Miracle-dz/UniFAR-FTUs huggingface dataset:
An isoperimetric problem with two distinct solutions

In this paper we prove that among all convex domains of the plane with two axis of symmetry, the maximizer of the first non trivial Neumann eigenvalue $\mu_1$ with perimeter constraint is achieved by the square and the equilateral triangle. Part of the result follows from a new general bound on $\mu_1$ involving the minimal width over the area. Our main result partially answers to a question addressed in 2009 by R. S. Laugesen, I. Polterovich, and B. A. Siudeja.
Mechanistic forecasts of species responses to climate change: The promise of biophysical ecology

A core challenge in global change biology is to predict how species will respond to future environmental change and to manage these responses. To make such predictions and management actions robust to novel futures, we need to accurately characterize how organisms experience their environments and the biological mechanisms by which they respond. All organisms are thermodynamically connected to their environments through the exchange of heat and water at fine spatial and temporal scales and this exchange can be captured with biophysical models. Although mechanistic models based on biophysical ecology have a long history of development and application, their use in global change biology remains limited despite their enormous promise and increasingly accessible software. We contend that greater understanding and training in the theory and methods of biophysical ecology is vital to expand their application. Our review shows how biophysical models can be implemented to understand and predict climate change impacts on species' behavior, phenology, survival, distribution, and abundance. It also illustrates the types of outputs that can be generated, and the data inputs required for different implementations. Examples range from simple calculations of body temperature at a particular site and time, to more complex analyses of species' distribution limits based on projected energy and water balances, accounting for behavior and phenology. We outline challenges that currently limit the widespread application of biophysical models relating to data availability, training, and the lack of common software ecosystems. We also discuss progress and future developments that could allow these models to be applied to many species across large spatial extents and timeframes. Finally, we highlight how biophysical models are uniquely suited to solve global change biology problems that involve predicting and interpreting responses to environmental variability and extremes, multiple or shifting constraints, and novel abiotic or biotic environments.
Knitting Knots&the Framing Anomaly

We study the twisting fault emerging in circular knitting and its relation to the mathematical concepts of framing curves and the Gauss linking integral. We create three knitted bands with framing zero, one, and negative two, and use three different techniques to compute the framing using the Gauss linking integral. We also briefly mention the connection to in Chern-Simons gauge theory.
The electromagnetic vacuum field as an essential ingredient of the quantum-mechanical ontology

This paper provides elements in support of the random zero-point radiation ﬁeld ( zpf ) as an essential ontological ingredient needed to ex-plain distinctive properties of quantum-mechanical systems. We show that when an otherwise classical particle is connected to the zpf , a drastic, qualitative change in the dynamics takes place, leading eventually to the quantum dynamics. In particular, we demonstrate that in parallel with the evolution of the particle canonical variables into quantum operators satisfying the basic commutator [ˆ x, ˆ p ] = i ~ , also the ﬁeld canonical variables are transformed, giving rise to the corresponding creation and annihilation operators ˆ a † , ˆ a , satisfying (cid:2) ˆ a, ˆ a † (cid:3) = 1 . This allows for an explanation of quantum features such as quantum ﬂuctuations, stationary states and transitions, and establishes a natural contact with (nonrela-tivistic) quantum electrodynamics. Hilbert space, a mathematical structure—gives
L-GreCo: An Efficient and General Framework for Layerwise-Adaptive Gradient Compression

Data-parallel distributed training of deep neural networks (DNN) has gained very widespread adoption, but can still experience communication bottlenecks. To address this issue, entire families of compression mechanisms have been developed, including quantization, sparsification, and low-rank approximation, some of which are seeing significant practical adoption. Despite this progress, almost all known compression schemes apply compression uniformly across DNN layers, although layers are heterogeneous in terms of parameter count and their impact on model accuracy. In this work, we provide a general framework for adapting the degree of compression across the model's layers dynamically during training, improving the overall compression, while leading to substantial speedups, without sacrificing accuracy. Our framework, called L-GreCo, is based on an adaptive algorithm, which automatically picks the optimal compression parameters for model layers guaranteeing the best compression ratio while satisfying an error constraint. Extensive experiments over image classification and language modeling tasks shows that L-GreCo is effective across all existing families of compression methods, and achieves up to 2.5$\times$ training speedup and up to 5$\times$ compression improvement over efficient implementations of existing approaches, while recovering full accuracy. Moreover, L-GreCo is complementary to existing adaptive algorithms, improving their compression ratio by 50% and practical throughput by 66%.
A note on the equivalence between the conditional uncorrelation and the independence of random variables

