Miracle-dz/UniFAR-FTUs huggingface dataset:
On the Convergence of the Gradient Descent Method with Stochastic Fixed-point Rounding Errors under the Polyak-Lojasiewicz Inequality

When training neural networks with low-precision computation, rounding errors often cause stagnation or are detrimental to the convergence of the optimizers; in this paper we study the influence of rounding errors on the convergence of the gradient descent method for problems satisfying the Polyak-Lojasiewicz inequality. Within this context, we show that, in contrast, biased stochastic rounding errors may be beneficial since choosing a proper rounding strategy eliminates the vanishing gradient problem and forces the rounding bias in a descent direction. Furthermore, we obtain a bound on the convergence rate that is stricter than the one achieved by unbiased stochastic rounding. The theoretical analysis is validated by comparing the performances of various rounding strategies when optimizing several examples using low-precision fixed-point number formats.
Ghost Effect from Boltzmann Theory: Expansion with Remainder

Consider the limit $\varepsilon\rightarrow0$ of the steady Boltzmann problem \begin{align} v\cdot\nabla_x\mathfrak{F}=\varepsilon^{-1}Q[\mathfrak{F},\mathfrak{F}],\quad \mathfrak{F}\big|_{v\cdot n<0}=M_w\displaystyle\int_{v'\cdot n>0} \mathfrak{F}(v')|v'\cdot n|\mathrm{d}{v'}, \end{align} where $\displaystyle M_w(x_0,v):=\frac{1}{2\pi\big(T_w(x_0)\big)^2} \exp\bigg(-\frac{|v|^2}{2T_w(x_0)}\bigg)$ for $x_0\in\partial\Omega$ is the wall Maxwellian in the diffuse-reflection boundary condition. In the natural case of $|\nabla T_w|=O(1)$, for any constant $P>0$, the Hilbert expansion leads to \begin{align}\label{expansion} \mathfrak{F}\approx \mu+\varepsilon\bigg\{\mu\bigg(\rho_1+u_1\cdot v+T_1\frac{|v|^2-3T}{2}\bigg)-\mu^{\frac{1}{2}}\left(\mathscr{A}\cdot\frac{\nabla_xT}{2T^2}\right)\bigg\} \end{align} where $\displaystyle\mu(x,v):=\frac{\rho(x)}{\big(2\pi T(x)\big)^{\frac{3}{2}}} \exp\bigg(-\frac{|v|^2}{2T(x)}\bigg)$, and $(\rho,u_1,T)$ is determined by a Navier-Stokes-Fourier system with"ghost"effect. The goal of this paper is to construct $\mathfrak{F}$ in the form of \begin{align}\label{aa 08} \mathfrak{F}(x,v)=&\mu+\mu^{\frac{1}{2}}\Big(\varepsilon f_1+\varepsilon^2f_2\Big)+\mu_w^{\frac{1}{2}}\Big(\varepsilon f^B_1\Big)+\varepsilon^{\alpha}\mu^{\frac{1}{2}}R, \end{align} for interior solutions $f_1$, $f_2$ and boundary layer $f^B_1$, where $\mu_w$ is $\mu$ computed for $T=T_w$, and derive equation for the remainder $R$ with some constant $\alpha\geq1$. To prove the validity of the expansion suitable bounds on $R$ are needed, which are provided in the companion paper [Esposito-Guo-Rossana-Wu2023].
On the biharmonic hypersurfaces with three distinct principal curvatures in space forms

In [16] there was proved that any biharmonic hypersurface with at most three distinct principal curvatures in space forms has constant mean curvature. At the very last step of the proof, the argument relied on the fact that the resultant of two polynomials is a non-zero polynomial. In this paper we point out that, in fact, there is a case, and only one, when this resultant is the zero polynomial and therefore the original proof is not fully complete. Further, we prove that in this special case we still obtain that the hypersurface has constant mean curvature.
Time-Resolved PIV Measurements of Turbulent Flow in Rotating Rib-Roughened Channel With Coriolis and Buoyancy Forces

