Miracle-dz/UniFAR-FTUs huggingface dataset:
Theoretical Analysis of Quartz Plate Acoustic Wave Resonators and Sensors Using Three-Dimensional Equations of Anisotropic Elasticity or Piezoelectricity

This is a review of theoretical results from the three-dimensional equations of anisotropic elasticity or linear piezoelectricity on waves and vibrations in quartz crystal plates. It covers both the classical results on acoustic wave resonators and the relatively new applications in acoustic wave sensors. It discusses the basic thickness modes with various complications due to electrodes, mass loading, contact with fluids, and air gaps, etc. as well as the more complicated transversely varying modes. These results are fundamental for the understanding and design optimization of the widely used quartz crystal plate resonators and sensors.
A Law of Robustness beyond Isoperimetry

We study the robust interpolation problem of arbitrary data distributions supported on a bounded space and propose a two-fold law of robustness. Robust interpolation refers to the problem of interpolating $n$ noisy training data points in $\mathbb{R}^d$ by a Lipschitz function. Although this problem has been well understood when the samples are drawn from an isoperimetry distribution, much remains unknown concerning its performance under generic or even the worst-case distributions. We prove a Lipschitzness lower bound $\Omega(\sqrt{n/p})$ of the interpolating neural network with $p$ parameters on arbitrary data distributions. With this result, we validate the law of robustness conjecture in prior work by Bubeck, Li, and Nagaraj on two-layer neural networks with polynomial weights. We then extend our result to arbitrary interpolating approximators and prove a Lipschitzness lower bound $\Omega(n^{1/d})$ for robust interpolation. Our results demonstrate a two-fold law of robustness: i) we show the potential benefit of overparametrization for smooth data interpolation when $n=\mathrm{poly}(d)$, and ii) we disprove the potential existence of an $O(1)$-Lipschitz robust interpolating function when $n=\exp(\omega(d))$.
EMOTE: An Explainable architecture for Modelling the Other Through Empathy

We can usually assume others have goals analogous to our own. This assumption can also, at times, be applied to multi-agent games - e.g. Agent 1's attraction to green pellets is analogous to Agent 2's attraction to red pellets. This"analogy"assumption is tied closely to the cognitive process known as empathy. Inspired by empathy, we design a simple and explainable architecture to model another agent's action-value function. This involves learning an"Imagination Network"to transform the other agent's observed state in order to produce a human-interpretable"empathetic state"which, when presented to the learning agent, produces behaviours that mimic the other agent. Our approach is applicable to multi-agent scenarios consisting of a single learning agent and other (independent) agents acting according to fixed policies. This architecture is particularly beneficial for (but not limited to) algorithms using a composite value or reward function. We show our method produces better performance in multi-agent games, where it robustly estimates the other's model in different environment configurations. Additionally, we show that the empathetic states are human interpretable, and thus verifiable.
Asymptotics for Palette Sparsification

It is shown that the following holds for each $\varepsilon>0$. For $G$ an $n$-vertex graph of maximum degree $D$ and"lists"$L_v$ ($v \in V(G)$) chosen independently and uniformly from the ($(1+\varepsilon)\ln n$)-subsets of $\{1, . , D+1\}$, \[ G \text{ admits a proper coloring } \sigma \text{ with } \sigma_v \in L_v \forall v \] with probability tending to 1 as $D \to \infty$. This is an asymptotically optimal version of a recent"palette sparsification"theorem of Assadi, Chen, and Khanna.
NEW SPECTROSCOPIC TECHNIQUE BASED ON COADDITION OF SURFACE BRIGHTNESS FLUCTUATIONS: NGC 4449 AND ITS STELLAR TIDAL STREAM

