Miracle-dz/UniFAR-FTUs huggingface dataset:
Accelerated Quality-Diversity through Massive Parallelism

Quality-Diversity (QD) optimization algorithms are a well-known approach to generate large collections of diverse and high-quality solutions. However, derived from evolutionary computation, QD algorithms are population-based methods which are known to be data-inefficient and requires large amounts of computational resources. This makes QD algorithms slow when used in applications where solution evaluations are computationally costly. A common approach to speed up QD algorithms is to evaluate solutions in parallel, for instance by using physical simulators in robotics. Yet, this approach is limited to several dozen of parallel evaluations as most physics simulators can only be parallelized more with a greater number of CPUs. With recent advances in simulators that run on accelerators, thousands of evaluations can now be performed in parallel on single GPU/TPU. In this paper, we present QDax, an accelerated implementation of MAP-Elites which leverages massive parallelism on accelerators to make QD algorithms more accessible. We show that QD algorithms are ideal candidates to take advantage of progress in hardware acceleration. We demonstrate that QD algorithms can scale with massive parallelism to be run at interactive timescales without any significant effect on the performance. Results across standard optimization functions and four neuroevolution benchmark environments shows that experiment runtimes are reduced by two factors of magnitudes, turning days of computation into minutes. More surprising, we observe that reducing the number of generations by two orders of magnitude, and thus having significantly shorter lineage does not impact the performance of QD algorithms. These results show that QD can now benefit from hardware acceleration, which contributed significantly to the bloom of deep learning.
FORML: Learning to Reweight Data for Fairness

Machine learning models are trained to minimize the mean loss for a single metric, and thus typically do not consider fairness and robustness. Ne-glecting such metrics in training can make these models prone to fairness violations when training data are imbalanced or test distributions differ. This work introduces F airness O ptimized R eweighting via M eta- L earning (FORML), a training algorithm that balances fairness and robustness with accuracy by jointly learning training sample weights and neural network parameters. The approach increases model fairness by learning to balance the contributions from both over-and under-represented sub-groups through dynamic reweighting of the data learned from a user-speciﬁed held-out set representative of the distribution under which fairness is desired. FORML improves equality of opportunity fairness criteria on image classiﬁcation tasks, reduces bias of corrupted labels, and facilitates building more fair datasets via data condensation. These improve-ments are achieved without pre-processing data or post-processing model outputs, without learning an additional weighting function, without chang-ing model architecture, and while maintaining accuracy on the original predictive metric.
Asymptotic behaviour of rotating convection-driven dynamos in the plane layer geometry

Abstract Dynamos driven by rotating convection in the plane layer geometry are investigated numerically for a range of Ekman number ($E$), magnetic Prandtl number ($Pm$) and Rayleigh number ($Ra$). The primary purpose of the investigation is to compare results of the simulations with previously developed asymptotic theory that is applicable in the limit of rapid rotation. We find that all of the simulations are in the quasi-geostrophic regime in which the Coriolis and pressure gradient forces are approximately balanced at leading order, whereas all other forces, including the Lorentz force, act as perturbations. Agreement between simulation output and asymptotic scalings for the energetics, flow speeds, magnetic field amplitude and length scales is found. The transition from large-scale dynamos to small-scale dynamos is well described by the magnetic Reynolds number based on the small convective length scale, $\widetilde {Rm}$, with large-scale dynamos preferred when $\widetilde {Rm} \lesssim O(1)$. The magnitude of the large-scale magnetic field is observed to saturate and become approximately constant with increasing Rayleigh number. Energy spectra show that all length scales present in the flow field and the small-scale magnetic field are consistent with a scaling of $E^{1/3}$, even in the turbulent regime. For a fixed value of $E$, we find that the viscous dissipation length scale is approximately constant over a broad range of $Ra$; the ohmic dissipation length scale is approximately constant within the large-scale dynamo regime, but transitions to a $\widetilde {Rm}^{-1/2}$ scaling in the small-scale dynamo regime.
Linear transformations of vertex operator presentations of Hall-Littlewood polynomials