It is well known that while the independence of random variables implies zero correlation, the opposite is not true. Namely, uncorrelated random variables are not necessarily independent. In this note we show that the implication could be reversed if we consider the localised version of the correlation coefficient. More specifically, we show that if random variables are conditionally (locally) uncorrelated for any quantile conditioning sets, then they are independent. For simplicity, we focus on the absolutely continuous case. Also, we illustrate potential usefulness of the stated result using two simple examples.
Symmetries, flat minima, and the conserved quantities of gradient flow

Empirical studies of the loss landscape of deep networks have revealed that many local minima are connected through low-loss valleys. Yet, little is known about the theoretical origin of such valleys. We present a general framework for finding continuous symmetries in the parameter space, which carve out low-loss valleys. Our framework uses equivariances of the activation functions and can be applied to different layer architectures. To generalize this framework to nonlinear neural networks, we introduce a novel set of nonlinear, data-dependent symmetries. These symmetries can transform a trained model such that it performs similarly on new samples, which allows ensemble building that improves robustness under certain adversarial attacks. We then show that conserved quantities associated with linear symmetries can be used to define coordinates along low-loss valleys. The conserved quantities help reveal that using common initialization methods, gradient flow only explores a small part of the global minimum. By relating conserved quantities to convergence rate and sharpness of the minimum, we provide insights on how initialization impacts convergence and generalizability.
Generate, Discriminate and Contrast: A Semi-Supervised Sentence Representation Learning Framework

Most sentence embedding techniques heavily rely on expensive human-annotated sentence pairs as the supervised signals. Despite the use of large-scale unlabeled data, the performance of unsupervised methods typically lags far behind that of the supervised counterparts in most downstream tasks. In this work, we propose a semi-supervised sentence embedding framework, GenSE, that effectively leverages large-scale unlabeled data. Our method include three parts: 1) Generate: A generator/discriminator model is jointly trained to synthesize sentence pairs from open-domain unlabeled corpus; 2) Discriminate: Noisy sentence pairs are filtered out by the discriminator to acquire high-quality positive and negative sentence pairs; 3) Contrast: A prompt-based contrastive approach is presented for sentence representation learning with both annotated and synthesized data. Comprehensive experiments show that GenSE achieves an average correlation score of 85.19 on the STS datasets and consistent performance improvement on four domain adaptation tasks, significantly surpassing the state-of-the-art methods and convincingly corroborating its effectiveness and generalization ability.
Edgeless-GNN: Unsupervised Representation Learning for Edgeless Nodes

We study the problem of embedding <italic>edgeless</italic> nodes such as users who newly enter the underlying network, while using graph neural networks (GNNs) widely studied for effective representation learning of graphs. Our study is motivated by the fact that GNNs cannot be straightforwardly adopted for our problem since message passing to such edgeless nodes having no connections is impossible. To tackle this challenge, we propose <inline-formula><tex-math notation="LaTeX">$\mathsf{Edgeless-GNN}$</tex-math><alternatives><mml:math><mml:mrow><mml:mi mathvariant="sans-serif">Edgeless</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="sans-serif">GNN</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href="shin-ieq1-3292240.gif"/></alternatives></inline-formula>, a novel inductive framework that enables GNNs to generate node embeddings even for edgeless nodes through <italic>unsupervised learning</italic>. Specifically, we start by constructing a proxy graph based on the similarity of node attributes as the GNN's computation graph defined by the underlying network. The known network structure is used to train model parameters, whereas a <italic>topology-aware</italic> loss function is established such that our model judiciously learns the network structure by encoding positive, negative, and second-order relations between nodes. For the edgeless nodes, we <italic>inductively</italic> infer embeddings by expanding the computation graph. By evaluating the performance of various downstream machine learning tasks, we empirically demonstrate that <inline-formula><tex-math notation="LaTeX">$\mathsf{Edgeless-GNN}$</tex-math><alternatives><mml:math><mml:mrow><mml:mi mathvariant="sans-serif">Edgeless</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="sans-serif">GNN</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href="shin-ieq2-3292240.gif"/></alternatives></inline-formula> exhibits (a) superiority over state-of-the-art inductive network embedding methods for edgeless nodes, (b) effectiveness of our topology-aware loss function, (c) robustness to incomplete node attributes, and (d) a linear scaling with the graph size.
Self-supervised predictive coding and multimodal fusion advance patient deterioration prediction in fine-grained time resolution

