Miracle-dz/UniFAR-FTUs huggingface dataset:
The Complexity of Optimizing Atomic Congestion

Atomic congestion games are a classic topic in network design, routing, and algorithmic game theory, and are capable of modeling congestion and flow optimization tasks in various application areas. While both the price of anarchy for such games as well as the computational complexity of computing their Nash equilibria are by now well-understood, the computational complexity of computing a system-optimal set of strategies - that is, a centrally planned routing that minimizes the average cost of agents - is severely understudied in the literature. We close this gap by identifying the exact boundaries of tractability for the problem through the lens of the parameterized complexity paradigm. After showing that the problem remains highly intractable even on extremely simple networks, we obtain a set of results which demonstrate that the structural parameters which control the computational (in)tractability of the problem are not vertex-separator based in nature (such as, e.g., treewidth), but rather based on edge separators. We conclude by extending our analysis towards the (even more challenging) min-max variant of the problem.
Fractional Deep Reinforcement Learning for Age-Minimal Mobile Edge Computing

Mobile edge computing (MEC) is a promising paradigm for real-time applications with intensive computational needs (e.g., autonomous driving), as it can reduce the processing delay. In this work, we focus on the timeliness of computational-intensive updates, measured by Age-of-Information (AoI), and study how to jointly optimize the task updating and offloading policies for AoI with fractional form. Specifically, we consider edge load dynamics and formulate a task scheduling problem to minimize the expected time-average AoI. The uncertain edge load dynamics, the nature of the fractional objective, and hybrid continuous-discrete action space (due to the joint optimization) make this problem challenging and existing approaches not directly applicable. To this end, we propose a fractional reinforcement learning (RL) framework and prove its convergence. We further design a model-free fractional deep RL (DRL) algorithm, where each device makes scheduling decisions with the hybrid action space without knowing the system dynamics and decisions of other devices. Experimental results show that our proposed algorithms reduce the average AoI by up to 57.6% compared with several non-fractional benchmarks.
Controlling Data Access Load in Distributed Systems

Distributed systems store data objects redundantly to balance the data access load over multiple nodes. Load balancing performance depends mainly on 1) the level of storage redundancy and 2) the assignment of data objects to storage nodes. We analyze the performance implications of these design choices by considering four practical storage schemes that we refer to as clustering, cyclic, block and random design. We formulate the problem of load balancing as maintaining the load on any node below a given threshold. Regarding the level of redundancy, we find that the desired load balance can be achieved in a system of $n$ nodes only if the replication factor $d = \Omega(\log(n)^{1/3})$, which is a necessary condition for any storage design. For clustering and cyclic designs, $d = \Omega(\log(n))$ is necessary and sufficient. For block and random designs, $d = \Omega(\log(n))$ is sufficient but unnecessary. Whether $d = \Omega(\log(n)^{1/3})$ is sufficient remains open. The assignment of objects to nodes essentially determines which objects share the access capacity on each node. We refer to the number of nodes jointly shared by a set of objects as the \emph{overlap} between those objects. We find that many consistently slight overlaps between the objects (block, random) are better than few but occasionally significant overlaps (clustering, cyclic). However, when the demand is ''skewed beyond a level'' the impact of overlaps becomes the opposite. We derive our results by connecting the load-balancing problem to mathematical constructs that have been used to study other problems. For a class of storage designs containing the clustering and cyclic design, we express load balance in terms of the maximum of moving sums of i.i. d. random variables, which is known as the scan statistic. For random design, we express load balance by using the occupancy metric for random allocation with complexes.
Signature of pressure-induced topological phase transition in ZrTe$_5$

The layered van der Waals material ZrTe$_5$ is known as a candidate topological insulator (TI), however its topological phase and the relation with other properties such as an apparent Dirac semimetallic state is still a subject of debate. We employ a semiclassical multicarrier transport (MCT) model to analyze the magnetotransport of ZrTe$_5$ nanodevices at hydrostatic pressures up to 2 GPa. The temperature dependence of the MCT results between 10 and 300 K is assessed in the context of thermal activation, and we obtain the positions of conduction and valence band edges in the vicinity of the chemical potential. We find evidence of the closing and subsequent re-opening of the band gap with increasing pressure, which is consistent with a phase transition from weak to strong TI. This matches expectations from ab initio band structure calculations, as well as previous observations that CVT-grown ZrTe$_5$ is in a weak TI phase in ambient conditions.
A charge-preserving method for solving graph neural diffusion networks

