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The main goal of this paper is to obtain upper bounds for the regularity of graded deficiency modules in the spirit of the one obtained by Kumini--Murai in the monomial case building upon the spectral sequence formalism developed by \`Alvarez Montaner, Boix and Zarzuela. This spectral sequence formalism allows us not only to recover Kumini--Murai's upper bound for monomial ideals, but also to extend it for other types of rings, which include toric face rings and some binomial edge rings, producing to the best of our knowledge new upper bounds for the regularity of graded deficiency modules of this type of rings., Comment: 14 pages, comments are welcome

Task Arithmetic is a model merging technique that enables the combination of multiple models' capabilities into a single model through simple arithmetic in the weight space, without the need for additional fine-tuning or access to the original training data. However, the factors that determine the success of Task Arithmetic remain unclear. In this paper, we examine Task Arithmetic for multi-task learning by framing it as a one-shot Federated Learning problem. We demonstrate that Task Arithmetic is mathematically equivalent to the commonly used algorithm in Federated Learning, called Federated Averaging (FedAvg). By leveraging well-established theoretical results from FedAvg, we identify two key factors that impact the performance of Task Arithmetic: data heterogeneity and training heterogeneity. To mitigate these challenges, we adapt several algorithms from Federated Learning to improve the effectiveness of Task Arithmetic. Our experiments demonstrate that applying these algorithms can often significantly boost performance of the merged model compared to the original Task Arithmetic approach. This work bridges Task Arithmetic and Federated Learning, offering new theoretical perspectives on Task Arithmetic and improved practical methodologies for model merging.

Twisting two-dimensional van der Waals magnets allows the formation and control of different spin-textures, as skyrmions or magnetic domains. Beyond the rotation angle, different spin reversal processes can be engineered by increasing the number of magnetic layers forming the twisted van der Waals heterostructure. Here, we consider pristine monolayers and bilayers of the A-type antiferromagnet CrSBr as building blocks. By rotating 90 degrees these units, we fabricate symmetric (monolayer/monolayer and bilayer/bilayer) and asymmetric (monolayer/bilayer) heterostructures. The magneto-transport properties reveal the appearance of magnetic hysteresis, which is highly dependent upon the magnitude and direction of the applied magnetic field and is determined not only by the twist-angle but also by the number of layers forming the stack. This high tunability allows switching between volatile and non-volatile magnetic memory at zero-field and controlling the appearance of abrupt magnetic reversal processes at either negative or positive field values on demand. The phenomenology is rationalized based on the different spin-switching processes occurring in the layers, as supported by micromagnetic simulations. Our results highlight the combination between twist-angle and number of layers as key elements for engineering spin-switching reversals in twisted magnets, of interest towards the miniaturization of spintronic devices and realizing novel spin textures., Comment: 18 pages, 5 figures

Visual Language Models (VLMs) are now increasingly being merged with Large Language Models (LLMs) to enable new capabilities, particularly in terms of improved interactivity and open-ended responsiveness. While these are remarkable capabilities, the contribution of LLMs to enhancing the longstanding key problem of classifying an image among a set of choices remains unclear. Through extensive experiments involving seven models, ten visual understanding datasets, and multiple prompt variations per dataset, we find that, for object and scene recognition, VLMs that do not leverage LLMs can achieve better performance than VLMs that do. Yet at the same time, leveraging LLMs can improve performance on tasks requiring reasoning and outside knowledge. In response to these challenges, we propose a pragmatic solution: a lightweight fix involving a relatively small LLM that efficiently routes visual tasks to the most suitable model for the task. The LLM router undergoes training using a dataset constructed from more than 2.5 million examples of pairs of visual task and model accuracy. Our results reveal that this lightweight fix surpasses or matches the accuracy of state-of-the-art alternatives, including GPT-4V and HuggingGPT, while improving cost-effectiveness.

