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In modern machine learning, models can often fit training data in numerous ways, some of which perform well on unseen (test) data, while others do not. Remarkably, in such cases gradient descent frequently exhibits an implicit bias that leads to excellent performance on unseen data. This implicit bias was extensively studied in supervised learning, but is far less understood in optimal control (reinforcement learning). There, learning a controller applied to a system via gradient descent is known as policy gradient, and a question of prime importance is the extent to which a learned controller extrapolates to unseen initial states. This paper theoretically studies the implicit bias of policy gradient in terms of extrapolation to unseen initial states. Focusing on the fundamental Linear Quadratic Regulator (LQR) problem, we establish that the extent of extrapolation depends on the degree of exploration induced by the system when commencing from initial states included in training. Experiments corroborate our theory, and demonstrate its conclusions on problems beyond LQR, where systems are non-linear and controllers are neural networks. We hypothesize that real-world optimal control may be greatly improved by developing methods for informed selection of initial states to train on., Comment: Accepted to ICML 2024

Graph generation is a fundamental problem in various domains, including chemistry and social networks. Recent work has shown that molecular graph generation using recurrent neural networks (RNNs) is advantageous compared to traditional generative approaches which require converting continuous latent representations into graphs. One issue which arises when treating graph generation as sequential generation is the arbitrary order of the sequence which results from a particular choice of graph flattening method. In this work we propose using RNNs, taking into account the non-sequential nature of graphs by adding an Orderless Regularization (OLR) term that encourages the hidden state of the recurrent model to be invariant to different valid orderings present under the training distribution. We demonstrate that sequential graph generation models benefit from our proposed regularization scheme, especially when data is scarce. Our findings contribute to the growing body of research on graph generation and provide a valuable tool for various applications requiring the synthesis of realistic and diverse graph structures., Comment: 16 pages, 3 figures

Tensor robust principal component analysis (robust PCA) has been applied to the lightning images. Robust PCA aims to classify the images into low-rank and sparse components. The low rank and sparse components correspond to static background separation and the dynamic (lightning) part of the images correspondingly. After classification, Singular Value Decomposition (SVD) unfold technique has been applied to sparse tensor, which transforms the tensor to spatial-temporal spaces in the form of vector matrixes. Spectral evolution shows the evolution of the polarization of the UV-Vis spectra. The contour maps of 2D energy density plots reveal the zero-point energy fluctuations of the bosons, fermions, and virtual matters from early to late stages. Detection of such fluctuations in the early stages can help to remote sensing of the lightning. 3D vector(ether) field representation of the sparse tensor of the brightest lightning reveals the butterfly effect of the black holes with the signatures of flapping. There is a correlation between the approximate entropy and the chaos trends of the 3D vector field analyzed by the Lyapunov exponent. In the brightest frame, the fractal dimension measures 0.8004, which is close to the Fibonacci Hamiltonian.

Overparameterization in deep learning typically refers to settings where a trained neural network (NN) has representational capacity to fit the training data in many ways, some of which generalize well, while others do not. In the case of Recurrent Neural Networks (RNNs), there exists an additional layer of overparameterization, in the sense that a model may exhibit many solutions that generalize well for sequence lengths seen in training, some of which extrapolate to longer sequences, while others do not. Numerous works have studied the tendency of Gradient Descent (GD) to fit overparameterized NNs with solutions that generalize well. On the other hand, its tendency to fit overparameterized RNNs with solutions that extrapolate has been discovered only recently and is far less understood. In this paper, we analyze the extrapolation properties of GD when applied to overparameterized linear RNNs. In contrast to recent arguments suggesting an implicit bias towards short-term memory, we provide theoretical evidence for learning low-dimensional state spaces, which can also model long-term memory. Our result relies on a dynamical characterization which shows that GD (with small step size and near-zero initialization) strives to maintain a certain form of balancedness, as well as on tools developed in the context of the moment problem from statistics (recovery of a probability distribution from its moments). Experiments corroborate our theory, demonstrating extrapolation via learning low-dimensional state spaces with both linear and non-linear RNNs., Comment: Accepted to ICLR 2023, 9 pages, 2 figures plus supplementary

When using recurrent neural networks (RNNs) it is common practice to apply trained models to sequences longer than those seen in training. This "extrapolating" usage deviates from the traditional statistical learning setup where guarantees are provided under the assumption that train and test distributions are identical. Here we set out to understand when RNNs can extrapolate, focusing on a simple case where the data generating distribution is memoryless. We first show that even with infinite training data, there exist RNN models that interpolate perfectly (i.e., they fit the training data) yet extrapolate poorly to longer sequences. We then show that if gradient descent is used for training, learning will converge to perfect extrapolation under certain assumptions on initialization. Our results complement recent studies on the implicit bias of gradient descent, showing that it plays a key role in extrapolation when learning temporal prediction models., Comment: 8 pages, 5 figures (plus appendix), AISTATS2022

