Miracle-dz/UniFAR-FTUs huggingface dataset:
Capacity for Electromagnetic Information Theory

Traditional channel capacity based on onedimensional time domain mismatches the four-dimensional electromagnetic fields, thus it cannot fully exploit the information in the spatial dimensions. Therefore, electromagnetic information theory based on the four-dimensional electromagnetic fields becomes necessary to reveal the fundamental theoretical capacity bound of the communication systems. Existing works on electromagnetic information theory focused on deterministic signals and degrees of freedom, which were unable to derive the capacity due to the lack of entropy definition. In this paper, we first model the communication between two continuous regions by random field. Then, we analyze a special case with parallel linear source and destination to derive the capacity bound. Specifically, for parallel infinite-length source and destination, we analyze the mutual information by spatial spectral density and derive the best current distribution on the source to achieve the maximum mutual information, i.e., the capacity. Then, we analyze the scenario with infinite-length source and finite-length destination. We use Mercer expansion to derive the mutual information between the source and the destination. Finally, for a practical model with finite-length source and destination, we analyze its Mercer expansion and reveal its connection with the infinitelength case. The capacity we analyzed reveals the theoretical limit of the communication rate between two continuous regions.
A Novel 1D State Space for Efficient Music Rhythmic Analysis

Inferring music time structures has a broad range of applications in music production, processing and analysis. Scholars have proposed various methods to analyze different aspects of time structures, such as beat, downbeat, tempo and meter. Many state-of-the-art (SOFA) methods, however, are computationally expensive. This makes them inapplicable in real-world industrial settings where the scale of the music collections can be millions. This paper proposes a new state space and a semi-Markov model for music time structure analysis. The proposed approach turns the commonly used 2D state spaces into a 1D model through a jump-back reward strategy. It reduces the state spaces size drastically. We then utilize the proposed method for causal, joint beat, downbeat, tempo, and meter tracking, and compare it against several previous methods. The proposed method delivers similar performance with the SOFA joint causal models with a much smaller state space and a more than 30 times speedup.
Can we learn gradients by Hamiltonian Neural Networks?

In this work, we propose a meta-learner based on ODE neural networks that learns gradients. This approach makes the optimizer is more flexible inducing an automatic inductive bias to the given task. Using the simplest Hamiltonian Neural Network we demonstrate that our method outperforms a meta-learner based on LSTM for an artificial task and the MNIST dataset with ReLU activations in the optimizee. Furthermore, it also surpasses the classic optimization methods for the artificial task and achieves comparable results for MNIST.
Effects of the Symmetries and Related Orders to the Thermalization of Many-Body Localized System

In this paper, we discuss the effects of the symmetries and related topological orders to the thermalization of many-body localized system. We consider the onedimensional fermion chain system with open boundary condition, whose boundaries are characterized by Sachdev-Ye-Kitaev (SYK) intercation. Just like in the SYK model and the tendor models, there are many-body quantum chaos in out-of-timeordered correlation when the system is being thermalized by the interactions (usually nonuniform and being randomly distributed), and satisfies the eigenstate thermalization hypothesis (ETH). While the continuous or discrete symmetries usually protect the related topological orders against the thermalization, which may lead to the localization of quantum states and generate large degeneracy. We discuss these effects in terms of the fermionic or spin languages. In many-body localized phase, a large number of degenerate ETH-violated states can be found in both the frustration-free AKLT model or the integrable biquadratic (Wishart) SYK model. The quantum scars appear when such degenerate states are embeded into an ETH-satisfying spectrum of the Hilbert space enlarged by a much larger number of bosonic flavors (e.g., SU(M) multiplets degeneracy). Usually, the emergence of quantum chaos require large limits of boson flavorM and the number of coupled (undegenerate) states (N ; which related to ZN symmetry). Further, the boson (or excitations) flavor number M can often to related to the fermion number N through the duality transformations, in which case the ZM symmetry is possible to generted by SU(M) model and leads to asymptotic degeneracy in large-M limit.
Efficiently Modeling Long Sequences with Structured State Spaces

