Miracle-dz/UniFAR-FTUs huggingface dataset:
A generalization of diversity for intersecting families

Let $\mathcal{F}\subseteq \binom{[n]}{r}$ be an intersecting family of sets and let $\Delta(\mathcal{F})$ be the maximum degree in $\mathcal{F}$, i.e., the maximum number of edges of $\mathcal{F}$ containing a fixed vertex. The \emph{diversity} of $\mathcal{F}$ is defined as $d(\mathcal{F}) := |\mathcal{F}| - \Delta(\mathcal{F})$. Diversity can be viewed as a measure of distance from the `trivial' maximum-size intersecting family given by the Erd\H os-Ko-Rado Theorem. Indeed, the diversity of this family is $0$. Moreover, the diversity of the largest non-trivial intersecting family \`a la Hilton-Milner is $1$. It is known that the maximum possible diversity of an intersecting family $\mathcal{F}\subseteq \binom{[n]}{r}$ is $\binom{n-3}{r-2}$ as long as $n$ is large enough. We introduce a generalization called the \emph{$C$-weighted diversity} of $\mathcal{F}$ as $d_C(\mathcal{F}) := |\mathcal{F}| - C \cdot \Delta(\mathcal{F})$. We determine the maximum value of $d_C(\mathcal{F})$ for intersecting families $\mathcal{F} \subseteq \binom{[n]}{r}$ and characterize the maximal families for $C\in \left[0,\frac{7}{3}\right)$ as well as give general bounds for all $C$. Our results imply, for large $n$, a recent conjecture of Frankl and Wang concerning a related diversity-like measure. Our primary technique is a variant of Frankl's Delta-system method.
A quantum-enhanced support vector machine for galaxy classification

Galaxy morphology, a key tracer of the evolution of a galaxy’s physical structure, has motivated extensive research on machine learning techniques for efficient and accurate galaxy classification. The emergence of quantum computers has generated optimism about the potential for significantly improving the accuracy of such classifications by leveraging the large dimensionality of quantum Hilbert space. This paper presents a quantum-enhanced support vector machine algorithm for classifying galaxies based on their morphology. The algorithm requires the computation of a kernel matrix, a task that is performed on a simulated quantum computer using a quantum circuit conjectured to be intractable on classical computers. The result shows similar performance between classical and quantum-enhanced support vector machine algorithms. For a training size of 40k, the receiver operating characteristic curve for differentiating ellipticals and spirals has an under-curve area (ROC AUC) of 0.946 ± 0.005 for both classical and quantum-enhanced algorithms. Additionally, we demonstrate for a small dataset that the performance of a noise-mitigated quantum SVM algorithm on a quantum device is in agreement with simulation. Finally, a necessary condition for achieving a potential quantum advantage is presented. This investigation is among the very first applications of quantum machine learning in astronomy and highlights their potential for further application in this field.
CALICO: Self-Supervised Camera-LiDAR Contrastive Pre-training for BEV Perception

Perception is crucial in the realm of autonomous driving systems, where bird's eye view (BEV)-based architectures have recently reached state-of-the-art performance. The desirability of self-supervised representation learning stems from the expensive and laborious process of annotating 2D and 3D data. Although previous research has investigated pretraining methods for both LiDAR and camera-based 3D object detection, a unified pretraining framework for multimodal BEV perception is missing. In this study, we introduce CALICO, a novel framework that applies contrastive objectives to both LiDAR and camera backbones. Specifically, CALICO incorporates two stages: point-region contrast (PRC) and region-aware distillation (RAD). PRC better balances the region- and scene-level representation learning on the LiDAR modality and offers significant performance improvement compared to existing methods. RAD effectively achieves contrastive distillation on our self-trained teacher model. CALICO's efficacy is substantiated by extensive evaluations on 3D object detection and BEV map segmentation tasks, where it delivers significant performance improvements. Notably, CALICO outperforms the baseline method by 10.5% and 8.6% on NDS and mAP. Moreover, CALICO boosts the robustness of multimodal 3D object detection against adversarial attacks and corruption. Additionally, our framework can be tailored to different backbones and heads, positioning it as a promising approach for multimodal BEV perception.
Optimal Sets and Solution Paths of ReLU Networks

We develop an analytical framework to characterize the set of optimal ReLU neural networks by reformulating the non-convex training problem as a convex program. We show that the global optima of the convex parameterization are given by a polyhedral set and then extend this characterization to the optimal set of the non-convex training objective. Since all stationary points of the ReLU training problem can be represented as optima of sub-sampled convex programs, our work provides a general expression for all critical points of the non-convex objective. We then leverage our results to provide an optimal pruning algorithm for computing minimal networks, establish conditions for the regularization path of ReLU networks to be continuous, and develop sensitivity results for minimal ReLU networks.
Controllable Motion Diffusion Model

