Miracle-dz/UniFAR-FTUs huggingface dataset:
Shattering in Pure Spherical Spin Glasses

We prove the existence of a shattered phase within the replica-symmetric phase of the pure spherical $p$-spin models for $p$ sufficiently large. In this phase, we construct a decomposition of the sphere into well-separated small clusters, each of which has exponentially small Gibbs mass, yet which together carry all but an exponentially small fraction of the Gibbs mass. We achieve this via quantitative estimates on the derivative of the Franz--Parisi potential, which measures the Gibbs mass profile around a typical sample. Corollaries on dynamics are derived, in particular we show the two-times correlation function of stationary Langevin dynamics must have an exponentially long plateau. We further show that shattering implies disorder chaos for the Gibbs measure in the optimal transport sense; this is known to imply failure of sampling algorithms which are stable under perturbation in the same metric.
False Sense of Security: Leveraging XAI to Analyze the Reasoning and True Performance of Context-less DGA Classifiers

The problem of revealing botnet activity through Domain Generation Algorithm (DGA) detection seems to be solved, considering that available deep learning classifiers achieve accuracies of over 99.9%. However, these classifiers provide a false sense of security as they are heavily biased and allow for trivial detection bypass. In this work, we leverage explainable artificial intelligence (XAI) methods to analyze the reasoning of deep learning classifiers and to systematically reveal such biases. We show that eliminating these biases from DGA classifiers considerably deteriorates their performance. Nevertheless we are able to design a context-aware detection system that is free of the identified biases and maintains the detection rate of state-of-the art deep learning classifiers. In this context, we propose a visual analysis system that helps to better understand a classifier’s reasoning, thereby increasing trust in and transparency of detection methods and facilitating decision-making.
Class-Incremental Mixture of Gaussians for Deep Continual Learning

Continual learning models for stationary data focus on learning and retaining concepts coming to them in a sequential manner. In the most generic class-incremental environment, we have to be ready to deal with classes coming one by one, without any higher-level grouping. This requirement invalidates many previously proposed methods and forces researchers to look for more flexible alternative approaches. In this work, we follow the idea of centroid-driven methods and propose end-to-end incorporation of the mixture of Gaussians model into the continual learning framework. By employing the gradient-based approach and designing losses capable of learning discriminative features while avoiding degenerate solutions, we successfully combine the mixture model with a deep feature extractor allowing for joint optimization and adjustments in the latent space. Additionally, we show that our model can effectively learn in memory-free scenarios with fixed extractors. In the conducted experiments, we empirically demonstrate the effectiveness of the proposed solutions and exhibit the competitiveness of our model when compared with state-of-the-art continual learning baselines evaluated in the context of image classification problems.
Two-sample and change-point inference for non-Euclidean valued time series

