Miracle-dz/UniFAR-FTUs huggingface dataset:
Mean eigenvector self-overlap in the real and complex elliptic Ginibre ensembles at strong and weak non-Hermiticity

We study the mean diagonal overlap of left and right eigenvectors associated with complex eigenvalues in $N\times N$ non-Hermitian random Gaussian matrices. In well known works by Chalker and Mehlig the expectation of this (self-)overlap was computed for the complex Ginibre ensemble as $N\to \infty$. In the present work, we consider the same quantity in the real and complex elliptic Ginibre ensembles characterized by correlations between off-diagonal entries controlled by a parameter $\tau\in[0,1]$, with $\tau=1$ corresponding to the Hermitian limit. We derive exact expressions for the mean diagonal overlap in both ensembles at any finite $N$, for any eigenvalue off the real axis. We further investigate several scaling regimes as $N\rightarrow \infty$, both in the limit of strong non-Hermiticity keeping a fixed $\tau\in[0,1)$ and in the weak non-Hermiticity limit, with $\tau$ approaching unity in such a way that $N(1-\tau)$ remains finite.
Get More with LESS: Synthesizing Recurrence with KV Cache Compression for Efficient LLM Inference

Many computational factors limit broader deployment of large language models. In this paper, we focus on a memory bottleneck imposed by the key-value (KV) cache, a computational shortcut that requires storing previous KV pairs during decoding. While existing KV cache methods approach this problem by pruning or evicting large swaths of relatively less important KV pairs to dramatically reduce the memory footprint of the cache, they can have limited success in tasks that require recollecting a majority of previous tokens. To alleviate this issue, we propose LESS, a simple integration of a (nearly free) constant sized cache with eviction-based cache methods, such that all tokens can be queried at later decoding steps. Its ability to retain information throughout time shows merit on a variety of tasks where we demonstrate LESS can help reduce the performance gap from caching everything, sometimes even matching it, all while being efficient.
Integrated Topology and Traffic Engineering for Reconfigurable Datacenter Networks

The state-of-the-art topologies of datacenter networks are fixed, based on electrical switching technology, and by now, we understand their throughput and cost well. For the past years, researchers have been developing novel optical switching technologies that enable the emergence of reconfigurable datacenter networks (RDCNs) that support dynamic psychical topologies. The art of network design of dynamic topologies, i.e., 'Topology Engineering,' is still in its infancy. Different designs offer distinct advantages, such as faster switch reconfiguration times or demand-aware topologies, and to date, it is yet unclear what design maximizes the throughput. This paper aims to improve our analytical understanding and formally studies the throughput of reconfigurable networks by presenting a general and unifying model for dynamic networks and their topology and traffic engineering. We use our model to study demand-oblivious and demand-aware systems and prove new upper bounds for the throughput of a system as a function of its topology and traffic schedules. Next, we offer a novel system design that combines both demand-oblivious and demand-aware schedules, and we prove its throughput supremacy under a large family of demand matrices. We evaluate our design numerically for sparse and dense traffic and show that our approach can outperform other designs by up to 25% using common network parameters.
On the Impact of Biological Risk in Aquaculture Valuation and Decision Making

This paper explores the impact of stochastic mortality and disease on animal-based commodities, with a specific emphasis on aquaculture, particularly in the context of salmon farming. The investigation delves into the stochastic nature of mortality and treatment plans based on historical data related to salmon lice. Given that salmon lice pose a significant challenge in salmon farming, with associated treatment costs estimated to be comparable to feeding expenses, their removal is imperative to ensure the survival of the salmon and comply with the Norwegian government's stipulation of maintaining 0.5 lice per fish. We propose a new model that considers the relationship between hosts and parasites to estimate the number of treatments required and their overall cost. An important aspect of this model is its incorporation of stochastic effectiveness for each removal. After calibrating the model to the available data, the study examines the stochastic behavior's impact on the optimal harvesting decision in comparison to deterministic mortality models. The results indicate an approximate $1.5\,\%$ increase in the value of the salmon farm when employing the harvesting rule based on the stochastic host-parasite model as opposed to a deterministic model.
Approximation of relation functions and attention mechanisms

Inner products of neural network feature maps arises in a wide variety of machine learning frameworks as a method of modeling relations between inputs. This work studies the approximation properties of inner products of neural networks. It is shown that the inner product of a multi-layer perceptron with itself is a universal approximator for symmetric positive-definite relation functions. In the case of asymmetric relation functions, it is shown that the inner product of two different multi-layer perceptrons is a universal approximator. In both cases, a bound is obtained on the number of neurons required to achieve a given accuracy of approximation. In the symmetric case, the function class can be identified with kernels of reproducing kernel Hilbert spaces, whereas in the asymmetric case the function class can be identified with kernels of reproducing kernel Banach spaces. Finally, these approximation results are applied to analyzing the attention mechanism underlying Transformers, showing that any retrieval mechanism defined by an abstract preorder can be approximated by attention through its inner product relations. This result uses the Debreu representation theorem in economics to represent preference relations in terms of utility functions.
From Architectures to Applications: A Review of Neural Quantum States

