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The meteoric rise of online games has created a need for accurate skill rating systems for tracking improvement and fair matchmaking. Although many skill rating systems are deployed, with various theoretical foundations, less work has been done at analysing the real-world performance of these algorithms. In this paper, we perform an empirical analysis of Elo, Glicko2 and TrueSkill through the lens of surrogate modelling, where skill ratings influence future matchmaking with a configurable acquisition function. We look both at overall performance and data efficiency, and perform a sensitivity analysis based on a large dataset of Counter-Strike: Global Offensive matches.

NEXCERA has been recently introduced as novel ceramic-based material for spacers of ultra-stable laser cavities with a zero-crossing coefficient of thermal expansion at room temperature. Brownian thermal noise currently limits the performance of these cavities, and the mechanical loss factor, a critical parameter in estimating this noise, remains unknown for NEXCERA. In this work, we investigate the mechanical loss factor of NEXCERA N117B at room temperature across different resonance frequencies using the Gentle Nodal Suspension technique. We measure a promising loss factor of $\phi = 1.89\times 10^{-5}$, indicating NEXCERA's potential for ultra-stable laser cavities. Based on these results, we calculate the thermal noise when NEXCERA is used as a spacer and compare its overall performance as a spacer material to widely used materials such as ULE and Zerodur, considering various substrate materials. Our findings suggest that NEXCERA is a strong candidate due to its lower thermal noise and reduced linear drift rate., Comment: 10 pages, 10 figures

In this note we prove (under mild hypotheses) that $f$ is a nontrivial character of $\mathbb{F}_p$ if and only if the Fourier transform of $f$ has magnitude 1 somewhere in $\mathbb{F}_p^\times$. This implies a converse to a theorem of Gauss on the magnitude of the Gauss sum, in addition to other consequences., Comment: 4 pages. Comments very welcome!

For half a century, artificial intelligence research has attempted to reproduce the human qualities of abstraction and reasoning - creating computer systems that can learn new concepts from a minimal set of examples, in settings where humans find this easy. While specific neural networks are able to solve an impressive range of problems, broad generalisation to situations outside their training data has proved elusive.In this work, we look at several novel approaches for solving the Abstraction & Reasoning Corpus (ARC), a dataset of abstract visual reasoning tasks introduced to test algorithms on broad generalization. Despite three international competitions with $100,000 in prizes, the best algorithms still fail to solve a majority of ARC tasks and rely on complex hand-crafted rules, without using machine learning at all. We revisit whether recent advances in neural networks allow progress on this task. First, we adapt the DreamCoder neurosymbolic reasoning solver to ARC. DreamCoder automatically writes programs in a bespoke domain-specific language to perform reasoning, using a neural network to mimic human intuition. We present the Perceptual Abstraction and Reasoning Language (PeARL) language, which allows DreamCoder to solve ARC tasks, and propose a new recognition model that allows us to significantly improve on the previous best implementation.We also propose a new encoding and augmentation scheme that allows large language models (LLMs) to solve ARC tasks, and find that the largest models can solve some ARC tasks. LLMs are able to solve a different group of problems to state-of-the-art solvers, and provide an interesting way to complement other approaches. We perform an ensemble analysis, combining models to achieve better results than any system alone. Finally, we publish the arckit Python library to make future research on ARC easier., Comment: 32 pages main text, 17 pages

The accurate prediction of survival times for patients with severe diseases remains a critical challenge despite recent advances in artificial intelligence. This study introduces "SurvTimeSurvival: Survival Analysis On Patients With Multiple Visits/Records", utilizing the Transformer model to not only handle the complexities of time-varying covariates but also covariates data. We also tackle the data sparsity issue common to survival analysis datasets by integrating synthetic data generation into the learning process of our model. We show that our method outperforms state-of-the-art deep learning approaches on both covariates and time-varying covariates datasets. Our approach aims not only to enhance the understanding of individual patient survival trajectories across various medical conditions, thereby improving prediction accuracy, but also to play a pivotal role in designing clinical trials and creating new treatments., Comment: Accepted as Findings Track in Machine Learning For Health (ML4H) 2023

We prove the existence of "murmurations" in the family of holomorphic modular forms of level $1$ and weight $k\to\infty$, that is, correlations between their root numbers and Hecke eigenvalues at primes growing in proportion to the analytic conductor. This is the first demonstration of murmurations in an archimedean family., Comment: 30 pages

