Miracle-dz/UniFAR-FTUs huggingface dataset:
Elliptical Halbach magnet and gradient modules for low-field portable MRI

Objective. To develop methods to design the complete magnetic system for a truly portable MRI scanner for neurological and musculoskeletal (MSK) applications, optimized for field homogeneity, field of view (FoV) and gradient performance compared to existing low-weight configurations. Approach. We explore optimal elliptic-bore Halbach configurations based on discrete arrays of permanent magnets. In this way, we seek to improve the field homogeneity and remove constraints to the extent of the gradient coils typical of Halbach magnets. Specifically, we have optimized a tightly-packed distribution of magnetic Nd$_2$Fe$_14$B cubes with differential evolution algorithms, and a second array of shimming magnets with interior point and differential evolution methods. We have also designed and constructed an elliptical set of gradient coils that extend over the whole magnet length, maximizing the distance between the lobe centers. These are optimized with a target field method minimizing a cost function that considers also heat dissipation. Main result. We have employed the new toolbox to build the main magnet and gradient modules for a portable MRI scanner designed for point-of-care and residential use. The elliptical Halbach bore has semi-axes of 10&14 cm and the magnet generates a field of 87 mT homogeneous down to 5,700 ppm (parts per million) in a 20 cm diameter FoV, it weighs 216 kg and has a width of 65 cm and a height of 72 cm. Gradient efficiencies go up to around 0.8 mT/m/A, for a maximum of 12 mT/m with in 0.5 ms with 15 A&15 V amplifier. The distance between lobes is 28 cm, significantly increased with respect to other Halbach-based scanners. Heat dissipation is around 25 W at maximum power, and gradient deviations from linearity are below 20% in a 20 cm sphere.
Linear and smooth oriented equivalence of orthogonal representations of finite groups

Let $n\le 5$ be an integer, and let $\Gamma$ be a finite group. We prove that if $\rho , \rho': \Gamma \to O(n)$ are two representations that are conjugate by an orientation-preserving diffeomorphism, then they are conjugate by an element of $SO(n)$. In the process, we prove that if $G \subset O(4)$ is a finite group, then exactly one of the following is true: the elements of $G$ have a common invariant $1$-dimensional subspace in $\mathbb{R}^4$; some element of $G$ has no invariant $1$-dimensional subspace; or $G$ is conjugate to a specific group $K \subset O(4)$ of order $16$.
Adaptive Bounding Box Uncertainties via Two-Step Conformal Prediction

Quantifying a model's predictive uncertainty is essential for safety-critical applications such as autonomous driving. We consider quantifying such uncertainty for multi-object detection. In particular, we leverage conformal prediction to obtain uncertainty intervals with guaranteed coverage for object bounding boxes. One challenge in doing so is that bounding box predictions are conditioned on the object's class label. Thus, we develop a novel two-step conformal approach that propagates uncertainty in predicted class labels into the uncertainty intervals for the bounding boxes. This broadens the validity of our conformal coverage guarantees to include incorrectly classified objects, ensuring their usefulness when maximal safety assurances are required. Moreover, we investigate novel ensemble and quantile regression formulations to ensure the bounding box intervals are adaptive to object size, leading to a more balanced coverage across sizes. Validating our two-step approach on real-world datasets for 2D bounding box localization, we find that desired coverage levels are satisfied with actionably tight predictive uncertainty intervals.
Zero-Sum Stochastic Games with Vanishing Stage Duration and Public Signals

We consider the behaviour of $\lambda$-discounted zero-sum games as the discount factor $\lambda$ tends to 0 (that is, the players are more and more patient), in the context of games with stage duration. In stochastic games with stage duration h, players act at times 0, h, 2h, . , and the payoff and leaving probabilities are proportional to h. When h tends to 0, such games approximate games in continuous time. The asymptotic behavior of the values (when both $\lambda$ and h tend to 0) was already studied in the case of stochastic games with perfect observation of the state and in the state-blind case. We consider the same question for the case of stochastic games with imperfect observation of the state. In such games, players are given at each stage a public signal that depends only on the current state. Our main result states that there exists a stochastic game with public signals, with no limit value (as the discount factor $\lambda$ goes to 0) if stage duration is 1, but with a limit value when stage duration h and discount factor $\lambda$ both tend to 0. Informally speaking, it means that the limit value in discrete time does not exist, but the limit value in continuous time (i.e., when h tends to 0) exists. Such a situation is impossible in the case of stochastic games with perfect observation of the state.
Near-Interpolators: Rapid Norm Growth and the Trade-Off between Interpolation and Generalization

