Miracle-dz/UniFAR-FTUs huggingface dataset:
On the one dimensional cubic NLS in a critical space

In this note we study the initial value problem in a critical space for the one dimensional Schrödinger equation with a cubic non-linearity and under some smallness conditions. In particular the initial data is given by a sequence of Dirac deltas with different amplitudes but equispaced. This choice is motivated by a related geometrical problem; the one describing the flow of curves in three dimensions moving in the direction of the binormal with a velocity that is given by the curvature.
The MineRL BASALT Competition on Learning from Human Feedback

The last decade has seen a significant increase of interest in deep learning research, with many public successes that have demonstrated its potential. As such, these systems are now being incorporated into commercial products. With this comes an additional challenge: how can we build AI systems that solve tasks where there is not a crisp, well-defined specification? While multiple solutions have been proposed, in this competition we focus on one in particular: learning from human feedback. Rather than training AI systems using a predefined reward function or using a labeled dataset with a predefined set of categories, we instead train the AI system using a learning signal derived from some form of human feedback, which can evolve over time as the understanding of the task changes, or as the capabilities of the AI system improve. The MineRL BASALT competition aims to spur forward research on this important class of techniques. We design a suite of four tasks in Minecraft for which we expect it will be hard to write down hardcoded reward functions. These tasks are defined by a paragraph of natural language: for example,"create a waterfall and take a scenic picture of it", with additional clarifying details. Participants must train a separate agent for each task, using any method they want. Agents are then evaluated by humans who have read the task description. To help participants get started, we provide a dataset of human demonstrations on each of the four tasks, as well as an imitation learning baseline that leverages these demonstrations. Our hope is that this competition will improve our ability to build AI systems that do what their designers intend them to do, even when the intent cannot be easily formalized. Besides allowing AI to solve more tasks, this can also enable more effective regulation of AI systems, as well as making progress on the value alignment problem.
Imaging Dynamics Beneath Turbid Media via Parallelized Single‐Photon Detection

Noninvasive optical imaging through dynamic scattering media has numerous important biomedical applications but still remains a challenging task. While standard diffuse imaging methods measure optical absorption or fluorescent emission, it is also well‐established that the temporal correlation of scattered coherent light diffuses through tissue much like optical intensity. Few works to date, however, have aimed to experimentally measure and process such temporal correlation data to demonstrate deep‐tissue video reconstruction of decorrelation dynamics. In this work, a single‐photon avalanche diode array camera is utilized to simultaneously monitor the temporal dynamics of speckle fluctuations at the single‐photon level from 12 different phantom tissue surface locations delivered via a customized fiber bundle array. Then a deep neural network is applied to convert the acquired single‐photon measurements into video of scattering dynamics beneath rapidly decorrelating tissue phantoms. The ability to reconstruct images of transient (0.1–0.4 s) dynamic events occurring up to 8 mm beneath a decorrelating tissue phantom with millimeter‐scale resolution is demonstrated, and it is highlighted how the model can flexibly extend to monitor flow speed within buried phantom vessels.
Ionisation potentials and electron affinity of oganesson with relativistic coupled cluster method

We present high accuracy relativistic coupled cluster calculations of the first and second ionisation potentials and the electron affinity of the heaviest element in the Periodic Table, Og. The results were extrapolated to the basis set limit and augmented with the higher order excitations (up to perturbative quadruples), the Breit contribution, and the QED self energy and vacuum polarisation corrections. We have performed an extensive investigation of the effect of the various computational parameters on the calculated properties, which allowed us to assign realistic uncertainties on our predictions. Similar study on the lighter homologue of Og, Rn, yields excellent agreement with experiment for the first ionisation potential and a reliable prediction for the second ionisation potential.
The Hybrid Euler-Hadamard Product Formula for Dirichlet $L$-functions in $\mathbb{F}_q [T]$

For Dirichlet L-functions in Fq[T ] we obtain a hybrid Euler-Hadamard product formula. We make a splitting conjecture, namely that the 2k-th moment of the Dirichlet L-functions at 1 2 , averaged over primitive characters of modulus R, is asymptotic to (as degR −→ ∞) the 2k-th moment of the Euler product multiplied by the 2k-th moment of the Hadamard product. We explicitly obtain the main term of the 2k-th moment of the Euler product, and we conjecture via random matrix theory the main term of the 2k-th moment of the Hadamard product. With the splitting conjecture, this directly leads to a conjecture for the 2k-th moment of Dirichlet Lfunctions. Finally, we lend support for the splitting conjecture by proving the cases k = 1, 2. This work is the function field analogue of the work of Bui and Keating. A notable difference in the function field setting is that the Euler-Hadamard product formula is exact, in that there is no error term.
Stochastic Algorithms for Self-consistent Calculations of Electronic Structures