We present a new spectroscopic technique based in part on targeting the upward fluctuations of the surface brightness for studying the internal stellar kinematics and metallicities of galaxies of low surface brightness effects both to galaxies and streams beyond the Local Group. The distance to these systems makes them unsuitable for targeting individual red giant branch (RGB) stars (tip of RGB at mag) and their surface brightness is too low ( mag arcsec−2) for integrated light spectroscopic measurements. This technique overcomes these two problems by targeting individual objects that are brighter than the tip of the RGB. We apply this technique to the star-forming dwarf galaxy NGC 4449 and its stellar stream. We use Keck/DEIMOS data to measure the line-of-sight radial velocity out to ∼7 kpc in the east side of the galaxy and ∼8 kpc along the stream. We find that the two systems are likely gravitationally bound to each other and have heliocentric radial velocities of 227.3 ± 10.7 km s−1 and 225.8 ± 16.0 km s−1, respectively. Neither the stream nor the near half of the galaxy shows a significant velocity gradient. We estimate the stellar metallicity of the stream based on the equivalent width of its calcium triplet lines and find [Fe/H] , which is consistent with the metallicity–luminosity relation for dwarf galaxies in the Local Group. Whether the stream's progenitor was moderately or severely stripped cannot be constrained with this uncertainty in metallicity. We demonstrate that this new technique can be used to measure the kinematics and (possibly) the metallicity of the numerous faint satellites and stellar streams in the halos of nearby (∼4 Mpc) galaxies.
Optimal Sampling-based Motion Planning in Gaussian Belief Space for Minimum Sensing Navigation

In this paper, we consider the motion planning problem in Gaussian belief space for minimum sensing navigation. Despite the extensive use of sampling-based algorithms and their rigorous analysis in the deterministic setting, there has been little formal analysis of the quality of their solutions returned by sampling algorithms in Gaussian belief space. This paper aims to address this lack of research by examining the asymptotic behavior of the cost of solutions obtained from Gaussian belief space based sampling algorithms as the number of samples increases. To that end, we propose a sampling based motion planning algorithm termed Information Geometric PRM* (IG-PRM*) for generating feasible paths that minimize a weighted sum of the Euclidean and an information-theoretic cost and show that the cost of the solution that is returned is guaranteed to approach the global optimum in the limit of large number of samples. Finally, we consider an obstacle-free scenario and compute the optimal solution using the"move and sense"strategy in literature. We then verify that the cost returned by our proposed algorithm converges to this optimal solution as the number of samples increases.
AI Chain on Large Language Model for Unsupervised Control Flow Graph Generation for Statically-Typed Partial Code

Control Flow Graphs (CFGs) are essential for visualizing, understanding and analyzing program behavior. For statically-typed programming language like Java, developers obtain CFGs by using bytecode-based methods for compilable code and Abstract Syntax Tree (AST)-based methods for partially uncompilable code. However, explicit syntax errors during AST construction and implicit semantic errors caused by bad coding practices can lead to behavioral loss and deviation of CFGs.To address the issue, we propose a novel approach that leverages the error-tolerant and understanding ability of pre-trained Large Language Models (LLMs) to generate CFGs. Our approach involves a Chain of Thought (CoT) with four steps: structure hierarchy extraction, nested code block extraction, CFG generation of nested code blocks, and fusion of all nested code blocks' CFGs. To address the limitations of the original CoT's single-prompt approach (i.e., completing all steps in a single generative pass), which can result in an ``epic'' prompt with hard-to-control behavior and error accumulation, we break down the CoT into an AI chain with explicit sub-steps. Each sub-step corresponds to a separate AI-unit, with an effective prompt assigned to each unit for interacting with LLMs to accomplish a specific purpose.Our experiments confirmed that our method outperforms existing CFG tools in terms of node and edge coverage, especially for incomplete or erroneous code. We also conducted an ablation experiment and confirmed the effectiveness of AI chain design principles: Hierarchical Task Breakdown, Unit Composition, and Mix of AI Units and Non-AI Units.Our work opens up new possibilities for building foundational software engineering tools based on LLMs, as opposed to traditional program analysis methods.
A combined volume penalization/selective frequency damping approach for immersed boundary methods: Application to moving geometries