The present contribution addresses the effect of Coriolis and buoyancy forces in a rotating rectangular channel having one wall provided with ribs perpendicular to the flow direction. Time-resolved PIV measurements are performed in a rotating facility where both the channel model and the measurement system rotate on a turntable at 134 rpm. Air is used as working fluid. The Reynolds number defined by the bulk velocity and the hydraulic diameter is 15000, and a rotation number of 0.38 is obtained both in clockwise and counter-clockwise sense. The ribbed wall, machined out of copper, is heated to a uniform temperature of about 100°C by means of electrical resistances. This allows to obtain a centrifugal buoyancy number of 0.31. Velocity fields are measured along the channel symmetry plane using a continuous laser diode and a high-speed camera. Both ensemble-averaged and time-resolved measurements are performed. In the latter case the realizations are acquired at 3.3 KHz, allowing to resolve the fine temporal flow scales. The effects of the rotational buoyancy with respect to the action of the Coriolis forces alone are highlighted. Particular attention is drawn to the extension of the separated area behind the rib, as well as to the length scales and time scales of the structures generated on the separated shear layer behind the ribs. Vortical structures are identified as regions of strong swirl having both spatial and temporal coherence. The rotational buoyancy near the heated wall affects strongly the physical characteristics, distribution and trajectory of such structures, which are critical for the turbulent transport and heat transfer.Copyright © 2012 by ASME
Partially disordered Heisenberg antiferromagnet with short-range stripe correlations

Zero-point quantum fluctuations of a N\'eel order can produce effective interactions between quasi-orphan spins weakly coupled to the lattice. On the $\sqrt{3}\times\sqrt{3}-$distorted triangular lattice, this phenomenon leads to a correlated partially disordered phase. In this article, we use matrix product state methods to study a similar model: the $S=1/2$ stuffed square lattice. Tunning the exchange amplitudes we go from a square lattice plus orphan central spins at $J'/J =0$, to the union jack lattice at $J'/J=1$, and a square lattice including all spins at $J/J'=0$. We calculate the complete antiferromagnetic phase diagram, dominated by ferrimagnetic and N\'eel orders, and compare with existing results. Most importantly, we find a partially disordered phase in the weakly frustrated regime. In this phase, the N\'eel order from the square lattice is unaffected, while the central spins form a collective state with exponentially decaying double striped correlations. We also study the role of quantum fluctuations by introducing an ordering staggered magnetic field on the square sublattice, and find that the central spins order ferromagnetically when fluctuations from the N\'eel order are suppressed.
Time-Conditioned Generative Modeling of Object-Centric Representations for Video Decomposition and Prediction

When perceiving the world from multiple viewpoints, humans have the ability to reason about the complete objects in a compositional manner even when an object is completely occluded from certain viewpoints. Meanwhile, humans are able to imagine novel views after observing multiple viewpoints. Recent remarkable advances in multi-view object-centric learning still leaves some unresolved problems: 1) The shapes of partially or completely occluded objects can not be well reconstructed. 2) The novel viewpoint prediction depends on expensive viewpoint annotations rather than implicit rules in view representations. In this paper, we introduce a time-conditioned generative model for videos. To reconstruct the complete shape of an object accurately, we enhance the disentanglement between the latent representations of objects and views, where the latent representations of time-conditioned views are jointly inferred with a Transformer and then are input to a sequential extension of Slot Attention to learn object-centric representations. In addition, Gaussian processes are employed as priors of view latent variables for video generation and novel-view prediction without viewpoint annotations. Experiments on multiple datasets demonstrate that the proposed model can make object-centric video decomposition, reconstruct the complete shapes of occluded objects, and make novel-view predictions.
Non-uniqueness in plane fluid flows

