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Adversarial attacks on explainability models have drastic consequences when explanations are used to understand the reasoning of neural networks in safety critical systems. Path methods are one such class of attribution methods susceptible to adversarial attacks. Adversarial learning is typically phrased as a constrained optimisation problem. In this work, we propose algebraic adversarial examples and study the conditions under which one can generate adversarial examples for integrated gradients. Algebraic adversarial examples provide a mathematically tractable approach to adversarial examples.

The sub-Jovian desert is a region in the mass-period and radius-period parameter space, typically encompassing short-period ranges between super-Earths and hot Jupiters, that exhibits an intrinsic dearth of planets. This scarcity is likely shaped by photoevaporation caused by the stellar irradiation received by giant planets that have migrated inward. We report the detection and characterization of TOI-3568 b, a transiting super-Neptune with a mass of $26.4\pm1.0$ M$_\oplus$, a radius of $5.30\pm0.27$ R$_\oplus$, a bulk density of $0.98\pm0.15$ g cm$^{-3}$, and an orbital period of 4.417965(5) d situated in the vicinity of the sub-Jovian desert. This planet orbiting a K dwarf star with solar metallicity, was identified photometrically by TESS. It was characterized as a planet by our high-precision radial velocity monitoring program using MAROON-X at Gemini North, supplemented by additional observations from the SPICE large program with SPIRou at CFHT. We performed a Bayesian MCMC joint analysis of the TESS and ground-based photometry, MAROON-X and SPIRou radial velocities, to measure the orbit, radius, and mass of the planet, as well as a detailed analysis of the high-resolution flux and polarimetric spectra to determine the physical parameters and elemental abundances of the host star. Our results reveal TOI-3568 b as a hot super-Neptune, rich in hydrogen and helium with a core of heavier elements with a mass between 10 and 25 M$_\oplus$. We analyzed the photoevaporation status of TOI-3568 b and found that it experiences one of the highest EUV luminosities among planets with a mass M$_{\rm p}$ $<2$ M$_{\rm Nep}$, yet it has an evaporation lifetime exceeding 5 Gyr. Positioned in the transition between two significant populations of exoplanets on the mass-period and energy diagrams, this planet presents an opportunity to test theories concerning the origin of the sub-Jovian desert., Comment: Accepted for publication in A&A on September 4, 2024

Text-to-image diffusion models have been widely adopted in real-world applications due to their ability to generate realistic images from textual descriptions. However, recent studies have shown that these methods are vulnerable to backdoor attacks. Despite the significant threat posed by backdoor attacks on text-to-image diffusion models, countermeasures remain under-explored. In this paper, we address this research gap by demonstrating that state-of-the-art backdoor attacks against text-to-image diffusion models can be effectively mitigated by a surprisingly simple defense strategy - textual perturbation. Experiments show that textual perturbations are effective in defending against state-of-the-art backdoor attacks with minimal sacrifice to generation quality. We analyze the efficacy of textual perturbation from two angles: text embedding space and cross-attention maps. They further explain how backdoor attacks have compromised text-to-image diffusion models, providing insights for studying future attack and defense strategies. Our code is available at https://github.com/oscarchew/t2i-backdoor-defense., Comment: ECCV 2024 Workshop The Dark Side of Generative AIs and Beyond

A Lagrangian gravity-wave parameterization (MS-GWaM, Multi-Scale Gravity-Wave Model) that allows for fully transient wave-mean-flow interaction and horizontal propagation is applied to orographic gravity waves for the first time. Both linear and nonlinear mountain waves are modeled in idealized simulations within the pseudo-incompressible flow solver PincFlow. Two-dimensional flows over monochromatic orographies are considered, using MS-GWaM either in its fully transient implementation or in a steady-state implementation that represents classic mountain-wave parameterizations. Comparisons of wave-resolving simulations (not using MS-GWaM) and coarse-resolution simulations (using MS-GWaM) show that allowing for transience leads to a significantly more accurate forcing of the resolved mean flow. The model is able to reproduce the transient forcing of linearly generated mountain waves that slowly propagate upwards, in contrast to the instantaneous distribution of wave energy in classic parameterizations. At high altitudes, wave breaking induces a wind reversal that is captured by the transient model but inhibited in steady-state simulations, due to the assumption of critical level formation. This shows that transience can have a substantial impact in the interaction between mountain waves and mean flow., Comment: 42 pages, 12 figures. This work has been submitted to the Journal of the Atmospheric Sciences. Copyright in this work may be transferred without further notice

The Janis-Newman-Winicour (JNW) spacetime possesses a naked singularity, although it represents an exact particle-like solution to the Einstein-Klein-Gordon theory with a massless scalar field. Here, we investigate the possible formation of a naked singularity in the JNW spacetime, using the thin-shell approximation to describe the gravitational collapse. By introducing different matter contents to construct thin-shells, we demonstrate the impossibility of naked singularity formation during the gravitational collapse unless the causality or null energy condition of the thin-shell is violated. Therefore, the weak cosmic censorship is satisfied even with the naked singularity of the JNW spacetime., Comment: 13 pages, 6 figures

Atoms in Rydberg states are an important building block for emerging quantum technologies. While the excitation to the Rydberg orbitals are typically achieved in more than tens of nanoseconds, the physical limit is in fact much faster, at the ten picoseconds level. Here, we tackle such ultrafast Rydberg excitation of a Rubidium atom by designing a dedicated pulsed laser system generating 480 nm pulses of 10 ps duration. In particular, we improved upon our previous design by using an injection-seeded optical parametric amplifier (OPA) to obtain stable pulsed energy, decreasing the fluctuation from 30 % to 6 %. We then succeeded in ultrafast excitation of Rydberg atoms with excitation probability of ~90 %, not limited anymore by energy fluctuation but rather by the atomic state preparation, addressable in future works. This achievement broadens the range of applications of Rydberg atoms.