High-order numerical techniques and immersed boundary methods (IBMs) are gaining popularity to avoid constructing body-fitted meshes while accurately resolving complex flows on Cartesian grids. Recently, we have presented a new treatment for the immersed boundary method based on the combination of volume penalization and selective frequency damping (SFD) [J. Kou and E. Ferrer, “A combined volume penalization/selective frequency damping approach for immersed boundary methods applied to high-order schemes,” J. Comput. Phys. 472, 111678 (2023). ], that offers improved accuracy for nonmoving geometries. The objective of SFD is to remove nonphysical, high-frequency oscillations inside the solid body and by doing so enhance the accuracy in the fluid region. The present paper extends the new immersed boundary treatment to moving geometries. The convergence of this approach is first validated by the method of manufactured solutions, where we design a one-dimensional advection–diffusion case, with a moving interface, to validate the numerical accuracy. Second, we simulate an unsteady flow past a plunging circular cylinder (Navier–Stokes solver). In this case, we show that the combination of volume penalization and SFD provides improved accuracy for moving geometries.
Attribute-Efficient PAC Learning of Low-Degree Polynomial Threshold Functions with Nasty Noise

The concept class of low-degree polynomial threshold functions (PTFs) plays a fundamental role in machine learning. In this paper, we study PAC learning of $K$-sparse degree-$d$ PTFs on $\mathbb{R}^n$, where any such concept depends only on $K$ out of $n$ attributes of the input. Our main contribution is a new algorithm that runs in time $({nd}/{\epsilon})^{O(d)}$ and under the Gaussian marginal distribution, PAC learns the class up to error rate $\epsilon$ with $O(\frac{K^{4d}}{\epsilon^{2d}} \cdot \log^{5d} n)$ samples even when an $\eta \leq O(\epsilon^d)$ fraction of them are corrupted by the nasty noise of Bshouty et al. (2002), possibly the strongest corruption model. Prior to this work, attribute-efficient robust algorithms are established only for the special case of sparse homogeneous halfspaces. Our key ingredients are: 1) a structural result that translates the attribute sparsity to a sparsity pattern of the Chow vector under the basis of Hermite polynomials, and 2) a novel attribute-efficient robust Chow vector estimation algorithm which uses exclusively a restricted Frobenius norm to either certify a good approximation or to validate a sparsity-induced degree-$2d$ polynomial as a filter to detect corrupted samples.
Spreads in Effective Learning Rates: The Perils of Batch Normalization During Early Training

Excursions in gradient magnitude pose a persistent challenge when training deep networks. In this paper, we study the early training phases of deep normalized ReLU networks, accounting for the induced scale invariance by examining effective learning rates (LRs). Starting with the well-known fact that batch normalization (BN) leads to exponentially exploding gradients at initialization, we develop an ODE-based model to describe early training dynamics. Our model predicts that in the gradient flow, effective LRs will eventually equalize, aligning with empirical findings on warm-up training. Using large LRs is analogous to applying an explicit solver to a stiff non-linear ODE, causing overshooting and vanishing gradients in lower layers after the first step. Achieving overall balance demands careful tuning of LRs, depth, and (optionally) momentum. Our model predicts the formation of spreads in effective LRs, consistent with empirical measurements. Moreover, we observe that large spreads in effective LRs result in training issues concerning accuracy, indicating the importance of controlling these dynamics. To further support a causal relationship, we implement a simple scheduling scheme prescribing uniform effective LRs across layers and confirm accuracy benefits.
Factually Consistent Summarization via Reinforcement Learning with Textual Entailment Feedback

Despite the seeming success of contemporary grounded text generation systems, they often tend to generate factually inconsistent text with respect to their input.This phenomenon is emphasized in tasks like summarization, in which the generated summaries should be corroborated by their source article. In this work we leverage recent progress on textual entailment models to directly address this problem for abstractive summarization systems.We use reinforcement learning with reference-free, textual-entailment rewards to optimize for factual consistency and explore the ensuing trade-offs, as improved consistency may come at the cost of less informative or more extractive summaries.Our results, according to both automatic metrics and human evaluation, show that our method considerably improves the faithfulness, salience and conciseness of the generated summaries.
On Masked Pre-training and the Marginal Likelihood