Abstract. We study the effect of linear transformations on quantum fields with applications to vertex operator presentations of symmetric functions. Properties of linearly transformed quantum fields and corresponding transformations of Hall-Littlewood polynomials are described, including preservation of commutation relations, stability, explicit combinatorial formulas and generating functions. We prove that specializations of linearly transformed Hall-Littlewood polynomials describe all polynomial tau functions of the KP and the BKP hierarchy. Examples of linear transformations are related to multiparameter symmetric functions, Grothendieck polynomials, deformations by cyclotomic polynomials, and some other variations of Schur symmetric functions that exist in the literature.
Optical biosensor based on a photonic crystal with a defective layer designed to determine the concentration of SARS-CoV-2 in water

We propose a new optical biosensor based on a SiO2/Si photonic crystal with a defect layer, which can determine the concentration of SARS-CoV-2 in water by the defect mode shift. Two models of the dependence of the refractive index of the defect layer on the concentration of the pathogen in water were considered. The optimal parameters of the photonic crystal in our device were determined such as the thickness of the SiO2 and Si layers of the ideal photonic crystal of 0.720 and 0.275 μm, respectively, and the optimal thickness of the defect layer of 1.87 μm was also determined. It was also demonstrated that in the presence of absorption in the structure under study, it is much more advantageous to operate in the reflection mode compared to the transmission mode. Finally, the wavelength dependence of the defect mode on the SARS-CoV-2 concentration was obtained and the sensitivity of the sensor was determined to be 1020 nm/RIU.
The Drinfel'd centres of String 2-groups

Let G be a compact connected Lie group and k ∈ H 4 ( B G, Z ) a cohomology class. The String 2-group G k is the central extension of G by the 2-group [ ∗ /U (1)] classiﬁed by k . It has a close relationship to the level k extension of the loop group LG . We compute the Drinfel’d centre of G k as a smooth 2-group. When G is semisimple, we prove that the Drinfel’d centre is equal to the invertible part of the category of positive energy representations of LG at level k (as long as we exclude factors of E 8 at level 2)
Robust Binary Models by Pruning Randomly-initialized Networks

Robustness to adversarial attacks was shown to require a larger model capacity, and thus a larger memory footprint. In this paper, we introduce an approach to obtain robust yet compact models by pruning randomly-initialized binary networks. Unlike adversarial training, which learns the model parameters, we initialize the model parameters as either +1 or -1, keep them fixed, and find a subnetwork structure that is robust to attacks. Our method confirms the Strong Lottery Ticket Hypothesis in the presence of adversarial attacks, and extends this to binary networks. Furthermore, it yields more compact networks with competitive performance than existing works by 1) adaptively pruning different network layers; 2) exploiting an effective binary initialization scheme; 3) incorporating a last batch normalization layer to improve training stability. Our experiments demonstrate that our approach not only always outperforms the state-of-the-art robust binary networks, but also can achieve accuracy better than full-precision ones on some datasets. Finally, we show the structured patterns of our pruned binary networks.
Density Profile of the Ambient Circumnuclear Medium in Seyfert 1 Galaxies

The shape of the ambient circumnuclear medium (ACM) density profile can probe the history of accretion onto the central supermassive black holes in galaxies and the circumnuclear environment. However, due to the limitations of instrument resolution, the density profiles of the ACM for most galaxies remain largely unknown. In this work, we propose a novel method to measure the ACM density profile of active galactic nuclei (AGNs) by the equilibrium between the radiation pressure on the warm absorbers (WAs, a type of AGN outflow) and the drag pressure from the ACM. We study the correlation between the outflow velocity and ionization parameter of WAs in each of the five Seyfert 1 galaxies (NGC 3227, NGC 3783, NGC 4051, NGC 4593, and NGC 5548), inferring that the density profile of the ACM is between n ∝ r −1.7 and n ∝ r −2.15 (n is number density and r is distance) from 0.01 pc to parsec scales in these five AGNs. Our results indicate that the ACM density profile in Seyfert 1 galaxies is steeper than the prediction by the spherically symmetric Bondi accretion model and the simulated results of the hot accretion flow, but more in line with the prediction by the standard thin-disk model.
Entropic force and real-time dynamics of holographic quarkonium in a magnetic field