The aim of this paper is to give a systematic mathematical interpretation of the diffusion problem on which Graph Neural Networks (GNNs) models are based. The starting point of our approach is a dissipative functional leading to dynamical equations which allows us to study the symmetries of the model. We discuss the conserved charges and provide a charge-preserving numerical method for solving the dynamical equations. In any dynamical system and also in GRAph Neural Diffusion (GRAND), knowing the charge values and their conservation along the evolution flow could provide a way to understand how GNNs and other networks work with their learning capabilities.
An Edge-Coupled Magnetostatic Bandpass Filter

This paper reports on the design, fabrication, and characterization of an edge-coupled magnetostatic forward volume wave bandpass filter. Using micromachining techniques, the filter is fabricated from a yttrium iron garnet (YIG) film grown on a gadolinium gallium garnet (GGG) substrate with inductive transducers. By adjusting an out-of-plane magnetic field, we demonstrate linear center frequency tuning for a $4^{\text{th}}$-order filter from 4.5 GHz to 10.1 GHz while retaining a fractional bandwidth of 0.3%, an insertion loss of 6.94 dB, and a -35dB rejection. We characterize the filter nonlinearity in the passband and stopband with IIP3 measurements of -4.85 dBm and 25.84 dBm, respectively. When integrated with a tunable magnetic field, this device is an octave tunable narrowband channel-select filter.
Runtime Analysis of the SMS-EMOA for Many-Objective Optimization

The widely used multiobjective optimizer NSGA-II was recently proven to have considerable difficulties in many-objective optimization. In contrast, experimental results in the literature show a good performance of the SMS-EMOA, which can be seen as a steady-state NSGA-II that uses the hypervolume contribution instead of the crowding distance as the second selection criterion. This paper conducts the first rigorous runtime analysis of the SMS-EMOA for many-objective optimization. To this aim, we first propose a many-objective counterpart, the m-objective mOJZJ problem, of the bi-objective OJZJ benchmark, which is the first many-objective multimodal benchmark used in a mathematical runtime analysis. We prove that SMS-EMOA computes the full Pareto front of this benchmark in an expected number of O(M^2 n^k) iterations, where n denotes the problem size (length of the bit-string representation), k the gap size (a difficulty parameter of the problem), and M=(2n/m-2k+3)^(m/2) the size of the Pareto front. This result together with the existing negative result on the original NSGA-II shows that in principle, the general approach of the NSGA-II is suitable for many-objective optimization, but the crowding distance as tie-breaker has deficiencies. We obtain three additional insights on the SMS-EMOA. Different from a recent result for the bi-objective OJZJ benchmark, the stochastic population update often does not help for mOJZJ. It results in a 1/Θ(min(Mk^(1/2)/2^(k/2),1)) speed-up, which is Θ(1) for large m such as m>k. On the positive side, we prove that heavy-tailed mutation still results in a speed-up of order k^(0.5+k-β). Finally, we conduct the first runtime analyses of the SMS-EMOA on the bi-objective OneMinMax and LOTZ benchmarks and show that it has a performance comparable to the GSEMO and the NSGA-II.
Hausdorff dimension and exact approximation order in $\mathbb{R}^n$

Given a non-increasing function $\psi\colon\mathbb{N}\to\mathbb{R}^+$ such that $s^{\frac{n+1}{n}}\psi(s)$ tends to zero as $s$ goes to infinity, we show that the set of points in $\mathbb{R}^n$ that are exactly $\psi$-approximable is non-empty, and we compute its Hausdorff dimension. For $n\geq 2$, this answers questions of Jarn\'{i}k and of Beresnevich, Dickinson, and Velani.
Spectrum Degeneracies from Quantum Evanescence

We identify degeneracies in the energy spectra of quantum theories that occur at integer values of the continuous parameter $N$ of an analytically continued global $O(N)$ symmetry. The degeneracies are enforced by the requirement that evanescent states fall out of the spectrum. They occur between different irreducible representations of the analytic continuation of $O(N)$ and hold non-perturbatively. We give examples in the spectra of the critical $O(N)$ model.
Self-Supervised Disentangled Representation Learning for Robust Target Speech Extraction

Speech signals are inherently complex as they encompass both global acoustic characteristics and local semantic information. However, in the task of target speech extraction, certain elements of global and local semantic information in the reference speech, which are irrelevant to speaker identity, can lead to speaker confusion within the speech extraction network. To overcome this challenge, we propose a self-supervised disentangled representation learning method. Our approach tackles this issue through a two-phase process, utilizing a reference speech encoding network and a global information disentanglement network to gradually disentangle the speaker identity information from other irrelevant factors. We exclusively employ the disentangled speaker identity information to guide the speech extraction network. Moreover, we introduce the adaptive modulation Transformer to ensure that the acoustic representation of the mixed signal remains undisturbed by the speaker embeddings. This component incorporates speaker embeddings as conditional information, facilitating natural and efficient guidance for the speech extraction network. Experimental results substantiate the effectiveness of our meticulously crafted approach, showcasing a substantial reduction in the likelihood of speaker confusion.
Quintom cosmology from an effective $BF$ theory