Data objects taking value in a general metric space have become increasingly common in modern data analysis. In this paper, we study two important statistical inference problems, namely, two-sample testing and change-point detection, for such non-Euclidean data under temporal dependence. Typical examples of non-Euclidean valued time series include yearly mortality distributions, time-varying networks, and covariance matrix time series. To accommodate unknown temporal dependence, we advance the self-normalization (SN) technique (Shao, 2010) to the inference of non-Euclidean time series, which is substantially different from the existing SN-based inference for functional time series that reside in Hilbert space (Zhang et al., 2011). Theoretically, we propose new regularity conditions that could be easier to check than those in the recent literature, and derive the limiting distributions of the proposed test statistics under both null and local alternatives. For change-point detection problem, we also derive the consistency for the change-point location estimator, and combine our proposed change-point test with wild binary segmentation to perform multiple change-point estimation. Numerical simulations demonstrate the effectiveness and robustness of our proposed tests compared with existing methods in the literature. Finally, we apply our tests to two-sample inference in mortality data and change-point detection in cryptocurrency data.
Nonlinear and Nonreciprocal Transport Effects in Untwinned Thin Films of Ferromagnetic Weyl Metal 
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The identification of distinct charge transport features, deriving from nontrivial bulk band and surface states, has been a challenging subject in the field of topological systems. In topological Dirac and Weyl semimetals, nontrivial conical bands with Fermi-arc surface states give rise to negative longitudinal magnetoresistance due to chiral anomaly effect and unusual thickness dependent quantum oscillation from Weyl-orbit effect, which were demonstrated recently in experiments. In this work, we report the experimental observations of large nonlinear and nonreciprocal transport effects for both longitudinal and transverse channels in an untwinned Weyl metal of SrRuO$_3$ thin film grown on a SrTiO$_{3}$ substrate. From rigorous measurements with bias current applied along various directions with respect to the crystalline principal axes, the magnitude of nonlinear Hall signals from the transverse channel exhibits a simple sin$\alpha$ dependence at low temperatures, where $\alpha$ is the angle between bias current direction and orthorhombic [001]$_{\rm o}$, reaching a maximum when current is along orthorhombic [1-10]$_{\rm o}$. On the contrary, the magnitude of nonlinear and nonreciprocal signals in the longitudinal channel attains a maximum for bias current along [001]$_{\rm o}$, and it vanishes for bias current along [1-10]$_{\rm o}$. The observed $\alpha$-dependent nonlinear and nonreciprocal signals in longitudinal and transverse channels reveal a magnetic Weyl phase with an effective Berry curvature dipole along [1-10]$_{\rm o}$ from surface states, accompanied by 1D chiral edge modes along [001]$_{\rm o}$.
Tracking the long-term GW phase evolution for HM Cancri-like binaries with LISA

From prolonged X-ray and optical data of the ultra-compact binary HM Cancri, two groups recently measured the second derivative of its orbital frequency. The space gravitational wave (GW) detector LISA will detect $\sim10^4$ Galactic binaries and their second frequency derivatives will be interesting observational targets for LISA. Here, we forecast the GW signal analysis for HM Cancri, as an ideal reference system for these numerous binaries. We find that, in its nominal operation period $T\sim4$yr, LISA is unlikely to realize a sufficient measurement precision for the reported second frequency derivative of this binary. However, because of a strong dependence on the time baseline, the precision will be drastically improved by extending the operation period of LISA or combining it with other missions (e.g., Taiji and TianQin) in a sequential order.
Yin-Yang balance : a dialectical view of variational principles of physics

The aim of this work is to provide a possible philosophical motivation to the variational principles of physics and a possible way to unify the axiomatic formulations of classical mechanics and statistical mechanics. The leitmotif of this work is a dialectical view of the world: any smooth motion in nature is the consequence of the interplay and dynamical balance between pairs of opposite, mutually exclusive but complementary and mutually transformable essences or elements of the motion. This dynamical balance is expressed by an invariant variational relationship between all the pairs of opposite elements in the considered phenomenon. Derivation of several principles of physics from this idea is given. ha l-0 03 10 43 7, v er si on 1 8 Au g 20 08
Trajectory Alignment: Understanding the Edge of Stability Phenomenon via Bifurcation Theory

Cohen et al. (2021) empirically study the evolution of the largest eigenvalue of the loss Hessian, also known as sharpness, along the gradient descent (GD) trajectory and observe the Edge of Stability (EoS) phenomenon. The sharpness increases at the early phase of training (referred to as progressive sharpening), and eventually saturates close to the threshold of $2 / \text{(step size)}$. In this paper, we start by demonstrating through empirical studies that when the EoS phenomenon occurs, different GD trajectories (after a proper reparameterization) align on a specific bifurcation diagram independent of initialization. We then rigorously prove this trajectory alignment phenomenon for a two-layer fully-connected linear network and a single-neuron nonlinear network trained with a single data point. Our trajectory alignment analysis establishes both progressive sharpening and EoS phenomena, encompassing and extending recent findings in the literature.
On the power of graph neural networks and the role of the activation function