Memristors stand out as promising components in the landscape of memory and computing. Memristors are generally defined by a conductance equation containing a state variable that imparts a memory effect. The current-voltage cycling causes transitions of the conductance, determined by different physical mechanisms such as the formation of conducting filaments in an insulating surrounding. Here we provide a unified description of the set and reset processes, by means of a single voltage activated relaxation time of the memory variable. This approach is based on the Hodgkin-Huxley model that is widely used to describe action potentials dynamics in neurons. We focus on halide perovskite memristors and their intersection with neuroscience-inspired computing. We show that the modelling approach adeptly replicates the experimental traits of both volatile and nonvolatile memristors. Its versatility extends across various device materials and configurations, capturing nuanced behaviors such as scan rate- and upper vertex-dependence. The model also describes well the response to sequences of voltage pulses that cause synaptic potentiation effects. This model serves as a potent tool for comprehending and probing the underlying mechanisms of memristors, by indicating the relaxation properties that control observable response, which opens the way for a detailed physical interpretation.

Single photons emitters (SPEs) are key components in quantum information applications and are commonly generated in 2D materials by inhomogeneous strain engineering. Here, we report an alternative approach that involves a 2D semiconductor/2D magnet heterostructure. The optical study of the WSe2/CrSBr heterostructures reveals several new emission lines at lower energies compared to characteristic WSe2 emissions, that are assigned to localized excitons. Further investigation demonstrates that one of these emergent lines is an SPE with a strong valley polarization response and large energy shift with the field-induced metamagnetic transition in CrSBr, linking it to the magnetic proximity effect of the adjacent CrSBr layer. In contrast to previous reports on WSe2 that only allow tuning of the SPEs by out-of-plane magnetic field, our emitter is sensitive to both in- and out-of-plane fields. Our findings demonstrate the potential of this approach for improved control and polarization of SPEs in 2D materials., Comment: 17 pages, 4 figures, plus suporting information

We extend Ravagnani's MacWilliams duality theory to the settings of rank metric codes over finite chain rings, relating the sequences of $q$-binomial moments of a rank metric code over this class of rings with those of its dual.

Starting from a single layer of NbS$_2$ grown on graphene by molecular beam epitaxy, the single unit cell thick 2D materials Nb$_{5/3}$S$_3$-2D and Nb$_2$S$_3$-2D are created using two different pathways. Either annealing under sulfur-deficient conditions at progressively higher temperatures or deposition of increasing amounts of Nb at elevated temperature result in phase-pure Nb$_{5/3}$S$_3$-2D followed by Nb$_2$S$_3$-2D. The materials are characterized by scanning tunneling microscopy, scanning tunneling spectroscopy and X-ray photoemission spectroscopy. The experimental assessment combined with systematic density functional theory calculations reveals their structure. The 2D materials are covalently bound without any van der Waals gap. Their stacking sequence and structure are at variance with expectations based on corresponding bulk materials highlighting the importance of surface and interface effects in structure formation.

Configural processing, the perception of spatial relationships among an object's components, is crucial for object recognition. However, the teleology and underlying neurocomputational mechanisms of such processing are still elusive, notwithstanding decades of research. We hypothesized that processing objects via configural cues provides a more robust means to recognizing them relative to local featural cues. We evaluated this hypothesis by devising identification tasks with composite letter stimuli and comparing different neural network models trained with either only local or configural cues available. We found that configural cues yielded more robust performance to geometric transformations such as rotation or scaling. Furthermore, when both features were simultaneously available, configural cues were favored over local featural cues. Layerwise analysis revealed that the sensitivity to configural cues emerged later relative to local feature cues, possibly contributing to the robustness to pixel-level transformations. Notably, this configural processing occurred in a purely feedforward manner, without the need for recurrent computations. Our findings with letter stimuli were successfully extended to naturalistic face images. Thus, our study provides neurocomputational evidence that configural processing emerges in a na\"ive network based on task contingencies, and is beneficial for robust object processing under varying viewing conditions.