Due to the exponential growth of the Hilbert space dimension with system size, the simulation of quantum many-body systems has remained a persistent challenge until today. Here, we review a relatively new class of variational states for the simulation of such systems, namely neural quantum states (NQS), which overcome the exponential scaling by compressing the state in terms of the network parameters rather than storing all exponentially many coefficients needed for an exact parameterization of the state. We introduce the commonly used NQS architectures and their various applications for the simulation of ground and excited states, finite temperature and open system states as well as NQS approaches to simulate the dynamics of quantum states. Furthermore, we discuss NQS in the context of quantum state tomography.
Eulerian Formulation of the Tensor-Based Morphology Equations for Strain-Based Blood Damage Modeling

The development of blood-handling medical devices, such as ventricular assist devices, requires the analysis of their biocompatibility. Among other aspects, this includes hemolysis, i.e., red blood cell damage. For this purpose, computational fluid dynamics (CFD) methods are employed to predict blood flow in prototypes. The most basic hemolysis models directly estimate red blood cell damage from fluid stress in the resulting flow field. More advanced models explicitly resolve cell deformation. On the downside, these models are typically written in a Lagrangian formulation, i.e., they require pathline tracking. We present a new Eulerian description of cell deformation, enabling the evaluation of the solution across the whole domain. The resulting hemolysis model can be applied to any converged CFD simulation due to one-way coupling with the fluid velocity field. We discuss the efficient numerical treatment of the model equations in a stabilized finite element context. We validate the model by comparison to the original Lagrangian formulation in selected benchmark flows. Two more complex test cases demonstrate the method's capabilities in real-world applications. The results highlight the advantages over previous hemolysis models. In conclusion, the model holds great potential for the design process of future generations of medical devices.
Thinking twice inside the box: is Wigner's friend really quantum?

There has been a surge of recent interest in the Wigner's friend paradox, sparking several novel thought experiments and no-go theorems. The main narrative has been that Wigner's friend highlights a counterintuitive feature that is unique to quantum theory, and which is closely related to the quantum measurement problem. Here, we challenge this view. We argue that the gist of the Wigner's friend paradox can be reproduced without assuming quantum physics, and that it underlies a much broader class of enigmas in the foundations of physics and philosophy. To show this, we first consider several recently proposed extended Wigner's friend scenarios, and demonstrate that their implications for the absoluteness of observations can be reproduced by classical thought experiments that involve the duplication of agents. Crucially, some of these classical scenarios are technologically much easier to implement than their quantum counterparts. Then, we argue that the essential structural ingredient of all these scenarios is a feature that we call"Restriction A": essentially, that a physical theory cannot give us a probabilistic description of the observations of all agents. Finally, we argue that this difficulty is at the core of other puzzles in the foundations of physics and philosophy, and demonstrate this explicitly for cosmology's Boltzmann brain problem. Our analysis suggests that Wigner's friend should be studied in a larger context, addressing a frontier of human knowledge that exceeds the boundaries of quantum physics: to obtain reliable predictions for experiments in which these predictions can be privately but not intersubjectively verified.
Directional Convergence Near Small Initializations and Saddles in Two-Homogeneous Neural Networks

This paper examines gradient flow dynamics of two-homogeneous neural networks for small initializations, where all weights are initialized near the origin. For both square and logistic losses, it is shown that for sufficiently small initializations, the gradient flow dynamics spend sufficient time in the neighborhood of the origin to allow the weights of the neural network to approximately converge in direction to the Karush-Kuhn-Tucker (KKT) points of a neural correlation function that quantifies the correlation between the output of the neural network and corresponding labels in the training data set. For square loss, it has been observed that neural networks undergo saddle-to-saddle dynamics when initialized close to the origin. Motivated by this, this paper also shows a similar directional convergence among weights of small magnitude in the neighborhood of certain saddle points.
Modeling the Spatial Distribution of Urban Population Density and Its Evolution in Guangzhou

On the basis of the third,fourth and fifth population census and implying Geography Information System technique to get spatial data,the author studies and models the distribution of urban population density and its evolution in Guangzhou.It is indicated that the Clark Model can best describe spatial distribution of urban population density and its evolution since 1982 in Guangzhou,and with the lapse of time,fit of the model become better and better.In the future,this Clark Model of population density will evolves into the Newling model.
Controllability and feedback stabilizability in a nonuniform framework

