Miracle-dz/UniFAR-FTUs huggingface dataset:
Hierarchical Latent Structure for Multi-Modal Vehicle Trajectory Forecasting

Variational autoencoder (VAE) has widely been utilized for modeling data distributions because it is theoretically elegant, easy to train, and has nice manifold representations. However, when applied to image reconstruction and synthesis tasks, VAE shows the limitation that the generated sample tends to be blurry. We observe that a similar problem, in which the generated trajectory is located between adjacent lanes, often arises in VAE-based trajectory forecasting models. To mitigate this problem, we introduce a hierarchical latent structure into the VAE-based forecasting model. Based on the assumption that the trajectory distribution can be approximated as a mixture of simple distributions (or modes), the low-level latent variable is employed to model each mode of the mixture and the high-level latent variable is employed to represent the weights for the modes. To model each mode accurately, we condition the low-level latent variable using two lane-level context vectors computed in novel ways, one corresponds to vehicle-lane interaction and the other to vehicle-vehicle interaction. The context vectors are also used to model the weights via the proposed mode selection network. To evaluate our forecasting model, we use two large-scale real-world datasets. Experimental results show that our model is not only capable of generating clear multi-modal trajectory distributions but also outperforms the state-of-the-art (SOTA) models in terms of prediction accuracy. Our code is available at https://github.com/d1024choi/HLSTrajForecast.
Optimal Clustering by Lloyd Algorithm for Low-Rank Mixture Model

This paper investigates the computational and statistical limits in clustering matrix-valued observations. We propose a low-rank mixture model (LrMM), adapted from the classical Gaussian mixture model (GMM) to treat matrix-valued observations, which assumes low-rankness for population center matrices. A computationally efficient clustering method is designed by integrating Lloyd's algorithm and low-rank approximation. Once well-initialized, the algorithm converges fast and achieves an exponential-type clustering error rate that is minimax optimal. Meanwhile, we show that a tensor-based spectral method delivers a good initial clustering. Comparable to GMM, the minimax optimal clustering error rate is decided by the separation strength, i.e., the minimal distance between population center matrices. By exploiting low-rankness, the proposed algorithm is blessed with a weaker requirement on the separation strength. Unlike GMM, however, the computational difficulty of LrMM is characterized by the signal strength, i.e., the smallest non-zero singular values of population center matrices. Evidence is provided showing that no polynomial-time algorithm is consistent if the signal strength is not strong enough, even though the separation strength is strong. Intriguing differences between estimation and clustering under LrMM are discussed. The merits of low-rank Lloyd's algorithm are confirmed by comprehensive simulation experiments. Finally, our method outperforms others in the literature on real-world datasets.
Learning Temporally Extended Skills in Continuous Domains as Symbolic Actions for Planning

Problems which require both long-horizon planning and continuous control capabilities pose significant challenges to existing reinforcement learning agents. In this paper we introduce a novel hierarchical reinforcement learning agent which links temporally extended skills for continuous control with a forward model in a symbolic discrete abstraction of the environment's state for planning. We term our agent SEADS for Symbolic Effect-Aware Diverse Skills. We formulate an objective and corresponding algorithm which leads to unsupervised learning of a diverse set of skills through intrinsic motivation given a known state abstraction. The skills are jointly learned with the symbolic forward model which captures the effect of skill execution in the state abstraction. After training, we can leverage the skills as symbolic actions using the forward model for long-horizon planning and subsequently execute the plan using the learned continuous-action control skills. The proposed algorithm learns skills and forward models that can be used to solve complex tasks which require both continuous control and long-horizon planning capabilities with high success rate. It compares favorably with other flat and hierarchical reinforcement learning baseline agents and is successfully demonstrated with a real robot.
Closing the Gap Between Directed Hopsets and Shortcut Sets

For an n-vertex directed graph $G = (V,E)$, a $\beta$-\emph{shortcut set} $H$ is a set of additional edges $H \subseteq V \times V$ such that $G \cup H$ has the same transitive closure as $G$, and for every pair $u,v \in V$, there is a $uv$-path in $G \cup H$ with at most $\beta$ edges. A natural generalization of shortcut sets to distances is a $(\beta,\epsilon)$-\emph{hopset} $H \subseteq V \times V$, where the requirement is that $H$ and $G \cup H$ have the same shortest-path distances, and for every $u,v \in V$, there is a $(1+\epsilon)$-approximate shortest path in $G \cup H$ with at most $\beta$ edges. There is a large literature on the tradeoff between the size of a shortcut set / hopset and the value of $\beta$. We highlight the most natural point on this tradeoff: what is the minimum value of $\beta$, such that for any graph $G$, there exists a $\beta$-shortcut set (or a $(\beta,\epsilon)$-hopset) with $O(n)$ edges? Not only is this a natural structural question in its own right, but shortcuts sets / hopsets form the core of many distributed, parallel, and dynamic algorithms for reachability / shortest paths. Until very recently the best known upper bound was a folklore construction showing $\beta = O(n^{1/2})$, but in a breakthrough result Kogan and Parter [SODA 2022] improve this to $\beta = \tilde{O}(n^{1/3})$ for shortcut sets and $\tilde{O}(n^{2/5})$ for hopsets. Our result is to close the gap between shortcut sets and hopsets. That is, we show that for any graph $G$ and any fixed $\epsilon$ there is a $(\tilde{O}(n^{1/3}),\epsilon)$ hopset with $O(n)$ edges. More generally, we achieve a smooth tradeoff between hopset size and $\beta$ which exactly matches the tradeoff of Kogan and Parter for shortcut sets (up to polylog factors). Using a very recent black-box reduction of Kogan and Parter, our new hopset implies improved bounds for approximate distance preservers.
SDFEst: Categorical Pose and Shape Estimation of Objects From RGB-D Using Signed Distance Fields