Masked pre-training removes random input dimensions and learns a model that can predict the missing values. Empirical results indicate that this intuitive form of self-supervised learning yields models that generalize very well to new domains. A theoretical understanding is, however, lacking. This paper shows that masked pre-training with a suitable cumulative scoring function corresponds to maximizing the model's marginal likelihood, which is de facto the Bayesian model selection measure of generalization. Beyond shedding light on the success of masked pre-training, this insight also suggests that Bayesian models can be trained with appropriately designed self-supervision. Empirically, we confirm the developed theory and explore the main learning principles of masked pre-training in large language models.
Is novelty predictable?

Machine learning-based design has gained traction in the sciences, most notably in the design of small molecules, materials, and proteins, with societal applications ranging from drug development and plastic degradation to carbon sequestration. When designing objects to achieve novel property values with machine learning, one faces a fundamental challenge: how to push past the frontier of current knowledge, distilled from the training data into the model, in a manner that rationally controls the risk of failure. If one trusts learned models too much in extrapolation, one is likely to design rubbish. In contrast, if one does not extrapolate, one cannot find novelty. Herein, we ponder how one might strike a useful balance between these two extremes. We focus in particular on designing proteins with novel property values, although much of our discussion is relevant to machine learning-based design more broadly.
Low-Cost GNSS Simulators With Wireless Clock Synchronization for Indoor Positioning

In regions where global navigation satellite systems (GNSS) signals are unavailable, such as underground areas and tunnels, GNSS simulators can be deployed for transmitting simulated GNSS signals. Then, a GNSS receiver in the simulator coverage outputs the position based on the received GNSS signals (e.g., Global Positioning System (GPS) L1 signals in this study) transmitted by the corresponding simulator. This approach provides periodic position updates to GNSS users while deploying a small number of simulators without modifying the hardware and software of user receivers. However, the simulator clock should be synchronized to the GNSS satellite clock to generate almost identical signals to the live-sky GNSS signals, which is necessary for seamless indoor and outdoor positioning handover. The conventional clock synchronization method based on the wired connection between each simulator and an outdoor GNSS antenna causes practical difficulty and increases the cost of deploying the simulators. This study proposes a wireless clock synchronization method based on a private time server and time delay calibration. Additionally, we derived the constraints for determining the optimal simulator coverage and separation between adjacent simulators. The positioning performance of the proposed GPS simulator-based indoor positioning system was demonstrated in the underground testbed for a driving vehicle with a GPS receiver and a pedestrian with a smartphone. The average position errors were 3.7 m for the vehicle and 9.6 m for the pedestrian during the field tests with successful indoor and outdoor positioning handovers. Since those errors are within the coverage of each deployed simulator, it is confirmed that the proposed system with wireless clock synchronization can effectively provide periodic position updates to users where live-sky GNSS signals are unavailable.
Existential closedeness and the structure of bimodules of II$_1$ factors

We prove that if a separable II$_1$ factor $M$ is existentially closed, then every $M$-bimodule is weakly contained in the trivial $M$-bimodule, $\text{L}^2(M)$, and, equivalently, every normal completely positive map on $M$ is a pointwise 2-norm limit of maps of the form $x\mapsto\sum_{i=1}^ka_i^*xa_i$, for some $k\in\mathbb N$ and $(a_i)_{i=1}^k\subset M$. This provides the first examples of non-hyperfinite separable II$_1$ factors $M$ with the latter properties. We also obtain new characterizations of $M$-bimodules which are weakly contained in the trivial or coarse $M$-bimodule and of relative amenability inside $M$. Additionally, we give an operator algebraic presentation of the proof of the existence of existentially closed II$_1$ factors. While existentially closed II$_1$ factors have property Gamma, by adapting this proof we construct non-Gamma II$_1$ factors which are existentially closed in every weakly coarse extension.
Efficient Deep Learning of Robust Policies from MPC using Imitation and Tube-Guided Data Augmentation

