Miracle-dz/UniFAR-FTUs huggingface dataset:
The coupled hirota equation with a 3*3 lax pair: painleve-type asymptotics in transition zone

We consider the Painleve asymptotics for a solution of integrable coupled Hirota equationwith a 3*3 Lax pair whose initial data decay rapidly at infinity. Using Riemann-Hilbert techniques and Deift-Zhou nonlinear steepest descent arguments, in a transition zone defined by /x/t-1/(12a)/t^2/3<=C, where C>0 is a constant, it turns out that the leading-order term to the solution can be expressed in terms of the solution of a coupled Painleve II equation associated with a 3*3 matrix Riemann-Hilbert problem.
Asymptotically homogeneous solutions of the supercritical Lane-Emden system

We consider the Lane-Emden system-$\Delta$u = |v| p-1 v,-$\Delta$v = |u| q-1 u in R d. When p $\ge$ q $\ge$ 1, it is known that there exists a positive radial stable solution (u, v) $\in$ C 2 (R d) if and only if d $\ge$ 11 and (p, q) lies on or above the so-called Joseph-Lundgren curve introduced in [5]. In this paper, we prove that for d $\le$ 10, there is no positive stable solution (or merely stable outside a compact set and (p, q) does not lie on the critical Sobolev hyperbola), while for d $\ge$ 11, the Joseph-Lundgren curve is indeed the dividing line for the existence of such solutions, if one assumes in addition that they are asymptotically homogeneous (see Definition 1 below). Most of our results are optimal improvements of previous works in the litterature.
Factorisation Homology for Class $\cal S$ Theories

Based on recent advancements in algebraic geometry, algebraic topology, and higher-categorical structures, we show how ground state degeneracies in closed stratified manifolds can be used for describing class ${\cal S}$ theories whose AGT dual requires generalised Moore-Segal bordism operators lacking reparametrisation-invariance.
NVS-Adapter: Plug-and-Play Novel View Synthesis from a Single Image

Transfer learning of large-scale Text-to-Image (T2I) models has recently shown impressive potential for Novel View Synthesis (NVS) of diverse objects from a single image. While previous methods typically train large models on multi-view datasets for NVS, fine-tuning the whole parameters of T2I models not only demands a high cost but also reduces the generalization capacity of T2I models in generating diverse images in a new domain. In this study, we propose an effective method, dubbed NVS-Adapter, which is a plug-and-play module for a T2I model, to synthesize novel multi-views of visual objects while fully exploiting the generalization capacity of T2I models. NVS-Adapter consists of two main components; view-consistency cross-attention learns the visual correspondences to align the local details of view features, and global semantic conditioning aligns the semantic structure of generated views with the reference view. Experimental results demonstrate that the NVS-Adapter can effectively synthesize geometrically consistent multi-views and also achieve high performance on benchmarks without full fine-tuning of T2I models. The code and data are publicly available in ~\href{https://postech-cvlab.github. io/nvsadapter/}{https://postech-cvlab.github. io/nvsadapter/}.
Astronomical Image Blurring from Transversely Correlated Quantum Gravity Fluctuations

Quantum fluctuations in spacetime can, in some cases, lead to distortion in astronomical images of faraway objects. In particular, a stochastic model of quantum gravity predicts an accumulated fluctuation in the path length $\Delta L$ with variance $\langle \Delta L^2\rangle\sim l_pL$ over a distance $L$, similar to a random walk, and assuming no spatial correlation above length $l_p$; it has been argued that such an effect is ruled out by observation of sharp images from distant stars. However, in other theories, such as the pixellon (modeled on the Verlinde-Zurek (VZ) effect), quantum fluctuations can still accumulate as in the random walk model while simultaneously having large distance correlations in the fluctuations. Using renormalization by analytic continuation, we derive the correlation transverse to the light propagation, and show that image distortion effects in the pixellon model are strongly suppressed in comparison to the random walk model, thus evading all existing and future constraints. We also find that the diffraction of light rays does not lead to qualitative changes in the blurring effect.
Quantum topological data analysis via the estimation of the density of states

