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Reclassification, the process by which English learner (EL) students exit EL classification, often determines ELs' access to mainstream academic coursework. While existing research finds that many students who demonstrate English proficiency do not reclassify, few studies evaluate policies that effectively reclassify eligible students. This study examines the impact of shifting reclassification responsibility from school districts to the state in Michigan. Using a difference-in-regression discontinuities design, we find that state-level responsibility increases reclassification rates by 35 percentage points compared to district-level responsibility. The effects are larger for Spanish speakers, indicating that state procedures may reduce linguistic bias. Our findings contribute to the literature on default policies in K-12 education and provide evidence on policies that promote equity in EL education.

Metcalfe et al (1) argue that the greatest potential for human-AI partnerships lies in their application to highly complex problem spaces. Herein, we discuss three different forms of hybrid team intelligence and posit that across all three forms, the hybridization of man and machine intelligence can be effective under the right conditions. We foresee two significant research and development (R&D) challenges underlying the creation of effective hybrid intelligence. First, rapid advances in machine intelligence and/or fundamental changes in human behaviors or capabilities over time can outpace R&D. Second, the future conditions under which hybrid intelligence will operate are unknown, but unlikely to be the same as the conditions of today. Overcoming both of these challenges requires a deep understanding of multiple human-centric and machine-centric disciplines that creates a large barrier to entry into the field. Herein, we outline an open, shareable research platform that creates a form of hybrid team intelligence that functions under representative future conditions. The intent for the platform is to facilitate new forms of hybrid intelligence research allowing individuals with human-centric or machine-centric backgrounds to rapidly enter the field and initiate research. Our hope is that through open, community research on the platform, state-of-the-art advances in human and machine intelligence can quickly be communicated across what are currently different R&D communities and allow hybrid team intelligence research to stay at the forefront of scientific advancement.

We establish the asymptotic implicit bias of gradient descent (GD) for generic non-homogeneous deep networks under exponential loss. Specifically, we characterize three key properties of GD iterates starting from a sufficiently small empirical risk, where the threshold is determined by a measure of the network's non-homogeneity. First, we show that a normalized margin induced by the GD iterates increases nearly monotonically. Second, we prove that while the norm of the GD iterates diverges to infinity, the iterates themselves converge in direction. Finally, we establish that this directional limit satisfies the Karush-Kuhn-Tucker (KKT) conditions of a margin maximization problem. Prior works on implicit bias have focused exclusively on homogeneous networks; in contrast, our results apply to a broad class of non-homogeneous networks satisfying a mild near-homogeneity condition. In particular, our results apply to networks with residual connections and non-homogeneous activation functions, thereby resolving an open problem posed by Ji and Telgarsky (2020)., Comment: 96 pages

In overparameterized logistic regression, gradient descent (GD) iterates diverge in norm while converging in direction to the maximum $\ell_2$-margin solution -- a phenomenon known as the implicit bias of GD. This work investigates additional regularization effects induced by early stopping in well-specified high-dimensional logistic regression. We first demonstrate that the excess logistic risk vanishes for early-stopped GD but diverges to infinity for GD iterates at convergence. This suggests that early-stopped GD is well-calibrated, whereas asymptotic GD is statistically inconsistent. Second, we show that to attain a small excess zero-one risk, polynomially many samples are sufficient for early-stopped GD, while exponentially many samples are necessary for any interpolating estimator, including asymptotic GD. This separation underscores the statistical benefits of early stopping in the overparameterized regime. Finally, we establish nonasymptotic bounds on the norm and angular differences between early-stopped GD and $\ell_2$-regularized empirical risk minimizer, thereby connecting the implicit regularization of GD with explicit $\ell_2$-regularization.

To precisely define the treatment effect of interest in a clinical trial, the ICH E9 estimand addendum describes that relevant so-called intercurrent events should be identified and strategies specified to deal with them. Handling intercurrent events with different strategies leads to different estimands. In this paper, we focus on estimands that involve addressing one intercurrent event with the treatment policy strategy and another with the hypothetical strategy. We define these estimands using potential outcomes and causal diagrams, considering the possible causal relationships between the two intercurrent events and other variables. We show that there are different causal estimand definitions and assumptions one could adopt, each having different implications for estimation, which is demonstrated in a simulation study. The different considerations are illustrated conceptually using a diabetes trial as an example.

The peculiar velocity field of the local Universe provides direct insights into its matter distribution and the underlying theory of gravity, and is essential in cosmological analyses for modelling deviations from the Hubble flow. Numerous methods have been developed to reconstruct the density and velocity fields at $z \lesssim 0.05$, typically constrained by redshift-space galaxy positions or by direct distance tracers such as the Tully-Fisher relation, the fundamental plane, or Type Ia supernovae. We introduce a validation framework to evaluate the accuracy of these reconstructions against catalogues of direct distance tracers. Our framework assesses the goodness-of-fit of each reconstruction using Bayesian evidence, residual redshift discrepancies, velocity scaling, and the need for external bulk flows. Applying this framework to a suite of reconstructions -- including those derived from the Bayesian Origin Reconstruction from Galaxies (BORG) algorithm and from linear theory -- we find that the non-linear BORG reconstruction consistently outperforms others. We highlight the utility of such a comparative approach for supernova or gravitational wave cosmological studies, where selecting an optimal peculiar velocity model is essential. Additionally, we present calibrated bulk flow curves predicted by the reconstructions and perform a density-velocity cross-correlation using a linear theory reconstruction to constrain the growth factor, yielding $S_8 = 0.69 \pm 0.034$. This result is in significant tension with Planck but agrees with other peculiar velocity studies., Comment: 25 pages, 16 figures. To be submitted to MNRAS, comments are welcome

Fixing Python dependency issues is a tedious and error-prone task for developers, who must manually identify and resolve environment dependencies and version constraints of third-party modules and Python interpreters. Researchers have attempted to automate this process by relying on large knowledge graphs and database lookup tables. However, these traditional approaches face limitations due to the variety of dependency error types, large sets of possible module versions, and conflicts among transitive dependencies. This study explores the potential of using large language models (LLMs) to automatically fix dependency issues in Python programs. We introduce PLLM (pronounced "plum"), a novel technique that employs retrieval-augmented generation (RAG) to help an LLM infer Python versions and required modules for a given Python file. PLLM builds a testing environment that iteratively (1) prompts the LLM for module combinations, (2) tests the suggested changes, and (3) provides feedback (error messages) to the LLM to refine the fix. This feedback cycle leverages natural language processing (NLP) to intelligently parse and interpret build error messages. We benchmark PLLM on the Gistable HG2.9K dataset, a collection of challenging single-file Python gists. We compare PLLM against two state-of-the-art automatic dependency inference approaches, namely PyEGo and ReadPyE, w.r.t. the ability to resolve dependency issues. Our results indicate that PLLM can fix more dependency issues than the two baselines, with +218 (+15.97%) more fixes over ReadPyE and +281 (+21.58%) over PyEGo. Our deeper analyses suggest that PLLM is particularly beneficial for projects with many dependencies and for specific third-party numerical and machine-learning modules. Our findings demonstrate the potential of LLM-based approaches to iteratively resolve Python dependency issues., Comment: Under submission to TOSEM, 2025