Astronomical observatories have been identified as substantial contributors to the carbon footprint of astrophysical research. Being part of the collaboration that currently develops the Medium-Sized Telescope (MST) of the Cherenkov Telescope Array, a ground-based observatory for very-high-energy gamma rays that will comprise 64 telescopes deployed on two sites, we assessed the environmental impacts of one MST on the Northern site by means of a Life Cycle Assessment. We identified resource use and climate change as the most significant impacts, being driven by telescope manufacturing and energy consumption during operations. We estimate life cycle greenhouse gas emissions of 2,660 +/- 274 tCO2 equivalent for the telescope, 44% of which arise from construction, 1% from on-site assembly and commissioning, and 55% from operations over 30 years. Environmental impacts can be reduced by using renewable energies during construction and operations, use of less electronic components and metal casting, and use of recycled materials. We propose complementing project requirements with environmental budgets as an effective measure for impact management and reductions., Comment: 32 pages, 4 main figures, 3 extended data figures

The layered metamagnet CrSBr offers a rich interplay between magnetic, optical and electrical properties that can be extended down to the two-dimensional (2D) limit. Despite the extensive research regarding the long-range magnetic order in magnetic van der Waals materials, short-range correlations have been loosely investigated. By using Small-Angle Neutron Scattering (SANS) we show the formation of short-range magnetic regions in CrSBr with correlation lengths that increase upon cooling up to ca. 3 nm at the antiferromagnetic ordering temperature (TN ~ 140 K). Interestingly, these ferromagnetic correlations start developing below 200 K, i.e., well above TN. Below TN, these correlations rapidly decrease and are negligible at low-temperatures. The experimental results are well-reproduced by an effective spin Hamiltonian, which pinpoints that the short-range correlations in CrSBr are intrinsic to the monolayer limit, and discard the appearance of any frustrated phase in CrSBr at low-temperatures within our experimental window between 2 and 200 nm. Overall, our results are compatible with a spin freezing scenario of the magnetic fluctuations in CrSBr and highlight SANS as a powerful technique for characterizing the rich physical phenomenology beyond the long-range order paradigm offered by van der Waals magnets., Comment: Main Text + Supplementary Information

Migratory and tissue resident cells exhibit highly branched morphologies to perform their function and to adapt to the microenvironment. Immune cells, for example, display transient branched shapes while exploring the surrounding tissues. In another example, to properly irrigate the tissues, blood vessels bifurcate thereby forcing the branching of cells moving on top or within the vessels. In both cases microenvironmental constraints force migrating cells to extend several highly dynamic protrusions. Here, we present a theoretical model for the shape dynamics and migration of cells that simultaneously span several junctions, which we validated by using micropatterns with an hexagonal array, and a neuronal network image analysis pipeline to monitor the macrophages and endothelial cell shapes and migration. In our model we describe how the actin retrograde flow controls branch extension, retraction and global cell polarization. We relate the noise in this flow to the residency times and trapping of the cell at the junctions of the network. In addition, we found that macrophages and endothelial cells display very different migration regimes on the network, with macrophages moving faster and having larger changes in cell length in comparison to endothelial cells. These results expose how cellular shapes and migration are intricately coupled inside complex geometries.

Distillation is the task of replacing a complicated machine learning model with a simpler model that approximates the original [BCNM06,HVD15]. Despite many practical applications, basic questions about the extent to which models can be distilled, and the runtime and amount of data needed to distill, remain largely open. To study these questions, we initiate a general theory of distillation, defining PAC-distillation in an analogous way to PAC-learning [Val84]. As applications of this theory: (1) we propose new algorithms to extract the knowledge stored in the trained weights of neural networks -- we show how to efficiently distill neural networks into succinct, explicit decision tree representations when possible by using the ``linear representation hypothesis''; and (2) we prove that distillation can be much cheaper than learning from scratch, and make progress on characterizing its complexity., Comment: 46 pages, 5 figures. Please reach out with comments! Feedback is welcome

Nowadays there is a large number of non-classical logics, each one best suited for reasoning about some issues in abstract fields, such as linguistics or epistemology, among others. Proving interesting properties for each one of them supposes a big workload for logicians and computer scientists. We want an approach into this problematic that is modular. To adress this issue, the report shows new insights in the construction of Atomic Logics introduced by Guillaume Aucher. Atomic Logics let us represent very general left and right introduction rules and they come along a new kind of rules based on display logics and residuation. A new approach is taken into the definition of Atomic Logics, which is now built on a class of actions for which we prove cut-elimination. We show that some of them are equivalent to Aucher's Atomic Logics and we prove cut-elimination and Craig Interpolation for a class of them. The introduced theory is applied to the non-associative Lambek Calculus throughout the report. It is accompanied by a computer-checked formalisation of the original syntax in the proof assistant Coq., Comment: Master's thesis