We develop a quantum topological data analysis (QTDA) protocol based on the estimation of the density of states (DOS) of the combinatorial Laplacian. Computing topological features of graphs and simplicial complexes is crucial for analyzing datasets and building explainable AI solutions. This task becomes computationally hard for simplicial complexes with over sixty vertices and high-degree topological features due to a combinatorial scaling. We propose to approach the task by embedding underlying hypergraphs as effective quantum Hamiltonians and evaluating their density of states from the time evolution. Specifically, we compose propagators as quantum circuits using the Cartan decomposition of effective Hamiltonians and sample overlaps of time-evolved states using multi-fidelity protocols. Next, we develop various post-processing routines and implement a Fourier-like transform to recover the rank (and kernel) of Hamiltonians. This enables us to estimate the Betti numbers, revealing the topological features of simplicial complexes. We test our protocol on noiseless and noisy quantum simulators and run examples on IBM quantum processors. We observe the resilience of the proposed QTDA approach to real-hardware noise even in the absence of error mitigation, showing the promise to near-term device implementations and highlighting the utility of global DOS-based estimators.
Mixture-of-Linear-Experts for Long-term Time Series Forecasting

Long-term time series forecasting (LTSF) aims to predict future values of a time series given the past values. The current state-of-the-art (SOTA) on this problem is attained in some cases by linear-centric models, which primarily feature a linear mapping layer. However, due to their inherent simplicity, they are not able to adapt their prediction rules to periodic changes in time series patterns. To address this challenge, we propose a Mixture-of-Experts-style augmentation for linear-centric models and propose Mixture-of-Linear-Experts (MoLE). Instead of training a single model, MoLE trains multiple linear-centric models (i.e., experts) and a router model that weighs and mixes their outputs. While the entire framework is trained end-to-end, each expert learns to specialize in a specific temporal pattern, and the router model learns to compose the experts adaptively. Experiments show that MoLE reduces forecasting error of linear-centric models, including DLinear, RLinear, and RMLP, in over 78% of the datasets and settings we evaluated. By using MoLE existing linear-centric models can achieve SOTA LTSF results in 68% of the experiments that PatchTST reports and we compare to, whereas existing single-head linear-centric models achieve SOTA results in only 25% of cases. Additionally, MoLE models achieve SOTA in all settings for the newly released Weather2K datasets.
Humans vs Large Language Models: Judgmental Forecasting in an Era of Advanced AI

This study investigates the forecasting accuracy of human experts versus Large Language Models (LLMs) in the retail sector, particularly during standard and promotional sales periods. Utilizing a controlled experimental setup with 123 human forecasters and five LLMs, including ChatGPT4, ChatGPT3.5, Bard, Bing, and Llama2, we evaluated forecasting precision through Mean Absolute Percentage Error. Our analysis centered on the effect of the following factors on forecasters performance: the supporting statistical model (baseline and advanced), whether the product was on promotion, and the nature of external impact. The findings indicate that LLMs do not consistently outperform humans in forecasting accuracy and that advanced statistical forecasting models do not uniformly enhance the performance of either human forecasters or LLMs. Both human and LLM forecasters exhibited increased forecasting errors, particularly during promotional periods and under the influence of positive external impacts. Our findings call for careful consideration when integrating LLMs into practical forecasting processes.
When Bio-Inspired Computing meets Deep Learning: Low-Latency, Accurate, & Energy-Efficient Spiking Neural Networks from Artificial Neural Networks