In this article we present new results about the expressivity of Graph Neural Networks (GNNs). We prove that for any GNN with piecewise polynomial activations, whose architecture size does not grow with the graph input sizes, there exists a pair of non-isomorphic rooted trees of depth two such that the GNN cannot distinguish their root vertex up to an arbitrary number of iterations. The proof relies on tools from the algebra of symmetric polynomials. In contrast, it was already known that unbounded GNNs (those whose size is allowed to change with the graph sizes) with piecewise polynomial activations can distinguish these vertices in only two iterations. It was also known prior to our work that with ReLU (piecewise linear) activations, bounded GNNs are weaker than unbounded GNNs [Aamand&Al., 2022]. Our approach adds to this result by extending it to handle any piecewise polynomial activation function, which goes towards answering an open question formulated by Grohe [Grohe,2021] more completely. Our second result states that if one allows activations that are not piecewise polynomial, then in two iterations a single neuron perceptron can distinguish the root vertices of any pair of nonisomorphic trees of depth two (our results hold for activations like the sigmoid, hyperbolic tan and others). This shows how the power of graph neural networks can change drastically if one changes the activation function of the neural networks. The proof of this result utilizes the Lindemann-Weierstrauss theorem from transcendental number theory.
Transport-entropy forms of direct and Converseblaschke-Santal{\'o} inequalities

We explore alternative functional or transport-entropy formulations of the Blaschke-Santal{\'o} inequality and of its conjectured counterpart due to Mahler. In particular, we obtain new direct and reverse Blaschke-Santal{\'o} inequalities for s-concave functions. We also obtain new sharp symmetrized transport-entropy inequalities for a large class of spherically invariant probability measures, including the uniform measure on the unit Euclidean sphere and generalized Cauchy and Barenblatt distributions. Finally, we show that the Mahler's conjecture is equivalent to some reinforced log-Sobolev type inequality on the sphere.
Unknotted Curves on Seifert Surfaces

We consider homologically essential simple closed curves on Seifert surfaces of genus one knots in $S^3$, and in particular those that are unknotted or slice in $S^3$. We completely characterize all such curves for most twist knots: they are either positive or negative braid closures; moreover, we determine exactly which of those are unknotted. A surprising consequence of our work is that the figure eight knot admits infinitely many unknotted essential curves up to isotopy on its genus one Seifert surface, and those curves are enumerated by Fibonacci numbers. On the other hand, we prove that many twist knots admit homologically essential curves that cannot be positive or negative braid closures. Indeed, among those curves, we exhibit an example of a slice but not unknotted homologically essential simple closed curve. We further investigate our study of unknotted essential curves for arbitrary Whitehead doubles of non-trivial knots, and obtain that there is a precisely one unknotted essential simple closed curve in the interior of the doubles' standard genus one Seifert surface. As a consequence of all these we obtain many new examples of 3-manifolds that bound contractible 4-manifolds.
The ‘antisymmetric’ programme: theoretical and typological implications

In more mature fields of inquiry, the existence of anomalies is no reason to reject a theory which provides non-trivial explanations for a significant set of relevant phenomena. It may, however, decree the superiority of one theory over another when one but not the other is able to explain the anomalies away (while retaining an explanation for the same basic set of phenomena). 2 A well-known anomaly of all theories of syntax in the Sixties, the Seventies and the Eighties was the existence of various (unexpected) left-right asymmetries in the syntax of natural languages, both within single languages, and cross-linguistically. For example, it was known since the mid-Sixties that while movement to the left (in a 'right branching' language like English) could apply over an unbounded domain, apparent movement to the right was 'upward bounded' (Ross I967: 307). More puzzling still was the subsequent observation that in what were then analysed as the mirror-image left branching languages of the OV type (see Chomsky (I964: I123, fn. 9)), no mirror-image unbounded movement to the right was attested either (see Bach (I97I: I6I), Bresnan (I972: 42 ff.)), despite a few occasional claims to the contrary.3 The various theories proposed, up to the Principles and Parameters theory of the Eighties and the early Nineties, were unable to provide an answer to
When Do Transformers Shine in RL? Decoupling Memory from Credit Assignment