We continue the study of a recently constructed holographic QCD model supplemented with magnetic ﬁeld. We consider the holographic dual of a quark, anti-quark pair and investigate its entropy beyond the deconﬁnement phase transition in terms of interquark distance, temperature and magnetic ﬁeld. We obtain a clear magnetic ﬁeld dependence in the strongly decreasing entropy near deconﬁnement and in the entropy variation for growing interquark separation. We uncover various supporting evidences for inverse magnetic catalysis. The emergent entropic force is found to become stronger with magnetic ﬁeld, promoting the quarkonium dissociation. We also probe the dynamical dissociation of the quarkonium state, ﬁnding a faster dissociation with magnetic ﬁeld. At least the static predictions should become amenable to a qualitative comparison with future lattice data.
Massless minimal quantum scalar field with an asymmetric self interaction in de Sitter spacetime

Massless minimally coupled quantum scalar field with an asymmetric self interaction, V(ϕ) = λϕ 4/4! + βϕ 3/3! (with λ > 0) is considered in the (3+1)-dimensional inflationary de Sitter spacetime. This potential is bounded from below irrespective of the sign of β. Earlier computations mostly considered the quartic part. Our chief motivation behind this study is to assess the vacuum expectation values of V(ϕ) and ϕ, both of which can be negative, and hence may lead to some screening of the inflationary cosmological constant value. First using the in-in formalism, the renormalised quantum correction to the cubic potential appearing in the energy-momentum tensor is computed at two loop, which is the leading order in this case. The quantum correction to the kinetic term at two loop are subleading compared to the above result at late cosmological times. Next, using some of these results we compute the renormalised vacuum expectation value of ϕ, by computing the tadpoles at 𝒪(β) and 𝒪(λβ). Due to the appearance of the de Sitter isometry breaking logarithms, the tadpoles cannot be completely renormalised away in this case, unlike the flat spacetime. All these results, as expected, show secularly growing logarithms at late cosmological times. We next use a recently proposed renormalisation group inspired formalism to resum perturbative secular effects, to compute a non-perturbative 〈ϕ〉 at late cosmological times. 〈ϕ〉 turns out to be approximately one order of magnitude less compared to the position of the classical minima ϕ = -3β/λ of V(ϕ). Estimation on the possible screening of the inflationary cosmological constant due to this 〈ϕ〉 is also presented.
Generic properties of $3$-dimensional Reeb flows: Birkhoff sections and entropy

In this paper we use broken book decompositions to study Reeb flows on closed $3$-manifolds. We show that if the Liouville measure of a nondegenerate contact form can be approximated by periodic orbits, then there is a Birkhoff section for the associated Reeb flow. In view of Irie's equidistribution theorem, this is shown to imply that the set of contact forms whose Reeb flows have a Birkhoff section contains an open and dense set in the $C^\infty$-topology. We also show that the set of contact forms whose Reeb flows have positive topological entropy is open and dense in the $C^\infty$-topology.
Pentagon relation in quantum cluster scattering diagrams

We formulate the pentagon relation for quantum dilogarithm elements in the structure group of a quantum cluster scattering diagram (QCSD). As an application, we show the nonpositivity of a certain class of nonskew-symmetric QCSDs. Also, we explicitly present various consistency relations for QCSDs of rank 2 completely or up to some degree, many of which are new in the literature.
Sequential Learning of the Topological Ordering for the Linear Non-Gaussian Acyclic Model with Parametric Noise