The convergence property of a stochastic algorithm for the self-consistent field (SCF) calculations of electron structures is studied. The algorithm is formulated by rewriting the electron charges as a trace/diagonal of a matrix function, which is subsequently expressed as a statistical average. The function is further approximated by using a Krylov subspace approximation. As a result, each SCF iteration only samples one random vector without having to compute all the orbitals. We consider the common practice of SCF iterations with damping and mixing. We prove with appropriate assumptions that the iterations converge in the mean-square sense, when the stochastic error has an almost sure bound. We also consider the scenario when such an assumption is weakened to a second moment condition, and prove the convergence in probability.
Speech Synthesis from Text and Ultrasound Tongue Image-based Articulatory Input

Articulatory information has been shown to be effective in improving the performance of HMM-based and DNN-based text-to-speech synthesis. Speech synthesis research focuses traditionally on text-to-speech conversion, when the input is text or an estimated linguistic representation, and the target is synthesized speech. However, a research field that has risen in the last decade is articulation-to-speech synthesis (with a target application of a Silent Speech Interface, SSI), when the goal is to synthesize speech from some representation of the movement of the articulatory organs. In this paper, we extend traditional (vocoder-based) DNN-TTS with articulatory input, estimated from ultrasound tongue images. We compare text-only, ultrasound-only, and combined inputs. Using data from eight speakers, we show that that the combined text and articulatory input can have advantages in limited-data scenarios, namely, it may increase the naturalness of synthesized speech compared to single text input. Besides, we analyze the ultrasound tongue recordings of several speakers, and show that misalignments in the ultrasound transducer positioning can have a negative effect on the final synthesis performance.
Wigner function with correlation damping.

We examine the effect of the decoherence-induced reduction of correlation length on a one-dimensional scattering problem by solving numerically the evolution equation for the Wigner function with decoherence proposed by Barletti et al. [J. Comput. Theor. Transp. 47, 209 (2018)2332-430910.1080/23324309.2018. 1520732]. The numerical solution is achieved by the splitting-scheme algorithm, suitably modified to include the decoherence term. Three cases are examined, corresponding to a reflection-dominated regime, a transmission-dominated regime, and an intermediate one. The dynamic evolution of the Wigner function is followed until the separation process of the reflected and of the transmitted packets is complete and it is observed for three different values of the correlation length. The outcomes show a broadening and flattening of the Wigner function which becomes progressively more pronounced as the correlation length is decreased. This results in a reduced reflection at low energies and in a reduced transmission at high energies.
Parking on Cayley trees&Frozen Erd\"os-R\'enyi

Consider a uniform rooted Cayley tree Tn with n vertices and let m cars arrive sequentially, independently, and uniformly on its vertices. Each car tries to park on its arrival node, and if the spot is already occupied, it drives towards the root of the tree and parks as soon as possible. Lackner & Panholzer [56] established a phase transition for this process when m ≈ 2 . In this work, we couple this model with a variant of the classical Erdős–Rényi random graph process. This enables us to describe the phase transition for the size of the components of parked cars using a modification of the multiplicative coalescent which we name the frozen multiplicative coalescent. The geometry of critical parked clusters is also studied. Those trees are very different from Bienaymé–Galton–Watson trees and should converge towards the growth-fragmentation trees canonically associated to the 3/2-stable process that already appeared in the study of random planar maps. Figure 1: First line: Parking on a random Cayley tree with 10000 vertices when resp. 4000, 5000 and 6000 cars have arrived (color and thickness indicate the flux of cars along the edges). Second line: The frozen Erdős–Rényi process at stages 400, 500, 600, 700 and 800 on a graph with 1000 vertices. ∗Université Paris-Saclay. E-mail: alice.contat@universite-paris-saclay.fr †Université Paris-Saclay and Institut Universitaire de France. E-mail: nicolas.curien@gmail.com 1 ar X iv :2 10 7. 02 11 6v 1 [ m at h. PR ] 5 J ul 2 02 1
Row‐sensing templates: A generic 3D sensor‐based approach to robot localization with respect to orchard row centerlines