Rich geometric understanding of the world is an important component of many robotic applications such as planning and manipulation. In this paper, we present a modular pipeline for pose and shape estimation of objects from RGB-D images given their category. The core of our method is a generative shape model, which we integrate with a novel initialization network and a differentiable renderer to enable 6D pose and shape estimation from a single or multiple views. We investigate the use of discretized signed distance fields as an efficient shape representation for fast analysis-by-synthesis optimization. Our modular framework enables multi-view optimization and extensibility. We demonstrate the benefits of our approach over state-of-the-art methods in several experiments on both synthetic and real data. We open-source our approach at https://github.com/roym899/sdfest.
Thermal Conductivity for p–(Bi, Sb)2Te3 Films of Topological Insulators

In this study, we investigated the temperature dependencies of the total, crystal lattice, and electronic thermal conductivities in films of topological insulators p–Bi0.5Sb1. 5Te3 and p–Bi2Te3 formed by discrete and thermal evaporation methods. The largest decrease in the lattice thermal conductivity because of the scattering of long-wavelength phonons on the grain interfaces was observed in the films of the solid-solution p–Bi0.5Sb1. 5Te3 deposited by discrete evaporation on the amorphous substrates of polyimide without thermal treatment. It was shown that in the p–Bi0.5Sb1. 5Te3 films with low thermal conductivity, the energy dependence of the relaxation time is enhanced, which is specific to the topological insulators. The electronic thermal conductivity was determined by taking into account the effective scattering parameter in the relaxation time approximation versus energy in the Lorentz number calculations. A correlation was established between the thermal conductivity and the peculiarities of the morphology of the interlayer surface (0001) in the studied films. Additionally, the total κ and the lattice κL thermal conductivities decrease, while the number of grains and the roughness of the surface (0001) increase in unannealed films compared to annealed ones. It was demonstrated that increasing the thermoelectric figure of merit ZT in the p–Bi0.5Sb1. 5Te3 films formed by discrete evaporation on a polyimide substrate is determined by an increase in the effective scattering parameter in topological insulators due to enhancement in the energy dependence of the relaxation time.
A Probabilistic Model Of Interaction Dynamics for Dyadic Face-to-Face Settings

—Natural conversations between humans often involve a large number of non-verbal nuanced expressions, displayed at key times throughout the conversation. Understanding and being able to model these complex interactions is essential for creating realistic human-agent communication, whether in the virtual or physical world. As social robots and intelligent avatars emerge in popularity and utility, being able to realistically model and generate these dynamic expressions throughout conversations is critical. We develop a probabilistic model to capture the interaction dynamics between pairs of participants in a face-to-face setting, allowing for the encoding of synchronous expressions between the interlocutors. This interaction encoding is then used to inﬂuence the generation when predicting one agent’s future dynamics, conditioned on the other’s current dynamics. FLAME features are extracted from videos containing natural conversations between subjects to train our interaction model. We successfully assess the efﬁcacy of our proposed model via quantitative metrics and qualitative metrics, and show that it successfully captures the dynamics of a pair of interacting dyads. We also test the model with a never-before-seen parent-infant dataset comprising of two different modes of communication between the dyads, and show that our model successfully delineates between the modes, based on their interacting dynamics.
Non-Convex Bilevel Games with Critical Point Selection Maps

Bilevel optimization problems involve two nested objectives, where an upper-level objective depends on a solution to a lower-level problem. When the latter is non-convex, multiple critical points may be present, leading to an ambiguous definition of the problem. In this paper, we introduce a key ingredient for resolving this ambiguity through the concept of a selection map which allows one to choose a particular solution to the lower-level problem. Using such maps, we define a class of hierarchical games between two agents that resolve the ambiguity in bilevel problems. This new class of games requires introducing new analytical tools in Morse theory to extend implicit differentiation, a technique used in bilevel optimization resulting from the implicit function theorem. In particular, we establish the validity of such a method even when the latter theorem is inapplicable due to degenerate critical points. Finally, we show that algorithms for solving bilevel problems based on unrolled optimization solve these games up to approximation errors due to finite computational power. A simple correction to these algorithms is then proposed for removing these errors.
Quasilinear rough evolution equations

