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Performative prediction is a framework accounting for the shift in the data distribution induced by the prediction of a model deployed in the real world. Ensuring rapid convergence to a stable solution where the data distribution remains the same after the model deployment is crucial, especially in evolving environments. This paper extends the Repeated Risk Minimization (RRM) framework by utilizing historical datasets from previous retraining snapshots, yielding a class of algorithms that we call Affine Risk Minimizers and enabling convergence to a performatively stable point for a broader class of problems. We introduce a new upper bound for methods that use only the final iteration of the dataset and prove for the first time the tightness of both this new bound and the previous existing bounds within the same regime. We also prove that utilizing historical datasets can surpass the lower bound for last iterate RRM, and empirically observe faster convergence to the stable point on various performative prediction benchmarks. We offer at the same time the first lower bound analysis for RRM within the class of Affine Risk Minimizers, quantifying the potential improvements in convergence speed that could be achieved with other variants in our framework.

Snort is a two-player game played on a simple graph in which the players take turns colouring vertices in their own colour, with the restriction that two adjacent vertices cannot have opposite colours. We will show that on triangular grids with one or two rows of triangles, and many of their variants, the first player will win when playing optimally.

Quantum key distribution (QKD) allows two users to exchange a provably secure key for cryptographic applications. In prepare-and-measure QKD protocols, the states must be indistinguishable to prevent information leakage to an eavesdropper performing a side-channel attack. Here, we measure the indistinguishability of quantum states in a prepare-and-measure three-state BB84 polarization-based decoy state protocol using resonant-cavity light-emitting diodes (RC-LEDs) as the source in the transmitter. We make the spatial, spectral, and temporal DOF of the generated quantum states nearly indistinguishable using a spatial filter single-mode fiber, a narrow-band spectral filter, and adjustable timing of the electrical pulses driving the RC-LEDs, respectively. The sources have fully indistinguishable transverse spatial modes. The measured fractional mutual information between an assumed eavesdropper and the legitimate receiver is $2.39\times10^{-5}$ due to the spectral distinguishability and $4.31\times10^{-5}$ for the temporal distinguishability. The source is integrated into a full QKD system operating in a laboratory environment, where we achieve a raw key rate of 532 Kbits/s with an average quantum bit error rate of 1.83\%. The low system size, weight, and power make it suitable for mobile platforms such as uncrewed aerial vehicles (drones) or automobiles.

We prove that several dynamically defined fractals in $\mathbb{C}$ and $\mathbb{C}^2$ which arise from different type of polynomial dynamical systems can not be the same objects. One of our main results is that the closure of Misiurewicz PCF cubic polynomials (the strong bifurcation locus) cannot be the Julia set of a regular polynomial endomorphism of $\mathbb{C}^2$. We also show that the Julia set of a H\'enon map and a polynomial endomorphism cannot coincide., Comment: 18 pages, comments welcome!

We present a novel positive kinetic scheme built on the efficient collide-and-stream algorithm of the lattice Boltzmann method (LBM) to address hyperbolic conservation laws. We focus on the compressible Euler equations with strong discontinuities. Starting from the work of Jin and Xin [20] and then [4,8], we show how the LBM discretization procedure can yield both first- and second-order schemes, referred to as vectorial LBM. Noticing that the first-order scheme is convex preserving under a specific CFL constraint, we develop a blending strategy that preserves both the conservation and simplicity of the algorithm. This approach employs convex limiters, carefully designed to ensure either positivity (of the density and the internal energy) preservation (PP) or well-defined local maximum principles (LMP), while minimizing numerical dissipation. On challenging test cases involving strong discontinuities and near-vacuum regions, we demonstrate the scheme accuracy, robustness, and ability to capture sharp discontinuities with minimal numerical oscillations., Comment: 23 pages, 10 figures

Hydro-generating units (HGUs) play a crucial role in integrating intermittent renewable energy sources into the power grid due to their flexible operational capabilities. This evolving role has led to an increase in transient events, such as startups, which impose significant stresses on turbines, leading to increased turbine fatigue and a reduced operational lifespan. Consequently, optimizing startup sequences to minimize stresses is vital for hydropower utilities. However, this task is challenging, as stress measurements on prototypes can be expensive and time-consuming. To tackle this challenge, we propose an innovative automated approach to optimize the startup parameters of HGUs with a limited budget of measured startup sequences. Our method combines active learning and black-box optimization techniques, utilizing virtual strain sensors and dynamic simulations of HGUs. This approach was tested in real-time during an on-site measurement campaign on an instrumented Francis turbine prototype. The results demonstrate that our algorithm successfully identified an optimal startup sequence using only seven measured sequences. It achieves a remarkable 42% reduction in the maximum strain cycle amplitude compared to the standard startup sequence. This study paves the way for more efficient HGU startup optimization, potentially extending their operational lifespans.