This paper explores the idea that information is an essential and distinctive feature of living systems. Unlike non-living systems, living systems actively acquire, process, and use information about their environments to respond to changing conditions, sustain themselves, and achieve other intrinsic goals. We discuss relevant theoretical frameworks such as ``semantic information'' and ``fitness value of information''. We also highlight the broader implications of our perspective for fields such as origins-of-life research and astrobiology. In particular, we touch on the transition to information-driven systems as a key step in abiogenesis, informational constraints as determinants of planetary habitability, and informational biosignatures for detecting life beyond Earth. We briefly discuss experimental platforms which offer opportunities to investigate these theoretical concepts in controlled environments. By integrating theoretical and experimental approaches, this perspective advances our understanding of life's informational dynamics and its universal principles across diverse scientific domains., Comment: 10 pages 4 figures 131 references

The EdResearch for Action "Overview Series" summarizes the research on key topics to provide K-12 education decision makers and advocates with an evidence base to ground discussions about how to best serve students. This research brief breaks down what is known about multilingual students classified as English Learners (ML-ELs), how ML-ELs perform in K-12 education, and what challenges they face. Key insights provided include: (1) research-based practices--such as bilingual program models--district and school leaders can use to support the academic success and linguistic development of ML-ELs; and (2) one-size-fits-all practices to avoid that can limit many students' opportunities to engage with rigorous content. [This brief was produced in collaboration with the University of Texas at Austin, College of Education.]

Process-supervised reward models (PRMs), which verify large language model (LLM) outputs step-by-step, have achieved significant success in mathematical and coding problems. However, their application to other domains remains largely unexplored. In this work, we train a PRM to provide step-level reward signals for clinical notes generated by LLMs from patient-doctor dialogues. Guided by real-world clinician expertise, we carefully designed step definitions for clinical notes and utilized Gemini-Pro 1.5 to automatically generate process supervision data at scale. Our proposed PRM, trained on the LLaMA-3.1 8B instruct model, outperformed both Gemini-Pro 1.5 and the vanilla outcome-supervised reward model (ORM) in two key evaluations: (1) selecting gold-reference samples from error-containing ones, achieving 98.8% accuracy (versus 70.0% for the vanilla ORM and 93.8% for Gemini-Pro 1.5), and (2) selecting physician-preferred notes, achieving 56.2% accuracy (compared to 37.5% for the vanilla ORM and 50.0% for Gemini-Pro 1.5). Additionally, we conducted ablation studies to determine optimal loss functions and data selection strategies, along with physician reader studies to explore predictors of downstream Best-of-N performance. Our promising results suggest the potential of PRMs to extend beyond the clinical domain, offering a scalable and effective solution for diverse generative tasks.

The creation of the ICH E9 (R1) estimands framework has led to more precise specification of the treatment effects of interest in the design and statistical analysis of clinical trials. However, it is unclear how the new framework relates to causal inference, as both approaches appear to define what is being estimated and have a quantity labelled an estimand. Using illustrative examples, we show that both approaches can be used to define a population-based summary of an effect on an outcome for a specified population and highlight the similarities and differences between these approaches. We demonstrate that the ICH E9 (R1) estimand framework offers a descriptive, structured approach that is more accessible to non-mathematicians, facilitating clearer communication of trial objectives and results. We then contrast this with the causal inference framework, which provides a mathematically precise definition of an estimand, and allows the explicit articulation of assumptions through tools such as causal graphs. Despite these differences, the two paradigms should be viewed as complementary rather than competing. The combined use of both approaches enhances the ability to communicate what is being estimated. We encourage those familiar with one framework to appreciate the concepts of the other to strengthen the robustness and clarity of clinical trial design, analysis, and interpretation.

Recent advances have revealed that the rate of convergence of the expected test error in deep supervised learning decays as a function of the intrinsic dimension and not the dimension $d$ of the input space. Existing literature defines this intrinsic dimension as the Minkowski dimension or the manifold dimension of the support of the underlying probability measures, which often results in sub-optimal rates and unrealistic assumptions. In this paper, we consider supervised deep learning when the response given the explanatory variable is distributed according to an exponential family with a $\beta$-H\"older smooth mean function. We consider an entropic notion of the intrinsic data-dimension and demonstrate that with $n$ independent and identically distributed samples, the test error scales as $\tilde{\mathcal{O}}\left(n^{-\frac{2\beta}{2\beta + \bar{d}_{2\beta}(\lambda)}}\right)$, where $\bar{d}_{2\beta}(\lambda)$ is the $2\beta$-entropic dimension of $\lambda$, the distribution of the explanatory variables. This improves on the best-known rates. Furthermore, under the assumption of an upper-bounded density of the explanatory variables, we characterize the rate of convergence as $\tilde{\mathcal{O}}\left( d^{\frac{2\lfloor\beta\rfloor(\beta + d)}{2\beta + d}}n^{-\frac{2\beta}{2\beta + d}}\right)$, establishing that the dependence on $d$ is not exponential but at most polynomial. We also demonstrate that when the explanatory variable has a lower bounded density, this rate in terms of the number of data samples, is nearly optimal for learning the dependence structure for exponential families.

