Miracle-dz/UniFAR-FTUs huggingface dataset:
Twin-width of graphs on surfaces

Twin-width is a width parameter introduced by Bonnet, Kim, Thomass\'e and Watrigant [FOCS'20, JACM'22], which has many structural and algorithmic applications. We prove that the twin-width of every graph embeddable in a surface of Euler genus $g$ is $18\sqrt{47g}+O(1)$, which is asymptotically best possible as it asymptotically differs from the lower bound by a constant multiplicative factor. Our proof also yields a quadratic time algorithm to find a corresponding contraction sequence. To prove the upper bound on twin-width of graphs embeddable in surfaces, we provide a stronger version of the Product Structure Theorem for graphs of Euler genus $g$ that asserts that every such graph is a subgraph of the strong product of a path and a graph with a tree-decomposition with all bags of size at most eight with a single exceptional bag of size $\max\{8,32g-27\}$.
Unsupervised Optical Flow Estimation with Dynamic Timing Representation for Spike Camera

Efficiently selecting an appropriate spike stream data length to extract precise information is the key to the spike vision tasks. To address this issue, we propose a dynamic timing representation for spike streams. Based on multi-layers architecture, it applies dilated convolutions on temporal dimension to extract features on multi-temporal scales with few parameters. And we design layer attention to dynamically fuse these features. Moreover, we propose an unsupervised learning method for optical flow estimation in a spike-based manner to break the dependence on labeled data. In addition, to verify the robustness, we also build a spike-based synthetic validation dataset for extreme scenarios in autonomous driving, denoted as SSES dataset. It consists of various corner cases. Experiments show that our method can predict optical flow from spike streams in different high-speed scenes, including real scenes. For instance, our method gets $15\%$ and $19\%$ error reduction from the best spike-based work, SCFlow, in $\Delta t=10$ and $\Delta t=20$ respectively which are the same settings as the previous works.
Mean-field interacting multi-type birth-death processes with a view to applications in phylodynamics

Multi-type birth-death processes underlie approaches for inferring evolutionary dynamics from phylogenetic trees across biological scales, ranging from deep-time species macroevolution to rapid viral evolution and somatic cellular proliferation. A limitation of current phylogenetic birth-death models is that they require restrictive linearity assumptions that yield tractable likelihoods, but that also preclude interactions between individuals. Many fundamental evolutionary processes -- such as environmental carrying capacity or frequency-dependent selection -- entail interactions, and may strongly influence the dynamics in some systems. Here, we introduce a multi-type birth-death process in mean-field interaction with an ensemble of replicas of the focal process. We prove that, under quite general conditions, the ensemble's stochastically evolving interaction field converges to a deterministic trajectory in the limit of an infinite ensemble. In this limit, the replicas effectively decouple, and self-consistent interactions appear as nonlinearities in the infinitesimal generator of the focal process. We investigate a special case that is amenable to calculations in the context of a phylogenetic birth-death model, and is rich enough to model both carrying capacity and frequency-dependent selection.
Tunneling, Page Curve and Black Hole Information

In a recent paper [1], we proposed that the quantum states of black hole responsible for the Bekenstein-Hawking entropy are given by Bell states of Fermi quanta in the interior of black hole. In this paper, we include the effect of tunneling on these entangled states and show that partial tunneling of these Bell states of Fermi quanta give rises to the Page curve of Hawking radiation. We also show that the entirety of information initially stored in the black hole is returned to the outside via the Hawking radiation.
Semiparametric Shape-restricted Estimators for Nonparametric Regression

Estimating the conditional mean function that relates predictive covariates to a response variable of interest is a fundamental task in economics and statistics. In this manuscript, we propose some general nonparametric regression approaches that are widely applicable based on a simple yet significant decomposition of nonparametric functions into a semiparametric model with shape-restricted components. For instance, we observe that every Lipschitz function can be expressed as a sum of a monotone function and a linear function. We implement well-established shape-restricted estimation procedures, such as isotonic regression, to handle the ``nonparametric"components of the true regression function and combine them with a simple sample-splitting procedure to estimate the parametric components. The resulting estimators inherit several favorable properties from the shape-restricted regression estimators. Notably, it is practically tuning parameter free, converges at the minimax optimal rate, and exhibits an adaptive rate when the true regression function is ``simple". We also confirm these theoretical properties and compare the practice performance with existing methods via a series of numerical studies.
What Happens During Finetuning of Vision Transformers: An Invariance Based Investigation