In this paper, we study the computation of sensitivities with respect to spot of path dependent financial derivatives by means of path weighting. We propose explicit path weighting formula and variance reduction adjustment in order to address the large variance happening when the first simulation time step is small. We also propose a covariance inflation technique to addresses the degenerator case when the covariance matrix is singular. The stock dynamics we consider is given in a general functional form, which includes the classical Black-Scholes model, the implied distribution model, and the local volatility model.

Emissions markets play a crucial role in reducing pollution by encouraging firms to minimize costs. However, their structure heavily relies on the decisions of policymakers, on the future economic activities, and on the availability of abatement technologies. This study examines how changes in regulatory standards, firms' abatement costs, and emissions levels affect allowance prices and firms' efforts to reduce emissions. This is done in a Radner equilibrium framework encompassing inter-temporal decision-making, uncertainty, and a comprehensive assessment of the market dynamics and outcomes. The results of this research have the potential to assist policymakers in enhancing the structure and efficiency of emissions trading systems, through an in-depth comprehension of the reactions of market stakeholders towards different market situations.

Deep learning has proven to be effective in a wide variety of loss minimization problems. However, many applications of interest, like minimizing projected Bellman error and min-max optimization, cannot be modelled as minimizing a scalar loss function but instead correspond to solving a variational inequality (VI) problem. This difference in setting has caused many practical challenges as naive gradient-based approaches from supervised learning tend to diverge and cycle in the VI case. In this work, we propose a principled surrogate-based approach compatible with deep learning to solve VIs. We show that our surrogate-based approach has three main benefits: (1) under assumptions that are realistic in practice (when hidden monotone structure is present, interpolation, and sufficient optimization of the surrogates), it guarantees convergence, (2) it provides a unifying perspective of existing methods, and (3) is amenable to existing deep learning optimizers like ADAM. Experimentally, we demonstrate our surrogate-based approach is effective in min-max optimization and minimizing projected Bellman error. Furthermore, in the deep reinforcement learning case, we propose a novel variant of TD(0) which is more compute and sample efficient.

In this note, we give a definitive basis for the dimension-eight operators leading to quartic -- but no cubic -- interactions among electroweak gauge bosons. These are often called anomalous quartic gauge couplings, or aQGCs. We distinguish in particular the CP-even ones from their CP-odd counterparts., Comment: LHC Effective Field Theory Working Group Note, 8 pages, 3 tables

Interpreting the decisions of Convolutional Neural Networks (CNNs) is essential for understanding their behavior, yet explainability remains a significant challenge, particularly for self-supervised models. Most existing methods for generating saliency maps rely on ground truth labels, restricting their use to supervised tasks. EigenCAM is the only notable label-independent alternative, leveraging Singular Value Decomposition to generate saliency maps applicable across CNN models, but it does not fully exploit the tensorial structure of feature maps. In this work, we introduce the Tucker Saliency Map (TSM) method, which applies Tucker tensor decomposition to better capture the inherent structure of feature maps, producing more accurate singular vectors and values. These are used to generate high-fidelity saliency maps, effectively highlighting objects of interest in the input. We further extend EigenCAM and TSM into multivector variants -Multivec-EigenCAM and Multivector Tucker Saliency Maps (MTSM)- which utilize all singular vectors and values, further improving saliency map quality. Quantitative evaluations on supervised classification models demonstrate that TSM, Multivec-EigenCAM, and MTSM achieve competitive performance with label-dependent methods. Moreover, TSM enhances explainability by approximately 50% over EigenCAM for both supervised and self-supervised models. Multivec-EigenCAM and MTSM further advance state-of-the-art explainability performance on self-supervised models, with MTSM achieving the best results., Comment: 29 pages, 20 figures