We present a collection of numerical bootstrap computations for 3d CFTs with a U(1) global symmetry. We test the accuracy of our method and fix conventions through a computation of bounds on the OPE coefficients for low-lying operators in the free fermion, free scalar, and generalised free vector field theories. We then compute new OPE bounds for scalar operators in the Gross-Neveu-Yukawa model, $O(2)$ model, and large $N$ limit of the $O(N)$ model. Additionally, we present a number of exclusion plots for such 3d CFTs. In particular, we look at the space of even and odd parity scalar operators in the low-lying spectrum that are compatible with crossing symmetry. As well as recovering the known theories, there are some kinks that indicate new unknown theories., Comment: 17 pages, 7 figures, 2 tables

When using multiple imputation (MI) for missing data, maintaining compatibility between the imputation model and substantive analysis is important for avoiding bias. For example, some causal inference methods incorporate an outcome model with exposure-confounder interactions that must be reflected in the imputation model. Two approaches for compatible imputation with multivariable missingness have been proposed: Substantive-Model-Compatible Fully Conditional Specification (SMCFCS) and a stacked-imputation-based approach (SMC-stack). If the imputation model is correctly specified, both approaches are guaranteed to be unbiased under the "missing at random" assumption. However, this assumption is violated when the outcome causes its own missingness, which is common in practice. In such settings, sensitivity analyses are needed to assess the impact of alternative assumptions on results. An appealing solution for sensitivity analysis is delta-adjustment using MI, specifically "not-at-random" (NAR)FCS. However, the issue of imputation model compatibility has not been considered in sensitivity analysis, with a naive implementation of NARFCS being susceptible to bias. To address this gap, we propose two approaches for compatible sensitivity analysis when the outcome causes its own missingness. The proposed approaches, NAR-SMCFCS and NAR-SMC-stack, extend SMCFCS and SMC-stack, respectively, with delta-adjustment for the outcome. We evaluate these approaches using a simulation study that is motivated by a case study, to which the methods were also applied. The simulation results confirmed that a naive implementation of NARFCS produced bias in effect estimates, while NAR-SMCFCS and NAR-SMC-stack were approximately unbiased. The proposed compatible approaches provide promising avenues for conducting sensitivity analysis to missingness assumptions in causal inference.

Contextuality is a key characteristic that separates quantum from classical phenomena and an important tool in understanding the potential advantage of quantum computation. However, when assessing the quantum resources available for quantum information processing, there is no formalism to determine whether a set of states can exhibit contextuality and whether such proofs of contextuality indicate anything about the resourcefulness of that set. Introducing a well-motivated notion of what it means for a set of states to be contextual, we establish a relationship between contextuality and antidistinguishability of sets of states. We go beyond the traditional notions of contextuality and antidistinguishability and treat both properties as resources, demonstrating that the degree of contextuality within a set of states has a direct connection to its level of antidistinguishability. If a set of states is contextual, then it must be weakly antidistinguishable and vice-versa. However, maximal contextuality emerges as a stronger property than traditional antidistinguishability., Comment: 8 pages, 2 figures

Federated Learning (FL) has emerged as a groundbreaking paradigm in collaborative machine learning, emphasizing decentralized model training to address data privacy concerns. While significant progress has been made in optimizing federated learning, the exploration of generalization error, particularly in heterogeneous settings, has been limited, focusing mainly on parametric cases. This paper investigates the generalization properties of deep federated regression within a two-stage sampling model. Our findings highlight that the intrinsic dimension, defined by the entropic dimension, is crucial for determining convergence rates when appropriate network sizes are used. Specifically, if the true relationship between response and explanatory variables is charecterized by a $\beta$-H\"older function and there are $n$ independent and identically distributed (i.i.d.) samples from $m$ participating clients, the error rate for participating clients scales at most as $\tilde{O}\left((mn)^{-2\beta/(2\beta + \bar{d}_{2\beta}(\lambda))}\right)$, and for non-participating clients, it scales as $\tilde{O}\left(\Delta \cdot m^{-2\beta/(2\beta + \bar{d}_{2\beta}(\lambda))} + (mn)^{-2\beta/(2\beta + \bar{d}_{2\beta}(\lambda))}\right)$. Here, $\bar{d}_{2\beta}(\lambda)$ represents the $2\beta$-entropic dimension of $\lambda$, the marginal distribution of the explanatory variables, and $\Delta$ characterizes the dependence between the sampling stages. Our results explicitly account for the "closeness" of clients, demonstrating that the convergence rates of deep federated learners depend on intrinsic rather than nominal high-dimensionality.

The safe and effective deployment of Large Language Models (LLMs) involves a critical step called alignment, which ensures that the model's responses are in accordance with human preferences. Prevalent alignment techniques, such as DPO, PPO and their variants, align LLMs by changing the pre-trained model weights during a phase called post-training. While predominant, these post-training methods add substantial complexity before LLMs can be deployed. Inference-time alignment methods avoid the complex post-training step and instead bias the generation towards responses that are aligned with human preferences. The best-known inference-time alignment method, called Best-of-N, is as effective as the state-of-the-art post-training procedures. Unfortunately, Best-of-N requires vastly more resources at inference time than standard decoding strategies, which makes it computationally not viable. In this work, we introduce Speculative Rejection, a computationally-viable inference-time alignment algorithm. It generates high-scoring responses according to a given reward model, like Best-of-N does, while being between 16 to 32 times more computationally efficient., Comment: NeurIPS 2024

Current and future large scale structure surveys aim to constrain the neutrino mass and the equation of state of dark energy. We aim to construct accurate and interpretable symbolic approximations to the linear and nonlinear matter power spectra as a function of cosmological parameters in extended $\Lambda$CDM models which contain massive neutrinos and non-constant equations of state for dark energy. This constitutes an extension of the syren-halofit emulators to incorporate these two effects, which we call syren-new (SYmbolic-Regression-ENhanced power spectrum emulator with NEutrinos and $W_0-w_a$). We also obtain a simple approximation to the derived parameter $\sigma_8$ as a function of the cosmological parameters for these models. Our results for the linear power spectrum are designed to emulate CLASS, whereas for the nonlinear case we aim to match the results of EuclidEmulator2. We compare our results to existing emulators and $N$-body simulations. Our analytic emulators for $\sigma_8$, the linear and nonlinear power spectra achieve root mean squared errors of 0.1%, 0.3% and 1.3%, respectively, across a wide range of cosmological parameters, redshifts and wavenumbers. We verify that emulator-related discrepancies are subdominant compared to observational errors and other modelling uncertainties when computing shear power spectra for LSST-like surveys. Our expressions have similar accuracy to existing (numerical) emulators, but are at least an order of magnitude faster, both on a CPU and GPU. Our work greatly improves the accuracy, speed and range of applicability of current symbolic approximations to the linear and nonlinear matter power spectra. We provide publicly available code for all symbolic approximations found., Comment: 18 pages, 15 figures

We identify regimes where post-selection can be used scalably in quantum error correction (QEC) to improve performance. We use statistical mechanical models to analytically quantify the performance and thresholds of post-selected QEC, with a focus on the surface code. Based on the non-equilibrium magnetization of these models, we identify a simple heuristic technique for post-selection that does not require a decoder. Along with performance gains, this heuristic allows us to derive analytic expressions for post-selected conditional logical thresholds and abort thresholds of surface codes. We find that such post-selected QEC is characterised by four distinct thermodynamic phases, and detail the implications of this phase space for practical, scalable quantum computation., Comment: 11 pages, comments welcome

We address the challenge of efficient auto-regressive generation in sequence prediction models by introducing FutureFill - a method for fast generation that applies to any sequence prediction algorithm based on convolutional operators. Our approach reduces the generation time requirement from quadratic to quasilinear relative to the context length. Additionally, FutureFill requires a prefill cache sized only by the number of tokens generated, which is smaller than the cache requirements for standard convolutional and attention-based models. We validate our theoretical findings with experimental evidence demonstrating correctness and efficiency gains in a synthetic generation task.