A central goal of sequence modeling is designing a single principled model that can address sequence data across a range of modalities and tasks, particularly on long-range dependencies. Although conventional models including RNNs, CNNs, and Transformers have specialized variants for capturing long dependencies, they still struggle to scale to very long sequences of $10000$ or more steps. A promising recent approach proposed modeling sequences by simulating the fundamental state space model (SSM) \( x'(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t) \), and showed that for appropriate choices of the state matrix \( A \), this system could handle long-range dependencies mathematically and empirically. However, this method has prohibitive computation and memory requirements, rendering it infeasible as a general sequence modeling solution. We propose the Structured State Space sequence model (S4) based on a new parameterization for the SSM, and show that it can be computed much more efficiently than prior approaches while preserving their theoretical strengths. Our technique involves conditioning \( A \) with a low-rank correction, allowing it to be diagonalized stably and reducing the SSM to the well-studied computation of a Cauchy kernel. S4 achieves strong empirical results across a diverse range of established benchmarks, including (i) 91\% accuracy on sequential CIFAR-10 with no data augmentation or auxiliary losses, on par with a larger 2-D ResNet, (ii) substantially closing the gap to Transformers on image and language modeling tasks, while performing generation $60\times$ faster (iii) SoTA on every task from the Long Range Arena benchmark, including solving the challenging Path-X task of length 16k that all prior work fails on, while being as efficient as all competitors.
FaceScape: 3D Facial Dataset and Benchmark for Single-View 3D Face Reconstruction

In this article, we present a large-scale detailed 3D face dataset, FaceScape, and the corresponding benchmark to evaluate single-view facial 3D reconstruction. By training on FaceScape data, a novel algorithm is proposed to predict elaborate riggable 3D face models from a single image input. FaceScape dataset releases 16,940 textured 3D faces, captured from 847 subjects and each with 20 specific expressions. The 3D models contain the pore-level facial geometry that is also processed to be topologically uniform. These fine 3D facial models can be represented as a 3D morphable model for coarse shapes and displacement maps for detailed geometry. Taking advantage of the large-scale and high-accuracy dataset, a novel algorithm is further proposed to learn the expression-specific dynamic details using a deep neural network. The learned relationship serves as the foundation of our 3D face prediction system from a single image input. Different from most previous methods, our predicted 3D models are riggable with highly detailed geometry under different expressions. We also use FaceScape data to generate the in-the-wild and in-the-lab benchmark to evaluate recent methods of single-view face reconstruction. The accuracy is reported and analyzed on the dimensions of camera pose and focal length, which provides a faithful and comprehensive evaluation and reveals new challenges. The unprecedented dataset, benchmark, and code have been released to the public for research purpose.
The Milky Way Revealed by Variable Stars. I. Sample Selection of RR Lyrae Stars and Evidence for Merger History

In order to study the Milky Way, RR Lyrae (RRL) variable stars identified by Gaia, ASAS-SN, and ZTF sky survey projects have been analyzed as tracers in this work. Photometric and spectroscopic information of 3417 RRLs including proper motions, radial velocity, and metallcity are obtained from observational data of Gaia, LAMOST, GALAH, APOGEE, and RAVE. Precise distances of RRLs with typical uncertainties less than 3% are derived by using a recent comprehensive period–luminosity–metallicity relation. Our results from kinematical and chemical analysis provide important clues for the assembly history of the Milky Way, especially for the Gaia–Sausage ancient merger. The kinematical and chemical trends found in this work are consistent with those of recent simulations that indicated that the Gaia–Sausage merger had a dual origin in the Galactic thick disk and halo. As recent similar works have found, the halo RRL sample in this work contains a subset of radially biased orbits besides a more isotropic component. This higher orbital anisotropy component amounts to β ≃ 0.8, and it contributes between 42% and 83% of the halo RRLs at 4 < R( kpc) < 20.
Symbolic Regression via Neural-Guided Genetic Programming Population Seeding

Symbolic regression is the process of identifying mathematical expressions that fit observed output from a black-box process. It is a discrete optimization problem generally believed to be NP-hard. Prior approaches to solving the problem include neural-guided search (e.g. using reinforcement learning) and genetic programming. In this work, we introduce a hybrid neural-guided/genetic programming approach to symbolic regression and other combinatorial optimization problems. We propose a neural-guided component used to seed the starting population of a random restart genetic programming component, gradually learning better starting populations. On a number of common benchmark tasks to recover underlying expressions from a dataset, our method recovers 65% more expressions than a recently published top-performing model using the same experimental setup. We demonstrate that running many genetic programming generations without interdependence on the neural-guided component performs better for symbolic regression than alternative formulations where the two are more strongly coupled. Finally, we introduce a new set of 22 symbolic regression benchmark problems with increased difficulty over existing benchmarks. Source code is provided at www.github. com/brendenpetersen/deep-symbolic-optimization.
Gap at 1 for the percolation threshold of Cayley graphs

We prove that the set of possible values for the percolation threshold $p_c$ of Cayley graphs has a gap at 1 in the sense that there exists $\varepsilon_0>0$ such that for every Cayley graph $G$ one either has $p_c(G)=1$ or $p_c(G) \leq 1-\varepsilon_0$. The proof builds on the new approach of Duminil-Copin, Goswami, Raoufi, Severo&Yadin to the existence of phase transition using the Gaussian free field, combined with the finitary version of Gromov's theorem on the structure of groups of polynomial growth of Breuillard, Green&Tao.
Amphiphilic polypeptides with prolonged enzymatic stability for the preparation of self-assembled nanobiomaterials

