Reviewerly/exHarmony huggingface dataset:
Neural network evidence of a weakly first order phase transition for the  two-dimensional 5-state Potts model

A universal (supervised) neural network (NN), which is only trained once on a one-dimensional lattice of 200 sites, is employed to study the phase transition of the two-dimensional (2D) 5-state ferromagnetic Potts model on the square lattice. In particular, the NN is obtained by using merely two artificially made configurations as the training set. Due to the elegant features of the considered NN, results associated with systems consisting of over 4000000 spins can be obtained with ease, and convincing evidence showing the investigated phase transition is weakly first order is reached. The outcomes demonstrated here can hardly be achieved with the standard NNs that are commonly used in the literature.
On the Overlooked Significance of Underutilized Contextual Features in Recent News Recommendation Models

Personalized news recommendation aims to provide attractive articles for readers by predicting their likelihood of clicking on a certain article. To accurately predict this probability, plenty of studies have been proposed that actively utilize content features of articles, such as words, categories, or entities. However, we observed that the articles' contextual features, such as CTR (click-through-rate), popularity, or freshness, were either neglected or underutilized recently. To prove that this is the case, we conducted an extensive comparison between recent deep-learning models and naive contextual models that we devised and surprisingly discovered that the latter easily outperforms the former. Furthermore, our analysis showed that the recent tendency to apply overly sophisticated deep-learning operations to contextual features was actually hindering the recommendation performance. From this knowledge, we design a purposefully simple contextual module that can boost the previous news recommendation models by a large margin.
A Special Case of Schematic Syntactic Unification

We present a unification problem based on first-order syntactic unification which ask whether every problem in a schematically-defined sequence of unification problems is unifiable, so called loop unification. Alternatively, our problem may be formulated as a recursive procedure calling first-order syntactic unification on certain bindings occurring in the solved form resulting from unification. Loop unification is closely related to Narrowing as the schematic constructions can be seen as a rewrite rule applied during unification, and primal grammars, as we deal with recursive term constructions. However, loop unification relaxes the restrictions put on variables as fresh as well as used extra variables may be introduced by rewriting. In this work we consider an important special case, so called semiloop unification. We provide a sufficient condition for unifiability of the entire sequence based on the structure of a sufficiently long initial segment. It remains an open question whether this condition is also necessary for semiloop unification and how it may be extended to loop unification.
Diagrammatic Analysis for Parameterized Quantum Circuits

Diagrammatic representations of quantum algorithms and circuits offer novel approaches to their design and analysis. In this work, we describe extensions of the ZX-calculus especially suitable for parameterized quantum circuits, in particular for computing observable expectation values as functions of or for fixed parameters, which are important algorithmic quantities in a variety of applications ranging from combinatorial optimization to quantum chemistry. We provide several new ZX-diagram rewrite rules and generalizations for this setting. In particular, we give formal rules for dealing with linear combinations of ZX-diagrams, where the relative complex-valued scale factors of each diagram must be kept track of, in contrast to most previously studied single-diagram realizations where these coefficients can be effectively ignored. This allows us to directly import a number useful relations from the operator analysis to ZX-calculus setting, including causal cone and quantum gate commutation rules. We demonstrate that the diagrammatic approach offers useful insights into algorithm structure and performance by considering several ansatze from the literature including realizations of hardware-efficient ansatze and QAOA. We find that by employing a diagrammatic representation, calculations across different ansatze can become more intuitive and potentially easier to approach systematically than by alternative means. Finally, we outline how diagrammatic approaches may aid in the design and study of new and more effective quantum circuit ansatze.
Invariance principle of random projection for the norm