Causal discovery, the learning of causality in a data mining scenario, has been of strong scien-tiﬁc and theoretical interest as a starting point to identify “what causes what? ” Contingent on assumptions, it is sometimes possible to identify an exact causal Directed Acyclic Graph (DAG), as opposed to a Markov equivalence class of graphs that gives ambiguity of causal directions. The focus of this paper is on one such case: a linear structural equation model with non-Gaussian noise, a model known as the Linear Non-Gaussian Acyclic Model (LiNGAM). Given a speciﬁed parametric noise model, we develop a novel sequential approach to estimate the causal ordering of a DAG. At each step of the procedure, only simple likelihood ratio scores are calculated on regression residuals to decide the next node to append to the current partial ordering. Under mild assumptions, the population version of our procedure provably identiﬁes a true ordering of the underlying causal DAG. We provide extensive numerical evidence to demonstrate that our sequential procedure is scalable to cases with possibly thousands of nodes and works well for high-dimensional data. We also conduct an application to a single-cell gene expression dataset to demonstrate our estimation procedure.
Challenging Common Assumptions in Convex Reinforcement Learning

The classic Reinforcement Learning (RL) formulation concerns the maximization of a scalar reward function. More recently, convex RL has been introduced to extend the RL formulation to all the objectives that are convex functions of the state distribution induced by a policy. Notably, convex RL covers several relevant applications that do not fall into the scalar formulation, including imitation learning, risk-averse RL, and pure exploration. In classic RL, it is common to optimize an infinite trials objective, which accounts for the state distribution instead of the empirical state visitation frequencies, even though the actual number of trajectories is always finite in practice. This is theoretically sound since the infinite trials and finite trials objectives can be proved to coincide and thus lead to the same optimal policy. In this paper, we show that this hidden assumption does not hold in the convex RL setting. In particular, we show that erroneously optimizing the infinite trials objective in place of the actual finite trials one, as it is usually done, can lead to a significant approximation error. Since the finite trials setting is the default in both simulated and real-world RL, we believe shedding light on this issue will lead to better approaches and methodologies for convex RL, impacting relevant research areas such as imitation learning, risk-averse RL, and pure exploration among others.
Learning strides in convolutional neural networks

Convolutional neural networks typically contain several downsampling operators, such as strided convolutions or pooling layers, that progressively reduce the resolution of intermediate representations. This provides some shift-invariance while reducing the computational complexity of the whole architecture. A critical hyperparameter of such layers is their stride: the integer factor of downsampling. As strides are not differentiable, finding the best configuration either requires cross-validation or discrete optimization (e.g. architecture search), which rapidly become prohibitive as the search space grows exponentially with the number of downsampling layers. Hence, exploring this search space by gradient descent would allow finding better configurations at a lower computational cost. This work introduces DiffStride, the first downsampling layer with learnable strides. Our layer learns the size of a cropping mask in the Fourier domain, that effectively performs resizing in a differentiable way. Experiments on audio and image classification show the generality and effectiveness of our solution: we use DiffStride as a drop-in replacement to standard downsampling layers and outperform them. In particular, we show that introducing our layer into a ResNet-18 architecture allows keeping consistent high performance on CIFAR10, CIFAR100 and ImageNet even when training starts from poor random stride configurations. Moreover, formulating strides as learnable variables allows us to introduce a regularization term that controls the computational complexity of the architecture. We show how this regularization allows trading off accuracy for efficiency on ImageNet.
Database Matching Under Column Repetitions

