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We prove local Calabi and higher order estimates for solutions to the continuity equation introduced by La Nave-Tian and extended to Hermitian metrics by Sherman-Weinkove. We apply the estimates to show that on a compact complex manifold the Chern scalar curvature of a solution must blow up at a finite-time singularity. Additionally, starting from certain classes of initial data on Oeljeklaus-Toma manifolds we prove Gromov-Hausdorff and smooth convergence of the metric to a particular non-negative $(1,1)$-form as $t\to\infty$., Comment: 20 pages

General physical scene understanding requires more than simply localizing and recognizing objects -- it requires knowledge that objects can have different latent properties (e.g., mass or elasticity), and that those properties affect the outcome of physical events. While there has been great progress in physical and video prediction models in recent years, benchmarks to test their performance typically do not require an understanding that objects have individual physical properties, or at best test only those properties that are directly observable (e.g., size or color). This work proposes a novel dataset and benchmark, termed Physion++, that rigorously evaluates visual physical prediction in artificial systems under circumstances where those predictions rely on accurate estimates of the latent physical properties of objects in the scene. Specifically, we test scenarios where accurate prediction relies on estimates of properties such as mass, friction, elasticity, and deformability, and where the values of those properties can only be inferred by observing how objects move and interact with other objects or fluids. We evaluate the performance of a number of state-of-the-art prediction models that span a variety of levels of learning vs. built-in knowledge, and compare that performance to a set of human predictions. We find that models that have been trained using standard regimes and datasets do not spontaneously learn to make inferences about latent properties, but also that models that encode objectness and physical states tend to make better predictions. However, there is still a huge gap between all models and human performance, and all models' predictions correlate poorly with those made by humans, suggesting that no state-of-the-art model is learning to make physical predictions in a human-like way. Project page: https://dingmyu.github.io/physion_v2/, Comment: Accepted by NeurIPS 2023 Datasets and Benchmarks Track

Kagome metals are widely recognized as versatile platforms for exploring novel topological properties, unconventional electronic correlations, magnetic frustration, and superconductivity. In the $R$V$_6$Sn$_6$ family of materials ($R$ = Sc, Y, Lu), ScV$_6$Sn$_6$ hosts an unusual charge density wave ground state as well as structural similarities with the $A$V$_3$Sb$_5$ system ($A$ = K, Cs, Rb). In this work, we combine Raman scattering spectroscopy with first-principles lattice dynamics calculations to reveal the charge density wave state in ScV$_6$Sn$_6$. In the low temperature phase, we find a five-fold splitting of the V-containing totally symmetric mode near 240 cm$^{-1}$ suggesting that the density wave acts to mix modes of $P$6/$mmm$ and $R$$\bar{3}$$m$ symmetry - an effect that we quantify by projecting phonons of the high symmetry state onto those of the lower symmetry structure. We also test the stability of the density wave state under compression and find that both physical and chemical pressure act to quench the effect. We discuss these findings in terms of symmetry and the structure-property trends that can be unraveled in this system.

Convolutional Neural Networks (CNNs) have reigned for a decade as the de facto approach to automated medical image diagnosis, pushing the state-of-the-art in classification, detection and segmentation tasks. Over the last years, vision transformers (ViTs) have appeared as a competitive alternative to CNNs, yielding impressive levels of performance in the natural image domain, while possessing several interesting properties that could prove beneficial for medical imaging tasks. In this work, we explore the benefits and drawbacks of transformer-based models for medical image classification. We conduct a series of experiments on several standard 2D medical image benchmark datasets and tasks. Our findings show that, while CNNs perform better if trained from scratch, off-the-shelf vision transformers can perform on par with CNNs when pretrained on ImageNet, both in a supervised and self-supervised setting, rendering them as a viable alternative to CNNs., Comment: Extended version of arXiv:2108.09038 originally published at the ICCV 2021 Workshop on Computer Vision for Automated Medical Diagnosis

High content imaging assays can capture rich phenotypic response data for large sets of compound treatments, aiding in the characterization and discovery of novel drugs. However, extracting representative features from high content images that can capture subtle nuances in phenotypes remains challenging. The lack of high-quality labels makes it difficult to achieve satisfactory results with supervised deep learning. Self-Supervised learning methods have shown great success on natural images, and offer an attractive alternative also to microscopy images. However, we find that self-supervised learning techniques underperform on high content imaging assays. One challenge is the undesirable domain shifts present in the data known as batch effects, which are caused by biological noise or uncontrolled experimental conditions. To this end, we introduce Cross-Domain Consistency Learning (CDCL), a self-supervised approach that is able to learn in the presence of batch effects. CDCL enforces the learning of biological similarities while disregarding undesirable batch-specific signals, leading to more useful and versatile representations. These features are organised according to their morphological changes and are more useful for downstream tasks -- such as distinguishing treatments and mechanism of action.