In the Emergency Department (ED), accurate prediction of critical events using Electronic Health Records (EHR) allows timely intervention and effective resource allocation. Though many studies have suggested automatic prediction methods, their coarse-grained time resolutions limit their practical usage. Therefore, in this study, we propose an hourly prediction method of critical events in ED, i.e., mortality and vasopressor need. Through extensive experiments, we show that both 1) bi-modal fusion between EHR text and time-series data and 2) self-supervised predictive regularization using L 2 loss between normalized context vector and EHR future time-series data improve predictive performance, especially the far-future prediction. Our uni-modal/bi-modal/bi-modal self-supervision scored 0.846/0.877/0.897 (0.824/0.855/0.886) and 0.817/0.820/0.858 (0.807/0.81/0.855) with mortality (far-future mortality) and with vasopressor need (far-future vasopressor need) prediction data in AUROC, respectively.
Sparse convex optimization toolkit: a mixed-integer framework

This paper proposes an open-source distributed solver for solving Sparse Convex Optimization (SCO) problems over computational networks. Motivated by past algorithmic advances in mixed-integer optimization, the Sparse Convex Optimization Toolkit (SCOT) adopts a mixed-integer approach to find exact solutions to SCO problems. In particular, SCOT combines various techniques to transform the original SCO problem into an equivalent convex Mixed-Integer Nonlinear Programming (MINLP) problem that can benefit from high-performance and parallel computing platforms. To solve the equivalent mixed-integer problem, we present the Distributed Hybrid Outer Approximation (DiHOA) algorithm that builds upon the LP/NLP-based branch-and-bound and is tailored for this specific problem structure. The DiHOA algorithm combines the so-called single- and multi-tree outer approximation, naturally integrates a decentralized algorithm for distributed convex nonlinear subproblems, and employs enhancement techniques such as quadratic cuts. Finally, we present detailed computational experiments that show the benefit of our solver through numerical benchmarks on 140 SCO problems with distributed datasets. To show the overall efficiency of SCOT we also provide solution profiles comparing SCOT to other state-of-the-art MINLP solvers.
QUASI-PROJECTIVE VARIETIES WITH ORBIFOLD FUNDAMENTAL GROUPS

In this work we study smooth complex quasi-projective varieties whose fundamental group is a free product of cyclic groups. In particular, we prove the existence of a (maybe irrational) pencil from the quasi-projective variety to a Riemann surface (endowed with an orbifold structure) which in- duces an isomorphism of (orbifold) fundamental groups. The orbifold structure is given by the multiple ﬁbers of the pencil. Associated with this result, we prove addition-deletion Lemmas of ﬁbers in the pencil which explain how these operations aﬀect the fundamental group of the quasi-projective variety. Our methods also allow us to produce curves whose fundamental group of their complement is a free product of cyclic groups, generalizing classical results on C p,q curves and torus type projective sextics, and showing how general this phenomenon is.
Learning Modular Robot Locomotion from Demonstrations

—Modular robots can be reconﬁgured to create a variety of designs from a small set of components. But constructing a robot’s hardware on its own is not enough– each robot needs a controller. One could create controllers for some designs individually, but developing policies for additional designs can be time consuming. This work presents a method that uses demonstrations from one set of designs to accelerate policy learning for additional designs. We leverage a learning framework in which a graph neural network is made up of modular components, each component corresponds to a type of module (e.g., a leg, wheel, or body) and these components can be recombined to learn from multiple designs at once. In this paper we develop a combined reinforcement and imitation learning algorithm. Our method is novel because the policy is optimized to both maximize a reward for one design, and simul- taneously imitate demonstrations from different designs, within one objective function. We show that when the modular policy is optimized with this combined objective, demonstrations from one set of designs inﬂuence how the policy behaves on a different design, decreasing the number of training iterations needed.
Epsilon regularity under scalar curvature and entropy lower bounds and volume upper bounds

Examples show that Riemannian manifolds with almost-Euclidean lower bounds on scalar curvature and Perelman entropy need not be close to Euclidean space in any metric space sense. Here we show that if one additionally assumes an almost-Euclidean upper bound on volumes of geodesic balls, then unit balls in such a space are Gromov-Hausdorﬀ close, and in fact bi-H¨older and bi- W 1 ,p homeomorphic, to Euclidean balls. We prove a compactness and limit space structure theorem under the same assumptions.
Decomposed Entropy and Estimation of Output Power in Deformed Microcavity Lasers

Park et al. showed that the Shannon entropy of the probability distribution of a single random variable for far-field profiles (FFPs) in deformed microcavity lasers can efficiently measure the directionality of deformed microcavity lasers. In this study, we instead consider two random variables of FFPs with joint probability distributions and introduce the decomposed (Shannon) entropy for the peak intensities of directional emissions. This provides a new foundation such that the decomposed entropy can estimate the degree of the output power at given FFPs without any further information.
Versatile Semantic Coded Transmission over MIMO Fading Channels