The attractive interaction in conventional BCS superconductors is provided by a bosonic mode. However, the pairing glue of most unconventional superconductors is unknown. The effect of electron-boson coupling is therefore extensively studied in these materials. A key signature are dispersion kinks that can be observed in the spectral function as abrupt changes in velocity and lifetime of quasiparticles. Here, we show the existence of two kinks in the unconventional iron-based superconductor RbFe$_2$As$_2$ using angle-resolved photoemission spectroscopy (ARPES) and dynamical mean field theory (DMFT). In addition, we observe the formation of a Hubbard band multiplet due to the combination of Coulomb interaction and Hund's rule coupling in this multiorbital systems. We demonstrate that the two dispersion kinks are a consequence of these strong many-body interactions. This interpretation is in line with a growing number of theoretical predictions for kinks in various general models of correlated materials. Our results provide a unifying link between iron-based superconductors and different classes of correlated, unconventional superconductors such as cuprates and heavy-fermion materials.

As robots become more common for both able-bodied individuals and those living with a disability, it is increasingly important that lay people be able to drive multi-degree-of-freedom platforms with low-dimensional controllers. One approach is to use state-conditioned action mapping methods to learn mappings between low-dimensional controllers and high DOF manipulators -- prior research suggests these mappings can simplify the teleoperation experience for users. Recent works suggest that neural networks predicting a local linear function are superior to the typical end-to-end multi-layer perceptrons because they allow users to more easily undo actions, providing more control over the system. However, local linear models assume actions exist on a linear subspace and may not capture nuanced actions in training data. We observe that the benefit of these mappings is being an odd function concerning user actions, and propose end-to-end nonlinear action maps which achieve this property. Unfortunately, our experiments show that such modifications offer minimal advantages over previous solutions. We find that nonlinear odd functions behave linearly for most of the control space, suggesting architecture structure improvements are not the primary factor in data-driven teleoperation. Our results suggest other avenues, such as data augmentation techniques and analysis of human behavior, are necessary for action maps to become practical in real-world applications, such as in assistive robotics to improve the quality of life of people living with w disability., Comment: 13 Pages, 7 Figures, presented at Collaborative AI and Modeling of Humans AAAI Bridge Program Submission

Given two sets of elements (such as cell types and drug compounds), researchers typically only have access to a limited subset of their interactions. The task of causal imputation involves using this subset to predict unobserved interactions. Squires et al. (2022) have proposed two estimators for this task based on the synthetic interventions (SI) estimator: SI-A (for actions) and SI-C (for contexts). We extend their work and introduce a novel causal imputation estimator, generalized synthetic interventions (GSI). We prove the identifiability of this estimator for data generated from a more complex latent factor model. On synthetic and real data we show empirically that it recovers or outperforms their estimators.

We consider multi-agent systems with cooperative interactions and study the convergence to consensus in the case of time-dependent lack of interaction. We prove a new condition ensuring consensus: we define a graph in which directed arrows correspond to connection functions that converge (in the weak sense) to some function with a positive integral on all intervals of the form $[t,+\infty)$. If the graph has a vertex reachable from all other indices, then the system converges to consensus. We show that this requirement generalizes some known sufficient conditions for convergence, such as the Persistent Excitation one. We also give a second new condition, transversal to the known ones: total connectedness of the undirected graph formed by the non-vanishing of limiting functions.

By merging models, AI systems can combine the distinct strengths of separate language models, achieving a balance between multiple capabilities without requiring substantial retraining. However, the integration process can be intricate due to differences in training methods and fine-tuning, typically necessitating specialized knowledge and repeated refinement. This paper explores model merging techniques across a spectrum of complexity, examining where automated methods like evolutionary strategies stand compared to hyperparameter-driven approaches such as DARE, TIES-Merging and simpler methods like Model Soups. In addition, we introduce Differentiable Adaptive Merging (DAM), an efficient, adaptive merging approach as an alternative to evolutionary merging that optimizes model integration through scaling coefficients, minimizing computational demands. Our findings reveal that even simple averaging methods, like Model Soups, perform competitively when model similarity is high, underscoring each technique's unique strengths and limitations. We open-sourced DAM, including the implementation code and experiment pipeline, on GitHub: https://github.com/arcee-ai/DAM., Comment: 11 pages, 1 figure, and 3 tables