The pretrain-finetune paradigm usually improves downstream performance over training a model from scratch on the same task, becoming commonplace across many areas of machine learning. While pretraining is empirically observed to be beneficial for a range of tasks, there is not a clear understanding yet of the reasons for this effect. In this work, we examine the relationship between pretrained vision transformers and the corresponding finetuned versions on several benchmark datasets and tasks. We present new metrics that specifically investigate the degree to which invariances learned by a pretrained model are retained or forgotten during finetuning. Using these metrics, we present a suite of empirical findings, including that pretraining induces transferable invariances in shallow layers and that invariances from deeper pretrained layers are compressed towards shallower layers during finetuning. Together, these findings contribute to understanding some of the reasons for the successes of pretrained models and the changes that a pretrained model undergoes when finetuned on a downstream task.
A fermion-parity qubit in a proximitized double quantum dot

Bound states in quantum dots coupled to superconductors can be in a coherent superposition of states with different electron number but with the same number parity. Electrostatic gating can tune this superposition to a sweet spot, where the quantum dot has the same mean electric charge independent of its electron-number parity. Here, we propose to encode quantum information in the local fermion parity of two tunnel-coupled quantum dots embedded in a Josephson junction. At the sweet spot, the qubit states have zero charge dipole moment. This protects the qubit from dephasing due to electric field fluctuations. Depending on the strength of the tunnel coupling between the dots, the system is further protected towards either relaxation (weak tunneling) or dephasing (strong tunneling) from noise coupling separately to each quantum dot. We describe initialization and readout as well as single-qubit and two-qubit gates by pulsing gate voltages.
The Effects of Interaction Conflicts, Levels of Automation, and Frequency of Automation on Human Automation Trust and Acceptance

In the presence of interaction conflicts, user trust in automation plays an important role in accepting intelligent environments such as smart homes. In this paper, a factorial research design is employed to investigate and compare the single and joint effects of Level of Automation (LoA), Frequency of Automated responses (FoA), and Conflict Intensity (CI) on human trust and acceptance of automation in the context of smart homes. To study these effects, we conducted web-based experiments to gather data from 324 online participants who experienced the system through a 3D simulation of a smart home. The findings show that the level and frequency of automation had an impact on user trust in smart environments. Furthermore, the results demonstrate that the users' acceptance of automated smart environments decreased in the presence of automation failures and interaction conflicts.
Multi-Object Tracking as Attention Mechanism

We propose a conceptually simple and thus fast multi-object tracking (MOT) model that does not require any attached modules, such as the Kalman filter, Hungarian algorithm, transformer blocks, or graph networks. Conventional MOT models are built upon the multi-step modules listed above, and thus the computational cost is high. Our proposed end-toend MOT model, TicrossNet, is composed of a base detector and a cross-attention module only. As a result, the overhead of tracking does not increase significantly even when the number of instances (Nt) increases. We show that TicrossNet runs in real-time; specifically, it achieves 32.6 FPS on MOT17 and 31.0 FPS on MOT20 (Tesla V100), which includes as many as >100 instances per frame. We also demonstrate that TicrossNet is robust to Nt; thus, it does not have to change the size of the base detector, depending on Nt, as is often done by other models for real-time processing.
Quartic polynomials in two variables do not represent all non-negative integers

In this paper, we prove that there does not exist $F \in \mathbb{Q}[x,y]$ of degree $4$ such that $F(\mathbb{Z}^2) = \mathbb{Z}_{\geq 0}$. In particular, this answers a question by John S. Lew and Bjorn Poonen for quartic polynomials.
Relativistic second-order viscous hydrodynamics from kinetic theory with extended relaxation-time approximation

We use the extended relaxation time approximation for the collision kernel, which incorporates a particle-energy dependent relaxation time, to derive second-order viscous hydrodynamics from the Boltzmann equation for a system of massless particles. The resulting transport coefficients are found to be sensitive to the energy dependence of the relaxation time and have significant influence on the fluid's evolution. Using the derived hydrodynamic equations, we study the evolution of a fluid undergoing (0+1)-dimensional expansion with Bjorken symmetry and investigate the fixed point structure inherent in the equations. Further, by employing a power law parametrization to describe the energy dependence of the relaxation time, we successfully reproduce the stable free-streaming fixed point for a specific power of the energy dependence. The impact of the energy-dependent relaxation time on the processes of isotropization and thermalization of an expanding plasma is discussed.
Shock cooling emission from explosions of red super-giants: II. An analytic model of deviations from blackbody emission