Generating realistic and controllable motions for virtual characters is a challenging task in computer animation, and its implications extend to games, simulations, and virtual reality. Recent studies have drawn inspiration from the success of diffusion models in image generation, demonstrating the potential for addressing this task. However, the majority of these studies have been limited to offline applications that target at sequence-level generation that generates all steps simultaneously. To enable real-time motion synthesis with diffusion models in response to time-varying control signals, we propose the framework of the Controllable Motion Diffusion Model (COMODO). Our framework begins with an auto-regressive motion diffusion model (A-MDM), which generates motion sequences step by step. In this way, simply using the standard DDPM algorithm without any additional complexity, our framework is able to generate high-fidelity motion sequences over extended periods with different types of control signals. Then, we propose our reinforcement learning-based controller and controlling strategies on top of the A-MDM model, so that our framework can steer the motion synthesis process across multiple tasks, including target reaching, joystick-based control, goal-oriented control, and trajectory following. The proposed framework enables the real-time generation of diverse motions that react adaptively to user commands on-the-fly, thereby enhancing the overall user experience. Besides, it is compatible with the inpainting-based editing methods and can predict much more diverse motions without additional fine-tuning of the basic motion generation models. We conduct comprehensive experiments to evaluate the effectiveness of our framework in performing various tasks and compare its performance against state-of-the-art methods.
A Note on the Spectrum of Magnetic Dirac Operators

In this article, we study the spectrum of the magnetic Dirac operator, and the magnetic Dirac operator with potential over complete Riemannian manifolds. We find sufficient conditions on the potentials as well as the manifold so that the spectrum is either maximal, or discrete. We also show that magnetic Dirac operators can have a dense set of eigenvalues.
The Object Folder Benchmark : Multisensory Learning with Neural and Real Objects

We introduce the ObjectFolder Benchmark, a benchmark suite of 10 tasks for multisensory object-centric learning, centered around object recognition, reconstruction, and manipulation with sight, sound, and touch. We also introduce the Objectfolder Real dataset, including the multisensory measurements for 100 real-world household objects, building upon a newly designed pipeline for collecting the 3D meshes, videos, impact sounds, and tactile readings of real-world objects. We conduct systematic benchmarking on both the 1,000 multisensory neural objects from Objectfolder, and the real multisensory data from Objectfolder Real. Our results demonstrate the importance of multisensory perception and reveal the respective roles of vision, audio, and touch for different object-centric learning tasks. By publicly releasing our dataset and benchmark suite, we hope to catalyze and enable new research in multisensory object-centric learning in computer vision, robotics, and beyond. Project page: https://objectfolder.stanford. edu
Image generation with shortest path diffusion

The field of image generation has made significant progress thanks to the introduction of Diffusion Models, which learn to progressively reverse a given image corruption. Recently, a few studies introduced alternative ways of corrupting images in Diffusion Models, with an emphasis on blurring. However, these studies are purely empirical and it remains unclear what is the optimal procedure for corrupting an image. In this work, we hypothesize that the optimal procedure minimizes the length of the path taken when corrupting an image towards a given final state. We propose the Fisher metric for the path length, measured in the space of probability distributions. We compute the shortest path according to this metric, and we show that it corresponds to a combination of image sharpening, rather than blurring, and noise deblurring. While the corruption was chosen arbitrarily in previous work, our Shortest Path Diffusion (SPD) determines uniquely the entire spatiotemporal structure of the corruption. We show that SPD improves on strong baselines without any hyperparameter tuning, and outperforms all previous Diffusion Models based on image blurring. Furthermore, any small deviation from the shortest path leads to worse performance, suggesting that SPD provides the optimal procedure to corrupt images. Our work sheds new light on observations made in recent works and provides a new approach to improve diffusion models on images and other types of data.
Visuomotor feedback tuning in the absence of visual error information

Large increases in visuomotor feedback gains occur during initial adaptation to novel dynamics, which we propose are due to increased internal model uncertainty. That is, large errors indicate increased uncertainty in our prediction of the environment, increasing feedback gains and co-contraction as a coping mechanism. Our previous work showed distinct patterns of visuomotor feedback gains during abrupt or gradual adaptation to a force field, suggesting two complementary processes: reactive feedback gains increasing with internal model uncertainty and the gradual learning of predictive feedback gains tuned to the environment. Here we further investigate what drives these changes visuomotor feedback gains in learning, by separating the effects of internal model uncertainty from visual error signal through removal of visual error information. Removing visual error information suppresses the visuomotor feedback gains in all conditions, but the pattern of modulation throughout adaptation is unaffected. Moreover, we find increased muscle co-contraction in both abrupt and gradual adaptation protocols, demonstrating that visuomotor feedback responses are independent from the level of co-contraction. Our result suggests that visual feedback benefits motor adaptation tasks through higher visuomotor feedback gains, but when it is not available participants adapt at a similar rate through increased co-contraction. We have demonstrated a direct connection between learning and predictive visuomotor feedback gains, independent from visual error signals. This further supports our hypothesis that internal model uncertainty drives initial increases in feedback gains.
Addressing Negative Transfer in Diffusion Models