The convex hull peeling of a point set consists in taking the convex hull, then removing the extreme points and iterating that procedure until no point remains. The boundary of each hull is called a layer. Following on from [15], we study the first layers generated by the peeling procedure when the point set is chosen as a homogeneous Poisson point process inside a polytope when the intensity goes to infinity. We focus on some specific functionals, namely the number of k-dimensional faces and the outer defect volume. Since the early works of R{\'e}nyi and Sulanke, it is well known that both the techniques and the rates are completely different for the convex hull when the underlying convex body has a smooth boundary or when it is itself a polytope. We expect such dichotomy to extend to the further layers of the peeling. More precisely we provide asymptotic limits for their expectation and variance as well as a central limit theorem. In particular, as in the unit ball, the growth rates do not depend on the layer. The method builds upon previous constructions for the convex hull contained in [9] and [18] and requires the assumption that the underlying polytope is simple.

Let $F$ be a totally real field. We study the root numbers $\epsilon(1/2, \pi)$ of self-dual cuspidal automorphic representations $\pi$ of $\mathrm{GL}_{2N}/F$ with conductor $\mathfrak n$ and regular integral infinitesimal character $\lambda$. If $\pi$ is orthogonal, then $\epsilon(1/2, \pi)$ is known to be identically one. We show that for symplectic representations, the root numbers $\epsilon(1/2, \pi)$ equidistribute between~$\pm 1$ as $\lambda \to \infty$, provided that there exists a prime dividing $\mathfrak n$ with power $>N$.We also study conjugate self-dual representations with respect to a CM extension $E/F$, where we obtain a similar result under the assumption that $\mathfrak n$ is divisible by a large enough power of a ramified prime and provide evidence that equidistribution does not hold otherwise. In cases where there are known to be associated Galois representations, we deduce root number equidistribution results for the corresponding families of $N$-dimensional Galois representations. The proof generalizes a classical argument for the case of $\mathrm{GL}_2/\mathbb Q$ by using Arthur's trace formula and the endoscopic classification for quasisplit classical groups similarly to a previous work (arxiv:2212.12138). The main new technical difficulty is evaluating endoscopic transfers of the required test functions at central elements., Comment: 81 pages, this version: improved exposition and many typo fixes and minor corrections. Comments are welcome!

The NetMob24 dataset offers a unique opportunity for researchers from a range of academic fields to access comprehensive spatiotemporal data sets spanning four countries (India, Mexico, Indonesia, and Colombia) over the course of two years (2019 and 2020). This dataset, developed in collaboration with Cuebiq (Also referred to as Spectus), comprises privacy-preserving aggregated data sets derived from mobile application (app) data collected from users who have voluntarily consented to anonymous data collection for research purposes. It is our hope that this reference dataset will foster the production of new research methods and the reproducibility of research outcomes.

A measurement of the double-spin asymmetry from electron-$^{3}$He scattering in the threshold region of two- and three-body breakup of $^{3}$He was performed at Jefferson Lab, for Q$^{2}$ values of 0.1 and 0.2 (GeV/$c$)$^{2}$. The results of this measurement serve as a stringent test of our understanding of few-body systems. When compared with calculations from plane wave impulse approximation and Faddeev theory, we found that the Faddeev calculations, which use modern nuclear potentials and prescriptions for meson-exchange currents, demonstrate an overall good agreement with data.

Blockchain promises to make online services more fault tolerant due to their inherent distributed nature. Their ability to execute arbitrary programs in different geo-distributed regions and on diverse operating systems make them an alternative of choice to our dependence on unique software whose recent failure affected 8.5 millions of machines. As of today, it remains, however, unclear whether blockchains can truly tolerate failures. In this paper, we assess the fault tolerance of blockchain. To this end, we inject failures in controlled deployments of five modern blockchain systems, namely Algorand, Aptos, Avalanche, Redbelly and Solana. We introduce a novel sensitivity metric, interesting in its own right, as the difference between the integrals of two cumulative distribution functions, one obtained in a baseline environment and one obtained in an adversarial environment. Our results indicate that (i) all blockchains except Redbelly are highly impacted by the failure of a small part of their network, (ii) Avalanche and Redbelly benefit from the redundant information needed for Byzantine fault tolerance while others are hampered by it, and more dramatically (iii) Avalanche and Solana cannot recover from localised transient failures., Comment: 16 pages, 6 figures