Light emission in the first hours and days following core-collapse supernovae (SNe) is dominated by the escape of photons from the expanding shock heated envelope. In a preceding paper, Paper I, we provided a simple analytic description of the time dependent luminosity, L, and color temperature, Tcol, valid up to H recombination (T ≈ 0.7 eV), for explosions of red supergiants with convective polytropic envelopes without significant circum-stellar medium (CSM). The analytic description was calibrated against ‘gray’ (frequency-independent) photon diffusion numeric calculations. Here we present the results of a large set of 1D multi-group (frequency-dependent) calculations, for a wide range of progenitor parameters (mass, radius, core/envelope mass ratios, metalicity) and explosion energies, using opacity tables that we constructed (and made publicly available), including the contributions of bound-bound and bound-free transitions. We provide an analytic description of the small, $\simeq 10~{{\%}}$ deviations of the spectrum from blackbody at low frequencies, hν < 3Tcol, and an improved (over Paper I) description of ‘line dampening’ for hν > 3Tcol. We show that the effects of deviations from initial polytropic density distribution are small, and so are the effects of ‘expansion opacity’ and deviations from LTE ionization and excitation (within our model assumptions). A recent study of a large set of type II SN observations finds that our model accounts well for the early multi-band data of more than 50 % of observed SNe (the others are likely affected by thick CSM), enabling the inference of progenitor properties, explosion velocity, and relative extinction.
VoxPoser: Composable 3D Value Maps for Robotic Manipulation with Language Models

Large language models (LLMs) are shown to possess a wealth of actionable knowledge that can be extracted for robot manipulation in the form of reasoning and planning. Despite the progress, most still rely on pre-defined motion primitives to carry out the physical interactions with the environment, which remains a major bottleneck. In this work, we aim to synthesize robot trajectories, i.e., a dense sequence of 6-DoF end-effector waypoints, for a large variety of manipulation tasks given an open-set of instructions and an open-set of objects. We achieve this by first observing that LLMs excel at inferring affordances and constraints given a free-form language instruction. More importantly, by leveraging their code-writing capabilities, they can interact with a vision-language model (VLM) to compose 3D value maps to ground the knowledge into the observation space of the agent. The composed value maps are then used in a model-based planning framework to zero-shot synthesize closed-loop robot trajectories with robustness to dynamic perturbations. We further demonstrate how the proposed framework can benefit from online experiences by efficiently learning a dynamics model for scenes that involve contact-rich interactions. We present a large-scale study of the proposed method in both simulated and real-robot environments, showcasing the ability to perform a large variety of everyday manipulation tasks specified in free-form natural language. Videos and code at https://voxposer.github. io
Substance or Style: What Does Your Image Embedding Know?

Probes are small networks that predict properties of underlying data from embeddings, and they provide a targeted, effective way to illuminate the information contained in embeddings. While analysis through the use of probes has become standard in NLP, there has been much less exploration in vision. Image foundation models have primarily been evaluated for semantic content. Better understanding the non-semantic information in popular embeddings (e.g., MAE, SimCLR, or CLIP) will shed new light both on the training algorithms and on the uses for these foundation models. We design a systematic transformation prediction task and measure the visual content of embeddings along many axes, including image style, quality, and a range of natural and artificial transformations. Surprisingly, six embeddings (including SimCLR) encode enough non-semantic information to identify dozens of transformations. We also consider a generalization task, where we group similar transformations and hold out several for testing. We find that image-text models (CLIP and ALIGN) are better at recognizing new examples of style transfer than masking-based models (CAN and MAE). Overall, our results suggest that the choice of pre-training algorithm impacts the types of information in the embedding, and certain models are better than others for non-semantic downstream tasks.
A Generalised Theory of Proportionality in Collective Decision Making

We consider a voting model, where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to be selected), various elections with diversity constraints, the model of public decisions (where decisions needs to be taken on a number of independent issues), and the model of collective scheduling. A critical property of voting is that it should be fair -- not only to individuals but also to groups of voters with similar opinions on the subject of the vote; in other words, the outcome of an election should proportionally reflect the voters' preferences. We formulate axioms of proportionality in this general model. Our axioms do not require predefining groups of voters; to the contrary, we ensure that the opinion of every subset of voters whose preferences are cohesive-enough are taken into account to the extent that is proportional to the size of the subset. Our axioms generalise the strongest known satisfiable axioms for the more specific models. We explain how to adapt two prominent committee election rules, Proportional Approval Voting (PAV) and Phragm\'{e}n Sequential Rule, as well as the concept of stable-priceability to our general model. The two rules satisfy our proportionality axioms if and only if the feasibility constraints are matroids.
Pyramid Deep Fusion Network for Two-Hand Reconstruction from RGB-D Images