Accurate robot localization relative to orchard row centerlines is essential for autonomous guidance where satellite signals are often obstructed by foliage. Existing sensor‐based approaches rely on various features extracted from images and point clouds. However, any selected features are not available consistently, because the visual and geometrical characteristics of orchard rows change drastically when tree types, growth stages, canopy management practices, seasons, and weather conditions change. In this study, we introduce a novel localization method that does not rely on features; instead, it relies on the concept of a row‐sensing template, which is the expected observation of a 3D sensor traveling in an orchard row, when the sensor is anywhere on the centerline and perfectly aligned with it. First, the template is built using a few measurements, provided that the sensor's true pose with respect to the centerline is available. Then, during navigation, the best pose estimate (and its confidence) is estimated by maximizing the match between the template and the sensed point cloud using particle‐filtering. The method can adapt to various orchards and conditions by rebuilding the template. Experiments were performed in a vineyard, and in an orchard in different seasons. Results showed that the lateral mean absolute error (MAE) was less than 3.6% of the row width, and the heading MAE was less than 1.72°. Localization was robust, as errors did not increase when less than 75% of measurement points were missing. The results indicate that template‐based localization can provide a generic approach for accurate and robust localization in real‐world orchards.
Advanced Turning Maneuver of a Many-Legged Robot Using Pitchfork Bifurcation

Legged robots have excellent terrestrial mobility for traversing diverse environments and, thus, have the potential to be deployed in a wide variety of scenarios. However, they are susceptible to falling and leg malfunction during locomotion. Although the use of a large number of legs can overcome these problems, it makes the body long and leads to many legs being constrained to contact with the ground to support the long body, which impedes maneuverability. To improve the locomotion maneuverability of such robots, this study focuses on dynamic instability, which induces rapid and large movement changes, and uses a 12-legged robot with a flexible body axis. Our previous work found that the straight walk of the robot becomes unstable through a Hopf bifurcation when the body-axis flexibility is changed, which induces body undulations. Furthermore, we developed a simple controller based on the Hopf bifurcation and showed that the instability facilitates the turning of the robot. In this study, we newly found that the straight walk becomes unstable through a pitchfork bifurcation when the body-axis flexibility is changed in a way different from that in our previous work. In addition, the pitchfork bifurcation induces a transition into a curved walk, whose curvature can be controlled by the body-axis flexibility. We developed a simple controller based on the pitchfork bifurcation characteristics and demonstrated that the robot can perform a turning maneuver superior to that with the previous controller. This study provides a novel design principle for maneuverable locomotion of many-legged robots using intrinsic dynamic properties.
Here’s What I’ve Learned: Asking Questions that Reveal Reward Learning

Robots can learn from humans by asking questions. In these questions, the robot demonstrates a few different behaviors and asks the human for their favorite. But how should robots choose which questions to ask? Today’s robots optimize for informative questions that actively probe the human’s preferences as efficiently as possible. But while informative questions make sense from the robot’s perspective, human onlookers may find them arbitrary and misleading. For example, consider an assistive robot learning to put away the dishes. Based on your answers to previous questions this robot knows where it should stack each dish; however, the robot is unsure about right height to carry these dishes. A robot optimizing only for informative questions focuses purely on this height: it shows trajectories that carry the plates near or far from the table, regardless of whether or not they stack the dishes correctly. As a result, when we see this question, we mistakenly think that the robot is still confused about where to stack the dishes! In this article, we formalize active preference-based learning from the human’s perspective. We hypothesize that—from the human’s point-of-view —the robot’s questions reveal what the robot has and has not learned. Our insight enables robots to use questions to make their learning process transparent to the human operator. We develop and test a model that robots can leverage to relate the questions they ask to the information these questions reveal. We then introduce a tradeoff between informative and revealing questions that considers both human and robot perspectives: a robot that optimizes for this tradeoff actively gathers information from the human while simultaneously keeping the human up to date with what it has learned. We evaluate our approach across simulations, online surveys, and in-person user studies. We find that robots, which consider the human’s point of view learn just as quickly as state-of-the-art baselines while also communicating what they have learned to the human operator. Videos of our user studies and results are available here: https://youtu.be/tC6y_jHN7Vw.
BAGUA: Scaling up Distributed Learning with System Relaxations

Recent years have witnessed a growing list of systems for distributed data-parallel training. Existing systems largely fit into two paradigms, i.e., parameter server and MPI-style collective operations. On the algorithmic side, researchers have proposed a wide range of techniques to lower the communication via "system relaxations": quantization, decentralization, and communication delay. However, most, if not all, existing systems only rely on standard synchronous and asynchronous stochastic gradient (SG) based optimization, therefore, cannot take advantage of all possible optimizations that the machine learning community has been developing recently. Given this emerging gap between the current landscapes of systems and theory, we build Bagua, a MPI-style communication library, providing a collection of primitives, that is both flexible and modular to support state-of-the-art system relaxation techniques of distributed training. Powered by this design, Bagua has a great ability to implement and extend various state-of-the-art distributed learning algorithms. In a production cluster with up to 16 machines (128 GPUs), Bagua can outperform PyTorch-DDP, Horovod and BytePS in the end-to-end training time by a significant margin (up to 2X) across a diverse range of tasks. Moreover, we conduct a rigorous tradeoff exploration showing that different algorithms and system relaxations achieve the best performance over different network conditions.
Linear Probing Revisited: Tombstones Mark the Death of Primary Clustering