The DARPA Subterranean Challenge is leading the development of robots capable of mapping underground mines and tunnels up to 8km in length and identify objects and people. Developing these autonomous abilities paves the way for future planetary cave and surface exploration missions. The Co-STAR team, competing in this challenge, is developing a hybrid aerial-ground vehicle, known as the Rollocopter. The current design of this vehicle is a drone with wheels attached. This allows for the vehicle to roll, actuated by the propellers, and fly only when necessary, hence benefiting from the reduced power consumption of the ground mode and the enhanced mobility of the aerial mode. This thesis focuses on the development and increased robustness of the local planning architecture for the Rollocopter. The first development of thesis is a local planner capable of collision avoidance. The local planning node provides the basic functionality required for the vehicle to navigate autonomously. The next stage was augmenting this with the ability to plan more reliably without localisation. This was then integrated with a hybrid mobility mode capable of rolling and flying to exploit power and mobility benefits of the respective configurations. A traversability analysis algorithm as well as determining the terrain that the vehicle is able to traverse is in the late stages of development for informing the decisions of the hybrid planner. A simulator was developed to test the planning algorithms and improve the robustness of the vehicle to different environments. The results presented in this thesis are related to the mobility of the rollocopter and the range of environments that the vehicle is capable of traversing. Videos are included in which the vehicle successfully navigates through dust-ridden tunnels, horizontal mazes, and areas with rough terrain., Comment: This thesis was submitted to The University of Sydney in partial fulfilment of the requirements for the degree of Bachelor of Engineering Honours (Aeronautical)(Space))

This paper presents an algorithm that finds a centroidal motion and footstep plan for a Spring-Loaded Inverted Pendulum (SLIP)-like bipedal robot model substantially faster than real-time. This is achieved with a novel representation of the dynamic footstep planning problem, where each point in the environment is considered a potential foothold that can apply a force to the center of mass to keep it on a desired trajectory. For a biped, up to two such footholds per time step must be selected, and we approximate this cardinality constraint with an iteratively reweighted $l_1$-norm minimization. Along with a linearizing approximation of an angular momentum constraint, this results in a quadratic program can be solved for a contact schedule and center of mass trajectory with automatic gait discovery. A 2 s planning horizon with 13 time steps and 20 surfaces available at each time is solved in 142 ms, roughly ten times faster than comparable existing methods in the literature. We demonstrate the versatility of this program in a variety of simulated environments., Comment: Accepted to IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2024

To maximize the amount of information extracted from cosmological datasets, simulations that accurately represent these observations are necessary. However, traditional simulations that evolve particles under gravity by estimating particle-particle interactions (N-body simulations) are computationally expensive and prohibitive to scale to the large volumes and resolutions necessary for the upcoming datasets. Moreover, modeling the distribution of galaxies typically involves identifying virialized dark matter halos, which is also a time- and memory-consuming process for large N-body simulations, further exacerbating the computational cost. In this study, we introduce CHARM, a novel method for creating mock halo catalogs by matching the spatial, mass, and velocity statistics of halos directly from the large-scale distribution of the dark matter density field. We develop multi-stage neural spline flow-based networks to learn this mapping at redshift z=0.5 directly with computationally cheaper low-resolution particle mesh simulations instead of relying on the high-resolution N-body simulations. We show that the mock halo catalogs and painted galaxy catalogs have the same statistical properties as obtained from $N$-body simulations in both real space and redshift space. Finally, we use these mock catalogs for cosmological inference using redshift-space galaxy power spectrum, bispectrum, and wavelet-based statistics using simulation-based inference, performing the first inference with accelerated forward model simulations and finding unbiased cosmological constraints with well-calibrated posteriors. The code was developed as part of the Simons Collaboration on Learning the Universe and is publicly available at \url{https://github.com/shivampcosmo/CHARM}., Comment: 12 pages and 8 figures. This is a Learning the Universe Publication

Fault-tolerant implementation of non-Clifford gates is a major challenge for achieving universal fault-tolerant quantum computing with quantum error-correcting codes. Magic state distillation is the most well-studied method for this but requires significant resources. Hence, it is crucial to tailor and optimize magic state distillation for specific codes from both logical- and physical-level perspectives. In this work, we perform such optimization for two-dimensional color codes, which are promising due to their higher encoding rates compared to surface codes, transversal implementation of Clifford gates, and efficient lattice surgery. We propose two distillation schemes based on the 15-to-1 distillation circuit and lattice surgery, which differ in their methods for handling faulty rotations. Our first scheme uses faulty T-measurement, offering resource efficiency when the target infidelity is above a certain threshold ($\sim 35p^3$ for physical error rate $p$). To achieve lower infidelities while maintaining resource efficiency, our second scheme exploits a distillation-free fault-tolerant magic state preparation protocol, achieving significantly lower infidelities (e.g., $\sim 10^{-19}$ for $p = 10^{-4}$) than the first scheme. Notably, our schemes outperform the best existing magic state distillation methods for color codes by up to about two orders of magnitude in resource costs for a given achievable target infidelity., Comment: 42 pages (22 pages for main text), 21 figures, 3 tables; v2 - updated combined MSD scheme (without autocorrection qubits) thanks to Sam Roberts's suggestion & additional comparison with a previous color code MSD scheme in Fig. 14