Examples of dynamical systems proposed by Z. Artstein and C. M. Dafermos admit non-unique solutions that track a one parameter family of closed circular orbits contiguous at a single point. Switching between orbits at this single point produces an infinite number of solutions with the same initial data. Dafermos appeals to a maximal entropy rate criterion to recover uniqueness. These results are here interpreted as non-unique Lagrange trajectories on a particular spatial region. The corresponding special velocity is proved consistent with plane steady compressible fluid flows that for specified pressure and mass density satisfy not only the Euler equations but also the Navier-Stokes equations for specially chosen volume and (positive) shear viscosities. The maximal entropy rate criterion recovers uniqueness.
ManyDG: Many-domain Generalization for Healthcare Applications

The vast amount of health data has been continuously collected for each patient, providing opportunities to support diverse healthcare predictive tasks such as seizure detection and hospitalization prediction. Existing models are mostly trained on other patients data and evaluated on new patients. Many of them might suffer from poor generalizability. One key reason can be overfitting due to the unique information related to patient identities and their data collection environments, referred to as patient covariates in the paper. These patient covariates usually do not contribute to predicting the targets but are often difficult to remove. As a result, they can bias the model training process and impede generalization. In healthcare applications, most existing domain generalization methods assume a small number of domains. In this paper, considering the diversity of patient covariates, we propose a new setting by treating each patient as a separate domain (leading to many domains). We develop a new domain generalization method ManyDG, that can scale to such many-domain problems. Our method identifies the patient domain covariates by mutual reconstruction and removes them via an orthogonal projection step. Extensive experiments show that ManyDG can boost the generalization performance on multiple real-world healthcare tasks (e.g., 3.7% Jaccard improvements on MIMIC drug recommendation) and support realistic but challenging settings such as insufficient data and continuous learning.
Logical Message Passing Networks with One-hop Inference on Atomic Formulas

Complex Query Answering (CQA) over Knowledge Graphs (KGs) has attracted a lot of attention to potentially support many applications. Given that KGs are usually incomplete, neural models are proposed to answer the logical queries by parameterizing set operators with complex neural networks. However, such methods usually train neural set operators with a large number of entity and relation embeddings from the zero, where whether and how the embeddings or the neural set operators contribute to the performance remains not clear. In this paper, we propose a simple framework for complex query answering that decomposes the KG embeddings from neural set operators. We propose to represent the complex queries into the query graph. On top of the query graph, we propose the Logical Message Passing Neural Network (LMPNN) that connects the local one-hop inferences on atomic formulas to the global logical reasoning for complex query answering. We leverage existing effective KG embeddings to conduct one-hop inferences on atomic formulas, the results of which are regarded as the messages passed in LMPNN. The reasoning process over the overall logical formulas is turned into the forward pass of LMPNN that incrementally aggregates local information to finally predict the answers' embeddings. The complex logical inference across different types of queries will then be learned from training examples based on the LMPNN architecture. Theoretically, our query-graph represenation is more general than the prevailing operator-tree formulation, so our approach applies to a broader range of complex KG queries. Empirically, our approach yields the new state-of-the-art neural CQA model. Our research bridges the gap between complex KG query answering tasks and the long-standing achievements of knowledge graph representation learning.
A noisy-input generalised additive model for relative sea-level change along the Atlantic coast of North America

We propose a Bayesian, noisy-input, spatial-temporal generalised additive model to examine regional relative sea-level (RSL) changes over time. The model provides probabilistic estimates of component drivers of regional RSL change via the combination of a univariate spline capturing a common regional signal over time, random slopes and intercepts capturing site-specific (local), long-term linear trends and a spatial-temporal spline capturing residual, non-linear, local variations. Proxy and instrumental records of RSL and corresponding measurement errors inform the model and a noisy-input method accounts for proxy temporal uncertainties. Results focus on the decomposition of RSL over the past 3000 years along the Atlantic coast of North America.
Data standardization for robust lip sync