We propose a new controllability property for linear time varying control systems in finite dimension: the nonuniform complete controllability, which is halfway between the classical Kalman's properties of complete controllability and uniform complete controllability. This new concept is described in terms of two gramian inequalities, which have a strong relation; as we prove in our first result; with the property of nonuniform bounded growth for the corresponding plant, also called uncontrolled part. On the other hand, the second result proves that if a control system is nonuniformly completely controllable and its plant has the property of nonuniform bounded growth, then there exist a linear feedback control leading to a nonuniformly exponentially stable closed--loop system.
Investigation of Ga interstitial and vacancy diffusion in $\beta$-Ga$_2$O$_3$ via split defects: a direct approach via master diffusion equations

The low symmetry of monoclinic $\beta$-Ga$_2$O$_3$ leads to elaborate intrinsic defects, such as Ga vacancies split amongst multiple lattice sites. These defects contribute to fast, anisotropic Ga diffusion, yet their complexity makes it challenging to understand dominant diffusion mechanisms. Here, we predict the 3D diffusivity tensors for Ga interstitials (Ga${_i^{3+}}$) and vacancies (V${_{Ga}^{3-}}$) via first principles and direct solution of the master diffusion equations. We first explore the maximum extent of configurationally complex ''$N$-split'' Ga interstitials and vacancies. With dominant low-energy defects identified, we enumerate all possible elementary hops connecting defect configurations to each other, including interstitialcy hops. Hopping barriers are obtained from nudged elastic band simulations. Finally, the comprehensive sets of (i) defect configurations and their energies and (ii) the hopping barriers that connect them are used to construct the master diffusion equations for both Ga${_i^{3+}}$ and V${_{Ga}^{3-}}$. The solution to these equations yields the Onsager transport coefficients, i.e. the components of the 3D diffusivity tensors $D_{{Ga}_i}$ and $D_{V_{Ga}}$ for Ga${_i^{3+}}$ and V${_{Ga}^{3-}}$, respectively. It further reveals the active diffusion paths along all crystallographic directions. We find that both Ga${_i^{3+}}$ and V${_{{Ga}}^{3-}}$ diffusion are fastest along the $c$-axis, due to 3-split defects that bridge neighboring unit cells along the $c$-axis and divert diffusing species around high-energy bottlenecks. Although isolated Ga${_i^{3+}}$ diffuse faster than isolated V${_{Ga}^{3-}}$, self-diffusion of Ga is predominantly mediated by V$_{Ga}^{3-}$ due to the higher V$_{Ga}^{3-}$ defect concentration under most thermodynamic environments.
Game of Trojans: Adaptive Adversaries Against Output-based Trojaned-Model Detectors

We propose and analyze an adaptive adversary that can retrain a Trojaned DNN and is also aware of SOTA output-based Trojaned model detectors. We show that such an adversary can ensure (1) high accuracy on both trigger-embedded and clean samples and (2) bypass detection. Our approach is based on an observation that the high dimensionality of the DNN parameters provides sufficient degrees of freedom to simultaneously achieve these objectives. We also enable SOTA detectors to be adaptive by allowing retraining to recalibrate their parameters, thus modeling a co-evolution of parameters of a Trojaned model and detectors. We then show that this co-evolution can be modeled as an iterative game, and prove that the resulting (optimal) solution of this interactive game leads to the adversary successfully achieving the above objectives. In addition, we provide a greedy algorithm for the adversary to select a minimum number of input samples for embedding triggers. We show that for cross-entropy or log-likelihood loss functions used by the DNNs, the greedy algorithm provides provable guarantees on the needed number of trigger-embedded input samples. Extensive experiments on four diverse datasets -- MNIST, CIFAR-10, CIFAR-100, and SpeechCommand -- reveal that the adversary effectively evades four SOTA output-based Trojaned model detectors: MNTD, NeuralCleanse, STRIP, and TABOR.
Kyanite eclogite thermobarometry and evidence for thrusting of UHP over HP metamorphic rocks, Nordøyane, Western Gneiss Region, Norway