Diffusion-based generative models have achieved remarkable success in various domains. It trains a shared model on denoising tasks that encompass different noise levels simultaneously, representing a form of multi-task learning (MTL). However, analyzing and improving diffusion models from an MTL perspective remains under-explored. In particular, MTL can sometimes lead to the well-known phenomenon of negative transfer, which results in the performance degradation of certain tasks due to conflicts between tasks. In this paper, we first aim to analyze diffusion training from an MTL standpoint, presenting two key observations: (O1) the task affinity between denoising tasks diminishes as the gap between noise levels widens, and (O2) negative transfer can arise even in diffusion training. Building upon these observations, we aim to enhance diffusion training by mitigating negative transfer. To achieve this, we propose leveraging existing MTL methods, but the presence of a huge number of denoising tasks makes this computationally expensive to calculate the necessary per-task loss or gradient. To address this challenge, we propose clustering the denoising tasks into small task clusters and applying MTL methods to them. Specifically, based on (O2), we employ interval clustering to enforce temporal proximity among denoising tasks within clusters. We show that interval clustering can be solved using dynamic programming, utilizing signal-to-noise ratio, timestep, and task affinity for clustering objectives. Through this, our approach addresses the issue of negative transfer in diffusion models by allowing for efficient computation of MTL methods. We validate the efficacy of proposed clustering and its integration with MTL methods through various experiments, demonstrating 1) improved generation quality and 2) faster training convergence of diffusion models.
Novel CMB constraints on the α parameter in alpha-attractor models

Cosmological α-attractors are a compelling class of inflationary models. They lead to universal predictions for large-scale observables, broadly independent from the functional form of the inflaton potential. In this work we derive improved analytical predictions for the large-scale observables, whose dependence on the duration of reheating and the parameter α is made explicit. We compare these with Planck and BICEP/Keck 2018 data in the framework of a Bayesian study, employing uniform logarithmic and linear priors for α. Our improved universal predictions allow direct constraints on the duration of reheating. Furthermore, while it is well-known that CMB constraints on the tensor-to-scalar ratio can be used to place an upper bound on the α parameter, we demonstrate that including the α-dependence of the scalar spectral tilt yields novel constraints on α. In particular, for small α, the scalar spectral tilt scales with log10 α, regardless of the specific potential shape. For decreasing α, this eventually puts the models in tension with CMB measurements, bounding the magnitude of α from below. Therefore, in addition to the upper bound from the tensor-to-scalar ratio, we derive the first lower bound on the magnitude of α for α-attractor T-models, log10 α = -4.2+5.4 -8.6 at 95% C.L.
Towards Interactive Image Inpainting via Sketch Refinement

One tough problem of image inpainting is to restore complex structures in the corrupted regions. It motivates interactive image inpainting which leverages additional hints, e.g., sketches, to assist the inpainting process. Sketch is simple and intuitive to end users, but meanwhile has free forms with much randomness. Such randomness may confuse the inpainting models, and incur severe artifacts in completed images. To address this problem, we propose a two-stage image inpainting method termed SketchRefiner. In the first stage, we propose using a cross-correlation loss function to robustly calibrate and refine the user-provided sketches in a coarse-to-fine fashion. In the second stage, we learn to extract informative features from the abstracted sketches in the feature space and modulate the inpainting process. We also propose an algorithm to simulate real sketches automatically and build a test protocol with different applications. Experimental results on public datasets demonstrate that SketchRefiner effectively utilizes sketch information and eliminates the artifacts due to the free-form sketches. Our method consistently outperforms the state-of-the-art ones both qualitatively and quantitatively, meanwhile revealing great potential in real-world applications. Our code and dataset are available.
Influences of Model Parameterization Schemes on the Response of Rainfall to Soil Moisture in the Central United States

Abstract The sensitivities of soil moisture impacts on summer rainfall in the central United States to different commonly used cumulus parameterization and surface flux schemes are examined using the PSU-NCAR MMS under different atmospheric and soil moisture conditions. The cumulus convection schemes used are the Kuo and Grell parameterization schemes, while the surface-moisture flux schemes used are the aerodynamic formulation and the Simple Biosphere (SiB) Model. Results show that a transient increase in soil moisture enhanced total rainfall over the simulation domain. The increase in soil moisture enhanced local rainfall when the lower atmosphere was thermally unstable and relatively dry, but it decreased the rainfall when the atmosphere was humid and lacked sufficient thermal forcing to initiate deep convection. Soil moisture impacts were noticeably stronger for the Kuo scheme, which simulated lighter peak rainfall, than those for the Grell scheme, which simulated heavier peak rainfall. The greater se.
Exposing Attention Glitches with Flip-Flop Language Modeling