Bio-inspired Spiking Neural Networks (SNN) are now demonstrating comparable accuracy to intricate convolutional neural networks (CNN), all while delivering remarkable energy and latency efficiency when deployed on neuromorphic hardware. In particular, ANN-to-SNN conversion has recently gained significant traction in developing deep SNNs with close to state-of-the-art (SOTA) test accuracy on complex image recognition tasks. However, advanced ANN-to-SNN conversion approaches demonstrate that for lossless conversion, the number of SNN time steps must equal the number of quantization steps in the ANN activation function. Reducing the number of time steps significantly increases the conversion error. Moreover, the spiking activity of the SNN, which dominates the compute energy in neuromorphic chips, does not reduce proportionally with the number of time steps. To mitigate the accuracy concern, we propose a novel ANN-to-SNN conversion framework, that incurs an exponentially lower number of time steps compared to that required in the SOTA conversion approaches. Our framework modifies the SNN integrate-and-fire (IF) neuron model with identical complexity and shifts the bias term of each batch normalization (BN) layer in the trained ANN. To mitigate the spiking activity concern, we propose training the source ANN with a fine-grained L1 regularizer with surrogate gradients that encourages high spike sparsity in the converted SNN. Our proposed framework thus yields lossless SNNs with ultra-low latency, ultra-low compute energy, thanks to the ultra-low timesteps and high spike sparsity, and ultra-high test accuracy, for example, 73.30% with only 4 time steps on the ImageNet dataset.
Unifying Correspondence, Pose and NeRF for Pose-Free Novel View Synthesis from Stereo Pairs

This work delves into the task of pose-free novel view synthesis from stereo pairs, a challenging and pioneering task in 3D vision. Our innovative framework, unlike any before, seamlessly integrates 2D correspondence matching, camera pose estimation, and NeRF rendering, fostering a synergistic enhancement of these tasks. We achieve this through designing an architecture that utilizes a shared representation, which serves as a foundation for enhanced 3D geometry understanding. Capitalizing on the inherent interplay between the tasks, our unified framework is trained end-to-end with the proposed training strategy to improve overall model accuracy. Through extensive evaluations across diverse indoor and outdoor scenes from two real-world datasets, we demonstrate that our approach achieves substantial improvement over previous methodologies, especially in scenarios characterized by extreme viewpoint changes and the absence of accurate camera poses.
SIFU: Side-view Conditioned Implicit Function for Real-world Usable Clothed Human Reconstruction

Creating high-quality 3D models of clothed humans from single images for real-world applications is crucial. Despite recent advancements, accurately reconstructing humans in complex poses or with loose clothing from in-the-wild images, along with predicting textures for unseen areas, remains a significant challenge. A key limitation of previous methods is their insufficient prior guidance in transitioning from 2D to 3D and in texture prediction. In response, we introduce SIFU (Side-view Conditioned Implicit Function for Real-world Usable Clothed Human Reconstruction), a novel approach combining a Side-view Decoupling Transformer with a 3D Consistent Texture Refinement pipeline.SIFU employs a cross-attention mechanism within the transformer, using SMPL-X normals as queries to effectively decouple side-view features in the process of mapping 2D features to 3D. This method not only improves the precision of the 3D models but also their robustness, especially when SMPL-X estimates are not perfect. Our texture refinement process leverages text-to-image diffusion-based prior to generate realistic and consistent textures for invisible views. Through extensive experiments, SIFU surpasses SOTA methods in both geometry and texture reconstruction, showcasing enhanced robustness in complex scenarios and achieving an unprecedented Chamfer and P2S measurement. Our approach extends to practical applications such as 3D printing and scene building, demonstrating its broad utility in real-world scenarios. Project page https://river-zhang.github. io/SIFU-projectpage/ .
Time scale dynamics of COVID-19 pandemic waves: The case of Greece (preprint)

The results of an alternative methodology for making predictions about the COVID-19 pandemic in Greece are presented. Instead of focusing on the various population profiles (subjected to instabilities introduced by the fitting process), this methodology focuses on the time scale that characterises the intensity and duration of the outbreak phase. Therefore, instead of predicting the peak of active cases, here their inflection point is predicted (the point where the increase of active cases stops accelerating and starts decelerating). Since the inflection point precedes the peak, this methodology can serve as an early warning of the peak. In addition, the paths between the various populations (healthy, exposed, infected, etc) that contribute the most to the outbreak phase are identified.
Ground States of Fermionic Nonlinear Schr\"{o}dinger Systems with Coulomb Potential II: The $L^2$-Critical Case