Due to their excellent biocompatibility and biodegradability, polypeptides have emerged as versatile bio-inspired scaffolds for the preparation of artificial biomaterials. In order to create self-assembled polypeptide nanoparticles with enhanced stability towards enzymatic degradation, we synthesized a series of random and block polypeptides based on lysine and α-aminoisobutyric acid (Aib) by the ring-opening polymerization of N-carboxyanhydrides (ROP NCA) of the corresponding amino acids. A conformational analysis carried out by means of FT-IR absorption and CD spectroscopies revealed a noticeable difference between random and block copolymers. In turn, the spatial organization of the polypeptide chains induced the formation of nanostructures of different types. The block copolymers self-assembled in vesicle-like structures, whereas polypeptides with randomly distributed monomers formed micelles. In contrast with the polymers with only natural amino acids, all nanoparticles based on Aib/Lys polypeptides showed strong resistance to proteolytic cleavage. The cytotoxicity and the kinetics of the cellular uptake of the prepared nanostructures were also studied. The results obtained could not only contribute to the understanding of long Aib polypeptide folding and self-assembling, but also pave the way to the design of nanomaterials with finely tuned properties in the fields of drug delivery and tissue engineering.
Atomic semigroup rings and the ascending chain condition on principal ideals

An integral domain is called atomic if every nonzero nonunit element factors into irreducibles. On the other hand, an integral domain is said to satisfy the ascending chain condition on principal ideals (ACCP) if every ascending chain of principal ideals stabilizes. It was asserted by P. Cohn back in the sixties that every atomic domain satisfies the ACCP, but such an assertion was refuted by A. Grams in the seventies with a neat counterexample. Still, atomic domains without the ACCP are notoriously elusive, and just a few classes have been found since Grams’ first construction. In the first part of this paper, we generalize Grams’ construction to provide new classes of atomic domains without the ACCP. In the second part of this paper, we construct a new class of atomic semigroup rings without the ACCP.
Multi-Task Learning based Convolutional Models with Curriculum Learning for the Anisotropic Reynolds Stress Tensor in Turbulent Duct Flow

The Reynolds-averaged Navier-Stokes (RANS) equations require accurate modeling of the anisotropic Reynolds stress tensor. Traditional closure models, while sophisticated, often only apply to restricted flow configurations. Researchers have started using machine learning approaches to tackle this problem by developing more general closure models informed by data. In this work we build upon recent convolutional neural network architectures used for turbulence modeling and propose a multi-task learning-based fully convolutional neural network that is able to accurately predict the normalized anisotropic Reynolds stress tensor for turbulent duct flows. Furthermore, we also explore the application of curriculum learning to data-driven turbulence modeling.
Scalars are universal: Equivariant machine learning, structured like classical physics

There has been enormous progress in the last few years in designing neural networks that respect the fundamental symmetries and coordinate freedoms of physical law. Some of these frameworks make use of irreducible representations, some make use of high-order tensor objects, and some apply symmetry-enforcing constraints. Different physical laws obey different combinations of fundamental symmetries, but a large fraction (possibly all) of classical physics is equivariant to translation, rotation, reflection (parity), boost (relativity), and permutations. Here we show that it is simple to parameterize universally approximating polynomial functions that are equivariant under these symmetries, or under the Euclidean, Lorentz, and Poincar\'e groups, at any dimensionality $d$. The key observation is that nonlinear O($d$)-equivariant (and related-group-equivariant) functions can be universally expressed in terms of a lightweight collection of scalars -- scalar products and scalar contractions of the scalar, vector, and tensor inputs. We complement our theory with numerical examples that show that the scalar-based method is simple, efficient, and scalable.
Tactile Sim-to-Real Policy Transfer via Real-to-Sim Image Translation

Simulation has recently become key for deep reinforcement learning to safely and efficiently acquire general and complex control policies from visual and proprioceptive inputs. Tactile information is not usually considered despite its direct relation to environment interaction. In this work, we present a suite of simulated environments tailored towards tactile robotics and reinforcement learning. A simple and fast method of simulating optical tactile sensors is provided, where high-resolution contact geometry is represented as depth images. Proximal Policy Optimisation (PPO) is used to learn successful policies across all considered tasks. A data-driven approach enables translation of the current state of a real tactile sensor to corresponding simulated depth images. This policy is implemented within a real-time control loop on a physical robot to demonstrate zero-shot sim-to-real policy transfer on several physically-interactive tasks requiring a sense of touch.
Bandit Learning with Delayed Impact of Actions