Substantial developments in pattern recognition and machine learning offer unique advancements to study the deeper structures of plasma physics. We have employed the Kernel principal component analysis(KPCA) of Argon glow discharge plasmas over time-resolved UV-Vis spectra for different pressure scans. 3D vector fields obtained by KPCA reveal the chaotic structure, strange attractors. The presence of the cross magnetic field (B=100G) and the addition of pressure increase the degree of chaos. Lower scale vector fields show that phonon sinks and traps and cool the plasma electron temperatures. The average electron and ion density profiles are provided by the 2D particle in cell simulation. Welch's transformation of the lower to higher scale vector fields illuminates the symmetric zero-point energy fluctuations of particles, antiparticles, and virtual particles. These positive and negative energies cancel each other and the combination of these energy fields form another type of fractal structure.

In many machine learning problems the output should not depend on the order of the input. Such "permutation invariant" functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly relevant for such problems, despite the inherent dependence of RNNs on order. We show that RNNs can be regularized towards permutation invariance, and that this can result in compact models, as compared to non-recurrent architectures. We implement this idea via a novel form of stochastic regularization. Existing solutions mostly suggest restricting the learning problem to hypothesis classes which are permutation invariant by design. Our approach of enforcing permutation invariance via regularization gives rise to models which are \textit{semi permutation invariant} (e.g. invariant to some permutations and not to others). We show that our method outperforms other permutation invariant approaches on synthetic and real world datasets., Comment: 9 pages, 5 figures, NeurIPS 2020

Argument generation is a challenging task whose research is timely considering its potential impact on social media and the dissemination of information. Here we suggest a pipeline based on GPT-2 for generating coherent claims, and explore the types of claims that it produces, and their veracity, using an array of manual and automatic assessments. In addition, we explore the interplay between this task and the task of Claim Retrieval, showing how they can complement one another., Comment: Accepted to Findings of EMNLP 2020

Pattern recognition and machine learning techniques are known to play an emerging role for studying underlying physics of light-matter interaction. While on the subject, photon condensation and Anti-Stokes cooling remain compelling phenomena of laser-underdense plasma interaction. In this work, the interaction of a 1064 nm continuum-wave laser with inductively-coupled plasma (ICP) of Mercury(Hg) has been studied by probabilistic pattern recognition over observed time resolved spectral data.3D vector fields obtained by the probabilistic pattern recognition over spectral database proficiently illuminates the analogue black hole (ABH) and its sonic horizon in which homoclinic orbit Whistler waves are exited. Vector spectra show the collective behavior of condensation and anti-Stokes cooling is due to the electronic transitions of Hg1 trapped by the phonon sink of ABH of laser. Modeling of subsonic phonon vector spectrum obtained by the probabilistic linear discriminant analysis(PLDA) estimates the 0.70 nanoKelvin of temperature of the sink region of ABH.

Identifying the quality of free-text arguments has become an important task in the rapidly expanding field of computational argumentation. In this work, we explore the challenging task of argument quality ranking. To this end, we created a corpus of 30,497 arguments carefully annotated for point-wise quality, released as part of this work. To the best of our knowledge, this is the largest dataset annotated for point-wise argument quality, larger by a factor of five than previously released datasets. Moreover, we address the core issue of inducing a labeled score from crowd annotations by performing a comprehensive evaluation of different approaches to this problem. In addition, we analyze the quality dimensions that characterize this dataset. Finally, we present a neural method for argument quality ranking, which outperforms several baselines on our own dataset, as well as previous methods published for another dataset., Comment: Accepted to AAAI 2020

We explore the task of automatic assessment of argument quality. To that end, we actively collected 6.3k arguments, more than a factor of five compared to previously examined data. Each argument was explicitly and carefully annotated for its quality. In addition, 14k pairs of arguments were annotated independently, identifying the higher quality argument in each pair. In spite of the inherent subjective nature of the task, both annotation schemes led to surprisingly consistent results. We release the labeled datasets to the community. Furthermore, we suggest neural methods based on a recently released language model, for argument ranking as well as for argument-pair classification. In the former task, our results are comparable to state-of-the-art; in the latter task our results significantly outperform earlier methods., Comment: Published at EMNLP 2019