Johnson-Lindenstrauss guarantees certain topological structure is preserved under random projections when project high dimensional deterministic vectors to low dimensional vectors. In this work, we try to understand how random matrix affect norms of random vectors. In particular we prove the distribution of the norm of random vector $X \in \mathbb{R}^n$, whose entries are i.i.d. random variables, is preserved by random projection $S:\mathbb{R}^n \to \mathbb{R}^m$. More precisely, \[ \frac{X^TS^TSX - mn}{\sqrt{σ^2 m^2n+2mn^2}} \xrightarrow[\quad m/n\to 0 \quad ]{ m,n\to \infty } \mathcal{N}(0,1) \] We also prove a concentration of the random norm transformed by either random projection or random embedding. Overall, our results showed random matrix has low distortion for the norm of random vectors with i.i.d. entries.
Gradient Masked Averaging for Federated Learning

Federated learning (FL) is an emerging paradigm that permits a large number of clients with heterogeneous data to coordinate learning of a unified global model without the need to share data amongst each other. A major challenge in federated learning is the heterogeneity of data across client, which can degrade the performance of standard FL algorithms. Standard FL algorithms involve averaging of model parameters or gradient updates to approximate the global model at the server. However, we argue that in heterogeneous settings, averaging can result in information loss and lead to poor generalization due to the bias induced by dominant client gradients. We hypothesize that to generalize better across non-i.i.d datasets, the algorithms should focus on learning the invariant mechanism that is constant while ignoring spurious mechanisms that differ across clients. Inspired from recent works in Out-of-Distribution generalization, we propose a gradient masked averaging approach for FL as an alternative to the standard averaging of client updates. This aggregation technique for client updates can be adapted as a drop-in replacement in most existing federated algorithms. We perform extensive experiments on multiple FL algorithms with in-distribution, real-world, feature-skewed out-of-distribution, and quantity imbalanced datasets and show that it provides consistent improvements, particularly in the case of heterogeneous clients.
A fast implementation of the Monster group

Let $\mathbb{M}$ be the Monster group, which is the largest sporadic finite simple group, and has first been constructed in 1982 by Griess. In 1985 Conway has constructed a 196884-dimensional rational epresentation $\rho$ of $\mathbb{M}$ with matrix entries in $\mathbb{Z}[\frac{1}{2}]$. We describe a new and very fast algorithm for performing the group operation in $\mathbb{M}$. For an odd integer $p > 1$ let $\rho_p$ be the representation $\rho$ with matrix entries taken modulo $p$. We use a generating set $\Gamma$ of $\mathbb{M}$, such that the operation of a generator in $\Gamma$ on an element of $\rho_p$ can easily be computed. We construct a triple $(v_1, v^+, v^-)$ of elements of the module $\rho_{15}$, such that an unknown $g \in \mathbb{M}$ can be effectively computed as a word in $\Gamma$ from the images $(v_1 g, v^+ g, v^- g)$. Our new algorithm based on this idea multiplies two random elements of $\mathbb{M}$ in less than 30~milliseconds on a standard PC with an Intel i7-8750H CPU at 4 GHz. This is more than 100000 times faster than estimated by Wilson in 2013.
The Complexity of Approximate Pattern Matching on De Bruijn Graphs

Aligning a sequence to a walk in a labeled graph is a problem of fundamental importance to Computational Biology. For finding a walk in an arbitrary graph with $|E|$ edges that exactly matches a pattern of length $m$, a lower bound based on the Strong Exponential Time Hypothesis (SETH) implies an algorithm significantly faster than $O(|E|m)$ time is unlikely [Equi et al., ICALP 2019]. However, for many special graphs, such as de Bruijn graphs, the problem can be solved in linear time [Bowe et al., WABI 2012]. For approximate matching, the picture is more complex. When edits (substitutions, insertions, and deletions) are only allowed to the pattern, or when the graph is acyclic, the problem is again solvable in $O(|E|m)$ time. When edits are allowed to arbitrary cyclic graphs, the problem becomes NP-complete, even on binary alphabets [Jain et al., RECOMB 2019]. These results hold even when edits are restricted to only substitutions. The complexity of approximate pattern matching on de Bruijn graphs remained open. We investigate this problem and show that the properties that make de Bruijn graphs amenable to efficient exact pattern matching do not extend to approximate matching, even when restricted to the substitutions only case with alphabet size four. We prove that determining the existence of a matching walk in a de Bruijn graph is NP-complete when substitutions are allowed to the graph. In addition, we demonstrate that an algorithm significantly faster than $O(|E|m)$ is unlikely for de Bruijn graphs in the case where only substitutions are allowed to the pattern. This stands in contrast to pattern-to-text matching where exact matching is solvable in linear time, like on de Bruijn graphs, but approximate matching under substitutions is solvable in subquadratic $O(n\sqrt{m})$ time, where $n$ is the text's length [Abrahamson, SIAM J. Computing 1987].
DP-REC: Private & Communication-Efficient Federated Learning