We consider a stochastic multi-armed bandit (MAB) problem with delayed impact of actions. In our setting, actions taken in the past impact the arm rewards in the subsequent future. This delayed impact of actions is prevalent in the real world. For example, the capability to pay back a loan for people in a certain social group might depend on historically how frequently that group has been approved loan applications. If banks keep rejecting loan applications to people in a disadvantaged group, it could create a feedback loop and further damage the chance of getting loans for people in that group. In this paper, we formulate this delayed and long-term impact of actions within the context of multi-armed bandits. We generalize the bandit setting to encode the dependency of this"bias"due to the action history during learning. The goal is to maximize the collected utilities over time while taking into account the dynamics created by the delayed impacts of historical actions. We propose an algorithm that achieves a regret of $\tilde{\mathcal{O}}(KT^{2/3})$ and show a matching regret lower bound of $\Omega(KT^{2/3})$, where $K$ is the number of arms and $T$ is the learning horizon. Our results complement the bandit literature by adding techniques to deal with actions with long-term impacts and have implications in designing fair algorithms.
AUTOMATIC KAPPA WEIGHTING FOR INSTRUMENTAL VARIABLE MODELS OF COMPLIER TREATMENT EFFECTS

We propose debiased machine learning estimators for complier parameters, such as local average treatment effect, with high dimensional covariates. To do so, we characterize the doubly robust moment function for the entire class of complier parameters as the combination of Wald and κ weight formulations. We directly estimate the κ weights, rather than their components, in order to eliminate the numerically unstable step of inverting propensity scores of high dimensional covariates. We prove our estimator is balanced, consistent, asymptotically normal, and semiparametrically efficient, and use it to estimate the effect of 401(k) participation on the distribution of net financial assets.
Extensions of Veech groups I: A hyperbolic action

Given a lattice Veech group in the mapping class group of a closed surface S$S$ , this paper investigates the geometry of Γ$\Gamma$ , the associated π1S$\pi _1S$ ‐extension group. We prove that Γ$\Gamma$ is the fundamental group of a bundle with a singular Euclidean‐by‐hyperbolic geometry. Our main result is that collapsing “obvious” product regions of the universal cover produces an action of Γ$\Gamma$ on a hyperbolic space, retaining most of the geometry of Γ$\Gamma$ . This action is a key ingredient in the sequel where we show that Γ$\Gamma$ is hierarchically hyperbolic and quasi‐isometrically rigid.
Adjacency Constraint for Efficient Hierarchical Reinforcement Learning

Goal-conditioned Hierarchical Reinforcement Learning (HRL) is a promising approach for scaling up reinforcement learning (RL) techniques. However, it often suffers from training inefficiency as the action space of the high-level, i.e., the goal space, is large. Searching in a large goal space poses difficulty for both high-level subgoal generation and low-level policy learning. In this article, we show that this problem can be effectively alleviated by restricting the high-level action space from the whole goal space to a <inline-formula><tex-math notation="LaTeX">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="zhang-ieq1-3192418.gif"/></alternatives></inline-formula>-step adjacent region of the current state using an adjacency constraint. We theoretically prove that in a deterministic Markov Decision Process (MDP), the proposed adjacency constraint preserves the optimal hierarchical policy, while in a stochastic MDP the adjacency constraint induces a bounded state-value suboptimality determined by the MDP's transition structure. We further show that this constraint can be practically implemented by training an adjacency network that can discriminate between adjacent and non-adjacent subgoals. Experimental results on discrete and continuous control tasks including challenging simulated robot locomotion and manipulation tasks show that incorporating the adjacency constraint significantly boosts the performance of state-of-the-art goal-conditioned HRL approaches.
Generative Occupancy Fields for 3D Surface-Aware Image Synthesis

The advent of generative radiance fields has significantly promoted the development of 3D-aware image synthesis. The cumulative rendering process in radiance fields makes training these generative models much easier since gradients are distributed over the entire volume, but leads to diffused object surfaces. In the meantime, compared to radiance fields occupancy representations could inherently ensure deterministic surfaces. However, if we directly apply occupancy representations to generative models, during training they will only receive sparse gradients located on object surfaces and eventually suffer from the convergence problem. In this paper, we propose Generative Occupancy Fields (GOF), a novel model based on generative radiance fields that can learn compact object surfaces without impeding its training convergence. The key insight of GOF is a dedicated transition from the cumulative rendering in radiance fields to rendering with only the surface points as the learned surface gets more and more accurate. In this way, GOF combines the merits of two representations in a unified framework. In practice, the training-time transition of start from radiance fields and march to occupancy representations is achieved in GOF by gradually shrinking the sampling region in its rendering process from the entire volume to a minimal neighboring region around the surface. Through comprehensive experiments on multiple datasets, we demonstrate that GOF can synthesize high-quality images with 3D consistency and simultaneously learn compact and smooth object surfaces. Code, models, and demo videos are available at https://sheldontsui.github. io/projects/GOF