We investigate $k$-superirreducible polynomials, by which we mean irreducible polynomials that remain irreducible under any polynomial substitution of positive degree at most $k$. Let $\mathbb F$ be a finite field of characteristic $p$. We show that no $2$-superirreducible polynomials exist in $\mathbb F[t]$ when $p=2$ and that no such polynomials of odd degree exist when $p$ is odd. We address the remaining case in which $p$ is odd and the polynomials have even degree by giving an explicit formula for the number of monic 2-superirreducible polynomials having even degree $d$. This formula is analogous to that given by Gauss for the number of monic irreducible polynomials of given degree over a finite field. We discuss the associated asymptotic behaviour when either the degree of the polynomial or the size of the finite field tends to infinity., Comment: 10 pages, revised version

Experiments aimed at searching for variations in the fine-structure constant $\alpha$ are based on spectroscopy of transitions in microscopic bound systems, such as atoms and ions, or resonances in optical cavities. The sensitivities of these systems to variations in $\alpha$ are typically on the order of unity and are fixed for a given system. For heavy atoms, highly charged ions and nuclear transitions, the sensitivity can be increased by benefiting from the relativistic effects and favorable arrangement of quantum states. This article proposes a new method for controlling the sensitivity factor of macroscopic physical systems. Specific concepts of optical cavities with tunable sensitivity to $\alpha$ are described. These systems show qualitatively different properties from those of previous studies of the sensitivity of macroscopic systems to variations in $\alpha$, in which the sensitivity was found to be fixed and fundamentally limited to an order of unity. Although possible experimental constraints attainable with the specific optical cavity arrangements proposed in this article do not yet exceed the present best constraints on $\alpha$ variations, this work paves the way for developing new approaches to searching for variations in the fundamental constants of physics.

We propose to use table-top-size ultra-stable optical cavities from the state-of-the-art optical atomic clocks as bar gravitational wave detectors for the frequencies higher than 2 kHz. We show that 2-20 kHz range of gravitational waves' spectrum can be accessed with instruments below 2 meters in size. The proposed cavities' materials and properties are being within the present-day technology grasp. The ultra-stable optical cavities allow detecting not only predicted gravitational wave signals from such sources as binary neutron star mergers and post-mergers, subsolar-mass primordial black-hole mergers, and collapsing stellar cores, but can reach new physics beyond standard model looking for ultralight bosons such as QCD axions and axion-like particles formed through black hole superradiance.

Unravelling protein distributions within individual cells is key to understanding their function and state and indispensable to developing new treatments. Here we present the Hybrid subCellular Protein Localiser (HCPL), which learns from weakly labelled data to robustly localise single-cell subcellular protein patterns. It comprises innovative DNN architectures exploiting wavelet filters and learnt parametric activations that successfully tackle drastic cell variability. HCPL features correlation-based ensembling of novel architectures that boosts performance and aids generalisation. Large-scale data annotation is made feasible by our "AI-trains-AI" approach, which determines the visual integrity of cells and emphasises reliable labels for efficient training. In the Human Protein Atlas context, we demonstrate that HCPL defines state-of-the-art in the single-cell classification of protein localisation patterns. To better understand the inner workings of HCPL and assess its biological relevance, we analyse the contributions of each system component and dissect the emergent features from which the localisation predictions are derived.

Information over-squashing is a phenomenon of inefficient information propagation between distant nodes on networks. It is an important problem that is known to significantly impact the training of graph neural networks (GNNs), as the receptive field of a node grows exponentially. To mitigate this problem, a preprocessing procedure known as rewiring is often applied to the input network. In this paper, we investigate the use of discrete analogues of classical geometric notions of curvature to model information flow on networks and rewire them. We show that these classical notions achieve state-of-the-art performance in GNN training accuracy on a variety of real-world network datasets. Moreover, compared to the current state-of-the-art, these classical notions exhibit a clear advantage in computational runtime by several orders of magnitude., Comment: 21 pages, 8 figures, 7 tables

As a structured prediction task, scene graph generation, given an input image, aims to explicitly model objects and their relationships by constructing a visually-grounded scene graph. In the current literature, such task is universally solved via a message passing neural network based mean field variational Bayesian methodology. The classical loose evidence lower bound is generally chosen as the variational inference objective, which could induce oversimplified variational approximation and thus underestimate the underlying complex posterior. In this paper, we propose a novel doubly reparameterized importance weighted structure learning method, which employs a tighter importance weighted lower bound as the variational inference objective. It is computed from multiple samples drawn from a reparameterizable Gumbel-Softmax sampler and the resulting constrained variational inference task is solved by a generic entropic mirror descent algorithm. The resulting doubly reparameterized gradient estimator reduces the variance of the corresponding derivatives with a beneficial impact on learning. The proposed method achieves the state-of-the-art performance on various popular scene graph generation benchmarks., Comment: arXiv admin note: substantial text overlap with arXiv:2205.07017

