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The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the Ising model on random graphs with an arbitrary degree distribution in the high-connectivity limit. Depending on the distribution of the threshold noise that governs the microscopic dynamics, the model evolves to nonequilibrium stationary states. We obtain an exact dynamical equation for the distribution of local magnetizations, from which we find the critical line that separates the paramagnetic from the ferromagnetic phase. For random graphs with a negative binomial degree distribution, we demonstrate that the stationary critical behavior as well as the long-time critical dynamics of the first two moments of the local magnetizations depend on the distribution of the threshold noise. In particular, for an algebraic threshold noise, these critical properties are determined by the power-law tails of the distribution of thresholds. We further show that the relaxation time of the average magnetization inside each phase exhibits the standard mean-field critical scaling. The values of all critical exponents considered here are independent of the variance of the negative binomial degree distribution. Our work highlights the importance of certain details of the microscopic dynamics for the critical behavior of nonequilibrium spin systems., Comment: 11 pages, 6 figures

In this work, we present a numerical investigation of a novel Lorentz-covariant parametrization to extract $x$-dependent GPDs using off-forward matrix elements of momentum-boosted hadrons coupled to non-local operators. The novelty of the method is the implementation of an asymmetric frame for the momentum transfer between the initial and final hadron state and the parametrization of the matrix elements into Lorentz-invariant amplitudes. The amplitudes can then be related to the standard light-cone GPDs. GPDs are defined in the symmetric frame, which requires a separate calculation for each value of the momentum transfer, increasing the computational cost significantly. The proposed method is powerful, as one can extract the GPDs at multiple values of the momentum transfer at the computational cost of a single value. For this proof-of-concept calculation, we use one ensemble of $N_f=2+1+1$ twisted mass fermions and a clover improvement with a pion mass of 260 MeV to calculate the proton unpolarized GPDs., Comment: 10 pages, 5 figures, contribution to the 39th International Symposium on Lattice Field Theory, Lattice 2022, Bonn, Germany

Modern machine learning requires system designers to specify aspects of the learning pipeline, such as losses, architectures, and optimizers. Meta-learning, or learning-to-learn, instead aims to learn those aspects, and promises to unlock greater capabilities with less manual effort. One particularly ambitious goal of meta-learning is to train general-purpose in-context learning algorithms from scratch, using only black-box models with minimal inductive bias. Such a model takes in training data, and produces test-set predictions across a wide range of problems, without any explicit definition of an inference model, training loss, or optimization algorithm. In this paper we show that Transformers and other black-box models can be meta-trained to act as general-purpose in-context learners. We characterize transitions between algorithms that generalize, algorithms that memorize, and algorithms that fail to meta-train at all, induced by changes in model size, number of tasks, and meta-optimization. We further show that the capabilities of meta-trained algorithms are bottlenecked by the accessible state size (memory) determining the next prediction, unlike standard models which are thought to be bottlenecked by parameter count. Finally, we propose practical interventions such as biasing the training distribution that improve the meta-training and meta-generalization of general-purpose in-context learning algorithms., Comment: Published at the NeurIPS 2022 Workshop on Meta-Learning. Full version currently under review

We propose a new approach to learned optimization where we represent the computation of an optimizer's update step using a neural network. The parameters of the optimizer are then learned by training on a set of optimization tasks with the objective to perform minimization efficiently. Our innovation is a new neural network architecture, Optimus, for the learned optimizer inspired by the classic BFGS algorithm. As in BFGS, we estimate a preconditioning matrix as a sum of rank-one updates but use a Transformer-based neural network to predict these updates jointly with the step length and direction. In contrast to several recent learned optimization-based approaches, our formulation allows for conditioning across the dimensions of the parameter space of the target problem while remaining applicable to optimization tasks of variable dimensionality without retraining. We demonstrate the advantages of our approach on a benchmark composed of objective functions traditionally used for the evaluation of optimization algorithms, as well as on the real world-task of physics-based visual reconstruction of articulated 3d human motion., Comment: Accepted to the IEEE/CVF Conference on Computer Vision and Pattern Recognition 2023 (CVPR) in Vancouver, Canada

While deep learning models have replaced hand-designed features across many domains, these models are still trained with hand-designed optimizers. In this work, we leverage the same scaling approach behind the success of deep learning to learn versatile optimizers. We train an optimizer for deep learning which is itself a small neural network that ingests gradients and outputs parameter updates. Meta-trained with approximately four thousand TPU-months of compute on a wide variety of optimization tasks, our optimizer not only exhibits compelling performance, but optimizes in interesting and unexpected ways. It requires no hyperparameter tuning, instead automatically adapting to the specifics of the problem being optimized. We open source our learned optimizer, meta-training code, the associated train and test data, and an extensive optimizer benchmark suite with baselines at velo-code.github.io.