The high-pressure crystal structure evolution of CH3NH3PbBr3 (MAPbBr3) perovskite has been investigated by single-crystal X-ray diffraction and synchrotron-based powder X-ray diffraction. Single-crystal X-ray diffraction reveals that the crystal structure of MAPbBr3 undergoes two phase transitions following the space-group sequence: Pm-3m-to-Im3-to-Pmn21. The transitions take place at around 0.8 and 1.8 GPa, respectively. This result is contradicting the previously reported phase transition sequence: Pm-3m-to-Im3-to-Pnma. In this work the crystal structures of each of the three phases are determined from single-crystal X-ray diffraction analysis which is later supported by Rietveld refinement of powder X-ray diffraction patterns. The pressure dependence of the crystal lattice parameters and unit-cell volumes are determined from the two aforementioned techniques, as well as the bulk moduli for each phase. The bandgap behaviour of MAPbBr3 has been studied up to around 4 GPa, by the means of single-crystal optical-absorption experiments. The evolution of the bandgap has been well explained using the pressure dependence of the Pb-Br bond distance and Pb-Br-Pb angles as determined from single-crystal X-ray diffraction experiments., Comment: 20 pages, 5 pages

The goal of this paper is to study Goldbach's conjecture for rings of regular functions of affine algebraic varieties over a field. Among our main results, we define the notion of Goldbach condition for Newton polytopes, and we prove in a constructive way that any polynomial in at least two variables over a field can be expressed as sum of at most $2r$ absolutely irreducible polynomials, where $r$ is the number of its non--zero monomials. We also study other weak forms of Goldbach's conjecture for localizations of these rings. Moreover, we prove the validity of Goldbach's conjecture for a particular instance of the so--called forcing algebras introduced by Hochster. Finally, we prove that, for a proper multiplicative closed set $S$ of $\mathbb{Z}$, the collection of elements of $S^{-1}\mathbb{Z}$ that can be written as finite sum of primes forms a dense subset of the real numbers, among other results., Comment: 27 pages, comments are welcome

Heat transport in two-dimensions is fundamentally different from that in three dimensions. As a consequence, the thermal properties of 2D materials are of great interest, both from scientific and application point of view. However, few techniques are available for accurate determination of these properties in ultrathin suspended membranes. Here, we present an optomechanical methodology for extracting the thermal expansion coefficient, specific heat and thermal conductivity of ultrathin membranes made of 2H-TaS2, FePS3, polycrystalline silicon, MoS2 and WSe2. The obtained thermal properties are in good agreement with values reported in the literature for the same materials. Our work provides an optomechanical method for determining thermal properties of ultrathin suspended membranes, that are difficult to measure otherwise. It can does provide a route towards improving our understanding of heat transport in the 2D limit and facilitates engineering of 2D structures with dedicated thermal performance., Comment: 14 pages, 10 figures

We discover that many natural-language prompts can be replaced by corresponding prompts that are unintelligible to humans but that provably elicit similar behavior in language models. We call these prompts "evil twins" because they are obfuscated and uninterpretable (evil), but at the same time mimic the functionality of the original natural-language prompts (twins). Remarkably, evil twins transfer between models. We find these prompts by solving a maximum-likelihood problem which has applications of independent interest., Comment: EMNLP 2024 Main, camera-ready

We investigate the capabilities of transformer models on relational reasoning tasks. In these tasks, models are trained on a set of strings encoding abstract relations, and are then tested out-of-distribution on data that contains symbols that did not appear in the training dataset. We prove that for any relational reasoning task in a large family of tasks, transformers learn the abstract relations and generalize to the test set when trained by gradient descent on sufficiently large quantities of training data. This is in contrast to classical fully-connected networks, which we prove fail to learn to reason. Our results inspire modifications of the transformer architecture that add only two trainable parameters per head, and that we empirically demonstrate improve data efficiency for learning to reason., Comment: 25 figures