In this article we analyze an effective action derived from a 7-dimensional $BF$ theory that, upon dimensional reduction, it transforms into an effective 4-dimensional action. Such resulting effective action involves a generic metric; however, we study a cosmological model described by a de Sitter universe, with a Hubble constant $H_{0}=67.70 \,\rm [km\, s^{-1}\,Mpc^{-1}]$. We compute the barotropic parameter $\omega \equiv p/\rho$ to analyze our solutions. Three different upshots are presented, where this model can transit from quintessence to the phantom regimes, crossing the theoretical phantom divide line. Thus the effective $BF$ action represents a quintom scenario.
Reconfigurable quantum photonic circuits based on quantum dots

Quantum photonic integrated circuits, composed of linear-optical elements, offer an efficient way for encoding and processing quantum information on-chip. At their core, these circuits rely on reconfigurable phase shifters, typically constructed from classical components such as thermo- or electro-optical materials, while quantum solid-state emitters such as quantum dots are limited to acting as single-photon sources. Here, we demonstrate the potential of quantum dots as reconfigurable phase shifters. We use numerical models based on established literature parameters to show that circuits utilizing these emitters enable high-fidelity operation and are scalable. Despite the inherent imperfections associated with quantum dots, such as imperfect coupling, dephasing, or spectral diffusion, our optimization shows that these do not significantly impact the unitary infidelity. Specifically, they do not increase the infidelity by more than 0.001 in circuits with up to 10 modes, compared to those affected only by standard nanophotonic losses and routing errors. For example, we achieve fidelities of 0.9998 in quantum-dot-based circuits enacting controlled-phase and -not gates without any redundancies. These findings demonstrate the feasibility of quantum emitter-driven quantum information processing and pave the way for cryogenically-compatible, fast, and low-loss reconfigurable quantum photonic circuits.
RetailKLIP : Finetuning OpenCLIP backbone using metric learning on a single GPU for Zero-shot retail product image classification

Retail product or packaged grocery goods images need to classified in various computer vision applications like self checkout stores, supply chain automation and retail execution evaluation. Previous works explore ways to finetune deep models for this purpose. But because of the fact that finetuning a large model or even linear layer for a pretrained backbone requires to run at least a few epochs of gradient descent for every new retail product added in classification range, frequent retrainings are needed in a real world scenario. In this work, we propose finetuning the vision encoder of a CLIP model in a way that its embeddings can be easily used for nearest neighbor based classification, while also getting accuracy close to or exceeding full finetuning. A nearest neighbor based classifier needs no incremental training for new products, thus saving resources and wait time.
Normality, Relativization, and Randomness

Normal numbers were introduced by Borel. Normality is certainly a weak notion of randomness; for instance, there are computable numbers which are absolutely normal. In the present paper, we introduce a relativization of normality to a fixed representation system. When we require normality with respect to large sets of such systems, we find variants of normality that imply randomness notions much stronger than absolute normality. The primary classes of numbers investigated in this paper are the supernormal numbers and the highly normal numbers, which we will define. These are relativizations of normality which are robust to all reasonable changes of representation. Among other results, we give a proof that the highly normal numbers are exactly those of computable dimension 1, which we think gives a more natural characterization than was previously known of this interesting class.
Probing Clifford Algebras Through Spin Groups: A Standard Model Perspective

Division algebras have demonstrated their utility in studying non-associative algebras and their connection to the Standard Model through complex Clifford algebras. This article focuses on exploring the connection between these complex Clifford algebras and their corresponding real Clifford algebras providing insight into geometric properties of bivector gauge symmetries. We first generate gauge symmetries in the complex Clifford algebra through a general Witt decomposition. Gauge symmetries act as a constraint on the underlying real Clifford algebra, where they're then translated from their complex form to their bivector counterpart. Spin group arguments allow the identification of bivector structures which preserve the gauge symmetry yielding the corresponding real Clifford algebra. We conclude that Standard Model gauge groups emerge from higher-dimensional Clifford algebras carrying Euclidean signatures, where particle states are recognized as a combination of basis elements corresponding to complex Euclidean Clifford algebras.
Episodic Return Decomposition by Difference of Implicitly Assigned Sub-Trajectory Reward