Tremendous progress has been made in reinforcement learning (RL) over the past decade. Most of these advancements came through the continual development of new algorithms, which were designed using a combination of mathematical derivations, intuitions, and experimentation. Such an approach of creating algorithms manually is limited by human understanding and ingenuity. In contrast, meta-learning provides a toolkit for automatic machine learning method optimisation, potentially addressing this flaw. However, black-box approaches which attempt to discover RL algorithms with minimal prior structure have thus far not outperformed existing hand-crafted algorithms. Mirror Learning, which includes RL algorithms, such as PPO, offers a potential middle-ground starting point: while every method in this framework comes with theoretical guarantees, components that differentiate them are subject to design. In this paper we explore the Mirror Learning space by meta-learning a "drift" function. We refer to the immediate result as Learnt Policy Optimisation (LPO). By analysing LPO we gain original insights into policy optimisation which we use to formulate a novel, closed-form RL algorithm, Discovered Policy Optimisation (DPO). Our experiments in Brax environments confirm state-of-the-art performance of LPO and DPO, as well as their transfer to unseen settings., Comment: NeurIPS 2022

While deep reinforcement learning (RL) agents have showcased strong results across many domains, a major concern is their inherent opaqueness and the safety of such systems in real-world use cases. To overcome these issues, we need agents that can quantify their uncertainty and detect out-of-distribution (OOD) states. Existing uncertainty estimation techniques, like Monte-Carlo Dropout or Deep Ensembles, have not seen widespread adoption in on-policy deep RL. We posit that this is due to two reasons: concepts like uncertainty and OOD states are not well defined compared to supervised learning, especially for on-policy RL methods. Secondly, available implementations and comparative studies for uncertainty estimation methods in RL have been limited. To overcome the first gap, we propose definitions of uncertainty and OOD for Actor-Critic RL algorithms, namely, proximal policy optimization (PPO), and present possible applicable measures. In particular, we discuss the concepts of value and policy uncertainty. The second point is addressed by implementing different uncertainty estimation methods and comparing them across a number of environments. The OOD detection performance is evaluated via a custom evaluation benchmark of in-distribution (ID) and OOD states for various RL environments. We identify a trade-off between reward and OOD detection performance. To overcome this, we formulate a Pareto optimization problem in which we simultaneously optimize for reward and OOD detection performance. We show experimentally that the recently proposed method of Masksembles strikes a favourable balance among the survey methods, enabling high-quality uncertainty estimation and OOD detection while matching the performance of original RL agents.

Learned optimizers -- neural networks that are trained to act as optimizers -- have the potential to dramatically accelerate training of machine learning models. However, even when meta-trained across thousands of tasks at huge computational expense, blackbox learned optimizers often struggle with stability and generalization when applied to tasks unlike those in their meta-training set. In this paper, we use tools from dynamical systems to investigate the inductive biases and stability properties of optimization algorithms, and apply the resulting insights to designing inductive biases for blackbox optimizers. Our investigation begins with a noisy quadratic model, where we characterize conditions in which optimization is stable, in terms of eigenvalues of the training dynamics. We then introduce simple modifications to a learned optimizer's architecture and meta-training procedure which lead to improved stability, and improve the optimizer's inductive bias. We apply the resulting learned optimizer to a variety of neural network training tasks, where it outperforms the current state of the art learned optimizer -- at matched optimizer computational overhead -- with regard to optimization performance and meta-training speed, and is capable of generalization to tasks far different from those it was meta-trained on., Comment: NeurIPS 2022

The spectral and localization properties of heterogeneous random graphs are determined by the resolvent distributional equations, which have so far resisted an analytic treatment. We solve analytically the resolvent equations of random graphs with an arbitrary degree distribution in the high-connectivity limit, from which we perform a thorough analysis of the impact of degree fluctuations on the spectral density, the inverse participation ratio, and the distribution of the local density of states. We show that all eigenvectors are extended and that the spectral density exhibits a logarithmic or a power-law divergence when the variance of the degree distribution is large enough. We elucidate this singular behaviour by showing that the distribution of the local density of states at the center of the spectrum displays a power-law tail determined by the variance of the degree distribution. In the regime of weak degree fluctuations the spectral density has a finite support, which promotes the stability of large complex systems on random graphs., Comment: 22 pages, 6 figures