We study the generalization capability of nearly-interpolating linear regressors: $\boldsymbol{\beta}$'s whose training error $\tau$ is positive but small, i.e., below the noise floor. Under a random matrix theoretic assumption on the data distribution and an eigendecay assumption on the data covariance matrix $\boldsymbol{\Sigma}$, we demonstrate that any near-interpolator exhibits rapid norm growth: for $\tau$ fixed, $\boldsymbol{\beta}$ has squared $\ell_2$-norm $\mathbb{E}[\|{\boldsymbol{\beta}}\|_{2}^{2}] = \Omega(n^{\alpha})$ where $n$ is the number of samples and $\alpha>1$ is the exponent of the eigendecay, i.e., $\lambda_i(\boldsymbol{\Sigma}) \sim i^{-\alpha}$. This implies that existing data-independent norm-based bounds are necessarily loose. On the other hand, in the same regime we precisely characterize the asymptotic trade-off between interpolation and generalization. Our characterization reveals that larger norm scaling exponents $\alpha$ correspond to worse trade-offs between interpolation and generalization. We verify empirically that a similar phenomenon holds for nearly-interpolating shallow neural networks.
Toward An Analytic Theory of Intrinsic Robustness for Dexterous Grasping

Conventional approaches to grasp planning require perfect knowledge of an object's pose and geometry. Uncertainties in these quantities induce uncertainties in the quality of planned grasps, which can lead to failure. Classically, grasp robustness refers to the ability to resist external disturbances after grasping an object. In contrast, this work studies robustness to intrinsic sources of uncertainty like object pose or geometry affecting grasp planning before execution. To do so, we develop a novel analytic theory of grasping that reasons about this intrinsic robustness by characterizing the effect of friction cone uncertainty on a grasp's force closure status. As a result, we show the Ferrari-Canny metric -- which measures the size of external disturbances a grasp can reject -- bounds the friction cone uncertainty a grasp can tolerate, and thus also measures intrinsic robustness. In tandem, we show that the recently proposed min-weight metric lower bounds the Ferrari-Canny metric, justifying it as a computationally-efficient, uncertainty-aware alternative. We validate this theory on hardware experiments versus a competitive baseline and demonstrate superior performance. Finally, we use our theory to develop an analytic notion of probabilistic force closure, which we show in simulation generates grasps that can incorporate uncertainty distributions over an object's geometry.
Effect of Ir growth pressure on the domain wall dynamics in Ta/Pt/Co/Ir/Ta stacks

The dynamical response of magnetic domain walls to external magnetic fields in ultra-thin multilayer magnetic films is determined not only by the composition and thickness of the layers but also by the growth conditions. Growth conditions can induce significant structural changes inside the layers and at the interfaces between them, affecting in particular the dynamics of domain walls, their mobility, elastic tension, and the pinning forces acting on them. In this work, we focus specifically on the effect of Ir layer growth pressure in Ta/Pt/Co/Ir/Ta ultra-thin multilayers films. Measurements of the DC magnetic properties, domain wall velocity and domain morphology in the creep regime for both constant and alternating field pulses, were performed for a batch of samples where the Ir layer was grown at different pressures. We find that the saturation magnetization, the effective anisotropy constant and the domain wall surface tension grow with increasing pressure and saturate at a threshold pressure, while the Dzyaloshinskii-Moriya field and the strength of the disorder remain practically unaltered over the range of pressures considered.
2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves II