Reinforcement learning (RL) algorithms face two distinct challenges: learning effective representations of past and present observations, and determining how actions influence future returns. Both challenges involve modeling long-term dependencies. The Transformer architecture has been very successful to solve problems that involve long-term dependencies, including in the RL domain. However, the underlying reason for the strong performance of Transformer-based RL methods remains unclear: is it because they learn effective memory, or because they perform effective credit assignment? After introducing formal definitions of memory length and credit assignment length, we design simple configurable tasks to measure these distinct quantities. Our empirical results reveal that Transformers can enhance the memory capability of RL algorithms, scaling up to tasks that require memorizing observations $1500$ steps ago. However, Transformers do not improve long-term credit assignment. In summary, our results provide an explanation for the success of Transformers in RL, while also highlighting an important area for future research and benchmark design. Our code is open-sourced at https://github.com/twni2016/Memory-RL
New Constraints on ALP Electron and Photon Couplings from ArgoNeuT and the MiniBooNE Beam Dump

Beam dumps and fixed-target experiments have been very sensitive probes of such particles and other physics beyond the Standard Model (BSM) by considering the production of new states from the primary interaction in the beam dump. In a proton beam dump, there are many secondary interactions taking place in electromagnetic showers which may be additional production channels for pseudoscalar bosons or axion-like particles (ALPs). The target-less configuration of the MiniBooNE experiment, which collected data from $1.86 \times 10^{20}$ protons impinging directly on the steel beam dump, is an excellent test of sensitivity to these production channels of ALPs in the MeV mass region. Using the null observation of the MiniBooNE dump mode data, we set new constraints on ALPs coupling to electrons and photons produced through a multitude of channels and detected via both scattering and decays in the MiniBooNE detector volume. We find that the null result rules out parameter space that was previously unconstrained by laboratory probes in the 10-100 MeV mass regime for both electron and photon couplings. Lastly, we make the case for performing a dedicated analysis with 1.25$\times 10^{20}$ POT of data collected by the ArgoNeuT experiment, which we show to have complementary sensitivity and set the stage for future searches.
On the Bipartite Entanglement Capacity of Quantum Networks

We consider the problem of multipath entanglement distribution to a pair of nodes in a quantum network consisting of devices with nondeterministic entanglement swapping capabilities. Multipath entanglement distribution enables a network to establish end-to-end entangled links across any number of available paths with preestablished link-level entanglement. Probabilistic entanglement swapping, on the other hand, limits the amount of entanglement that is shared between the nodes; this is especially the case when, due to practical constraints, swaps must be performed in temporal proximity to each other. Limiting our focus to the case where only bipartite entanglement is generated across the network, we cast the problem as an instance of generalized flow maximization between two quantum end nodes wishing to communicate. We propose a mixed-integer quadratically constrained program (MIQCP) to solve this flow problem for networks with arbitrary topology. We then compute the overall network capacity, defined as the maximum number of Einstein–Podolsky–Rosen (EPR) states distributed to users per time unit, by solving the flow problem for all possible network states generated by probabilistic entangled link presence and absence, and subsequently by averaging over all network state capacities. The MIQCP can also be applied to networks with multiplexed links. While our approach for computing the overall network capacity has the undesirable property that the total number of states grows exponentially with link multiplexing capability, it nevertheless yields an exact solution that serves as an upper bound comparison basis for the throughput performance of more easily implementable yet nonoptimal entanglement routing algorithms.
On the Composition of Randomized Query Complexity and Approximate Degree