Current machine learning methods for medical image analysis primarily focus on developing models tailored for their specific tasks, utilizing data within their target domain. These specialized models tend to be data-hungry and often exhibit limitations in generalizing to out-of-distribution samples. In this work, we show that employing models that incorporate multiple domains instead of specialized ones significantly alleviates the limitations observed in specialized models. We refer to this approach as multi-domain model and compare its performance to that of specialized models. For this, we introduce the incorporation of diverse medical image domains, including different imaging modalities like X-ray, MRI, CT, and ultrasound images, as well as various viewpoints such as axial, coronal, and sagittal views. Our findings underscore the superior generalization capabilities of multi-domain models, particularly in scenarios characterized by limited data availability and out-of-distribution, frequently encountered in healthcare applications. The integration of diverse data allows multi-domain models to utilize information across domains, enhancing the overall outcomes substantially. To illustrate, for organ recognition, multi-domain model can enhance accuracy by up to 8% compared to conventional specialized models.

Recent advancements in 2D materials have revealed the potential of van der Waals magnets, and specifically of their magnetic anisotropy that allows applications down to the 2D limit. Among these materials, CrSBr has emerged as a promising candidate, because its intriguing magnetic and electronic properties have appeal for both fundamental and applied research in spintronics or magnonics. Here, nano SQUID-on-tip (SOT) microscopy is used to obtain direct magnetic imaging of CrSBr flakes with thicknesses ranging from monolayer (N=1) to few-layer (N=5). The ferromagnetic order is preserved down to the monolayer, while the antiferromagnetic coupling of the layers starts from the bilayer case. For odd layers, at zero applied magnetic field, the stray field resulting from the uncompensated layer is directly imaged. The progressive spin reorientation along the out-of-plane direction (hard axis) is also measured with a finite applied magnetic field, allowing to evaluate the anisotropy constant, which remains stable down to the monolayer and is close to the bulk value. Finally, by selecting the applied magnetic field protocol, the formation of N\'eel magnetic domain walls is observed down to the single layer limit., Comment: Main text: 13 pages, 4 figures. Supplementary information: 10 pages, 7 figures, 1 table

Systematic generalization is a crucial aspect of intelligence, which refers to the ability to generalize to novel tasks by combining known subtasks and concepts. One critical factor that has been shown to influence systematic generalization is the diversity of training data. However, diversity can be defined in various ways, as data have many factors of variation. A more granular understanding of how different aspects of data diversity affect systematic generalization is lacking. We present new evidence in the problem of Visual Question Answering (VQA) that reveals that the diversity of simple tasks (i.e. tasks formed by a few subtasks and concepts) plays a key role in achieving systematic generalization. This implies that it may not be essential to gather a large and varied number of complex tasks, which could be costly to obtain. We demonstrate that this result is independent of the similarity between the training and testing data and applies to well-known families of neural network architectures for VQA (i.e. monolithic architectures and neural module networks). Additionally, we observe that neural module networks leverage all forms of data diversity we evaluated, while monolithic architectures require more extensive amounts of data to do so. These findings provide a first step towards understanding the interactions between data diversity design, neural network architectures, and systematic generalization capabilities., Comment: TMLR (https://openreview.net/forum?id=ZAin13msOp)

Magnetic imaging using nitrogen-vacancy (NV) spins in diamonds is a powerful technique for acquiring quantitative information about sub-micron scale magnetic order. A major challenge for its application in the research on two-dimensional (2D) magnets is the positioning of the NV centers at a well-defined, nanoscale distance to the target material required for detecting the small magnetic fields generated by magnetic monolayers. Here, we develop a diamond 'dry-transfer' technique, akin to the state-of-the-art 2D-materials assembly methods, and use it to place a diamond micro-membrane in direct contact with the 2D interlayer antiferromagnet CrSBr. We harness the resulting NV-sample proximity to spatially resolve the magnetic stray fields generated by the CrSBr, present only where the CrSBr thickness changes by an odd number of layers. From the magnetic stray field of a single uncompensated ferromagnetic layer in the CrSBr, we extract a monolayer magnetization of $M_\mathrm{CSB}$ = 0.46(2) T, without the need for exfoliation of monolayer crystals or applying large external magnetic fields. The ability to deterministically place NV-ensemble sensors into contact with target materials and detect ferromagnetic monolayer magnetizations paves the way for quantitative analysis of a wide range of 2D magnets assembled on arbitrary target substrates.