Privacy and communication efficiency are important challenges in federated training of neural networks, and combining them is still an open problem. In this work, we develop a method that unifies highly compressed communication and differential privacy (DP). We introduce a compression technique based on Relative Entropy Coding (REC) to the federated setting. With a minor modification to REC, we obtain a provably differentially private learning algorithm, DP-REC, and show how to compute its privacy guarantees. Our experiments demonstrate that DP-REC drastically reduces communication costs while providing privacy guarantees comparable to the state-of-the-art.
One-Step Abductive Multi-Target Learning with Diverse Noisy Label Samples

One-step abductive multi-target learning (OSAMTL) was proposed to handle complex noisy labels. In this paper, giving definition of diverse noisy label samples (DNLS), we propose one-step abductive multi-target learning with DNLS (OSAMTL-DNLS) to expand the methodology of original OSAMTL to better handle complex noisy labels.
Omnifont Persian OCR System Using Primitives

In this paper, we introduce a model-based omnifont Persian OCR system. The system uses a set of 8 primitive elements as structural features for recognition. First, the scanned document is preprocessed. After normalizing the preprocessed image, text rows and sub-words are separated and then thinned. After recognition of dots in sub-words, strokes are extracted and primitive elements of each sub-word are recognized using the strokes. Finally, the primitives are compared with a predefined set of character identification vectors in order to identify sub-word characters. The separation and recognition steps of the system are concurrent, eliminating unavoidable errors of independent separation of letters. The system has been tested on documents with 14 standard Persian fonts in 6 sizes. The achieved precision is 97.06%.
A Fine-Grained Analysis of Public Opinion toward Chinese Technology Companies on Reddit

In the face of the growing global influence and prevalence of Chinese technology companies, governments worldwide have expressed concern and mistrust toward these companies. There is a scarcity of research that specifically examines the widespread public response to this phenomenon on a large scale. This study aims to fill in the gap in understanding public opinion toward Chinese technology companies using Reddit data, a popular news-oriented social media platform. We employ the state-of-the-art transformer model to build a reliable sentiment classifier. We then use LDA to extract the topics associated with positive and negative comments. We also conduct content analysis by studying the changes in the semantic meaning of the companies' names over time. Our main findings include the following: 1) Notable difference exists in the proportions of positive comments (8.42%) and negative comments (14.12%); 2) Positive comments are mostly associated with the companies' consumer products, such as smartphones, laptops, and wearable electronics. Negative comments have a more diverse topic distribution (notable topics include criticism toward the platform, dissatisfaction with the companies' smartphone products, companies' ties to the Chinese government, data security concerns, 5G construction, and general political discussions); and 3) Characterization of each technology company is usually centered around a particular predominant theme related to the company, while real-world political events may trigger drastic changes in users' characterization.
Efficient realization of quantum algorithms with qudits

The development of a universal fault-tolerant quantum computer that can solve efficiently various difficult computational problems is an outstanding challenge for science and technology. In this work, we propose a technique for an efficient implementation of quantum algorithms with qudits. Our method is based on a transpilation of a circuit in the qubit form depending on the parameters of a qudit-based processor. This approach provides a qubit-to-qudit mapping and comparison to a standard realization of quantum algorithms, which highlights potential advantages of qudits. As an example, we consider a scheme for an efficient implementation of a $5$-qubit quantum algorithm with qudits. We expect that our findings are of importance for ongoing experiments with noisy intermediate-scale quantum devices.
Quantum speedups for treewidth