Imitation Learning (IL) has been increasingly employed to generate computationally efficient policies from task-relevant demonstrations provided by Model Predictive Control (MPC). However, commonly employed IL methods are often data- and computationally-inefficient, as they require a large number of MPC demonstrations, resulting in long training times, and they produce policies with limited robustness to disturbances not experienced during training. In this work, we propose an IL strategy to efficiently compress a computationally expensive MPC into a Deep Neural Network (DNN) policy that is robust to previously unseen disturbances. By using a robust variant of the MPC, called Robust Tube MPC (RTMPC), and leveraging properties from the controller, we introduce a computationally-efficient Data Aggregation (DA) method that enables a significant reduction of the number of MPC demonstrations and training time required to generate a robust policy. Our approach opens the possibility of zero-shot transfer of a policy trained from a single MPC demonstration collected in a nominal domain, such as a simulation or a robot in a lab/controlled environment, to a new domain with previously-unseen bounded model errors/perturbations. Numerical and experimental evaluations performed using linear and nonlinear MPC for agile flight on a multirotor show that our method outperforms strategies commonly employed in IL (such as DAgger and DR) in terms of demonstration-efficiency, training time, and robustness to perturbations unseen during training.
Graph Switching Dynamical Systems

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour into different regimes, or modes, each with simpler dynamics, and then learning the switching behaviour from one mode to another. Switching Dynamical Systems (SDS) are a powerful tool that automatically discovers these modes and mode-switching behaviour from time series data. While effective, these methods focus on independent objects, where the modes of one object are independent of the modes of the other objects. In this paper, we focus on the more general interacting object setting for switching dynamical systems, where the per-object dynamics also depends on an unknown and dynamically changing subset of other objects and their modes. To this end, we propose a novel graph-based approach for switching dynamical systems, GRAph Switching dynamical Systems (GRASS), in which we use a dynamic graph to characterize interactions between objects and learn both intra-object and inter-object mode-switching behaviour. We introduce two new datasets for this setting, a synthesized ODE-driven particles dataset and a real-world Salsa Couple Dancing dataset. Experiments show that GRASS can consistently outperforms previous state-of-the-art methods.
A new source for light dark matter isocurvature in low scale inflation

Light scalar and pseudoscalar particles are compelling dark matter candidates, with a vast running experimental program to discover them. Previous studies have shown that these light fields can generate sizable isocurvature perturbations in high scale inflationary models. Thereby, dark matter existence and cosmic microwave background measurements impose an upper bound on the inflationary scale. In this work, focusing on the axion case, we point out that light fields present during inflation can generate important isocurvature perturbations also in scenarios of low-scale inflation. In our mechanism, the axion field starts with some non-zero field value during inflation and rolls along its potential. Since inflation has a different duration in different patches of the universe, different regions will then have different values of the axion field, generating cold dark matter isocurvature modes. These modes are fully correlated with the adiabatic ones and share the same spectral index. In this scenario, the axion mass determines a lower bound on the Hubble parameter during inflation.
Neural Bee Colony Optimization: A Case Study in Public Transit Network Design

In this work we explore the combination of metaheuristics and learned neural network solvers for combinatorial optimization. We do this in the context of the transit network design problem, a uniquely challenging combinatorial optimization problem with real-world importance. We train a neural network policy to perform single-shot planning of individual transit routes, and then incorporate it as one of several sub-heuristics in a modified Bee Colony Optimization (BCO) metaheuristic algorithm. Our experimental results demonstrate that this hybrid algorithm outperforms the learned policy alone by up to 20% and the original BCO algorithm by up to 53% on realistic problem instances. We perform a set of ablations to study the impact of each component of the modified algorithm.