We investigate the abstract Cauchy problem for a quasilinear parabolic equation in a Banach space of the form du t − L t ( u t ) u t dt = N t ( u t ) dt + F ( u t ) · d X t , where X is a γ -Hölder rough path for γ ∈ (1 / 3 , 1 / 2) . We explore the mild formulation that combines functional analysis techniques and controlled rough paths theory which entail the local well-posedness of such equations. We apply our results to the stochastic Landau-Lifshitz-Gilbert and Shigesada-Kawasaki-Teramoto equation. In this framework we obtain a random dynamical system associated to the Landau-Lifshitz-Gilbert equation.
D ec 2 01 9 Ott-Antonsen ansatz is the only admissible truncation of a circular cumulant series

The cumulant representation is common in classical statistical physics for variables on the real line and the issue of closures of cumulant expansions is well elaborated. The case of phase variables significantly differs from the case of linear ones; the relevant order parameters are the KuramotoDaido ones but not the conventional moments. One can formally introduce ‘circular’ cumulants for Kuramoto-Daido order parameters, similar to the conventional cumulants for moments. The circular cumulant expansions allow to advance beyond the Ott-Antonsen theory and consider populations of real oscillators. First, we show that truncation of circular cumulant expansions, except for the Ott-Antonsen case, is forbidden. Second, we compare this situation to the case of the Gaussian distribution of a linear variable, where the second cumulant is nonzero and all the higher cumulants are zero, and elucidate why keeping up to the second cumulant is admissible for a linear variable, but forbidden for circular cumulants. Third, we discuss the implication of this truncation issue to populations of quadratic integrate-and-fire neurons [E. Montbrió, D. Pazó, A. Roxin, Phys. Rev. X 5, 021028 (2015)], where within the framework of macroscopic description, the firing rate diverges for any finite truncation of the cumulant series, and discuss how one should handle these situations. Fourth, we consider the cumulant-based low-dimensional reductions for macroscopic population dynamics in the context of this truncation issue. These reductions are applicable, where the cumulant series exponentially decay with the cumulant order, i.e., they form a geometric progression hierarchy. Fifth, we demonstrate the formation of this hierarchy for generic distributions on the circle and experimental data for coupled biological and electrochemical oscillators. Our main conclusion for applications is that, if the first and second circular cumulants are nonzero, there must be infinitely many nonzero higher cumulants. However, these higher cumulants can be small, in which case one can construct approximate equations for the dynamics of a finite number of leading cumulants.
Don't Start From Scratch: Leveraging Prior Data to Automate Robotic Reinforcement Learning

Reinforcement learning (RL) algorithms hold the promise of enabling autonomous skill acquisition for robotic systems. However, in practice, real-world robotic RL typically requires time consuming data collection and frequent human intervention to reset the environment. Moreover, robotic policies learned with RL often fail when deployed beyond the carefully controlled setting in which they were learned. In this work, we study how these challenges can all be tackled by effective utilization of diverse offline datasets collected from previously seen tasks. When faced with a new task, our system adapts previously learned skills to quickly learn to both perform the new task and return the environment to an initial state, effectively performing its own environment reset. Our empirical results demonstrate that incorporating prior data into robotic reinforcement learning enables autonomous learning, substantially improves sample-efficiency of learning, and enables better generalization. Project website: https://sites.google. com/view/ariel-berkeley/
Regularization by noise for rough differential equations driven by Gaussian rough paths

We consider the rough differential equation with drift driven by a Gaussian geometric rough path. Under natural conditions on the rough path, namely non-determinism, and uniform ellipticity conditions on the diffusion coefficient, we prove path-by-path well-posedness of the equation for poorly regular drifts. In the case of the fractional Brownian motion $B^H$ for $H>\frac14$, we prove that the drift may be taken to be $\kappa>0$ H\"older continuous and bounded for $\kappa>\frac32 - \frac1{2H}$. A flow transform of the equation and Malliavin calculus for Gaussian rough paths are used to achieve such a result.
Physical Attack on Monocular Depth Estimation with Optimal Adversarial Patches