As a continuation of \cite{me}, we consider ground states of the $N$ coupled fermionic nonlinear Schr\"{o}dinger system with a parameter $a $ and the Coulomb potential $V(x)$ in the $L^2$-critical case, where $a>0$ represents the attractive strength of the quantum particles. For any given $N\in\mathbb{N}^+$, we prove that the system admits ground states, if and only if the attractive strength $a$ satisfies $0<a<a^*_N$, where the critical constant $0<a^*_N<\infty$ is the same as the best constant of a dual finite-rank Lieb-Thirring inequality. By developing the so-called blow-up analysis of many-body fermionic problems, we also prove the mass concentration behavior of ground states for the system as $a\nearrow a_N^*$.
GateNet: A novel Neural Network Architecture for Automated Flow Cytometry Gating

Flow cytometry is widely used to identify cell populations in patient-derived fluids such as peripheral blood (PB) or cerebrospinal fluid (CSF). While ubiquitous in research and clinical practice, flow cytometry requires gating, i.e. cell type identification which requires labor-intensive and error-prone manual adjustments. To facilitate this process, we designed GateNet, the first neural network architecture enabling full end-to-end automated gating without the need to correct for batch effects. We train GateNet with over 8,000,000 events based on N=127 PB and CSF samples which were manually labeled independently by four experts. We show that for novel, unseen samples, GateNet achieves human-level performance (F1 score ranging from 0.910 to 0.997). In addition we apply GateNet to a publicly available dataset confirming generalization with an F1 score of 0.936. As our implementation utilizes graphics processing units (GPU), gating only needs 15 microseconds per event. Importantly, we also show that GateNet only requires ~10 samples to reach human-level performance, rendering it widely applicable in all domains of flow cytometry.
Probabilistic representation of the gradient of a killed diffusion semigroup: The half-space case

We introduce a probabilistic representation of the derivative of the semigroup associated to a multidimensional killed diffusion process defined on the half-space. The semigroup derivative is expressed as a functional of a process that is normally reflected when it hits the hyperplane. The representation of the derivative also involves a matrix-valued process which replaces the Jacobian of the underlying process that appears in the traditional pathwise derivative of a classical diffusion. The components of this matrix-valued process become zero except for those on the first row every time the reflected process touches the boundary. The results in this paper extend those in recent work of the authors, where the one-dimensional case was studied.
Irreducibility of Virasoro representations in Liouville CFT

In the context of Liouville conformal field theory, we construct the highest-weight representations of the Virasoro algebra at the degenerate values of the conformal weight (Kac table). We show that these modules are irreducible, giving a complete characterization of the algebraic structure of Liouville CFT. It also implies that all singular vectors vanish, which is one of the main assumptions usually made in theoretical physics. Our proof uses inputs from both probability theory and algebra, and gives new probabilistic content to the Kac table. Combining the information that singular vectors vanish with the main geometric properties of conformal blocks, we deduce that conformal blocks involving degenerate primary fields satisfy null-vector equations. These equations take the form of PDEs on the Teichm\"uller space of the underlying surface and generalize previous works in several directions.
A small latest Villafranchian (late early Pleistocene) rhinoceros from Pietrafitta (Perugia, Umbria, Central Italy), with notes on the Pirro and Westerhoven rhinoceroses

La mine de lignite de Pietrafitta a livre de nombreux restes de rhinoceros du Pleistocene ancien. Les restes craniens et dentaires, trop rares et mal preserves pour une attribution specifique, montrent parfois quelques traits du Stephanorhinus etruscus et du S. hundsheimensis. Une analyse comparative des vestiges postcraniens revele une similarite plus grande avec cette derniere espece. Malgre sa petite taille, le rhinoceros de Pietrafitta se refere au S. hundsheimensis. L'existence en Europe de rhinoceros similaires a celui de Pietrafitta (taille et morphologie) suggere pour origine possible du S. hundsheimensis une derivation du S. etruscus a travers cette espece de taille intermediaire
Counterfactual World Modeling for Physical Dynamics Understanding