In this paper, we study quantum algorithms for computing the exact value of the treewidth of a graph. Our algorithms are based on the classical algorithm by Fomin and Villanger (Combinatorica 32, 2012) that uses $O(2.616^n)$ time and polynomial space. We show three quantum algorithms with the following complexity, using QRAM in both exponential space algorithms: $\bullet$ $O(1.618^n)$ time and polynomial space; $\bullet$ $O(1.554^n)$ time and $O(1.452^n)$ space; $\bullet$ $O(1.538^n)$ time and space. In contrast, the fastest known classical algorithm for treewidth uses $O(1.755^n)$ time and space. The first two speed-ups are obtained in a fairly straightforward way. The first version uses additionally only Grover's search and provides a quadratic speedup. The second speedup is more time-efficient and uses both Grover's search and the quantum exponential dynamic programming by Ambainis et al. (SODA '19). The third version uses the specific properties of the classical algorithm and treewidth, with a modified version of the quantum dynamic programming on the hypercube. Lastly, as a small side result, we also give a new classical time-space tradeoff for computing treewidth in $O^*(2^n)$ time and $O^*(\sqrt{2^n})$ space.
Encoder Hurwitz Integers: The Hurwitz integers that have the ”division with small division” property

Abstract The residue class set of a Hurwitz integer is constructed by modulo function with primitive Hurwitz integer whose norm is a prime integer, i.e. prime Hurwitz integer. In this study, we consider primitive Hurwitz integer whose norm is both a prime integer and not a prime integer. If the norm of each element of the residue class set of a Hurwitz integer is less than the norm of the primitive Hurwitz integer used to construct the residue class set of the Hurwitz integer, then, the Euclid division algorithm works for this primitive Hurwitz integer. The Euclid division algorithm always works for prime Hurwitz integers. In other words, the prime Hurwitz integers and halves-integer primitive Hurwitz integers have the ”division with small remainder” property. However, this property is ignored in some studies that have a constructed Hurwitz residue class set that lies on primitive Hurwitz integers that their norms are not a prime integer and their components are in integers set. In this study, we solve this problem by defining Hurwitz integers that have the ”division with small remainder” property, namely, encoder Hurwitz integers set. Therefore, we can define appropriate metrics for codes over Lipschitz integers. Especially, Euclidean metric. Also, we investigate the performances of Hurwitz signal constellations (the left residue class set) obtained by modulo function with Hurwitz integers, which have the ”division with small remainder” property, over the additive white Gaussian noise (AWGN) channel by means of the constellation figure of merit (CFM), average energy, and signal-to-noise ratio (SNR).
A Quantum Internet Architecture

Entangled quantum communication is advancing rapidly, with laboratory and metropolitan testbeds under development, but to date there is no unifying Quantum Internet architecture. We propose a Quantum Internet architecture centered around the Quantum Recursive Network Architecture (QRNA), using RuleSet-based connections established using a two-pass connection setup. Scalability and internetworking (for both technological and administrative boundaries) are achieved using recursion in naming and connection control. In the near term, this architecture will support end-to-end, two-party entanglement on minimal hardware, and it will extend smoothly to multi-party entanglement and the use of quantum error correction on advanced hardware in the future. For a network internal gateway protocol, we recommend (but do not require) qDijkstra with seconds per Bell pair as link cost for routing; the external gateway protocol is designed to build recursively. The strength of our architecture is shown by assessing extensibility and demonstrating how robust protocol operation can be confirmed using the RuleSet paradigm.
CHAMP: Coherent Hardware-Aware Magnitude Pruning of Integrated Photonic  Neural Networks

We propose a novel hardware-aware magnitude pruning technique for coherent photonic neural networks. The proposed technique can prune 99.45% of network parameters and reduce the static power consumption by 98.23% with a negligible accuracy loss.
Harmless interpolation in regression and classification with structured features