The field of Grammatical Error Correction (GEC) has produced various systems to deal with focused phenomena or general text editing. We propose an automatic way to combine black-box systems. Our method automatically detects the strength of a system or the combination of several systems per error type, improving precision and recall while optimizing $F$ score directly. We show consistent improvement over the best standalone system in all the configurations tested. This approach also outperforms average ensembling of different RNN models with random initializations. In addition, we analyze the use of BERT for GEC - reporting promising results on this end. We also present a spellchecker created for this task which outperforms standard spellcheckers tested on the task of spellchecking. This paper describes a system submission to Building Educational Applications 2019 Shared Task: Grammatical Error Correction. Combining the output of top BEA 2019 shared task systems using our approach, currently holds the highest reported score in the open phase of the BEA 2019 shared task, improving F0.5 by 3.7 points over the best result reported., Comment: BEA 2019

We present a single-dish mapping algorithm with a number of advantages over traditional techniques. (1) Our algorithm makes use of weighted modeling, instead of weighted averaging, to interpolate between signal measurements. This smooths the data, but without blurring the data beyond instrumental resolution. Techniques that rely on weighted averaging blur point sources sometimes as much as 40%. (2) Our algorithm makes use of local, instead of global, modeling to separate astronomical signal from instrumental and/or environmental signal drift along the telescope's scans. Other techniques, such as basket weaving, model this drift with simple functional forms (linear, quadratic, etc.) across the entirety of scans, limiting their ability to remove such contaminants. (3) Our algorithm makes use of a similar, local modeling technique to separate astronomical signal from radio-frequency interference (RFI), even if only continuum data are available. (4) Unlike other techniques, our algorithm does not require data to be collected on a rectangular grid or regridded before processing. (5) Data from any number of observations, overlapping or not, may be appended and processed together. (6) Any pixel density may be selected for the final image. We present our algorithm, and evaluate it using both simulated and real data. We are integrating it into the image-processing library of the Skynet Robotic Telescope Network, which includes optical telescopes spanning four continents, and now also Green Bank Observatory's 20-meter diameter radio telescope in West Virginia. Skynet serves hundreds of professional users, and additionally tens of thousands of students, of all ages. Default data products are generated on the fly, but will soon be customizable after the fact., Comment: 50 pages, 54 figures, 4 tables, accepted for publication in ApJS

In this paper, the effects of electron beam on the X pinch produced spectra of L-shell Mo plasma have been investigated by principal component analysis (PCA), and this analysis is compared with that of line ratio diagnostics. Spectral database for PCA extraction was arranged using the non-LTE collisional radiative L-shell Mo model. PC vector spectra of L shell Mo including F, Ne, Na and Mg- like transitions were studied to investigate the polarization types of these transitions. PC1 vector spectra of F, Ne, Na and Mg- like transitions resulted in linear polarization of Stokes Q profiles. Besides, PC2 vector spectra showed linear polarization of Stokes U profiles of 2p53s of Ne like transitions which were recognized as responsive to the magnetic field (Trabert et al., 2017). 3D representation of PCA coefficients demonstrated that addition of electron beam to the non-LTE model generates the quantized collective clusters which are translations of each other and follow V-shaped cascade trajectories except for the case f = 0.0. The extracted principal coefficients were used as a database for the Artifical Neural Network (ANN) to estimate the plasma electron temperature, density and beam fractions of time integrated spatially resolved L-shell Mo X-pinch plasma spectrum. PCA based ANN provides advantage in reducing the network topology with a more efficient Backpropagation supervised learning algorithm. The modeled plasma electron temperature is about Te~660 eV and density ne=1x1020 cm-3 in the presence of the fraction of the beams with f~0.1 and centered energy of 5 keV.

Here, we have employed Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) to analyze Mie calculated UV-Vis spectra of gold nanospheres (GNS). Eigen spectra of PCA perform the Fano type resonances.3D vector field spectra reveal the Homoclinic orbit Lorenz attractor. Quantum confinement effects are observed by 3D representation of LDA. Standing wave patterns resulting from oscillations of ion acoustic phonon and electron waves are illustrated through the eigen spectra of LDA. Such capabilities of GNPs have brought high attention for the high energy density physics applications. Furthermore, accurate prediction of gold nanoparticle (GNP) sizes using machine learning could provide rapid analysis without the need for expensive analysis. Two hybrid algorithms consist of unsupervised PCA and two different supervised ANN have been used to estimate the diameters of GNPs. PCA based artificial neural network (ANN) were found to estimate the diameters with a high accuracy.