For any Boolean functions $f$ and $g$, the question whether $R(f\circ g) = \tilde{\Theta}(R(f)R(g))$, is known as the composition question for the randomized query complexity. Similarly, the composition question for the approximate degree asks whether $\widetilde{deg}(f\circ g) = \tilde{\Theta}(\widetilde{deg}(f)\cdot\widetilde{deg}(g))$. These questions are two of the most important and well-studied problems, and yet we are far from answering them satisfactorily. It is known that the measures compose if one assumes various properties of the outer function $f$ (or inner function $g$). This paper extends the class of outer functions for which $\text{R}$ and $\widetilde{\text{deg}}$ compose. A recent landmark result (Ben-David and Blais, 2020) showed that $R(f \circ g) = \Omega(noisyR(f)\cdot R(g))$. This implies that composition holds whenever $noisyR(f) = \Tilde{\Theta}(R(f))$. We show two results: (1)When $R(f) = \Theta(n)$, then $noisyR(f) = \Theta(R(f))$. (2) If $\text{R}$ composes with respect to an outer function, then $\text{noisyR}$ also composes with respect to the same outer function. On the other hand, no result of the type $\widetilde{deg}(f \circ g) = \Omega(M(f) \cdot \widetilde{deg}(g))$ (for some non-trivial complexity measure $M(\cdot)$) was known to the best of our knowledge. We prove that $\widetilde{deg}(f\circ g) = \widetilde{\Omega}(\sqrt{bs(f)} \cdot \widetilde{deg}(g)),$ where $bs(f)$ is the block sensitivity of $f$. This implies that $\widetilde{\text{deg}}$ composes when $\widetilde{\text{deg}}(f)$ is asymptotically equal to $\sqrt{\text{bs}(f)}$. It is already known that both $\text{R}$ and $\widetilde{\text{deg}}$ compose when the outer function is symmetric. We also extend these results to weaker notions of symmetry with respect to the outer function.
Continual Learning as Computationally Constrained Reinforcement Learning

An agent that efficiently accumulates knowledge to develop increasingly sophisticated skills over a long lifetime could advance the frontier of artificial intelligence capabilities. The design of such agents, which remains a long-standing challenge of artificial intelligence, is addressed by the subject of continual learning. This monograph clarifies and formalizes concepts of continual learning, introducing a framework and set of tools to stimulate further research.
Metastable cosmic strings

Many symmetry breaking patterns in grand unified theories (GUTs) give rise to cosmic strings that eventually decay when pairs of GUT monopoles spontaneously nucleate along the string cores. These strings are known as metastable cosmic strings and have intriguing implications for particle physics and cosmology. In this article, we discuss the current status of metastable cosmic strings, with a focus on possible GUT embeddings and connections to inflation, neutrinos, and gravitational waves (GWs). The GW signal emitted by a network of metastable cosmic strings in the early universe differs, in particular, from the signal emitted by topologically stable strings by a suppression at low frequencies. Therefore, if the underlying symmetry breaking scale is close to the GUT scale, the resulting GW spectrum can be accessible at current ground-based interferometers as well as at future space-based interferometers, such as LISA, and at the same time account for the signal in the most recent pulsar timing data sets. Metastable cosmic strings thus nourish the hope that future GW observations might shed light on fundamental physics close to the GUT scale.
Decay characterization of solutions to the viscous Camassa–Holm equations

In this paper we study the decay characterization in the space HσK(Rn) of solutions to the viscous Camassa–Holm equations (VCHE) in the whole space Rn (n=2,3,4), namely, where m+2p⩽K, r∗=r∗(v0) is the decay character of the initial datum v0∈HσK(Rn). We also get the optimal lower bounds for decay rates of solutions to VCHE when −n/2<r∗⩽1. In particular, when v0∈HσK(Rn)∩L1(Rn) has decay character r∗(v0)=0, then we recover the previous results of Bjorland and Schonbek (2008 Ann. Inst. Henri Poincaré Anal. Non Linéaire 25 907–36).