Recent times have witnessed an increasing number of applications of deep neural networks towards solving tasks that require superior cognitive abilities, e.g., playing Go, generating art, ChatGPT, etc. Such a dramatic progress raises the question: how generalizable are neural networks in solving problems that demand broad skills? To answer this question, we propose SMART: a Simple Multimodal Algorithmic Reasoning Task and the associated SMART-101 dataset, for evaluating the abstraction, deduction, and generalization abilities of neural networks in solving visuo-linguistic puzzles designed specifically for children in the 6--8 age group. Our dataset consists of 101 unique puzzles; each puzzle comprises a picture and a question, and their solution needs a mix of several elementary skills, including arithmetic, algebra, and spatial reasoning, among others. To scale our dataset towards training deep neural networks, we programmatically generate entirely new instances for each puzzle, while retaining their solution algorithm. To benchmark performances on SMART-101, we propose a vision and language meta-learning model using varied state-of-the-art backbones. Our experiments reveal that while powerful deep models offer reasonable performances on puzzles in a supervised setting, they are not better than random accuracy when analyzed for generalization. We also evaluate the recent ChatGPT and other large language models on a subset of SMART-101 and find that while these models show convincing reasoning abilities, the answers are often incorrect., Comment: Extended version of CVPR 2023 paper. For the SMART-101 dataset, see http://smartdataset.github.io/smart101

It is well-known that upper bounds for moments of the Riemann zeta function $\zeta(s)$ have implications for subconvexity bounds. In this paper we explore some implications in the opposite direction using functional analysis in the right-half of the critical strip. The main results characterise potential transitions in the behaviour of the moments., Comment: 17 pages

The ground state of the spin-1 Affleck, Kennedy, Lieb and Tasaki (AKLT) model is a paradigmatic example of both a matrix product state and a symmetry-protected topological phase, and additionally holds promise as a resource state for measurement-based quantum computation. Having a nonzero correlation length, the AKLT state cannot be exactly prepared by a constant-depth unitary circuit composed of local gates. In this work, we demonstrate that this no-go limit can be evaded by augmenting a constant-depth circuit with fusion measurements, such that the total preparation time is independent of system size and entirely deterministic. We elucidate our preparation scheme using the language of tensor networks, and furthermore show that the $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry of the AKLT state directly affords this speed-up over previously known preparation methods. To demonstrate the practical advantage of measurement-assisted preparation on noisy intermediate-scale quantum (NISQ) devices, we carry out our protocol on an IBM Quantum processor. We measure both the string order and entanglement spectrum of prepared AKLT chains and, employing these as metrics, find improved results over the known (purely unitary) sequential preparation approach. We conclude with a demonstration of quantum teleportation using the AKLT state prepared by our measurement-assisted scheme. This work thus serves to provide an efficient strategy to prepare a specific resource in the form of the AKLT state and, more broadly, experimentally demonstrates the possibility for realizable improvement in state preparation afforded by measurement-based circuit depth reduction strategies on NISQ-era devices., Comment: 17 pages, 8 figures. Supplemental Material: 13 pages, 11 figures

The world is filled with articulated objects that are difficult to determine how to use from vision alone, e.g., a door might open inwards or outwards. Humans handle these objects with strategic trial-and-error: first pushing a door then pulling if that doesn't work. We enable these capabilities in autonomous agents by proposing "Hypothesize, Simulate, Act, Update, and Repeat" (H-SAUR), a probabilistic generative framework that simultaneously generates a distribution of hypotheses about how objects articulate given input observations, captures certainty over hypotheses over time, and infer plausible actions for exploration and goal-conditioned manipulation. We compare our model with existing work in manipulating objects after a handful of exploration actions, on the PartNet-Mobility dataset. We further propose a novel PuzzleBoxes benchmark that contains locked boxes that require multiple steps to solve. We show that the proposed model significantly outperforms the current state-of-the-art articulated object manipulation framework, despite using zero training data. We further improve the test-time efficiency of H-SAUR by integrating a learned prior from learning-based vision models.