In this paper we present BayesLDM, a system for Bayesian longitudinal data modeling consisting of a high-level modeling language with specific features for modeling complex multivariate time series data coupled with a compiler that can produce optimized probabilistic program code for performing inference in the specified model. BayesLDM supports modeling of Bayesian network models with a specific focus on the efficient, declarative specification of dynamic Bayesian Networks (DBNs). The BayesLDM compiler combines a model specification with inspection of available data and outputs code for performing Bayesian inference for unknown model parameters while simultaneously handling missing data. These capabilities have the potential to significantly accelerate iterative modeling workflows in domains that involve the analysis of complex longitudinal data by abstracting away the process of producing computationally efficient probabilistic inference code. We describe the BayesLDM system components, evaluate the efficiency of representation and inference optimizations and provide an illustrative example of the application of the system to analyzing heterogeneous and partially observed mobile health data., Comment: Accepted at IEEE/ACM international conference on Connected Health: Applications, Systems and Engineering Technologies (CHASE) 2022

Traditionally, lattice QCD computations of generalized parton distributions (GPDs) have been carried out in a symmetric frame, where the transferred momentum is symmetrically distributed between the incoming and outgoing hadrons. However, such frames are inconvenient since they require a separate calculation for each value of the momentum transfer, increasing significantly the computational cost. In this work, by focusing on the quasi-distribution approach, we lay the foundation for faster and more effective lattice QCD calculations of GPDs exploiting asymmetric frames, with freedom in the transferred momentum distribution. An important ingredient of our approach is the Lorentz covariant parameterization of the matrix elements in terms of Lorentz-invariant amplitudes, which allows one to relate matrix elements in different frames. We also use this amplitude approach to propose a new definition of quasi-GPDs that is frame-independent and, more importantly, may lead to smaller power corrections in the matching relations to the light-cone GPDs. We demonstrate the efficacy of the formalism through numerical calculations using one ensemble of $N_f$=2+1+1 twisted mass fermions with a clover improvement. The value of the light-quark masses lead to a pion mass of about 260 MeV. Concentrating on the proton, and limiting ourselves to a vanishing longitudinal momentum transfer to the target, we extract the invariant amplitudes from matrix element calculations in both the symmetric and asymmetric frame, and obtain results for the twist-2 light-cone GPDs for unpolarized quarks, that is, $H$ and $E$., Comment: 39 pages, 19 figures, matches with published version

Robustness to adversarial perturbations has been explored in many areas of computer vision. This robustness is particularly relevant in vision-based reinforcement learning, as the actions of autonomous agents might be safety-critic or impactful in the real world. We investigate the susceptibility of vision-based reinforcement learning agents to gradient-based adversarial attacks and evaluate a potential defense. We observe that Bottleneck Attention Modules (BAM) included in CNN architectures can act as potential tools to increase robustness against adversarial attacks. We show how learned attention maps can be used to recover activations of a convolutional layer by restricting the spatial activations to salient regions. Across a number of RL environments, BAM-enhanced architectures show increased robustness during inference. Finally, we discuss potential future research directions., Comment: 5 pages, 2 figures, 3 tables

In most superconductors electrons form Cooper pairs in a spin-singlet state mediated by either phonons or by long-range interactions such as spin fluctuations. The superconductor UTe$_2$ is a rare material wherein electrons are believed to form pairs in a unique spin-triplet state with potential topological properties. While spin-triplet pairing may be mediated by ferromagnetic or antiferromagnetic fluctuations, experimentally, the magnetic properties of UTe$_2$ are unclear. By way of muon spin rotation/relaxation ($\mu$SR) measurements on independently grown UTe$_2$ single crystals we demonstrate the existence of magnetic clusters that gradually freeze into a disordered spin frozen state at low temperatures. Our findings suggest that inhomogeneous freezing of magnetic clusters is linked to the ubiquitous residual linear term in the temperature dependence of the specific heat ($C$) and the low-temperature upturn in $C/T$ versus $T$. The omnipresent magnetic inhomogeneity has potential implications for experiments aimed at establishing the intrinsic low-temperature properties of UTe$_2$., Comment: 33 pages, 9 figures

The Australian continent contributes substantially to the year-to-year variability of the global terrestrial carbon dioxide (CO2) sink. However, the scarcity of in-situ observations in remote areas prevents deciphering the processes that force the CO2 flux variability. Here, examining atmospheric CO2 measurements from satellites in the period 2009-2018, we find recurrent end-of-dry-season CO2 pulses over the Australian continent. These pulses largely control the year-to-year variability of Australia's CO2 balance, due to 2-3 times higher seasonal variations compared to previous top-down inversions and bottom-up estimates. The CO2 pulses occur shortly after the onset of rainfall and are driven by enhanced soil respiration preceding photosynthetic uptake in Australia's semi-arid regions. The suggested continental-scale relevance of soil rewetting processes has large implications for our understanding and modelling of global climate-carbon cycle feedbacks., Comment: 28 pages (including supplementary materials), 3 main figures, 7 supplementary figures; v2 changes: Last name of first author changed