Lip sync is a fundamental audio-visual task. However, existing lip sync methods fall short of being robust to the incred-ible diversity of videos taken in the wild, and the majority of the diversity is caused by compound distracting factors that could degrade existing lip sync methods. To address these is-sues, this paper proposes a data standardization pipeline that can produce standardized expressive images while preserving lip motion information from the input and reducing the effects of compound distracting factors. Based on recent advances in 3D face reconstruction, we ﬁrst create a model that can consistently disentangle expressions, with lip motion information embedded. Then, to reduce the effects of compound distracting factors on synthesized images, we synthesize images with only expressions from the input, intentionally setting all other attributes at predeﬁned values independent of the input. Using synthesized images, existing lip sync methods improve their data efﬁciency and robustness, and they achieve competitive performance for the active speaker detection task.
Sequential composition of propositional logic programs

This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for arbitrary programs. We show that the immediate consequence operator of a program can be represented via composition which allows us to compute its least model without any explicit reference to operators. This bridges the conceptual gap between the syntax and semantics of a propositional logic program in a mathematically satisfactory way.
Social Opinion Formation and Decision Making Under Communication Trends

This work studies the learning process over social networks under partial and random information sharing. In traditional social learning models, agents exchange full belief information with each other while trying to infer the true state of nature. We study the case where agents share information about only one hypothesis, namely, the trending topic, which can be randomly changing at every iteration. We show that agents can learn the true hypothesis even if they do not discuss it, at rates comparable to traditional social learning. We also show that using one's own belief as a prior for estimating the neighbors’ non-transmitted beliefs might create opinion clusters that prevent learning with full confidence. This phenomenon occurs when a single hypothesis corresponding to the truth is exchanged exclusively during all times. Such a practice, however, avoids the complete rejection of the truth under any information exchange procedure — something that could happen if priors were uniform.
Toward Robust Manufacturing Scheduling: Stochastic Job-Shop Scheduling

Manufacturing plays a significant role in economic development, production, exports, and job creation, which ultimately contribute to improving the quality of life. The presence of manufacturing defects is, however, inevitable leading to products being discarded, i.e. scrapped. In some cases, defective products can be repaired through rework. Scrap and rework cause a longer completion time, which can contribute to orders being shipped late. Moreover, the presence of uncertainties and combinatorial complexity significantly increases the difficulty of complex manufacturing scheduling. This paper tackles this challenge, exemplified by a case study on stochastic job-shop scheduling in low-volume, high-variety manufacturing contexts. To ensure on-time delivery, high-quality solutions are required, and near-optimal solutions must be obtained within strict time constraints to ensure smooth operations on the job-shop floor. To efficiently solve the stochastic job-shop scheduling (JSS) problem, a recently-developed Surrogate"Level-Based"Lagrangian Relaxation is used to reduce computational effort while efficiently exploiting the geometric convergence potential inherent to Polyak's stepsizing formula thereby leading to fast convergence. Numerical testing demonstrates that the new method is two orders of magnitude faster as compared to commercial solvers.
StyleGAN-T: Unlocking the Power of GANs for Fast Large-Scale Text-to-Image Synthesis

Text-to-image synthesis has recently seen significant progress thanks to large pretrained language models, large-scale training data, and the introduction of scalable model families such as diffusion and autoregressive models. However, the best-performing models require iterative evaluation to generate a single sample. In contrast, generative adversarial networks (GANs) only need a single forward pass. They are thus much faster, but they currently remain far behind the state-of-the-art in large-scale text-to-image synthesis. This paper aims to identify the necessary steps to regain competitiveness. Our proposed model, StyleGAN-T, addresses the specific requirements of large-scale text-to-image synthesis, such as large capacity, stable training on diverse datasets, strong text alignment, and controllable variation vs. text alignment tradeoff. StyleGAN-T significantly improves over previous GANs and outperforms distilled diffusion models - the previous state-of-the-art in fast text-to-image synthesis - in terms of sample quality and speed.
KINETIC THEORY OF NONSPHERICAL MOLECULES. V

