common methods such as variational autoencoders (VAEs) apply variational inference for training the neural network, but optimizing these models is often non-trivial. The encoder adds to the complexity of the model and introduces an amortization gap and the quality of the variational approximation is usually unknown. Additionally, the balance of the loss terms of the objective function heavily influences performance. Therefore, we argue that it is worthwhile to investigate a much simpler approximation which finds representations and their distribution by maximizing the model likelihood via back-propagation. In this approach, there is no encoder, and we therefore call it a Deep Generative Decoder (DGD). Using the CIFAR10 data set, we show that the DGD is easier and faster to optimize than the VAE, achieves more consistent low reconstruction errors of test data, and alleviates the problem of balancing the reconstruction and distribution loss terms. Although the model in its simple form cannot compete with stateof-the-art image generation approaches, it obtains better image generation scores than the variational approach on the CIFAR10 data. We demonstrate on MNIST data how the use of a Gaussian mixture with priors can lead to a clear separation of classes in a 2D representation space, and how the DGD can be used with labels to obtain a supervised representation.
Revisiting Latent-Space Interpolation via a Quantitative Evaluation Framework

Latent-space interpolation is commonly used to demonstrate the generalization ability of deep latent variable models. Various algorithms have been proposed to calculate the best trajectory between two encodings in the latent space. In this work, we show how data labeled with semantically continuous attributes can be utilized to conduct a quantitative evaluation of latent-space interpolation algorithms, for variational autoencoders. Our framework can be used to complement the standard qualitative comparison, and also enables evaluation for domains (such as graph) in which the visualization is difficult. Interestingly, our experiments reveal that the superiority of interpolation algorithms could be domain-dependent. While normalised interpolation works best for the image domain, spherical linear interpolation achieves the best performance in the graph domain. Next, we propose a simple-yet-effective method to restrict the latent space via a bottleneck structure in the encoder. We find that all interpolation algorithms evaluated in this work can benefit from this restriction. Finally, we conduct interpolation-aware training with the labeled attributes, and show that this explicit supervision can improve the interpolation performance.
Exploring the Importance of F0 Trajectories for Speaker Anonymization using X-vectors and Neural Waveform Models

Voice conversion for speaker anonymization is an emerging field in speech processing research. Many state-of-the-art approaches are based on the resynthesis of the phoneme posteriorgrams (PPG), the fundamental frequency (F0) of the input signal together with modified X-vectors. Our research focuses on the role of F0 for speaker anonymization, which is an understudied area. Utilizing the VoicePrivacy Challenge 2020 framework and its datasets we developed and evaluated eight low-complexity F0 modifications prior resynthesis. We found that modifying the F0 can improve speaker anonymization by as much as 8% with minor word-error rate degradation.
An open question about powers of log(n) in quasi-Monte Carlo

The commonly quoted error rate for QMC integration with an infinite low discrepancy sequence is O (n−1 log(n)). This holds uniformly over d dimensional integrands of Hardy-Krause variation one when using n evaluation points. Implicit in the rate is that for any sequence of QMC points the integrand can be chosen to depend on n. If we have a fixed integrand, should we expect to need those powers of log(n) as n → ∞? That is, do those powers provide a realistic idea of the progress that the algorithm makes as n → ∞? This paper poses an open question about whether there is any f and any (t, d)-sequence for which the absolute error exceeds a positive multiple of log(n)/n infinitely often for some r > 1. For r = 1, such functions are known from the discrepancy literature even for d = 1. An empirical search when d = 2 for integrands designed to exploit known weaknesses in certain point sets showed no evidence that r > 1 is needed. An example with d = 3 and n up to 2100 appears to require r > 1. Of course neither of these resolve the open problem.
Conjugate linear perturbations of Dirac operators and Majorana fermions

We study a canonical class of perturbations of Dirac operators that are defined in any dimension and on any Hermitian Clifford module bundle. These operators generalize the 2-dimensional Jackiw–Rossi operator, which describes electronic excitations on topological superconductors. We also describe the low energy spectrum of these operators on complete surfaces, under mild hypotheses.
Internal Feedback in Biological Control: Diversity, Delays, and Standard Theory

Neural architectures in organisms support efficient and robust control that is beyond the capability of engineered architectures. Unraveling the function of such architectures is challenging; their components are highly diverse and heterogeneous in their morphology, physiology, and biochemistry, and often obey severe speed-accuracy tradeoffs; they also contain many cryptic internal feedback pathways (IFPs). We claim that IFPs are crucial architectural features that strategically combine highly diverse components to give rise to optimal performance. We demonstrate this in a case study, and additionally describe how sensing and actuation delays in standard control (state feedback, full control, output feedback) give rise to independent and separable sources of IFPs. Our case study is an LQR problem with two types of sensors, one fast but sparse and one dense but slow. Controllers using only one type of sensor perform poorly, often failing even to stabilize; controllers using both types of sensors perform extremely well, demonstrating a strong diversity-enabled sweet spot (DESS). We demonstrate that IFPs are key in enabling this DESS, and additionally that with IFPs removed, controllers with delayed sensing perform poorly. The existence of strong DESS and IFP in this simple example suggest that these are fundamental architectural features in any complex system with diverse components, such as organisms and cyberphysical systems.