We give refined methods for proving finiteness of the Chabauty--Coleman--Kim set $X(\mathbb{Q}_2 )_2 $, when $X$ is a hyperelliptic curve with a rational Weierstrass point. The main developments are methods for computing Selmer conditions at $2$ and $\infty$ for the mod 2 Bloch--Kato Selmer group associated to the higher Chow group $\mathrm{CH}^2 (\mathrm{Jac}(X),1)$. As a result we show that most genus 2 curves in the LMFDB of Mordell--Weil rank 2 with exactly one rational Weierstrass point satsify $\# X(\mathbb{Q}_2 )_2<\infty $. We also obtain a field-theoretic description of second descent on the Jacobian of a hyperelliptic curve (under some conditions).
A multiscale cavity method for sublinear-rank symmetric matrix factorization

We consider a statistical model for symmetric matrix factorization with additive Gaussian noise in the high-dimensional regime where the rank $M$ of the signal matrix to infer scales with its size $N$ as $M = o(N^{1/10})$. Allowing for a $N$-dependent rank offers new challenges and requires new methods. Working in the Bayesian-optimal setting, we show that whenever the signal has i.i. d. entries the limiting mutual information between signal and data is given by a variational formula involving a rank-one replica symmetric potential. In other words, from the information-theoretic perspective, the case of a (slowly) growing rank is the same as when $M = 1$ (namely, the standard spiked Wigner model). The proof is primarily based on a novel multiscale cavity method allowing for growing rank along with some information-theoretic identities on worst noise for the Gaussian vector channel. We believe that the cavity method developed here will play a role in the analysis of a broader class of inference and spin models where the degrees of freedom are large arrays instead of vectors.
Mantle Flow as a Trigger for Subduction Initiation: A Missing Element of the Wilson Cycle Concept

The classical Wilson Cycle concept, describing repeated opening and closing of ocean basins, hypothesizes spontaneous conversion of passive continental margins into subduction zones. This process, however, is impeded by the high strength of passive margins, and it has never occurred in Cenozoic times. Here using thermomechanical models, we show that additional forcing, provided by mantle flow, which is induced by neighboring subduction zones and midmantle slab remnants, can convert a passive margin into a subduction zone. Models suggest that this is a long‐term process, thus explaining the lack of Cenozoic examples. We speculate that new subduction zones may form in the next few tens of millions of years along the Argentine passive margin and the U.S. East Coast. Mantle suction force can similarly trigger subduction initiation along large oceanic fracture zones. We propose that new subduction zones will preferentially originate where subduction zones were active in the past, thus explaining the remarkable colocation of subduction zones during at least the last 400 Myr.
On the Generalization Ability of Unsupervised Pretraining

Recent advances in unsupervised learning have shown that unsupervised pre-training, followed by fine-tuning, can improve model generalization. However, a rigorous understanding of how the representation function learned on an unlabeled dataset affects the generalization of the fine-tuned model is lacking. Existing theoretical research does not adequately account for the heterogeneity of the distribution and tasks in pre-training and fine-tuning stage. To bridge this gap, this paper introduces a novel theoretical framework that illuminates the critical factor influencing the transferability of knowledge acquired during unsupervised pre-training to the subsequent fine-tuning phase, ultimately affecting the generalization capabilities of the fine-tuned model on downstream tasks. We apply our theoretical framework to analyze generalization bound of two distinct scenarios: Context Encoder pre-training with deep neural networks and Masked Autoencoder pre-training with deep transformers, followed by fine-tuning on a binary classification task. Finally, inspired by our findings, we propose a novel regularization method during pre-training to further enhances the generalization of fine-tuned model. Overall, our results contribute to a better understanding of unsupervised pre-training and fine-tuning paradigm, and can shed light on the design of more effective pre-training algorithms.
SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression

The advancements in Large Language Models (LLMs) have been hindered by their substantial sizes, which necessitate LLM compression methods for practical deployment. Singular Value Decomposition (SVD) offers a promising solution for LLM compression. However, state-of-the-art SVD-based LLM compression methods have two key limitations: truncating smaller singular values may lead to higher compression loss, and the lack of update on the remaining model parameters after SVD truncation. In this work, we propose SVD-LLM, a new SVD-based LLM compression method that addresses the limitations of existing methods. SVD-LLM incorporates a truncation-aware data whitening strategy to ensure a direct mapping between singular values and compression loss. Moreover, SVD-LLM adopts a layer-wise closed-form model parameter update strategy to compensate for accuracy degradation caused by SVD truncation. We evaluate SVD-LLM on a total of 11 datasets and seven models from three different LLM families at four different scales. Our results demonstrate the superiority of SVD-LLM over state-of-the-arts, especially at high model compression ratios. The source code is available at https://github.com/AIoT-MLSys-Lab/SVD-LLM.
Attention Prompt Tuning: Parameter-efficient Adaptation of Pre-trained Models for Spatiotemporal Modeling

In this paper, we introduce Attention Prompt Tuning (APT) - a computationally efficient variant of prompt tuning for video-based applications such as action recognition. Prompt tuning approaches involve injecting a set of learnable prompts along with data tokens during fine-tuning while keeping the backbone frozen. This approach greatly reduces the number of learnable parameters compared to full tuning. For image-based downstream tasks, normally a couple of learnable prompts achieve results close to those of full tuning. However, videos, which contain more complex spatiotemporal information, require hundreds of tunable prompts to achieve reasonably good results. This reduces the parameter efficiency observed in images and significantly increases latency and the number of floating-point operations (FLOPs) during inference. To tackle these issues, we directly inject the prompts into the keys and values of the non-local attention mechanism within the transformer block. Additionally, we introduce a novel prompt reparameterization technique to make APT more robust against hyperparameter selection. The proposed APT approach greatly reduces the number of FLOPs and latency while achieving a significant performance boost over the existing parameter-efficient tuning methods on UCF101, HMDB51, and SSv2 datasets for action recognition. The code and pre-trained models are available at https://github.com/wgcban/apt
Simplicity Bias of Transformers to Learn Low Sensitivity Functions

Transformers achieve state-of-the-art accuracy and robustness across many tasks, but an understanding of the inductive biases that they have and how those biases are different from other neural network architectures remains elusive. Various neural network architectures such as fully connected networks have been found to have a simplicity bias towards simple functions of the data; one version of this simplicity bias is a spectral bias to learn simple functions in the Fourier space. In this work, we identify the notion of sensitivity of the model to random changes in the input as a notion of simplicity bias which provides a unified metric to explain the simplicity and spectral bias of transformers across different data modalities. We show that transformers have lower sensitivity than alternative architectures, such as LSTMs, MLPs and CNNs, across both vision and language tasks. We also show that low-sensitivity bias correlates with improved robustness; furthermore, it can also be used as an efficient intervention to further improve the robustness of transformers.
GPU-Accelerated Vecchia Approximations of Gaussian Processes for Geospatial Data using Batched Matrix Computations

Gaussian processes (GPs) are commonly used for geospatial analysis, but they suffer from high computational complexity when dealing with massive data. For instance, the log-likelihood function required in estimating the statistical model parameters for geospatial data is a computationally intensive procedure that involves computing the inverse of a covariance matrix with size n X n, where n represents the number of geographical locations. As a result, in the literature, studies have shifted towards approximation methods to handle larger values of n effectively while maintaining high accuracy. These methods encompass a range of techniques, including low-rank and sparse approximations. Vecchia approximation is one of the most promising methods to speed up evaluating the log-likelihood function. This study presents a parallel implementation of the Vecchia approximation, utilizing batched matrix computations on contemporary GPUs. The proposed implementation relies on batched linear algebra routines to efficiently execute individual conditional distributions in the Vecchia algorithm. We rely on the KBLAS linear algebra library to perform batched linear algebra operations, reducing the time to solution compared to the state-of-the-art parallel implementation of the likelihood estimation operation in the ExaGeoStat software by up to 700X, 833X, 1380X on 32GB GV100, 80GB A100, and 80GB H100 GPUs, respectively. We also successfully manage larger problem sizes on a single NVIDIA GPU, accommodating up to 1M locations with 80GB A100 and H100 GPUs while maintaining the necessary application accuracy. We further assess the accuracy performance of the implemented algorithm, identifying the optimal settings for the Vecchia approximation algorithm to preserve accuracy on two real geospatial datasets: soil moisture data in the Mississippi Basin area and wind speed data in the Middle East.
Strong asymptotic giant branch stars' spectral features in distant quiescent galaxies: Impact on galaxy evolution