Deep learning has substantially boosted the performance of Monocular Depth Estimation (MDE), a critical component in fully vision-based autonomous driving (AD) systems (e.g., Tesla and Toyota). In this work, we develop an attack against learning-based MDE. In particular, we use an optimization-based method to systematically generate stealthy physical-object-oriented adversarial patches to attack depth estimation. We balance the stealth and effectiveness of our attack with object-oriented adversarial design, sensitive region localization, and natural style camouflage. Using real-world driving scenarios, we evaluate our attack on concurrent MDE models and a representative downstream task for AD (i.e., 3D object detection). Experimental results show that our method can generate stealthy, effective, and robust adversarial patches for different target objects and models and achieves more than 6 meters mean depth estimation error and 93% attack success rate (ASR) in object detection with a patch of 1/9 of the vehicle's rear area. Field tests on three different driving routes with a real vehicle indicate that we cause over 6 meters mean depth estimation error and reduce the object detection rate from 90.70% to 5.16% in continuous video frames.
Not Just Skipping: Understanding the Effect of Sponsored Content on Users' Decision-Making in Online Health Search

Advertisements (ads) are an innate part of search engine business models. To promote sales, advertisers are willing to pay search engines to promote their content to a prominent position in the search result page (SERP). This raises concerns about the search engine manipulation effect (SEME): the opinions of users can be influenced by the way search results are presented In this work, we investigate the connection between SEME and sponsored content in the health domain. We conduct a series of user studies in which participants need to evaluate the effectiveness of different non-prescription natural remedies for various medical conditions. We present participants SERPs with different intentionally created biases towards certain viewpoints, with or without sponsored content, and ask them to evaluate the effectiveness of the treatment solely based on the information presented to them. We investigate two types of sponsored content: 1). Direct marketing ads that directly market the product without expressing an opinion about its effectiveness; and 2). Indirect marketing ads that explicitly advocate the product's effectiveness on the condition in the query. Our results reveal a significant difference between the influence on users from these two types of ads. Though users mostly skip direct marketing ads, they do sometimes tilt users' decision-making. Indirect marketing ads affect both the users' examination behavior and their perception of the treatment's effectiveness. We further discover that the contrast between the indirect marketing ads and the viewpoint presented in the organic search results plays an important role in users' decision-making. When the contrast is high, users exhibit a strong preference towards a negative viewpoint, and when the contrast is low or none, users exhibit a preference toward a more positive viewpoint.
Partial Resampling of Imbalanced Data

Imbalanced data is a frequently encountered problem in machine learning. Despite a vast amount of literature on sampling techniques for imbalanced data, there is a limited number of studies that address the issue of the optimal sampling ratio. In this paper, we attempt to fill the gap in the literature by conducting a large scale study of the effects of sampling ratio on classification accuracy. We consider 10 popular sampling methods and evaluate their performance over a range of ratios based on 20 datasets. The results of the numerical experiments suggest that the optimal sampling ratio is between 0.7 and 0.8 albeit the exact ratio varies depending on the dataset. Furthermore, we find that while factors such the original imbalance ratio or the number of features do not play a discernible role in determining the optimal ratio, the number of samples in the dataset may have a tangible effect.
Efficient Stackelberg Strategies for Finitely Repeated Games

We study Stackelberg equilibria in finitely repeated games, where the leader commits to a strategy that picks actions in each round and can be adaptive to the history of play (i.e. they commit to an algorithm). In particular, we study static repeated games with no discounting. We give efficient algorithms for finding approximate Stackelberg equilibria in this setting, along with rates of convergence depending on the time horizon $T$. In many cases, these algorithms allow the leader to do much better on average than they can in the single-round Stackelberg. We give two algorithms, one computing strategies with an optimal $\frac{1}{T}$ rate at the expense of an exponential dependence on the number of actions, and another (randomized) approach computing strategies with no dependence on the number of actions but a worse dependence on $T$ of $\frac{1}{T^{0.25}}$. Both algorithms build upon a linear program to produce simple automata leader strategies and induce corresponding automata best-responses for the follower. We complement these results by showing that approximating the Stackelberg value in three-player finite-horizon repeated games is a computationally hard problem via a reduction from balanced vertex cover.
Epi-constructivism: Decidable sets of computable numbers as foundational objects for mathematics

It is well known that the R, the set of real numbers, is an abstract set, where almost all its elements cannot be described in any finite language. We investigate possible approaches to what might be called an epi-constructionist approach to mathematics. While most constructive mathematics is concerned with constructive proofs, the agenda here is that the objects that we study, specifically the class of numbers that we study, should be an enumerable set of finite symbol strings. These might also be called decidable constructive real numbers, that is our class of numbers should be a computable sets of explicitly represented computable numbers. There have been various investigations of the computable numbers going back to Turing. Most are however not expressed constructively, rather computable is a property assigned to some of the abstract real numbers. Other definitions define constructive real numbers without reference to the abstract R, but the construction is undecidable, i.e., we cannot determine if a given construction represents a computable real number or not. For example, we may define a real as a computable convergent sequence of rationals, but cannot in general decide if a given computable sequence is convergent. This paper explores several specific classes of decidable constructive real numbers that could form foundational objects for what we might call an epi-constructionist mathematics.