Why do large language models sometimes output factual inaccuracies and exhibit erroneous reasoning? The brittleness of these models, particularly when executing long chains of reasoning, currently seems to be an inevitable price to pay for their advanced capabilities of coherently synthesizing knowledge, pragmatics, and abstract thought. Towards making sense of this fundamentally unsolved problem, this work identifies and analyzes the phenomenon of attention glitches, in which the Transformer architecture's inductive biases intermittently fail to capture robust reasoning. To isolate the issue, we introduce flip-flop language modeling (FFLM), a parametric family of synthetic benchmarks designed to probe the extrapolative behavior of neural language models. This simple generative task requires a model to copy binary symbols over long-range dependencies, ignoring the tokens in between. We find that Transformer FFLMs suffer from a long tail of sporadic reasoning errors, some of which we can eliminate using various regularization techniques. Our preliminary mechanistic analyses show why the remaining errors may be very difficult to diagnose and resolve. We hypothesize that attention glitches account for (some of) the closed-domain hallucinations in natural LLMs.
Relation between critical current density and flux flow resistivity in Bi2223 bulk element for fault current limiter

The relationship between the critical current density and flux flow resistivity in a Bi2223 bulk for fault current limiter application was experimentally investigated. The distributions of J/sub c/ and voltage along the longitudinal direction were measured as well as the transport current. As a result, it was found that the flux flow resistivity is higher at positions of lower critical current. Measured results were numerically analyzed to obtain an empirical expression for the flux flow resistivity as a function of the critical current density, accumulated Joule heat and transport current.
Graphs with Large Girth and Small Cop Number

In this paper we consider the cop number of graphs with no, or few, short cycles. We show that when the girth of $G$ is at least $7$ and the minimum degree is sufficiently large, $\delta \geq (\ln{n})^{\frac{1}{1-\alpha}}$ where $\alpha \in (0,1)$, then $c(G) = o(n \delta^{1-\lfloor \frac{g}{4} \rfloor})$ as $n \rightarrow \infty$. This extends work of Frankl and implies that if $G$ is large and dense in the sense that $\delta \geq n^{\frac{2 + o(1)}{g-1}}$ while also having girth $g \geq 7$, then $G$ satisfies Meyniel's conjecture, that is $c(G) = O(\sqrt{n})$. Moreover, it implies that if $G$ is large and dense in the sense that there $\delta \geq n^{\epsilon}$ for some $\epsilon>0$, while also having girth $g \geq 7$, then there exists an $\alpha>0$ such that $c(G) = O(n^{1-\alpha})$, thereby satisfying the weak Meyniel's conjecture. Of course, this implies similar results for dense graphs with small, that is $O(n^{1-\alpha})$, numbers of short cycles, as each cycle can be broken by adding a single cop. We also, show that there are graphs $G$ with girth $g$ and minimum degree $\delta$ such that the cop number is at most $o(g (\delta-1)^{(1+o(1))\frac{g}{4}})$. This resolves a recent conjecture by Bradshaw, Hosseini, Mohar, and Stacho, by showing that the constant $\frac{1}{4}$ cannot be improved in the exponent of a lower bound $c(G) \geq \frac{1}{g} (\delta - 1)^{\lfloor \frac{g-1}{4}\rfloor}$.
Understanding Augmentation-based Self-Supervised Representation Learning via RKHS Approximation

Data augmentation is critical to the empirical success of modern self-supervised representation learning, such as contrastive learning and masked language modeling. However, a theoretical understanding of the exact role of augmentation remains limited. Recent work has built the connection between self-supervised learning and the approximation of the top eigenspace of a graph Laplacian operator, suggesting that learning a linear probe atop such representation can be connected to RKHS regression. Building on this insight, this work delves into a statistical analysis of augmentation-based pretraining. Starting from the isometry property, a geometric characterization of the target function given by the augmentation, we disentangle the effects of the model and the augmentation, and prove two generalization bounds that are free of model complexity. Our first bound works for an arbitrary encoder, where the prediction error is decomposed as the sum of an estimation error incurred by fitting a linear probe with RKHS regression, and an approximation error entailed by RKHS approximation. Our second bound specifically addresses the case where the encoder is near-optimal, that is it approximates the top-d eigenspace of the RKHS induced by the augmentation. A key ingredient in our analysis is the augmentation complexity, which we use to quantitatively compare different augmentations and analyze their impact on downstream performance.