The present work emphasizes the relevance of low-field NMR relaxometry to investigate colloid-polymer hydrogels by probing water dynamics across a wide range of formulations between $\rm 10^{\circ}C$ and $\rm 80^{\circ}C$. By examining the temperature dependence of the transverse relaxation time $T_2$, we demonstrate a clear link between the NMR response and the rheological behavior of the hydrogels. In particular, we show that NMR relaxometry targeting the solvent provides reliable insights into the hydrogel microstructure and allows the detection of phase transitions and aging processes. Our findings suggest that this solvent-focused technique could greatly benefit the soft matter community, complementing other experimental methods in the study of gels., Comment: 6 pages, 4 figures

Relighting radiance fields is severely underconstrained for multi-view data, which is most often captured under a single illumination condition; It is especially hard for full scenes containing multiple objects. We introduce a method to create relightable radiance fields using such single-illumination data by exploiting priors extracted from 2D image diffusion models. We first fine-tune a 2D diffusion model on a multi-illumination dataset conditioned by light direction, allowing us to augment a single-illumination capture into a realistic -- but possibly inconsistent -- multi-illumination dataset from directly defined light directions. We use this augmented data to create a relightable radiance field represented by 3D Gaussian splats. To allow direct control of light direction for low-frequency lighting, we represent appearance with a multi-layer perceptron parameterized on light direction. To enforce multi-view consistency and overcome inaccuracies we optimize a per-image auxiliary feature vector. We show results on synthetic and real multi-view data under single illumination, demonstrating that our method successfully exploits 2D diffusion model priors to allow realistic 3D relighting for complete scenes. Project site https://repo-sam.inria.fr/fungraph/generative-radiance-field-relighting/, Comment: Project site https://repo-sam.inria.fr/fungraph/generative-radiance-field-relighting/

The landscape of science and technology is characterized by its dynamic and evolving nature, constantly reshaped by new discoveries, innovations, and paradigm shifts. Moreover, science is undergoing a remarkable shift towards increasing interdisciplinary collaboration, where the convergence of diverse fields fosters innovative solutions to complex problems. Detecting emerging scientific topics is paramount as it enables industries, policymakers, and innovators to adapt their strategies, investments, and regulations proactively. As the common approach for detecting emerging technologies, despite being useful, bibliometric analyses may suffer from oversimplification and/or misinterpretation of complex interdisciplinary trends. In addition, relying solely on domain experts to pinpoint emerging technologies from science and technology trends might restrict the ability to systematically analyze extensive information and introduce subjective judgments into the interpretations. To overcome these drawbacks, in this work, we present an automated artificial intelligence-enabled framework, called WISDOM, for detecting emerging research themes using advanced topic modeling and weak signal analysis. The proposed approach can assist strategic planners and domain experts in more effectively recognizing and tracking trends related to emerging topics by swiftly processing and analyzing vast volumes of data, uncovering hidden cross-disciplinary patterns, and offering unbiased insights, thereby enhancing the efficiency and objectivity of the detection process. As the case technology, we assess WISDOM's performance in identifying emerging research as well as their trends, in the field of underwater sensing technologies using scientific papers published between 2004 and 2021., Comment: 18 pages, 7 figures

Computational modeling is an integral part of catalysis research. With it, new methodologies are being developed and implemented to improve the accuracy of simulations while reducing the computational cost. In particular, specific machine-learning techniques have been applied to build interatomic potential from ab initio results. Here, We report an energy-free machine-learning calculator that combines three individually trained neural networks to predict the energy and atomic forces of particulate matter. Three structures were investigated: a monometallic nanoparticle, a bimetallic nanoalloy, and a supported metal crystallites. Atomic energies were predicted via a graph neural network, leading to a mean absolute error (MAE) within 0.004 eV from Density Functional Theory (DFT) calculations. The task of predicting atomic forces was split over two feedforward networks, one predicting the force's norm and another its direction. The force prediction resulted in a MAE within 0.080 eV/A against DFT results. The interpretability of the graph neural network predictions was demonstrated by underlying the physics of the monometallic particle in the form of cohesion energy.