Two new ultimately thin vanadium rich 2D materials based on VS2 are created via molecular beam epitaxy and investigated using scanning tunneling microscopy, X-ray photoemission spectroscopy and density-functional theory calculations. The controlled synthesis of stoichiometric single-layer VS2 or either of the two vanadium-rich materials is achieved by varying the sample coverage and the sulphur pressure during annealing. Through annealing of small stoichiometric single-layer VS2 islands without S pressure, S-vacancies spontaneously order in 1D arrays, giving rise to patterned adsorption. Via the comparison of density-functional theory calculations with scanning tunneling microscopy data, the atomic structure of the S-depleted phase, with a stoichiometry of V4S7, is determined. By depositing larger amounts of vanadium and sulphur, which are subsequently annealed in a S-rich atmosphere, self-intercalated ultimately thin V5S8-derived layers are obtained, which host 2x2 V-layers between sheets of VS2. We provide atomic models for the thinnest V5S8-derived structures. Finally, we use scanning tunneling spectroscopy to investigate the charge density wave observed in the 2D V5S8-derived islands.

By default neural networks are not robust to changes in data distribution. This has been demonstrated with simple image corruptions, such as blurring or adding noise, degrading image classification performance. Many methods have been proposed to mitigate these issues but for the most part models are evaluated on single corruptions. In reality, visual space is compositional in nature, that is, that as well as robustness to elemental corruptions, robustness to compositions of corruptions is also needed. In this work we develop a compositional image classification task where, given a few elemental corruptions, models are asked to generalize to compositions of these corruptions. That is, to achieve compositional robustness. We experimentally compare empirical risk minimization with an invariance building pairwise contrastive loss and, counter to common intuitions in domain generalization, achieve only marginal improvements in compositional robustness by encouraging invariance. To move beyond invariance, following previously proposed inductive biases that model architectures should reflect data structure, we introduce a modular architecture whose structure replicates the compositional nature of the task. We then show that this modular approach consistently achieves better compositional robustness than non-modular approaches. We additionally find empirical evidence that the degree of invariance between representations of 'in-distribution' elemental corruptions fails to correlate with robustness to 'out-of-distribution' compositions of corruptions.

We identify incremental learning dynamics in transformers, where the difference between trained and initial weights progressively increases in rank. We rigorously prove this occurs under the simplifying assumptions of diagonal weight matrices and small initialization. Our experiments support the theory and also show that phenomenon can occur in practice without the simplifying assumptions., Comment: 39 pages, to appear in NeurIPS 2023

The Van der Waals semiconductor metamagnet CrSBr offers an ideal platform for studying the interplay between optical and magnetic properties in the two-dimensional limit. Here, we carried out an exhaustive optical characterization of this material by means of temperature and magnetic field dependent photoluminescence (PL) on flakes of different thicknesses down to the monolayer. We found a characteristic emission peak that is quenched upon switching the ferromagnetic layers from an antiparallel to a parallel configuration and exhibits a different temperature dependence from that of the peaks commonly ascribed to excitons. The contribution of this peak to the PL is boosted around 30-40 K, coinciding with the hidden order magnetic transition temperature. Our findings reveal the connection between the optical and magnetic properties via the ionization of magnetic donor vacancies. This behavior enables a useful tool for the optical reading of the magnetic states in atomically thin layers of CrSBr and shows the potential of the design of two-dimensional heterostructures with magnetic and excitonic properties., Comment: 20 pages, 5 figures