Real-world decision-making problems are usually accompanied by delayed rewards, which affects the sample efficiency of Reinforcement Learning, especially in the extremely delayed case where the only feedback is the episodic reward obtained at the end of an episode. Episodic return decomposition is a promising way to deal with the episodic-reward setting. Several corresponding algorithms have shown remarkable effectiveness of the learned step-wise proxy rewards from return decomposition. However, these existing methods lack either attribution or representation capacity, leading to inefficient decomposition in the case of long-term episodes. In this paper, we propose a novel episodic return decomposition method called Diaster (Difference of implicitly assigned sub-trajectory reward). Diaster decomposes any episodic reward into credits of two divided sub-trajectories at any cut point, and the step-wise proxy rewards come from differences in expectation. We theoretically and empirically verify that the decomposed proxy reward function can guide the policy to be nearly optimal. Experimental results show that our method outperforms previous state-of-the-art methods in terms of both sample efficiency and performance. The code is available at https://github.com/HxLyn3/Diaster.
When Graph Data Meets Multimodal: A New Paradigm for Graph Understanding and Reasoning

Graph data is ubiquitous in the physical world, and it has always been a challenge to efficiently model graph structures using a unified paradigm for the understanding and reasoning on various graphs. Moreover, in the era of large language models, integrating complex graph information into text sequences has become exceptionally difficult, which hinders the ability to interact with graph data through natural language instructions.The paper presents a new paradigm for understanding and reasoning about graph data by integrating image encoding and multimodal technologies. This approach enables the comprehension of graph data through an instruction-response format, utilizing GPT-4V's advanced capabilities. The study evaluates this paradigm on various graph types, highlighting the model's strengths and weaknesses, particularly in Chinese OCR performance and complex reasoning tasks. The findings suggest new direction for enhancing graph data processing and natural language interaction.
Density density correlation functions of chiral Luttinger liquids with a point contact impurity

The density density correlation function (most singular parts) of chiral Luttinger liquids forming the fractional quantum Hall effect (FQHE) edge is systematically derived in presence of a point-contact junction acting as a localised scalar impurity and is shown to be expressible as compact analytical functions with second order poles and involving the bare scale-independent reflection and transmission coefficients. The results are validated on comparison with standard fermionic perturbation theory. The linear response Hall conductance in the absence of a point-contact is recovered from the obtained density density correlation functions (DDCF). The system under consideration is inhomogeneous with broken translational invariance and for such systems in one dimension, the connected moments of the density fluctuation operator beyond second order need not be included in order to retreive the most singular parts of the correlations. The reason being that all odd moments of the density are zero and all higher order even moments are less singular than the quadratic moment. The implications of these results when used in conjunction with bosonization methods in presence of impurity backscattering is briefly discussed.
Analyzing Generalization in Policy Networks: A Case Study with the Double-Integrator System

Extensive utilization of deep reinforcement learning (DRL) policy networks in diverse continuous control tasks has raised questions regarding performance degradation in expansive state spaces where the input state norm is larger than that in the training environment. This paper aims to uncover the underlying factors contributing to such performance deterioration when dealing with expanded state spaces, using a novel analysis technique known as state division. In contrast to prior approaches that employ state division merely as a post-hoc explanatory tool, our methodology delves into the intrinsic characteristics of DRL policy networks. Specifically, we demonstrate that the expansion of state space induces the activation function $\tanh$ to exhibit saturability, resulting in the transformation of the state division boundary from nonlinear to linear. Our analysis centers on the paradigm of the double-integrator system, revealing that this gradual shift towards linearity imparts a control behavior reminiscent of bang-bang control. However, the inherent linearity of the division boundary prevents the attainment of an ideal bang-bang control, thereby introducing unavoidable overshooting. Our experimental investigations, employing diverse RL algorithms, establish that this performance phenomenon stems from inherent attributes of the DRL policy network, remaining consistent across various optimization algorithms.
Gaussian-SLAM: Photo-realistic Dense SLAM with Gaussian Splatting

We present a dense simultaneous localization and mapping (SLAM) method that uses 3D Gaussians as a scene representation. Our approach enables interactive-time reconstruction and photo-realistic rendering from real-world single-camera RGBD videos. To this end, we propose a novel effective strategy for seeding new Gaussians for newly explored areas and their effective online optimization that is independent of the scene size and thus scalable to larger scenes. This is achieved by organizing the scene into sub-maps which are independently optimized and do not need to be kept in memory. We further accomplish frame-to-model camera tracking by minimizing photometric and geometric losses between the input and rendered frames. The Gaussian representation allows for high-quality photo-realistic real-time rendering of real-world scenes. Evaluation on synthetic and real-world datasets demonstrates competitive or superior performance in mapping, tracking, and rendering compared to existing neural dense SLAM methods.