Agents often have individual goals which depend on a group's actions. If agents trust a forecast of collective action and adapt strategically, such prediction can influence outcomes non-trivially, resulting in a form of performative prediction. This effect is ubiquitous in scenarios ranging from pandemic predictions to election polls, but existing work has ignored interdependencies among predicted agents. As a first step in this direction, we study a collective risk dilemma where agents dynamically decide whether to trust predictions based on past accuracy. As predictions shape collective outcomes, social welfare arises naturally as a metric of concern. We explore the resulting interplay between accuracy and welfare, and demonstrate that searching for stable accurate predictions can minimize social welfare with high probability in our setting. By assuming knowledge of a Bayesian agent behavior model, we then show how to achieve better trade-offs and use them for mechanism design.

We study the creation and breakdown of a quantized vortex shear layer forming between a stationary Bose-Einstein condensate and a stirred-in persistent current. Once turbulence is established, we characterize the progressive clustering of the vortices, showing that the cluster number follows a power law decay with time, similar to decaying turbulence in other two-dimensional systems. Numerical study of the system demonstrates good agreement of the experimental data with a point vortex model that includes damping and noise. With increasing vortex number in the computational model, we observe a convergence of the power-law exponent to a fixed value., Comment: 8 pages, 8 figures

Originating in game theory, Shapley values are widely used for explaining a machine learning model's prediction by quantifying the contribution of each feature's value to the prediction. This requires a scalar prediction as in binary classification, whereas a multiclass probabilistic prediction is a discrete probability distribution, living on a multidimensional simplex. In such a multiclass setting the Shapley values are typically computed separately on each class in a one-vs-rest manner, ignoring the compositional nature of the output distribution. In this paper, we introduce Shapley compositions as a well-founded way to properly explain a multiclass probabilistic prediction, using the Aitchison geometry from compositional data analysis. We prove that the Shapley composition is the unique quantity satisfying linearity, symmetry and efficiency on the Aitchison simplex, extending the corresponding axiomatic properties of the standard Shapley value. We demonstrate this proper multiclass treatment in a range of scenarios., Comment: To be published in ECAI2024's proceedings

We present a dynamic hedging scheme for S&P 500 options, where rebalancing decisions are enhanced by integrating information about the implied volatility surface dynamics. The optimal hedging strategy is obtained through a deep policy gradient-type reinforcement learning algorithm, with a novel hybrid neural network architecture improving the training performance. The favorable inclusion of forward-looking information embedded in the volatility surface allows our procedure to outperform several conventional benchmarks such as practitioner and smiled-implied delta hedging procedures, both in simulation and backtesting experiments.

The recent work of Horikawa and Nakagawa (2024) claims that under a complete market admitting statistical arbitrage, the difference between the hedging position provided by deep hedging and that of the replicating portfolio is a statistical arbitrage. This raises concerns as it entails that deep hedging can include a speculative component aimed simply at exploiting the structure of the risk measure guiding the hedging optimisation problem. We test whether such finding remains true in a GARCH-based market model, which is an illustrative case departing from complete market dynamics. We observe that the difference between deep hedging and delta hedging is a speculative overlay if the risk measure considered does not put sufficient relative weight on adverse outcomes. Nevertheless, a suitable choice of risk measure can prevent the deep hedging agent from engaging in speculation.

Thanks to their parallel and sparse activity features, recurrent neural networks (RNNs) are well-suited for hardware implementation in low-power neuromorphic hardware. However, mapping rate-based RNNs to hardware-compatible spiking neural networks (SNNs) remains challenging. Here, we present a ${\Sigma}{\Delta}$-low-pass RNN (lpRNN): an RNN architecture employing an adaptive spiking neuron model that encodes signals using ${\Sigma}{\Delta}$-modulation and enables precise mapping. The ${\Sigma}{\Delta}$-neuron communicates analog values using spike timing, and the dynamics of the lpRNN are set to match typical timescales for processing natural signals, such as speech. Our approach integrates rate and temporal coding, offering a robust solution for the efficient and accurate conversion of RNNs to SNNs. We demonstrate the implementation of the lpRNN on Intel's neuromorphic research chip Loihi, achieving state-of-the-art classification results on audio benchmarks using 3-bit weights. These results call for a deeper investigation of recurrency and adaptation in event-based systems, which may lead to insights for edge computing applications where power-efficient real-time inference is required., Comment: 5 pages, 3 figures, accepted at ICONS 2024