$N$-body simulations are computationally expensive, so machine-learning (ML)-based emulation techniques have emerged as a way to increase their speed. Although fast, surrogate models have limited trustworthiness due to potentially substantial emulation errors that current approaches cannot correct for. To alleviate this problem, we introduce COmoving Computer Acceleration (COCA), a hybrid framework interfacing ML with an $N$-body simulator. The correct physical equations of motion are solved in an emulated frame of reference, so that any emulation error is corrected by design. This approach corresponds to solving for the perturbation of particle trajectories around the machine-learnt solution, which is computationally cheaper than obtaining the full solution, yet is guaranteed to converge to the truth as one increases the number of force evaluations. Although applicable to any ML algorithm and $N$-body simulator, this approach is assessed in the particular case of particle-mesh cosmological simulations in a frame of reference predicted by a convolutional neural network, where the time dependence is encoded as an additional input parameter to the network. COCA efficiently reduces emulation errors in particle trajectories, requiring far fewer force evaluations than running the corresponding simulation without ML. We obtain accurate final density and velocity fields for a reduced computational budget. We demonstrate that this method shows robustness when applied to examples outside the range of the training data. When compared to the direct emulation of the Lagrangian displacement field using the same training resources, COCA's ability to correct emulation errors results in more accurate predictions. COCA makes $N$-body simulations cheaper by skipping unnecessary force evaluations, while still solving the correct equations of motion and correcting for emulation errors made by ML., Comment: 23 pages, 13 figures. Accepted for publication in A&A

New constraints on the expansion rate of the Universe seem to favor evolving dark energy in the form of thawing quintessence models, i.e., models for which a canonical, minimally coupled scalar field has, at late times, begun to evolve away from potential energy domination. We scrutinize the evidence for thawing quintessence by exploring what it predicts for the equation of state. We show that, in terms of the usual Chevalier-Polarski-Linder parameters, ($w_0$, $w_a$), thawing quintessence is, in fact, only marginally consistent with a compilation of the current data. Despite this, we embrace the possibility that thawing quintessence is dark energy and find constraints on the microphysics of this scenario. We do so in terms of the effective mass $m^2$ and energy scale $V_0$ of the scalar field potential. We are particularly careful to enforce un-informative, flat priors on these parameters so as to minimize their effect on the final posteriors. While the current data favors a large and negative value of $m^2$, when we compare these models to the standard $\Lambda$CDM model we find that there is scant evidence for thawing quintessence., Comment: Updated to match published PRD version

Automation transformed various aspects of our human civilization, revolutionizing industries and streamlining processes. In the domain of scientific inquiry, automated approaches emerged as powerful tools, holding promise for accelerating discovery, enhancing reproducibility, and overcoming the traditional impediments to scientific progress. This article evaluates the scope of automation within scientific practice and assesses recent approaches. Furthermore, it discusses different perspectives to the following questions: Where do the greatest opportunities lie for automation in scientific practice?; What are the current bottlenecks of automating scientific practice?; and What are significant ethical and practical consequences of automating scientific practice? By discussing the motivations behind automated science, analyzing the hurdles encountered, and examining its implications, this article invites researchers, policymakers, and stakeholders to navigate the rapidly evolving frontier of automated scientific practice.

Physics, as a fundamental science, aims to understand the laws of Nature and describe them in mathematical equations. While the physical reality manifests itself in a wide range of phenomena with varying levels of complexity, the equations that describe them display certain statistical regularities and patterns, which we begin to explore here. By drawing inspiration from linguistics, where Zipf's law states that the frequency of any word in a large corpus of text is roughly inversely proportional to its rank in the frequency table, we investigate whether similar patterns for the distribution of operators emerge in the equations of physics. We analyse three corpora of formulae and find, using sophisticated implicit-likelihood methods, that the frequency of operators as a function of their rank in the frequency table is best described by an exponential law with a stable exponent, in contrast with Zipf's inverse power-law. Understanding the underlying reasons behind this statistical pattern may shed light on Nature's modus operandi or reveal recurrent patterns in physicists' attempts to formalise the laws of Nature. It may also provide crucial input for symbolic regression, potentially augmenting language models to generate symbolic models for physical phenomena. By pioneering the study of statistical regularities in the equations of physics, our results open the door for a meta-law of Nature, a (probabilistic) law that all physical laws obey., Comment: 9 pages, 5 figures

The SKA Observatory, currently in the construction phase, will have two of the world's largest radio telescopes when completed in 2028. The scale of the project introduces unique challenges for the telescope software design and implementation at all levels, from user interfacing software down to the lower-level control of individual telescope elements. The Observation Execution Tool (OET) is part of the Observation Science Operations (OSO) suite of applications and is responsible for orchestrating the highest level of telescope control through the execution of telescope control scripts. One of the main challenges for the OET is creating a design that can robustly run concurrent observations on multiple subarrays while remaining responsive to the user. The Scaled Agile Framework (SAFe) development process followed by the SKA project also means the software should be allow to iterative implementation and easily accommodate new and changing requirements. This paper concentrates on the design decisions and challenges in the development of the OET, how we have solved some of the specific technical problems and details on how we remain flexible for future requirements., Comment: 6 pages, 2 figures, submitted to 2024 SPIE Astronomical Telescopes + Instrumentation, Software and Cyberinfrastructure for Astronomy VIII conference

The Observatory Science Operations (OSO) subsystem of the SKAO consists of a range of complex tools which will be used to propose, design, schedule and execute observations. Bridging the gap between the science and telescope domains is the key responsibility of OSO, requiring considerations of usability, performance, availability and accessibility, amongst others. This paper describes the state of the observatory software as we approach construction milestones, how the applications meet these requirements using a modern technology architecture, and challenges so far.

Electronic structure methods built around double-electron excitations have a rich history in quantum chemistry. However, it seems to be the case that such methods are only suitable in particular situations and are not naturally equipped to simultaneously handle the variety of electron correlations that might be present in chemical systems. To this end, the current work seeks a computationally efficient, low-rank, "ultimate" coupled cluster method based exclusively on $T_2$ and its products which can effectively emulate more "complete" methods that explicitly consider higher-rank, $T_{2m}$ operators. We introduce a hierarchy of methods designed to systematically account for higher, even order cluster operators - like $T_4, T_6, \cdots, T_{2m}$ - by invoking tenets of the factorization theorem of perturbation theory and expectation-value coupled cluster theory. It is shown that each member within this methodological hierarchy is defined such that both the wavefunction and energy are correct through some order in many-body perturbation theory (MBPT), and can be extended up to arbitrarily high orders in $T_2$. The efficacy of such approximations are determined by studying the potential energy surface of several prototypical systems that are chosen to represent both non-dynamic, static, and dynamic correlation regimes. We find that the proposed hierarchy of augmented $T_2$ methods essentially reduce to standard CCD for problems where dynamic electron correlations dominate, but offer improvements in situations where non-dynamic and static correlations become relevant. A notable highlight of this work is that the cheapest methods in this hierarchy - which are correct through fifth-order in MBPT - consistently emulate the behavior of the $\mathcal{O}(N^{10})$ CCDQ method, yet only require a $\mathcal{O}(N^{6})$ algorithm by virtue of factorized intermediates.