Accurately recovering the dense 3D mesh of both hands from monocular images poses considerable challenges due to occlusions and projection ambiguity. Most of the existing methods extract features from color images to estimate the root-aligned hand meshes, which neglect the crucial depth and scale information in the real world. Given the noisy sensor measurements with limited resolution, depth-based methods predict 3D keypoints rather than a dense mesh. These limitations motivate us to take advantage of these two complementary inputs to acquire dense hand meshes on a real-world scale. In this work, we propose an end-to-end framework for recovering dense meshes for both hands, which employ single-view RGB-D image pairs as input. The primary challenge lies in effectively utilizing two different input modalities to mitigate the blurring effects in RGB images and noises in depth images. Instead of directly treating depth maps as additional channels for RGB images, we encode the depth information into the unordered point cloud to preserve more geometric details. Specifically, our framework employs ResNet50 and PointNet++ to derive features from RGB and point cloud, respectively. Additionally, we introduce a novel pyramid deep fusion network (PDFNet) to aggregate features at different scales, which demonstrates superior efficacy compared to previous fusion strategies. Furthermore, we employ a GCN-based decoder to process the fused features and recover the corresponding 3D pose and dense mesh. Through comprehensive ablation experiments, we have not only demonstrated the effectiveness of our proposed fusion algorithm but also outperformed the state-of-the-art approaches on publicly available datasets. To reproduce the results, we will make our source code and models publicly available at {\url{https://github.com/zijinxuxu/PDFNet}}.
TreeFormer: A Semi-Supervised Transformer-Based Framework for Tree Counting From a Single High-Resolution Image

Automatic tree density estimation and counting using single aerial and satellite images is a challenging task in photogrammetry and remote sensing, yet has an important role in forest management. In this article, we propose the first semi-supervised transformer-based framework for tree counting which reduces the expensive tree annotations for remote sensing images. Our method, termed as TreeFormer, first develops a pyramid tree representation module based on transformer blocks to extract multiscale features during the encoding stage. Contextual attention-based feature fusion (CAFF) and tree density regressor (TDR) modules are further designed to utilize the robust features from the encoder to estimate tree density maps in the decoder. Moreover, we propose a pyramid learning strategy that includes local tree density consistency and local tree count ranking losses to utilize unlabeled images in the training process. Finally, the tree counter token (TCT) is introduced to regulate the network by computing the global tree counts for both labeled and unlabeled images. Our model was evaluated on two benchmark tree counting datasets, Jiangsu and Yosemite, as well as a new dataset, KCL-London, created by ourselves. Our TreeFormer outperforms the state-of-the-art semi-supervised methods under the same setting and exceeds the fully-supervised methods using the same number of labeled images. The codes and datasets are available at https://github.com/HAAClassic/TreeFormer.
On the association of secondary hairpin growth and surface pressure gradient for oscillating foils

The correspondence of secondary spanwise structures and pressure gradient is numerically evaluated for a foil, performing heaving and pitching motion, at a range of phase offsets (90$^\circ$ $\le \phi \le$ 270$^\circ$) and reduced frequency (0.32 $\le St_c \le$ 0.56). The Reynolds number is $Re =$ 8000. The wake is shown to be dominated by secondary hairpin-like structures that are formed due to an elliptic instability prompted by the paired primary and secondary leading edge vortex ($LEV$). The weaker secondary $LEV$ undergoes a core deformation, resulting in streamwise vorticity outflux across the span of the foil, and hence, the growth of hairpin-like structures. Evaluating pressure gradients on the surface of the foil reveals a unique fundamental measure to quantitatively characterize the growth of these coherent structures. Their dominant presence can be directly linked to the growth of the secondary $LEV$ formed due to the large-scale interactions under localized adverse pressure gradients. These promote a streamwise flow compression in neighboring regions of the primary $LEV$. This association also presents a vivid consistency across a range of kinematics. Therefore, this correspondence provides a novel procedure to investigate the mechanisms involved in the formation of secondary structures in the wake of an oscillating foil.
Bag of Views: An Appearance-Based Approach to Next-Best-View Planning for 3D Reconstruction

UAV-based intelligent data acquisition for 3D reconstruction and monitoring of infrastructure has experienced an increasing surge of interest due to recent advancements in image processing and deep learning-based techniques. View planning is an essential part of this task that dictates the information capture strategy and heavily impacts the quality of the 3D model generated from the captured data. Recent methods have used prior knowledge or partial reconstruction of the target to accomplish view planning for active reconstruction; the former approach poses a challenge for complex or newly identified targets while the latter is computationally expensive. In this work, we present Bag-of-Views (BoV), a fully appearance-based model used to assign utility to the captured views for both offline dataset refinement and online next-best-view (NBV) planning applications targeting the task of 3D reconstruction. With this contribution, we also developed the View Planning Toolbox (VPT), a lightweight package for training and testing machine learning-based view planning frameworks, custom view dataset generation of arbitrary 3D scenes, and 3D reconstruction. Through experiments which pair a BoV-based reinforcement learning model with VPT, we demonstrate the efficacy of our model in reducing the number of required views for high-quality reconstructions in dataset refinement and NBV planning.