In this note we study common preperiodic points of rational maps of the Riemann Sphere. We show that given any degrees $d_1,d_2\geq2$, outside a Zariski closed subset of the space of pairs of rational maps $(f,g)$ of degree $d_1$ and $d_2$ respectively, the maps $f$ and $g$ share at most a uniformly bounded number of common preperiodic points. This generalizes a result of DeMarco and Mavraki to maps of possibly different degrees. Our main contribution is the use of H\"older properties of the Green function of a rational map to obtain height estimates., Comment: 23 pages, accepted for publication in Simons Symposium Proceedings

We study the production of three electroweak gauge bosons at the LHC, in the effective field theory of the standard model, at dimension six and next-to-leading order in QCD. We present results for inclusive cross-sections and differential distributions, finding that these QCD corrections are large, often vary across the phase-space and notably differ from those observed in the standard model. We then explore the potential of the recently observed triboson production processes for improving the sensitivity brought by electroweak precision observables and diboson data. The additional sensitivity we observe is dominated by resonant Higgs boson contributions, with decays to photon pairs in particular. A global analysis including Higgs boson data is therefore needed for a fair assessment of the future reach of triboson measurements on heavy new physics., Comment: 37 pages, 9 figures, 14 tables

This article seeks to contribute to a nuanced understanding of the integration of Design Structure Matrix (DSM) and genetic algorithms in the context of Complex Systems modelling described within Model-Based System Engineering approach. By examining coupling minimization as a critical aspect of advanced systems engineering practices, we aim to provide a scholarly exploration, blending theoretical insights with practical applications. The objective is to equip systems architects with analytical tools integrated within their Model Based Systems Engineering (MBSE) environment for exploring the design space of component interactions, facilitating the identification of optimal system architectures., Comment: ERTS2024, SEE; 3AF, Jun 2024, Toulouse, France

Tools from optimal transport (OT) theory have recently been used to define a notion of quantile function for directional data. In practice, regularization is mandatory for applications that require out-of-sample estimates. To this end, we introduce a regularized estimator built from entropic optimal transport, by extending the definition of the entropic map to the spherical setting. We propose a stochastic algorithm to directly solve a continuous OT problem between the uniform distribution and a target distribution, by expanding Kantorovich potentials in the basis of spherical harmonics. In addition, we define the directional Monge-Kantorovich depth, a companion concept for OT-based quantiles. We show that it benefits from desirable properties related to Liu-Zuo-Serfling axioms for the statistical analysis of directional data. Building on our regularized estimators, we illustrate the benefits of our methodology for data analysis.

Bi$_2$Se$_3$ has been the focus of intense interest over the past decade due to its topological properties. Bi surfaces are known to form on Bi$_2$Se$_3$ upon exposure to atmosphere, but their electronic structure has not been investigated. We report band structure measurements of such Bi surfaces using angle-resolved photoemission spectroscopy. Measured spectra can be well explained by the band structure of a single bilayer of Bi on Bi$_2$Se$_3$, and show that Bi surfaces consistently dominate the photoemission signal for air exposure times of at least 1 hour. These results demonstrate that atmospheric effects should be taken into consideration when identifying two-dimensional transport channels, and when designing surface-sensitive measurements of Bi$_2$Se$_3$, ideally limiting air exposure to no more than a few minutes.

We give a new proof of a Fourier interpolation result first proved by Radchenko-Viazovska, deriving it from a vanishing result of the first cohomology of a Fuchsian group with coefficients in the Weil representation.

We conducted extensive experiments on domain adaptation of the Meta-Llama-3-70B-Instruct model on SEC data, exploring its performance on both general and domain-specific benchmarks. Our focus included continual pre-training (CPT) and model merging, aiming to enhance the model's domain-specific capabilities while mitigating catastrophic forgetting. Through this study, we evaluated the impact of integrating financial regulatory data into a robust language model and examined the effectiveness of our model merging techniques in preserving and improving the model's instructive abilities. The model is accessible at hugging face: https://huggingface.co/arcee-ai/Llama-3-SEC-Base, arcee-ai/Llama-3-SEC-Base. This is an intermediate checkpoint of our final model, which has seen 20B tokens so far. The full model is still in the process of training. This is a preprint technical report with thorough evaluations to understand the entire process., Comment: 8 pages, 6 figures