Age-dating and weighting stellar populations in galaxies at various cosmic epochs are essential steps to study galaxy formation through cosmic times. Evolutionary population synthesis models with different input physics are used towards this aim. In particular, the contribution from the thermally pulsing asymptotic-giant-branch (TP-AGB) stellar phase, which peaks for intermediate-age 0.6-2 Gyr systems, has been debated upon for decades. Here we report the detection of strong cool star signatures in the rest-frame near-infrared spectra of three young (~1 Gyr), massive (~10^10 Msun) quiescent galaxies at large look-back time, z=1-2, using JWST/NIRSpec. The co-existence of oxygen- and carbon-type absorption features, spectral edges and features from rare species such as Vanadium, and possibly Zirconium, reveal a strong contribution from TP-AGB stars. Population synthesis models with significant TP-AGB contribution reproduce the observations considerably better than those with weak TP-AGB, which are those commonly used. These findings call for revisions of published stellar population fitting results, pointing to lower masses and younger ages, with additional implications on cosmic dust production and chemical enrichment. These results will stimulate new generations of improved models informed by these and future observations.
Homotopical commutative rings and bispans

We prove that commutative semirings in a cartesian closed presentable $\infty$-category, as defined by Groth, Gepner, and Nikolaus, are equivalent to product-preserving functors from the $(2,1)$-category of bispans of finite sets. In other words, we identify the latter as the Lawvere theory for commutative semirings in the $\infty$-categorical context. This implies that connective commutative ring spectra can be described as grouplike product-preserving functors from bispans of finite sets to spaces. A key part of the proof is a localization result for $\infty$-categories of spans, and more generally for $\infty$-categories with factorization systems, that may be of independent interest.
Universal Chemical Formula Dependence of $Ab$ $Initio$ Low-Energy Effective Hamiltonian in Single-Layer Carrier Doped Cuprate Superconductors -- Study by Hierarchical Dependence Extraction Algorithm

We explore the possibility to control the superconducting (SC) transition temperature at optimal hole doping $T_{c}^{\rm opt}$ in cuprates by tuning the chemical formula (CF). $T_{c}^{\rm opt}$ can be theoretically predicted from the parameters of the \textit{ab initio} low-energy effective Hamiltonian (LEH) with one antibonding (AB) Cu$3d_{x^2-y^2}$/O$2p_{\sigma}$ orbital per Cu atom in the CuO$_2$ plane, notably the nearest neighbor hopping amplitude $|t_1|$ and the ratio $u=U/|t_1|$, where $U$ is the onsite effective Coulomb repulsion. However, the CF dependence of $|t_1|$ and $u$ is a highly nontrivial question. In this paper, we propose the universal dependence of $|t_1|$ and $u$ on the CF and structural features in hole doped cuprates with a single CuO$_2$ layer sandwiched between block layers. To do so, we perform extensive \textit{ab initio} calculations of $|t_1|$ and $u$ and analyze the results by employing a machine learning method called Hierarchical Dependence Extraction (HDE). The main results are the following: (a) $|t_1|$ has a main-order dependence on the radii $R_{\rm X}$ and $R_{\rm A}$ of the apical anion X and cation A in the block layer. ($|t_1|$ increases when $R_{\rm X}$ or $R_{\rm A}$ decreases.) (b) $u$ has a main-order dependence on the negative ionic charge $Z_{\rm X}$ of X and the hole doping $\delta$ of the AB orbital. ($u$ decreases when $|Z_{\rm X}|$ increases or $\delta$ increases.) We elucidate and discuss the microscopic mechanism of (a,b). We demonstrate the predictive power of the HDE by showing the consistency between (a,b) and results from previous works. The present results provide a basis for optimizing SC properties in cuprates and possibly akin materials. Also, the HDE method offers a general platform to identify dependencies between physical quantities.