First introduced in 1954, linear probing is one of the oldest data structures in computer science, and due to its unrivaled data locality, it continues to be one of the fastest hash tables in practice. It is widely believed and taught, however, that linear probing should never be used at high load factors; this is because primary-clustering effects cause insertions at load factor $1 - 1 /x$ to take expected time $\Theta(x^2)$ (rather than the ideal $\Theta(x)$). The dangers of primary clustering, first discovered by Knuth in 1963, have been taught to generations of computer scientists, and have influenced the design of some of many widely used hash tables. We show that primary clustering is not a foregone conclusion. We demonstrate that small design decisions in how deletions are implemented have dramatic effects on the asymptotic performance of insertions, so that, even if a hash table operates continuously at a load factor $1 - \Theta(1/x)$, the expected amortized cost per operation is $\tilde{O}(x)$. This is because tombstones created by deletions actually cause an anti-clustering effect that combats primary clustering. We also present a new variant of linear probing (which we call graveyard hashing) that completely eliminates primary clustering on \emph{any} sequence of operations: if, when an operation is performed, the current load factor is $1 - 1/x$ for some $x$, then the expected cost of the operation is $O(x)$. One corollary is that, in the external-memory model with a data blocks of size $B$, graveyard hashing offers the following remarkable guarantee: at any load factor $1 - 1/x$ satisfying $x = o(B)$, graveyard hashing achieves $1 + o(1)$ expected block transfers per operation. Past external-memory hash tables have only been able to offer a $1 + o(1)$ guarantee when the block size $B$ is at least $\Omega(x^2)$.
Finite step Rigidity of Hitchin representations and special Margulis-Smilga spacetimes

In this article we use the “escape from subvarieties lemma” introduced by Eskin–Mozes–Oh to prove finite step rigidity results for the Jordan-Lyapunov projection spectra of Hitchin representations and the Margulis-Smilga invariant spectra of some special Margulis-Smilga spacetimes. In the process, we also prove a similar finite step rigidity result for the Cartan spectra of representations of a finitely generated group inside a connected semisimple real algebraic Lie group with trivial center.
Multi-objective congestion control

Decades of research on Internet congestion control (CC) have produced a plethora of algorithms that optimize for different performance objectives. Applications face the challenge of choosing the most suitable algorithm based on their needs, and it takes tremendous efforts and expertise to customize CC algorithms when new demands emerge. In this paper, we explore a basic question: can we design a single CC algorithm to satisfy different objectives? We propose MOCC, the first multi-objective congestion control algorithm that attempts to address this question. The core of MOCC is a novel multi-objective reinforcement learning framework for CC to automatically learn the correlations between different application requirements and the corresponding optimal control policies. Under this framework, MOCC further applies transfer learning to transfer the knowledge from past experience to new applications, quickly adapting itself to a new objective even if it is unforeseen. We provide both user-space and kernel-space implementation of MOCC. Real-world Internet experiments and extensive simulations show that MOCC supports well multi-objective, competing or outperforming the best existing CC algorithms on each individual objectives, and quickly adapting to new application objectives in 288 seconds (14.2× faster than prior work) without compromising old ones.
Improve Agents without Retraining: Parallel Tree Search with Off-Policy Correction

Tree Search (TS) is crucial to some of the most influential successes in reinforcement learning. Here, we tackle two major challenges with TS that limit its usability: \textit{distribution shift} and \textit{scalability}. We first discover and analyze a counter-intuitive phenomenon: action selection through TS and a pre-trained value function often leads to lower performance compared to the original pre-trained agent, even when having access to the exact state and reward in future steps. We show this is due to a distribution shift to areas where value estimates are highly inaccurate and analyze this effect using Extreme Value theory. To overcome this problem, we introduce a novel off-policy correction term that accounts for the mismatch between the pre-trained value and its corresponding TS policy by penalizing under-sampled trajectories. We prove that our correction eliminates the above mismatch and bound the probability of sub-optimal action selection. Our correction significantly improves pre-trained Rainbow agents without any further training, often more than doubling their scores on Atari games. Next, we address the scalability issue given by the computational complexity of exhaustive TS that scales exponentially with the tree depth. We introduce Batch-BFS: a GPU breadth-first search that advances all nodes in each depth of the tree simultaneously. Batch-BFS reduces runtime by two orders of magnitude and, beyond inference, enables also training with TS of depths that were not feasible before. We train DQN agents from scratch using TS and show improvement in several Atari games compared to both the original DQN and the more advanced Rainbow. The code for BCTS can be found in \url{https://github.com/NVlabs/bcts}.