Artificially intelligent agents are increasingly being integrated into human decision-making: from large language model (LLM) assistants to autonomous vehicles. These systems often optimize their individual objective, leading to conflicts, particularly in general-sum games where naive reinforcement learning agents empirically converge to Pareto-suboptimal Nash equilibria. To address this issue, opponent shaping has emerged as a paradigm for finding socially beneficial equilibria in general-sum games. In this work, we introduce Advantage Alignment, a family of algorithms derived from first principles that perform opponent shaping efficiently and intuitively. We achieve this by aligning the advantages of interacting agents, increasing the probability of mutually beneficial actions when their interaction has been positive. We prove that existing opponent shaping methods implicitly perform Advantage Alignment. Compared to these methods, Advantage Alignment simplifies the mathematical formulation of opponent shaping, reduces the computational burden and extends to continuous action domains. We demonstrate the effectiveness of our algorithms across a range of social dilemmas, achieving state-of-the-art cooperation and robustness against exploitation., Comment: 25 Pages, 8 figures

Fusing outputs from automatic speaker verification (ASV) and spoofing countermeasure (CM) is expected to make an integrated system robust to zero-effort imposters and synthesized spoofing attacks. Many score-level fusion methods have been proposed, but many remain heuristic. This paper revisits score-level fusion using tools from decision theory and presents three main findings. First, fusion by summing the ASV and CM scores can be interpreted on the basis of compositional data analysis, and score calibration before fusion is essential. Second, the interpretation leads to an improved fusion method that linearly combines the log-likelihood ratios of ASV and CM. However, as the third finding reveals, this linear combination is inferior to a non-linear one in making optimal decisions. The outcomes of these findings, namely, the score calibration before fusion, improved linear fusion, and better non-linear fusion, were found to be effective on the SASV challenge database., Comment: Proceedings of Interspeech, DOI: 10.21437/Interspeech.2024-422. Code: https://github.com/nii-yamagishilab/SpeechSPC-mini

The rapid progress in generative models has resulted in impressive leaps in generation quality, blurring the lines between synthetic and real data. Web-scale datasets are now prone to the inevitable contamination by synthetic data, directly impacting the training of future generated models. Already, some theoretical results on self-consuming generative models (a.k.a., iterative retraining) have emerged in the literature, showcasing that either model collapse or stability could be possible depending on the fraction of generated data used at each retraining step. However, in practice, synthetic data is often subject to human feedback and curated by users before being used and uploaded online. For instance, many interfaces of popular text-to-image generative models, such as Stable Diffusion or Midjourney, produce several variations of an image for a given query which can eventually be curated by the users. In this paper, we theoretically study the impact of data curation on iterated retraining of generative models and show that it can be seen as an \emph{implicit preference optimization mechanism}. However, unlike standard preference optimization, the generative model does not have access to the reward function or negative samples needed for pairwise comparisons. Moreover, our study doesn't require access to the density function, only to samples. We prove that, if the data is curated according to a reward model, then the expected reward of the iterative retraining procedure is maximized. We further provide theoretical results on the stability of the retraining loop when using a positive fraction of real data at each step. Finally, we conduct illustrative experiments on both synthetic datasets and on CIFAR10 showing that such a procedure amplifies biases of the reward model.

The Conditional Gradient (or Frank-Wolfe) method is one of the most well-known methods for solving constrained optimization problems appearing in various machine learning tasks. The simplicity of iteration and applicability to many practical problems helped the method to gain popularity in the community. In recent years, the Frank-Wolfe algorithm received many different extensions, including stochastic modifications with variance reduction and coordinate sampling for training of huge models or distributed variants for big data problems. In this paper, we present a unified convergence analysis of the Stochastic Frank-Wolfe method that covers a large number of particular practical cases that may have completely different nature of stochasticity, intuitions and application areas. Our analysis is based on a key parametric assumption on the variance of the stochastic gradients. But unlike most works on unified analysis of other methods, such as SGD, we do not assume an unbiasedness of the real gradient estimation. We conduct analysis for convex and non-convex problems due to the popularity of both cases in machine learning. With this general theoretical framework, we not only cover rates of many known methods, but also develop numerous new methods. This shows the flexibility of our approach in developing new algorithms based on the Conditional Gradient approach. We also demonstrate the properties of the new methods through numerical experiments., Comment: Appears in: The 27th International Conference on Artificial Intelligence and Statistics (AISTATS 2024). 42 pages, 13 algorithms, 8 figures, 3 tables. Reference: https://proceedings.mlr.press/v238/nazykov24a.html