I introduce a new approach to semantic information based upon the influence of erasure operations (interventions) upon distributions of a system's future trajectories through its phase space. Semantic (meaningful) information is distinguished from syntactic information by the property of having some intrinsic causal power on the future of a given system. As Shannon famously stated, syntactic information is a simple property of probability distributions (the elementary Shannon expression), or correlations between two subsystems and thus does not tell us anything about the meaning of a given message. Kolchinsky & Wolpert (2018) introduced a powerful framework for computing semantic information, which employs interventions upon the state of a system (either initial or dynamic) to erase syntactic information that might influence the viability of a subsystem (such as an organism in an environment). In this work I adapt this framework such that rather than using the viability of a subsystem, we simply observe the changes in future trajectories through a system's phase space as a result of informational interventions (erasures or scrambling). This allows for a more general formalisation of semantic information that does not assume a primary role for the viability of a subsystem (to use examples from Kolchinsky & Wolpert (2018), a rock, a hurricane, or a cell). Many systems of interest have a semantic component, such as a neural network, but may not have such an intrinsic connection to viability as living organisms or dissipative structures. Hence this simple approach to semantic information could be applied to any living, non-living or technological system in order to quantify whether a given quantity of syntactic information within it also has semantic or causal power.

Coupled cluster theory has had a momentous impact on the ab initio prediction of molecular properties, and remains a staple ingratiate in high-accuracy thermochemical model chemistries. However, these methods require inclusion of at least some connected quadruple excitations, which generally scale at best as $\mathcal{O}(N^9)$ with the number of basis functions. It very difficult to predict, a priori, the effect correlation past CCSD(T) has on a give reaction energies. The purpose of this work is to examine cost-effective quadruple corrections based on the factorization theorem of many-body perturbation theory that may address these challenges. We show that the $\mathcal{O}(N^7)$, factorized CCSD(TQ${}_\text{f}$) method introduces minimal error to predicted correlation and reaction energies as compared to the $\mathcal{O}(N^9)$ CCSD(TQ). Further, we examine the performance of Goodson's continued fraction method in the estimation of CCSDT(Q)${}_\Lambda$ contributions to reaction energies, as well as a "new" method related to %TAE[(T)] that we refer to as a scaled perturbation estimator. We find that the scaled perturbation estimator based upon CCSD(TQ${}_\text{f}$)/cc-pVDZ is capable of predicting CCSDT(Q)${}_\Lambda$/cc-pVDZ contributions to reaction energies with an average error of 0.07 kcal mol${}^{-1}$ and a RMST of 0.52 kcal mol${}^{-1}$ when applied to a test-suite of nearly 3000 reactions. This offers a means by which to reliably ballpark how important post-CCSD(T) contributions are to reaction energies while incurring no more than CCSD(T) formal cost and a little mental math.

The Knowledge Is Power Program (KIPP) is the nation's largest network of public charter schools. KIPP began as a network of charter middle schools designed to serve underserved communities, with the goal of closing achievement gaps and preparing students to succeed in college. KIPP has since expanded its model to include elementary and high schools in most regions, and expanded its goals to include preparing students to persist in multiple postsecondary pathways. In this report, we present the results of the second phase of a long-term tracking study that follows 2,066 students who applied to enter 21 oversubscribed KIPP middle schools through an admission lottery in 2008, 2009, or 2011. [For the first phase study "Long-Term Impacts of KIPP Middle Schools on College Enrollment and Early College Persistence," see ED603636.]

Coupled cluster methods based exclusively on double excitations are comparatively "cheap" and interesting model chemistries, as they are typically able to capture the bulk of the dynamical electron correlation effects. The trade-off in such approximations is that the effect of neglected excitations, particularly single excitations, can be considerable. Using standard and electron pair-restricted $T_2$ operators to define two flavors of unitary coupled cluster doubles (UCCD) methods, we investigate the extent in which missing single excitations can be recovered from low-order corrections in many-body perturbation theory (MBPT) within the unitary coupled cluster (UCC) formalism. Our analysis includes the derivations of finite-order, UCC energy functionals which are used as a basis to define perturbative estimates of missed single excitations. This leads to the novel UCCD[4S] and UCCD[6S] methods, which consider energy corrections for missing singles excitations through fourth- and sixth-order in MBPT, respectively. We also apply the same methodology to the electron pair-restricted ansatz, but the improvements are only marginal. Our findings show that augmenting UCCD with these post hoc perturbative corrections can lead to UCCSD-quality results.

The typical training of neural networks using large stepsize gradient descent (GD) under the logistic loss often involves two distinct phases, where the empirical risk oscillates in the first phase but decreases monotonically in the second phase. We investigate this phenomenon in two-layer networks that satisfy a near-homogeneity condition. We show that the second phase begins once the empirical risk falls below a certain threshold, dependent on the stepsize. Additionally, we show that the normalized margin grows nearly monotonically in the second phase, demonstrating an implicit bias of GD in training non-homogeneous predictors. If the dataset is linearly separable and the derivative of the activation function is bounded away from zero, we show that the average empirical risk decreases, implying that the first phase must stop in finite steps. Finally, we demonstrate that by choosing a suitably large stepsize, GD that undergoes this phase transition is more efficient than GD that monotonically decreases the risk. Our analysis applies to networks of any width, beyond the well-known neural tangent kernel and mean-field regimes., Comment: Clarify our results on sigmoid neural networks

Empirically, large-scale deep learning models often satisfy a neural scaling law: the test error of the trained model improves polynomially as the model size and data size grow. However, conventional wisdom suggests the test error consists of approximation, bias, and variance errors, where the variance error increases with model size. This disagrees with the general form of neural scaling laws, which predict that increasing model size monotonically improves performance. We study the theory of scaling laws in an infinite dimensional linear regression setup. Specifically, we consider a model with $M$ parameters as a linear function of sketched covariates. The model is trained by one-pass stochastic gradient descent (SGD) using $N$ data. Assuming the optimal parameter satisfies a Gaussian prior and the data covariance matrix has a power-law spectrum of degree $a>1$, we show that the reducible part of the test error is $\Theta(M^{-(a-1)} + N^{-(a-1)/a})$. The variance error, which increases with $M$, is dominated by the other errors due to the implicit regularization of SGD, thus disappearing from the bound. Our theory is consistent with the empirical neural scaling laws and verified by numerical simulation.