—Motivated by synchronization errors in the sampling of time-indexed databases, matching of random databases under random column repetitions (including deletions) is investigated. Column histograms are used as a permutation-invariant feature to detect the repetition pattern, whose asymptotic-uniqueness is proved using information-theoretic tools. Repetition detection is followed by a row matching scheme. Considering this overall scheme, sufﬁcient conditions for successful database matching in terms of the database growth rate are derived. A modiﬁed version of Fano’s inequality leads to a tight necessary condition for successful matching, establishing the matching capacity under column repetitions. This capacity is equal to the erasure bound, which assumes the repetition locations are known a-priori.
Complex cobordism with involutions and geometric orientations

We calculate the cobordism ring Ω C2 ∗ of stably almost complex manifolds with involution, and investigate the C2-spectrum ΩC2 which represents it. We introduce the notion of a geometrically oriented C2-spectrum, which extends the notion of a complex oriented C2-spectrum, and of which ΩC2 is the universal example. Examples, in addition to ΩC2 , include the Eilenberg-Maclane spectrum C2 and the connective cover kC2 of C2-equivariant K-theory. On the algebraic side, we define and study filtered C2-equivariant formal group laws, which are the algebraic structures determined by geometrically oriented C2-spectra. We prove some of the fundamental properties of filtered C2-equivariant formal group laws, as well as a universality statement for the filtered C2-equivariant formal group law determined by ΩC2 .
Circle Squaring with Pieces of Small Boundary and Low Borel Complexity

Tarski’s Circle Squaring Problem from 1925 asks whether it is possible to partition a disk in the plane into ﬁnitely many pieces and reassemble them via isometries to yield a partition of a square of the same area. It was ﬁnally resolved by Laczkovich in 1990 in the aﬃrmative. Recently, several new proofs have emerged which achieve circle squaring with better structured pieces: namely, pieces which are Lebesgue measurable and have the property of Baire (Grabowski–M´ath´e–Pikhurko) or even are Borel (Marks– Unger). Inthis paper, we show that circle squaring is possible with Borel pieces of positive Lebesgue measure whose boundaries have upper Minkowski dimension less than 2 (in particular, each piece is Jordan measurable). We also improve the Borel complexity of the pieces: namely, we show that each piece can be taken to be a Boolean combination of F σ sets. This is a consequence of our more general result that applies to any two bounded subsets of R k , k (cid:62) 1, of equal positive measure whose boundaries have upper Minkowski dimension smaller than k .
Value distribution of exponential polynomials and their role in the theories of complex differential equations and oscillation theory

An exponential polynomial is a finite linear sum of terms P(z)eQ(z)$P(z)e^{Q(z)}$ , where P(z)$P(z)$ and Q(z)$Q(z)$ are polynomials. The early results on the value distribution of exponential polynomials can be traced back to Georg Pólya's paper published in 1920, while the latest results have come out in 2022. Despite of over a century of research work, many intriguing problems on value distribution of exponential polynomials still remain unsolved. The role of exponential polynomials and their quotients in the theories of linear/non‐linear differential equations, oscillation theory and differential‐difference equations will also be discussed. Thirteen open problems are given to motivate the readers for further research in these topics.
Regression Transformer: Concurrent Conditional Generation and Regression by Blending Numerical and Textual Tokens

We report the Regression Transformer (RT), a method that abstracts regression as a conditional sequence modeling problem. The RT casts continuous properties as sequences of numerical tokens and encodes them jointly with conventional to-kens. This yields a dichotomous model that can seamlessly transition between solving regression tasks and conditional generation tasks; solely governed by the mask location. We propose several extensions to the XLNet objective and adopt an alternating training scheme to concurrently optimize property prediction and conditional text generation based on a self-consistency loss. Our experiments on both chemical and protein languages demonstrate that the performance of traditional regression models can be surpassed despite training with cross entropy loss. Importantly, priming the same model with continuous properties yields a highly competitive conditional generative models that outperforms specialized approaches in a constrained property optimization benchmark. In sum, the Regression Transformer opens the door for ”swiss army knife” models that excel at both regression and conditional generation. This ﬁnds application particularly in property-driven, local exploration of the chemical or protein space.