Artifacts on magnetic resonance scans are a serious challenge for both radiologists and computer-aided diagnosis systems. Most commonly, artifacts are caused by motion of the patients, but can also arise from device-specific abnormalities such as noise patterns. Irrespective of the source, artifacts can not only render a scan useless, but can potentially induce misdiagnoses if left unnoticed. For instance, an artifact may masquerade as a tumor or other abnormality. Retrospective artifact correction (RAC) is concerned with removing artifacts after the scan has already been taken. In this work, we propose a method capable of retrospectively removing eight common artifacts found in native-resolution MR imagery. Knowledge of the presence or location of a specific artifact is not assumed and the system is, by design, capable of undoing interactions of multiple artifacts. Our method is realized through the design of a novel volumetric transformer-based neural network that generalizes a \emph{window-centered} approach popularized by the Swin transformer. Unlike Swin, our method is (i) natively volumetric, (ii) geared towards dense prediction tasks instead of classification, and (iii), uses a novel and more global mechanism to enable information exchange between windows. Our experiments show that our reconstructions are considerably better than those attained by ResNet, V-Net, MobileNet-v2, DenseNet, CycleGAN and BicycleGAN. Moreover, we show that the reconstructed images from our model improves the accuracy of FSL BET, a standard skull-stripping method typically applied in diagnostic workflows., Comment: BMVC22

The practical benefits of hybrid quantum information processing hardware that contains continuous-variable objects (bosonic modes such as mechanical or electromagnetic oscillators) in addition to traditional (discrete-variable) qubits have recently been demonstrated by experiments with bosonic codes that reach the break-even point for quantum error correction and by efficient Gaussian boson sampling simulation of the Franck-Condon spectra of triatomic molecules that is well beyond the capabilities of current qubit-only hardware. The goal of this Co-design Center for Quantum Advantage (C2QA) project is to develop an instruction set architecture (ISA) for hybrid qubit/bosonic mode systems that contains an inventory of the fundamental operations and measurements that are possible in such hardware. The corresponding abstract machine model (AMM) would also contain a description of the appropriate error models associated with the gates, measurements and time evolution of the hardware. This information has been implemented as an extension of Qiskit. Qiskit is an opensource software development toolkit (SDK) for simulating the quantum state of a quantum circuit on a system with Python 3.7+ and for running the same circuits on prototype hardware within the IBM Quantum Lab. We introduce the Bosonic Qiskit software to enable the simulation of hybrid qubit/bosonic systems using the existing Qiskit software development kit. This implementation can be used for simulating new hybrid systems, verifying proposed physical systems, and modeling systems larger than can currently be constructed. We also cover tutorials and example use cases included within the software to study Jaynes- Cummings models, bosonic Hubbard models, plotting Wigner functions and animations, and calculating maximum likelihood estimations using Wigner functions.

Strongly contracting dynamical systems have numerous properties (e.g., incremental ISS), find widespread applications (e.g., in controls and learning), and their study is receiving increasing attention. This work starts with the simple observation that, given a strongly contracting system, its adjoint dynamical system is also strongly contracting, with the same rate, with respect to the dual norm, under time reversal. As main implication of this dual contractivity, we show that the classic Method of Successive Approximations (MSA), an indirect method in optimal control, is a contraction mapping for short optimization intervals or large contraction rates. Consequently, we establish new convergence conditions for the MSA algorithm, which further imply uniqueness of the optimal control and sufficiency of Pontryagin's minimum principle under additional assumptions.

We study the continuity equation of La Nave-Tian, extended to the Hermitian setting by Sherman-Weinkove, on Hopf and Inoue surfaces. We prove a priori estimates for solutions in both cases, and Gromov-Hausdorff convergence of Inoue surfaces to a circle., Comment: 15 pages

Vision transformers have demonstrated the potential to outperform CNNs in a variety of vision tasks. But the computational and memory requirements of these models prohibit their use in many applications, especially those that depend on high-resolution images, such as medical image classification. Efforts to train ViTs more efficiently are overly complicated, necessitating architectural changes or intricate training schemes. In this work, we show that standard ViT models can be efficiently trained at high resolution by randomly dropping input image patches. This simple approach, PatchDropout, reduces FLOPs and memory by at least 50% in standard natural image datasets such as ImageNet, and those savings only increase with image size. On CSAW, a high-resolution medical dataset, we observe a 5 times savings in computation and memory using PatchDropout, along with a boost in performance. For practitioners with a fixed computational or memory budget, PatchDropout makes it possible to choose image resolution, hyperparameters, or model size to get the most performance out of their model., Comment: IEEE/CVF Winter Conference on Applications of Computer Vision (WACV)