Machine learning is vulnerable to adversarial manipulation. Previous literature has demonstrated that at the training stage attackers can manipulate data and data sampling procedures to control model behaviour. A common attack goal is to plant backdoors i.e. force the victim model to learn to recognise a trigger known only by the adversary. In this paper, we introduce a new class of backdoor attacks that hide inside model architectures i.e. in the inductive bias of the functions used to train. These backdoors are simple to implement, for instance by publishing open-source code for a backdoored model architecture that others will reuse unknowingly. We demonstrate that model architectural backdoors represent a real threat and, unlike other approaches, can survive a complete re-training from scratch. We formalise the main construction principles behind architectural backdoors, such as a link between the input and the output, and describe some possible protections against them. We evaluate our attacks on computer vision benchmarks of different scales and demonstrate the underlying vulnerability is pervasive in a variety of training settings.

We present the measurements of the photoionisation cross sections of the excited $^1$P$_1$ and $^3$S$_1$ states of ultracold $^{88}$Sr atoms at 389.889 nm wavelength, which is the magic wavelength of the $^{1}$S$_{0}$-${}^{3}$P${}_{0}$ clock transition. The photoionisation cross section of the $^1$P$_1$ state is determined from the measured ionisation rates of $^{88}$Sr in the magneto-optical trap in the $^1$P$_1$ state to be 2.20(50)$\times$10$^{-20}$ m$^2$, while the photoionisation cross section of $^{88}$Sr in the $^3$S$_1$ state is inferred from the photoionisation-induced reduction in the number of atoms transferred through the $^3\text{S}_1$ state in an operating optical lattice clock to be $1.38(66)\times$10$^{-18}$ m$^2$. Furthermore, the resulting limitations of employing a blue-detuned magic wavelength optical lattice in strontium optical lattice clocks are evaluated. We estimated photoionisation induced loss rates of atoms at 389.889 nm wavelength under typical experimental conditions and made several suggestions on how to mitigate these losses. In particular, the large photoionisation induced losses for the $^3$S$_1$ state would make the use of the $^3$S$_1$ state in the optical cycle in a blue-detuned optical lattice unfeasible and would instead require the less commonly used $^3$D$_{1,2}$ states during the detection part of the optical clock cycle., Comment: Copyright 2022 Optica Publishing Group. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved

Active optical frequency standards provide interesting alternatives to their passive counterparts. Particularly, such a clock alone continuously generates highly-stable narrow-line laser radiation. Thus a local oscillator is not required to keep the optical phase during a dead time between interrogations as in passive clocks, but only to boost the active clock's low output power to practically usable levels with the current state of technology. Here we investigate the spectral properties and the stability of active clocks, including homogeneous and inhomogeneous broadening effects. We find that for short averaging times the stability is limited by photon shot noise from the limited emitted laser power and at long averaging times by phase diffusion of the laser output. Operational parameters for best long-term stability were identified. Using realistic numbers for an active clock with $^{87}$Sr we find that an optimized stability of $\sigma_y(\tau) \approx 4\times10^{-18}/\sqrt{\tau [\mathrm{s}]}$ is achievable., Comment: 15 pages

Scene graph generation is a structured prediction task aiming to explicitly model objects and their relationships via constructing a visually-grounded scene graph for an input image. Currently, the message passing neural network based mean field variational Bayesian methodology is the ubiquitous solution for such a task, in which the variational inference objective is often assumed to be the classical evidence lower bound. However, the variational approximation inferred from such loose objective generally underestimates the underlying posterior, which often leads to inferior generation performance. In this paper, we propose a novel importance weighted structure learning method aiming to approximate the underlying log-partition function with a tighter importance weighted lower bound, which is computed from multiple samples drawn from a reparameterizable Gumbel-Softmax sampler. A generic entropic mirror descent algorithm is applied to solve the resulting constrained variational inference task. The proposed method achieves the state-of-the-art performance on various popular scene graph generation benchmarks.

Recent work showed that hybrid networks, which combine predefined and learnt filters within a single architecture, are more amenable to theoretical analysis and less prone to overfitting in data-limited scenarios. However, their performance has yet to prove competitive against the conventional counterparts when sufficient amounts of training data are available. In an attempt to address this core limitation of current hybrid networks, we introduce an Efficient Hybrid Network (E-HybridNet). We show that it is the first scattering based approach that consistently outperforms its conventional counterparts on a diverse range of datasets. It is achieved with a novel inductive architecture that embeds scattering features into the network flow using Hybrid Fusion Blocks. We also demonstrate that the proposed design inherits the key property of prior hybrid networks -- an effective generalisation in data-limited scenarios. Our approach successfully combines the best of the two worlds: flexibility and power of learnt features and stability and predictability of scattering representations., Comment: Accepted to ICPR-2022