Semantic communications have shown great potential to boost the end-to-end transmission performance. To further improve the system efﬁciency, in this paper, we propose a class of novel semantic coded transmission (SCT) schemes over multiple-input multiple-output (MIMO) fading channels. In particular, we propose a high-efﬁciency SCT system supporting concurrent transmission of multiple streams, which can maximize the multiplexing gain of end-to-end semantic communication system. By jointly considering the entropy distribution on the source semantic features and the wireless MIMO channel states, we design a spatial multiplexing mechanism to realize adaptive coding rate allocation and stream mapping. As a result, source content and channel environment will be seamlessly coupled, which maximizes the coding gain of SCT system. More-over, our SCT system is versatile: a single model can support various transmission rates. The whole model is optimized under the con-straint of transmission rate-distortion (RD) tradeoff. Experimental results verify that our scheme substantially increases the throughput of semantic communication system. It also outperforms traditional MIMO communication systems under realistic fading channels.
Disorder-induced quantum phase transitions in three-dimensional topological insulators and superconductors

We discuss the effects of disorder in time-reversal invariant topological insulators and superconductors in three spatial dimensions. For three-dimensional topological insulator in symplectic (AII) symmetry class, the phase diagram in the presence of disorder and a mass term, which drives a transition between trivial and topological insulator phases, is computed numerically by the transfer matrix method. The numerics is supplemented by a field theory analysis (the large-$N_f$ expansion where $N_f$ is the number of valleys or Dirac cones), from which we obtain the correlation length exponent, and several anomalous dimensions at a non-trivial critical point separating a metallic phase and a Dirac semi-metal. A similar field theory approach is developed for disorder-driven transitions in symmetry class AIII, CI, and DIII. For these three symmetry classes, where topological superconductors are characterized by integer topological invariant, a complementary description is given in terms of the non-linear sigma model supplemented with a topological term which is a three-dimensional analogue of the Pruisken term in the integer quantum Hall effect.
Lita: Accelerating Distributed Training of Sparsely Activated Models

Scaling model parameters usually improves model quality, but at the price of high computation overhead. Sparsely activated models, usually in the form of Mixture of Experts (MoE) architecture, have constant computation cost over their dense counterparts, thus providing opportunities to train and serve a large model at a reasonable cost. However, the distributed training of an MoE model is prone to low efficiency, mainly due to the interleaved all-to-all communication during model computation. This paper makes three main contributions. First, we systematically analyze the all-to-all overhead in distributed training of MoE. Second, we propose a new communication scheduling scheme based on tensor partitioning that prioritizes the all-to-all operations over other communication, due to its blocking nature. Third, we introduce expert packing that reduces the all-to-all transfer size and incorporates optimizations to mitigate its overheads. Both techniques effectively tackle the all-to-all bottleneck, and we integrate them into a new system called Lina. Experiments on an A100 GPU testbed show that Lina improves the training step time of popular NLP models by up to 1.73x over the state-of-the-art.
Robust MelGAN: A robust universal neural vocoder for high-fidelity TTS

In current two-stage neural text-to-speech (TTS) paradigm, it is ideal to have a universal neural vocoder, once trained, which is robust to imperfect mel-spectrogram predicted from the acoustic model. To this end, we propose Robust MelGAN vocoder by solving the original multi-band MelGAN’s metallic sound problem and increasing its generalization ability. Specifically, we introduce a fine-grained network dropout strategy to the generator. With a specifically designed over-smooth handler which separates speech signal intro periodic and aperiodic components, we only perform network dropout to the aperodic components, which alleviates metallic sounding and maintains good speaker similarity. To further improve generalization ability, we introduce several data augmentation methods to augment fake data in the discriminator, including harmonic shift, harmonic noise and phase noise. Experiments show that Robust MelGAN can be used as a universal vocoder, significantly improving sound quality in TTS systems built on various types of data. 11Audio samples are available at https://RobustMelGAN.github. io/RobustMelGAN/
A unified LMI approach to reduced-order controllers: a matrix pencil perspective

This paper addresses the existence and design of reduced-order controllers for a rather general class of control design problems which can be characterized in the LMI framework. By incorporating certain matrix pencils into the LMI based formulation for solving the problems, this paper presents a unified controller degree bound for the problems in terms of the minimal rank of the matrix pencils with respect to their generalized eigenvalues in the unstable region and at infinity. When the full-order controller exists, this paper shows that there exists a reduced-order controller if one of the matrix pencils has unstable finite generalized eigenvalue(s) or infinite eigenstructure. Moreover, this paper demonstrates that the computational problem of finding the controllers with such new degree bound is convex by providing LMI based design methods for constructing the reduced-order controllers.