We study when the neural tangent kernel (NTK) approximation is valid for training a model with the square loss. In the lazy training setting of Chizat et al. 2019, we show that rescaling the model by a factor of $\alpha = O(T)$ suffices for the NTK approximation to be valid until training time $T$. Our bound is tight and improves on the previous bound of Chizat et al. 2019, which required a larger rescaling factor of $\alpha = O(T^2)$., Comment: Accepted to TMLR. Added proof flowchart

The crystal structure of CH3NH3PbBr3 perovskite has been investigated under high-pressure by synchrotron-based powder X-ray diffraction. We found that after the previously reported phase transitions in CH3NH3PbBr3 (Pm-3m->Im-3->Pmn21), which occur below 2 GPa, there is a third transition to a crystalline phase at 4.6 GPa. This transition is reported here for the first time contradicting previous studies which reported amorphization of CH3NH3PbBr3 between 2.3 and 4.6 GPa. Our X-ray diffraction measurements show that CH3NH3PbBr3 remains crystalline up to 7.6 GPa, the highest pressure covered by experiments. The new high-pressure phase is also described by the space group Pmn21, but the transition involves abrupt changes in the unit-cell parameters and a 3% decrease of the unit-cell volume. Our conclusions are confirmed by optical-absorption experiments and visual observations and by the fact that changes induced by pressure up to 10 GPa are reversible. The optical studies also allow for the determination of the pressure dependence of the band-gap energy which is discussed using the structural information obtained from X-ray diffraction., Comment: 15 pages, 4 figures

The temperature dependent order parameter provides important information on the nature of magnetism. Using traditional methods to study this parameter in two-dimensional (2D) magnets remains difficult, however, particularly for insulating antiferromagnetic (AF) compounds. Here, we show that its temperature dependence in AF MPS$_{3}$ (M(II) = Fe, Co, Ni) can be probed via the anisotropy in the resonance frequency of rectangular membranes, mediated by a combination of anisotropic magnetostriction and spontaneous staggered magnetization. Density functional calculations followed by a derived orbital-resolved magnetic exchange analysis confirm and unravel the microscopic origin of this magnetization inducing anistropic strain. We further show that the temperature and thickness dependent order parameter allows to deduce the material's critical exponents characterising magnetic order. Nanomechanical sensing of magnetic order thus provides a future platform to investigate 2D magnetism down to the single-layer limit., Comment: 9 pages, 4 figures, 1 table. Appended SI

Deep Neural Networks (DNNs) often fail in out-of-distribution scenarios. In this paper, we introduce a tool to visualize and understand such failures. We draw inspiration from concepts from neural electrophysiology, which are based on inspecting the internal functioning of a neural networks by analyzing the feature tuning and invariances of individual units. Deep Electrophysiology, in short Deephys, provides insights of the DNN's failures in out-of-distribution scenarios by comparative visualization of the neural activity in in-distribution and out-of-distribution datasets. Deephys provides seamless analyses of individual neurons, individual images, and a set of set of images from a category, and it is capable of revealing failures due to the presence of spurious features and novel features. We substantiate the validity of the qualitative visualizations of Deephys thorough quantitative analyses using convolutional and transformers architectures, in several datasets and distribution shifts (namely, colored MNIST, CIFAR-10 and ImageNet)., Comment: 12 pages, 8 figures

We investigate the time complexity of SGD learning on fully-connected neural networks with isotropic data. We put forward a complexity measure -- the leap -- which measures how "hierarchical" target functions are. For $d$-dimensional uniform Boolean or isotropic Gaussian data, our main conjecture states that the time complexity to learn a function $f$ with low-dimensional support is $\tilde\Theta (d^{\max(\mathrm{Leap}(f),2)})$. We prove a version of this conjecture for a class of functions on Gaussian isotropic data and 2-layer neural networks, under additional technical assumptions on how SGD is run. We show that the training sequentially learns the function support with a saddle-to-saddle dynamic. Our result departs from [Abbe et al. 2022] by going beyond leap 1 (merged-staircase functions), and by going beyond the mean-field and gradient flow approximations that prohibit the full complexity control obtained here. Finally, we note that this gives an SGD complexity for the full training trajectory that matches that of Correlational Statistical Query (CSQ) lower-bounds.