The ability to understand physical dynamics is essential to learning agents acting in the world. This paper presents Counterfactual World Modeling (CWM), a candidate pure vision foundational model for physical dynamics understanding. CWM consists of three basic concepts. First, we propose a simple and powerful temporally-factored masking policy for masked prediction of video data, which encourages the model to learn disentangled representations of scene appearance and dynamics. Second, as a result of the factoring, CWM is capable of generating counterfactual next-frame predictions by manipulating a few patch embeddings to exert meaningful control over scene dynamics. Third, the counterfactual modeling capability enables the design of counterfactual queries to extract vision structures similar to keypoints, optical flows, and segmentations, which are useful for dynamics understanding. We show that zero-shot readouts of these structures extracted by the counterfactual queries attain competitive performance to prior methods on real-world datasets. Finally, we demonstrate that CWM achieves state-of-the-art performance on the challenging Physion benchmark for evaluating physical dynamics understanding.
Adversarial Semi-Supervised Domain Adaptation for Semantic Segmentation: A New Role for Labeled Target Samples

Adversarial learning baselines for domain adaptation (DA) approaches in the context of semantic segmentation are under explored in semi-supervised framework. These baselines involve solely the available labeled target samples in the supervision loss. In this work, we propose to enhance their usefulness on both semantic segmentation and the single domain classifier neural networks. We design new training objective losses for cases when labeled target data behave as source samples or as real target samples. The underlying rationale is that considering the set of labeled target samples as part of source domain helps reducing the domain discrepancy and, hence, improves the contribution of the adversarial loss. To support our approach, we consider a complementary method that mixes source and labeled target data, then applies the same adaptation process. We further propose an unsupervised selection procedure using entropy to optimize the choice of labeled target samples for adaptation. We illustrate our findings through extensive experiments on the benchmarks GTA5, SYNTHIA, and Cityscapes. The empirical evaluation highlights competitive performance of our proposed approach.
Topological Obstructions and How to Avoid Them

Incorporating geometric inductive biases into models can aid interpretability and generalization, but encoding to a specific geometric structure can be challenging due to the imposed topological constraints. In this paper, we theoretically and empirically characterize obstructions to training encoders with geometric latent spaces. We show that local optima can arise due to singularities (e.g. self-intersection) or due to an incorrect degree or winding number. We then discuss how normalizing flows can potentially circumvent these obstructions by defining multimodal variational distributions. Inspired by this observation, we propose a new flow-based model that maps data points to multimodal distributions over geometric spaces and empirically evaluate our model on 2 domains. We observe improved stability during training and a higher chance of converging to a homeomorphic encoder.
TULIP: Transformer for Upsampling of LiDAR Point Cloud

LiDAR Upsampling is a challenging task for the perception systems of robots and autonomous vehicles, due to the sparse and irregular structure of large-scale scene contexts. Recent works propose to solve this problem by converting LiDAR data from 3D Euclidean space into an image super-resolution problem in 2D image space. Although their methods can generate high-resolution range images with fine-grained details, the resulting 3D point clouds often blur out details and predict invalid points. In this paper, we propose TULIP, a new method to reconstruct high-resolution LiDAR point clouds from low-resolution LiDAR input. We also follow a range image-based approach but specifically modify the patch and window geometries of a Swin-Transformer-based network to better fit the characteristics of range images. We conducted several experiments on three public real-world and simulated datasets. TULIP outperforms state-of-the-art methods in all relevant metrics and generates robust and more realistic point clouds than prior works.
General Tail Bounds for Non-Smooth Stochastic Mirror Descent

In this paper, we provide novel tail bounds on the optimization error of Stochastic Mirror Descent for convex and Lipschitz objectives. Our analysis extends the existing tail bounds from the classical light-tailed Sub-Gaussian noise case to heavier-tailed noise regimes. We study the optimization error of the last iterate as well as the average of the iterates. We instantiate our results in two important cases: a class of noise with exponential tails and one with polynomial tails. A remarkable feature of our results is that they do not require an upper bound on the diameter of the domain. Finally, we support our theory with illustrative experiments that compare the behavior of the average of the iterates with that of the last iterate in heavy-tailed noise regimes.