The rapid spread of West Nile Virus (WNV) is a growing concern. With no vaccines or specific medications available, prevention through mosquito control is the only solution to curb the spread. Mosquito traps, used to detect viral presence in mosquito populations, are essential tools for WNV surveillance. But how do we decide where to place a mosquito trap? And what makes a good trap location, anyway? We present a robust statistical approach to determine a mosquito trap's ability to predict human WNV cases in the Chicago metropolitan area and its suburbs. We then use this value to detect the landscape, demographic, and socioeconomic factors associated with a mosquito trap's predictive ability. This approach enables resource-limited mosquito control programs to identify better trap locations while reducing trap numbers to increase trap-based surveillance efficiency. The approach can also be applied to a wide range of different environmental surveillance programs., Comment: 22 pages, 9 figures

The Fine-Gray model for the subdistribution hazard is commonly used for estimating associations between covariates and competing risks outcomes. When there are missing values in the covariates included in a given model, researchers may wish to multiply impute them. Assuming interest lies in estimating the risk of only one of the competing events, this paper develops a substantive-model-compatible multiple imputation approach that exploits the parallels between the Fine-Gray model and the standard (single-event) Cox model. In the presence of right-censoring, this involves first imputing the potential censoring times for those failing from competing events, and thereafter imputing the missing covariates by leveraging methodology previously developed for the Cox model in the setting without competing risks. In a simulation study, we compared the proposed approach to alternative methods, such as imputing compatibly with cause-specific Cox models. The proposed method performed well (in terms of estimation of both subdistribution log hazard ratios and cumulative incidences) when data were generated assuming proportional subdistribution hazards, and performed satisfactorily when this assumption was not satisfied. The gain in efficiency compared to a complete-case analysis was demonstrated in both the simulation study and in an applied data example on competing outcomes following an allogeneic stem cell transplantation. For individual-specific cumulative incidence estimation, assuming proportionality on the correct scale at the analysis phase appears to be more important than correctly specifying the imputation procedure used to impute the missing covariates.

Enterprise security is increasingly being threatened by social engineering attacks, such as phishing, which deceive employees into giving access to enterprise data. To protect both the users themselves and enterprise data, more and more organizations provide cyber security training that seeks to teach employees/customers to identify and report suspicious content. By its very nature, such training seeks to focus on signals that are likely to persist across a wide range of attacks. Further, it expects the user to apply the learnings from these training on e-mail messages that were not filtered by existing, automatic enterprise security (e.g., spam filters and commercial phishing detection software). However, relying on such training now shifts the detection of phishing from an automatic process to a human driven one which is fallible especially when a user errs due to distraction, forgetfulness, etc. In this work we explore treating this type of detection as a natural language processing task and modifying training pipelines accordingly. We present a dataset with annotated labels where these labels are created from the classes of signals that users are typically asked to identify in such training. We also present baseline classifier models trained on these classes of labels. With a comparative analysis of performance between human annotators and the models on these labels, we provide insights which can contribute to the improvement of the respective curricula for both machine and human training., Comment: 10 pages, 2 Tables, 1 figure

Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a parameterized family of exclusive decoders, which are able to abort on decoding instances that are deemed too difficult. We develop new numerical sampling methods to quantify logical failure rates with exclusive decoders as well as the trade-off in terms of the amount of post-selection required. For the most discriminating of exclusive decoders, we demonstrate a threshold of 50\% under depolarizing noise for the surface code (or $32(1)\%$ for the fault-tolerant case with phenomenological measurement errors), and up to a quadratic improvement in logical failure rates below threshold. Furthermore, surprisingly, with a modest exclusion criterion, we identify a regime at low error rates where the exclusion rate decays with code distance, providing a pathway for scalable and time-efficient quantum computing with post-selection. We apply our exclusive decoder to the 15-to-1 magic state distillation protocol, and report a $75\%$ reduction in the number of physical qubits required, and a $60\%$ reduction in the total spacetime volume required, including accounting for repetitions required for post-selection. We also consider other applications, as an error mitigation technique, and in concatenated schemes. Our work highlights the importance of post-selection as a powerful tool in quantum error correction., Comment: 20 pages, 17 figures, comments welcome

Bias models relating the dark matter field to the spatial distribution of halos are widely used in current cosmological analyses. Many models predict halos purely from the local Eulerian matter density, yet bias models in perturbation theory require other local properties. We assess the validity of assuming that only the local dark matter density can be used to predict the number density of halos in a model-independent way and in the non-perturbative regime. Utilising $N$-body simulations, we study the properties of the halo counts field after spatial voxels with near-equal dark matter density have been permuted. If local-in-matter-density biasing were valid, the statistical properties of the permuted and un-permuted fields would be indistinguishable since both represent equally fair draws of the stochastic biasing model. If the Lagrangian radius is greater than approximately half the voxel size and for halos less massive than $\sim10^{15}\,h^{-1}{\rm\,M_\odot}$, we find the permuted halo field has a scale-dependent bias with greater than 25% more power on scales relevant for current surveys. These bias models remove small-scale power by not modelling correlations between neighbouring voxels, which substantially boosts large-scale power to conserve the field's total variance. This conclusion is robust to the choice of initial conditions and cosmology. Assuming local-in-matter-density halo biasing cannot, therefore, reproduce the distribution of halos across a large range of scales and halo masses, no matter how complex the model. One must either allow the biasing to be a function of other quantities and/or remove the assumption that neighbouring voxels are statistically independent., Comment: 10 pages, 5 figures. Accepted in ApJL

We analyse the search behaviour of genetic programming for symbolic regression in practically relevant but limited settings, allowing exhaustive enumeration of all solutions. This enables us to quantify the success probability of finding the best possible expressions, and to compare the search efficiency of genetic programming to random search in the space of semantically unique expressions. This analysis is made possible by improved algorithms for equality saturation, which we use to improve the Exhaustive Symbolic Regression algorithm; this produces the set of semantically unique expression structures, orders of magnitude smaller than the full symbolic regression search space. We compare the efficiency of random search in the set of unique expressions and genetic programming. For our experiments we use two real-world datasets where symbolic regression has been used to produce well-fitting univariate expressions: the Nikuradse dataset of flow in rough pipes and the Radial Acceleration Relation of galaxy dynamics. The results show that genetic programming in such limited settings explores only a small fraction of all unique expressions, and evaluates expressions repeatedly that are congruent to already visited expressions., Comment: This is an extended version of the article submitted to Parallel Problem Solving from Nature (PPSN) Conference 2024