Abstract Quantitative estimates of metamorphic conditions are combined with previously reported structural analysis to develop the thermotectonic evolution of two separate lithotectonic units metamorphosed during the Late Silurian-Early Devonian collision between Baltica and Laurentia. A structurally higher plate, regionally correlated with the Blåhø Nappe, contains kyanite eclogites associated with microdiamond-bearing kyanite-garnet-graphite gneiss on the north coast of Fjørtoft and correlated with kyanite eclogites at Nogva, Flemsøya. The kyanite eclogites, containing the assemblage kyanite- garnet-omphacite-coesite (now polycrystalline quartz pseudomorphs) ± zoisite ± phengite, yield conditions of 820 °C and 34-39 kbar at Fjørtoft and of 820 °C and 30-36 kbar at Nogva, best characterized by two recently recalibrated geothermobarometers. The conditions at Fjørtoft overlap the diamond-graphite phase boundary and represent the first quantitative petrologic determination of UHP diamond-forming conditions in crustal rocks outside the Dabie Mountains, China and the Kokchetav Massif, Kazahkstan. In a structurally lower plate, eclogitized mylonite with the assemblage kyanite-garnet-omphacite-quartz-oligoclase, produced from the mid-Proterozoic Haram Gabbro that has intruded diorite country rock, yields 780 °C and 18 kbar. This result agrees with other normal HP estimates by Mørk (1985) from partially to completely eclogitized gabbro in the same unit on Flemsøya. We propose that the UHP plate reached a maximum depth of 125 km and then experienced 65 km of exhumation during top-southeast thrusting that brought it into contact with the HP plate. Following this, both plates were exhumed together until reaching a depth of 37 km where they experienced extensive amphibolite-facies re-equilibration and top-west or left-lateral shearing. Temporal details of these histories were determined by monazite U-Th-Pb geochronology described in a companion paper
Nonparametric identification and efficient estimation of causal effects with instrumental variables

Instrumental variables are widely used in econometrics and epidemiology for identifying and estimating causal effects when an exposure of interest is confounded by unmeasured factors. Despite this popularity, the assumptions invoked to justify the use of instruments differ substantially across the literature. Similarly, statistical approaches for estimating the resulting causal quantities vary considerably, and often rely on strong parametric assumptions. In this work, we compile and organize structural conditions that nonparametrically identify conditional average treatment effects, average treatment effects among the treated, and local average treatment effects, with a focus on identification formulae invoking the conditional Wald estimand. Moreover, we build upon existing work and propose nonparametric efficient estimators of functionals corresponding to marginal and conditional causal contrasts resulting from the various identification paradigms. We illustrate the proposed methods on an observational study examining the effects of operative care on adverse events for cholecystitis patients, and a randomized trial assessing the effects of market participation on political views.
Learning Interpretable Concepts: Unifying Causal Representation Learning and Foundation Models

To build intelligent machine learning systems, there are two broad approaches. One approach is to build inherently interpretable models, as endeavored by the growing field of causal representation learning. The other approach is to build highly-performant foundation models and then invest efforts into understanding how they work. In this work, we relate these two approaches and study how to learn human-interpretable concepts from data. Weaving together ideas from both fields, we formally define a notion of concepts and show that they can be provably recovered from diverse data. Experiments on synthetic data and large language models show the utility of our unified approach.
An In-Depth Investigation of LEO Satellite Topology Design Parameters

Low Earth Orbit (LEO) satellite networks are rapidly gaining traction today. Although several real-world deployments exist, our preliminary analysis of LEO topology performance with the soon-to-be operational Inter-Satellite Links (ISLs) reveals several interesting characteristics that are difficult to explain based on our current understanding of topologies. For example, a real-world satellite shell with a low density of satellites offers better latency performance than another shell with nearly double the number of satellites. In this work, we conduct an in-depth investigation of LEO satellite topology design parameters and their impact on network performance while using the ISLs. In particular, we focus on three design parameters: the number of orbits in a shell, the inclination of orbits, and the number of satellites per orbit. Through an extensive analysis of real-world and synthetic satellite configurations, we uncover several interesting properties of satellite topologies. Notably, there exist thresholds for the number of satellites per orbit and the number of orbits below which the latency performance degrades significantly. Moreover, network delay between a pair of traffic endpoints depends on the alignment of the satellite's orbit (Inclination) with the geographic locations of endpoints.
Automated Unit Test Improvement using Large Language Models at Meta

This paper describes Meta's TestGen-LLM tool, which uses LLMs to automatically improve existing human-written tests. TestGen-LLM verifies that its generated test classes successfully clear a set of filters that assure measurable improvement over the original test suite, thereby eliminating problems due to LLM hallucination. We describe the deployment of TestGen-LLM at Meta test-a-thons for the Instagram and Facebook platforms. In an evaluation on Reels and Stories products for Instagram, 75% of TestGen-LLM's test cases built correctly, 57% passed reliably, and 25% increased coverage. During Meta's Instagram and Facebook test-a-thons, it improved 11.5% of all classes to which it was applied, with 73% of its recommendations being accepted for production deployment by Meta software engineers. We believe this is the first report on industrial scale deployment of LLM-generated code backed by such assurances of code improvement.