Overparametrized neural networks tend to perfectly fit noisy training data yet generalize well on test data. Inspired by this empirical observation, recent work has sought to understand this phenomenon of benign overfitting or harmless interpolation in the much simpler linear model. Previous theoretical work critically assumes that either the data features are statistically independent or the input data is high-dimensional; this precludes general nonparametric settings with structured feature maps. In this paper, we present a general and flexible framework for upper bounding regression and classification risk in a reproducing kernel Hilbert space. A key contribution is that our framework describes precise sufficient conditions on the data Gram matrix under which harmless interpolation occurs. Our results recover prior independent-features results (with a much simpler analysis), but they furthermore show that harmless interpolation can occur in more general settings such as features that are a bounded orthonormal system. Furthermore, our results show an asymptotic separation between classification and regression performance in a manner that was previously only shown for Gaussian features.
Prefixes of the Fibonacci word that end with a cube

We study the prefixes of the Fibonacci word that end with a cube. Using Walnut we obtain an exact description of the positions of the Fibonacci word at which a cube ends.
Partitioning Image Representation in Contrastive Learning

In contrastive learning in the image domain, the anchor and positive samples are forced to have as close representations as possible. However, forcing the two samples to have the same representation could be misleading because the data augmentation techniques make the two samples different. In this paper, we introduce a new representation, partitioned representation, which can learn both common and unique features of the anchor and positive samples in contrastive learning. The partitioned representation consists of two parts: the content part and the style part. The content part represents common features of the class, and the style part represents the own features of each sample, which can lead to the representation of the data augmentation method. We can achieve the partitioned representation simply by decomposing a loss function of contrastive learning into two terms on the two separate representations, respectively. To evaluate our representation with two parts, we take two framework models: Variational AutoEncoder (VAE) and BootstrapYour Own Latent(BYOL) to show the separability of content and style, and to confirm the generalization ability in classification, respectively. Based on the experiments, we show that our approach can separate two types of information in the VAE framework and outperforms the conventional BYOL in linear separability and a few-shot learning task as downstream tasks.
Model-Agnostic Hybrid Numerical Weather Prediction and Machine Learning  Paradigm for Solar Forecasting in the Tropics

Numerical weather prediction (NWP) and machine learning (ML) methods are popular for solar forecasting. However, NWP models have multiple possible physical parameterizations, which requires site-specific NWP optimization. This is further complicated when regional NWP models are used with global climate models with different possible parameterizations. In this study, an alternative approach is proposed and evaluated for four radiation models. Weather Research and Forecasting (WRF) model is run in both global and regional mode to provide an estimate for solar irradiance. This estimate is then post-processed using ML to provide a final prediction. Normalized root-mean-square error from WRF is reduced by up to 40-50% with this ML error correction model. Results obtained using CAM, GFDL, New Goddard and RRTMG radiation models were comparable after this correction, negating the need for WRF parameterization tuning. Other models incorporating nearby locations and sensor data are also evaluated, with the latter being particularly promising.
O-ViT: Orthogonal Vision Transformer

Inspired by the tremendous success of the self-attention mechanism in natural language processing, the Vision Transformer (ViT) creatively applies it to image patch sequences and achieves incredible performance. However, the scaled dot-product self-attention of ViT brings about scale ambiguity to the structure of the original feature space. To address this problem, we propose a novel method named Orthogonal Vision Transformer (O-ViT), to optimize ViT from the geometric perspective. O-ViT limits parameters of self-attention blocks to be on the norm-keeping orthogonal manifold, which can keep the geometry of the feature space. Moreover, O-ViT achieves both orthogonal constraints and cheap optimization overhead by adopting a surjective mapping between the orthogonal group and its Lie algebra.We have conducted comparative experiments on image recognition tasks to demonstrate O-ViT's validity and experiments show that O-ViT can boost the performance of ViT by up to 3.6%.