For robot arms to perform everyday tasks in unstructured environments, these robots must be able to manipulate a diverse range of objects. Today's robots often grasp objects with either soft grippers or rigid end-effectors. However, purely rigid or purely soft grippers have fundamental limitations: soft grippers struggle with irregular, heavy objects, while rigid grippers often cannot grasp small, numerous items. In this paper we therefore introduce RISOs, a mechanics and controls approach for unifying traditional RIgid end-effectors with a novel class of SOft adhesives. When grasping an object, RISOs can use either the rigid end-effector (pinching the item between non-deformable fingers) and/or the soft materials (attaching and releasing items with switchable adhesives). This enhances manipulation capabilities by combining and decoupling rigid and soft mechanisms. With RISOs robots can perform grasps along a spectrum from fully rigid, to fully soft, to rigid-soft, enabling real time object manipulation across a 1 million times range in weight (from 2 mg to 2 kg). To develop RISOs we first model and characterize the soft switchable adhesives. We then mount sheets of these soft adhesives on the surfaces of rigid end-effectors, and develop control strategies that make it easier for robot arms and human operators to utilize RISOs. The resulting RISO grippers were able to pick-up, carry, and release a larger set of objects than existing grippers, and participants also preferred using RISO. Overall, our experimental and user study results suggest that RISOs provide an exceptional gripper range in both capacity and object diversity. See videos of our user studies here: https://youtu.be/du085R0gPFI

We describe a challenging robotics deployment in a complex ecosystem to monitor a rich plant community. The study site is dominated by dynamic grassland vegetation and is thus visually ambiguous and liable to drastic appearance change over the course of a day and especially through the growing season. This dynamism and complexity in appearance seriously impact the stability of the robotics platform, as localisation is a foundational part of that control loop, and so routes must be carefully taught and retaught until autonomy is robust and repeatable. Our system is demonstrated over a 6-week period monitoring the response of grass species to experimental climate change manipulations. We also discuss the applicability of our pipeline to monitor biodiversity in other complex natural settings., Comment: to be presented at the Workshop on Field Robotics - ICRA 2024

Two-dimensional color codes are a promising candidate for fault-tolerant quantum computing, as they have high encoding rates, transversal implementation of logical Clifford gates, and resource-efficient magic state preparation schemes. However, decoding color codes presents a significant challenge due to their structure, where elementary errors violate three checks instead of just two (a key feature in surface code decoding), and the complexity of extracting syndrome is greater. We introduce an efficient color-code decoder that tackles these issues by combining two matching decoders for each color, generalized to handle circuit-level noise by employing detector error models. We provide comprehensive analyses of the decoder, covering its threshold and sub-threshold scaling both for bit-flip noise with ideal measurements and for circuit-level noise. Our simulations reveal that this decoding strategy nearly reaches the best possible scaling of logical failure ($p_\mathrm{fail} \sim p^{d/2}$) for both noise models, where $p$ is the noise strength, in the regime of interest for fault-tolerant quantum computing. While its noise thresholds are comparable with other matching-based decoders for color codes ($8.2\%$ for bit-flip noise and $0.46\%$ for circuit-level noise), the scaling of logical failure rates below threshold significantly outperforms the best matching-based decoders., Comment: 30 pages, 17 figures

There is a growing academic interest as well as commercial exploitation of millimetre-wave scanning radar for autonomous vehicle localisation and scene understanding. Although several datasets to support this research area have been released, they are primarily focused on urban or semi-urban environments. Nevertheless, rugged offroad deployments are important application areas which also present unique challenges and opportunities for this sensor technology. Therefore, the Oxford Offroad Radar Dataset (OORD) presents data collected in the rugged Scottish highlands in extreme weather. The radar data we offer to the community are accompanied by GPS/INS reference - to further stimulate research in radar place recognition. In total we release over 90GiB of radar scans as well as GPS and IMU readings by driving a diverse set of four routes over 11 forays, totalling approximately 154km of rugged driving. This is an area increasingly explored in literature, and we therefore present and release examples of recent open-sourced radar place recognition systems and their performance on our dataset. This includes a learned neural network, the weights of which we also release. The data and tools are made freely available to the community at https://oxford-robotics-institute.github.io/oord-dataset.

Rapid and accurate evaluation of the nonlinear matter power spectrum, $P(k)$, as a function of cosmological parameters and redshift is of fundamental importance in cosmology. Analytic approximations provide an interpretable solution, yet current approximations are neither fast nor accurate relative to numerical emulators. We use symbolic regression to obtain simple analytic approximations to the nonlinear scale, $k_\sigma$, the effective spectral index, $n_{\rm eff}$, and the curvature, $C$, which are required for the halofit model. We then re-optimise the coefficients of halofit to fit a wide range of cosmologies and redshifts. We explore the space of analytic expressions to fit the residuals between $P(k)$ and the optimised predictions of halofit. Our results are designed to match the predictions of EuclidEmulator2, but are validated against $N$-body simulations. Our symbolic expressions for $k_\sigma$, $n_{\rm eff}$ and $C$ have root mean squared fractional errors of 0.8%, 0.2% and 0.3%, respectively, for redshifts below 3 and a wide range of cosmologies. The re-optimised halofit parameters reduce the root mean squared fractional error (compared to EuclidEmulator2) from 3% to below 2% for wavenumbers $k=9\times10^{-3}-9 \, h{\rm Mpc^{-1}}$. We introduce syren-halofit (symbolic-regression-enhanced halofit), an extension to halofit containing a short symbolic correction which improves this error to 1%. Our method is 2350 and 3170 times faster than current halofit and hmcode implementations, respectively, and 2680 and 64 times faster than EuclidEmulator2 (which requires running class) and the BACCO emulator. We obtain comparable accuracy to EuclidEmulator2 and BACCO when tested on $N$-body simulations. Our work greatly increases the speed and accuracy of symbolic approximations to $P(k)$, making them significantly faster than their numerical counterparts without loss of accuracy., Comment: 11 pages, 8 figures. Accepted for publication in A&A

We consider gradient descent (GD) with a constant stepsize applied to logistic regression with linearly separable data, where the constant stepsize $\eta$ is so large that the loss initially oscillates. We show that GD exits this initial oscillatory phase rapidly -- in $\mathcal{O}(\eta)$ steps -- and subsequently achieves an $\tilde{\mathcal{O}}(1 / (\eta t) )$ convergence rate after $t$ additional steps. Our results imply that, given a budget of $T$ steps, GD can achieve an accelerated loss of $\tilde{\mathcal{O}}(1/T^2)$ with an aggressive stepsize $\eta:= \Theta( T)$, without any use of momentum or variable stepsize schedulers. Our proof technique is versatile and also handles general classification loss functions (where exponential tails are needed for the $\tilde{\mathcal{O}}(1/T^2)$ acceleration), nonlinear predictors in the neural tangent kernel regime, and online stochastic gradient descent (SGD) with a large stepsize, under suitable separability conditions., Comment: COLT 2024 camera ready