In the kinetic theory of rigid nonspherical molecules, discussed previously, the transport coefficients were expressed in terms of certain multi‐dimensional integrals, the brace expressions. In the present discussion these integrals are considered in detail. The integrations over the linear and angular velocities are carried out explicitly and the problem is further reduced to an integral of geometrical parameters over the surfaces of two bodies. The resulting expressions for the transport coefficients apply to any rigid nonspherical convex body in which the center of mass is a center of symmetry. As an example, the final integrations are carried out explicitly for the spherocylindrical model. The shear viscosity, the bulk viscosity, and the thermal conductivity, for this model are presented as functions of two parameters characteristic of the shape and mass distribution of the molecule.
First light and reionization epoch simulations (Flares) X: environmental galaxy bias and survey variance at high redshift

Upcoming deep galaxy surveys with JWST will probe galaxy evolution during the epoch of reionization (EoR, 5 ≤ z ≤ 10) over relatively compact areas (e.g. ∼300 arcmin2 for the JADES GTO survey). It is therefore imperative that we understand the degree of survey variance to evaluate how representative the galaxy populations in these studies will be. We use the First Light And Reionization Epoch Simulations (Flares) to measure the galaxy bias of various tracers over an unprecedentedly large range in overdensity for a hydrodynamic simulation, and use these relations to assess the impact of bias and clustering on survey variance in the EoR. Star formation is highly biased relative to the underlying dark matter distribution, with the mean ratio of the stellar to dark matter density varying by a factor of 100 between regions of low and high matter overdensity (smoothed on a scale of 14 h−1 cMpc). This is reflected in the galaxy distribution – the most massive galaxies are found solely in regions of high overdensity. As a consequence of the above, galaxies in the EoR are highly clustered, which can lead to a large variance in survey number counts. For mean number counts N ≲ 100 (1000), in a unit redshift slice of angular area 300 arcmin2 (1.4 deg2), the 2σ range in N is roughly a factor of four (two). We present relations between the expected variance and survey area for different survey geometries; these relations will be of use to observers wishing to understand the impact of survey variance on their results.
GBOSE: Generalized Bandit Orthogonalized Semiparametric Estimation

In sequential decision-making scenarios i.e. mobile health, recommendation systems, revenue management; contextual multi-armed bandit algorithms have garnered attention for their performance. But most of the existing algorithms are built on the assumption of a strictly parametric reward model, mostly linear in nature. In this work, we propose a new algorithm with a semi-parametric reward model with state-of-the-art complexity of upper bound on regret amongst existing semi-parametric algorithms. Our work expands the scope of another representative algorithm (Krishnamurthy et al., 2018) of state-of-the-art complexity with a similar reward model by proposing an algorithm built upon the same action ﬁltering procedures but provides explicit action selection distribution for scenarios involving more than two arms at a particular time step while requiring fewer computations. We derive the said complexity of the upper bound on regret and present simulation results that afﬁrm our method’s superiority out of all prevalent semi-parametric bandit algorithms for cases involving over two arms.
Seismo-acoustic field statistics in shallow water

The spatial statistics of the acoustic field in shallow water are strongly affected by interfacial roughness and volume fluctuations in the water column or the seabed. These features scatter energy, reducing the coherence of the acoustic field. This paper introduces a consistent, mode-based modeling framework for ocean scattering. First, the rough surface scattering theory of Kuperman and Schmidt is reformulated in terms of normal modes, resulting in computation times which are reduced by several orders of magnitude. Next, a perturbation theory describing scattering from sound speed and density fluctuations in acoustic media is developed. The scattering theories are combined with KRAKEN, creating a unified normal mode code for wave theory modeling of shallow-water spatial statistics. The scattered field statistics are found to be a complicated function of scattering mechanism, scatterer statistics, and acoustic environment. Bottom properties, including elasticity, strongly influence the scattered field.
Simulated maximum likelihood estimation of multivariate mixed‐Poisson regression models, with application

This paper proposes and implements simulated maximum likelihood estimation of bivariate count models with unrestricted correlation pattern of unobserved heterogeneity. The implementation incorporates both antithetic acceleration and adjustment for first-order simulation bias. Both the Monte Carlo simulation evidence and an application to health utilization data confirm that the method is reliable and feasible in data analysis.