Measuring grasp stability is an important skill for dexterous robot manipulation tasks, which can be inferred from haptic information with a tactile sensor. Control policies have to detect rotational displacement and slippage from tactile feedback, and determine a re-grasp strategy in term of location and force. Classic stable grasp task only trains control policies to solve for re-grasp location with objects of fixed center of gravity. In this work, we propose a revamped version of stable grasp task that optimises both re-grasp location and gripping force for objects with unknown and moving center of gravity. We tackle this task with a model-free, end-to-end Transformer-based reinforcement learning framework. We show that our approach is able to solve both objectives after training in both simulation and in a real-world setup with zero-shot transfer. We also provide performance analysis of different models to understand the dynamics of optimizing two opposing objectives., Comment: Accepted by ICIEA 2024

Neutral atoms trapped in microscopic optical tweezers have emerged as a growing platform for quantum science. Achieving homogeneity over the tweezers array is an important technical requirement, and our research focuses on improving it for holographic arrays generated with a Spatial Light Modulator (SLM). We present a series of optimization methods to calculate better holograms, fueled by precise measurement schemes. These innovations enable to achieve intensity homogeneity with a relative standard deviation of 0.3 %, shape variations below 0.5 %, and positioning errors within 70 nm. Such ultra-precise holographic optical tweezers arrays allow for the most demanding applications in quantum science with atomic arrays.

We consider large-scale, implicit-search-based solutions to the Shortest Path Problems on Graphs of Convex Sets (GCS). We propose GCS*, a forward heuristic search algorithm that generalizes A* search to the GCS setting, where a continuous-valued decision is made at each graph vertex, and constraints across graph edges couple these decisions, influencing costs and feasibility. Such mixed discrete-continuous planning is needed in many domains, including motion planning around obstacles and planning through contact. This setting provides a unique challenge for best-first search algorithms: the cost and feasibility of a path depend on continuous-valued points chosen along the entire path. We show that by pruning paths that are cost-dominated over their entire terminal vertex, GCS* can search efficiently while still guaranteeing cost optimality and completeness. To find satisficing solutions quickly, we also present a complete but suboptimal variation, pruning instead reachability-dominated paths. We implement these checks using polyhedral-containment or sampling-based methods. The sampling-based implementation is probabilistically complete and asymptotically cost optimal, and performs effectively even with minimal samples in practice. We demonstrate GCS* on planar pushing tasks where the combinatorial explosion of contact modes renders prior methods intractable and show it performs favorably compared to the state-of-the-art. Project website: https://shaoyuan.cc/research/gcs-star/

In this paper, we shall show that the vector-scalar potential ($\mathbf{A}$-$\Phi$) formulation, for many problems, can be further simplified by ignoring the scalar potential contribution and setting it to zero.

Solid-state quantum emitters are essential sources of single photons, and enhancing their emission rates is of paramount importance for applications in quantum communications, computing, and metrology. One approach is to couple quantum emitters with resonant photonic nanostructures, where the emission rate is enhanced due to the Purcell effect. Dielectric nanoantennas are promising as they provide strong emission enhancement compared to plasmonic ones, which suffer from high Ohmic loss. Here, we designed and fabricated a dielectric Fano resonator based on a pair of silicon (Si) ellipses and a disk, which supports the mode hybridization between quasi-bound-states-in-the-continuum (quasi-BIC) and Mie resonance. We demonstrated the performance of the developed resonant system by interfacing it with single photon emitters (SPEs) based on nitrogen-vacancy (NV-) centers in nanodiamonds (NDs). We observed that the interfaced emitters have a Purcell enhancement factor of ~10, with sub-ns emission lifetime and a polarization contrast of 9. Our results indicate a promising method for developing efficient and compact single-photon sources for integrated quantum photonics applications., Comment: 20 pages, 4 figures

With emerging prevalence beyond traditionally endemic regions, the global burden of dengue disease is forecasted to be one of the fastest growing. With limited direct treatment or vaccination currently available, prevention through vector control is widely believed to be the most effective form of managing outbreaks. This study examines traditional state space models (moving average, autoregressive, ARIMA, SARIMA), supervised learning techniques (XGBoost, SVM, KNN) and deep networks (LSTM, CNN, ConvLSTM) for forecasting weekly dengue cases in Singapore. Meteorological data and search engine trends were included as features for ML techniques. Forecasts using CNNs yielded lowest RMSE in weekly cases in 2019., Comment: 12 pages, 6 figures

Different languages have distinct phonetic systems and vary in their prosodic features making it challenging to develop a Text-to-Speech (TTS) model that can effectively synthesise speech in multilingual settings. Furthermore, TTS architecture needs to be both efficient enough to capture nuances in multiple languages and efficient enough to be practical for deployment. The standard approach is to build transformer based model such as SpeechT5 and train it on large multilingual dataset. As the size of these models grow the conventional fine-tuning for adapting these model becomes impractical due to heavy computational cost. In this paper, we proposes to integrate parameter-efficient transfer learning (PETL) methods such as adapters and hypernetwork with TTS architecture for multilingual speech synthesis. Notably, in our experiments PETL methods able to achieve comparable or even better performance compared to full fine-tuning with only $\sim$2.5\% tunable parameters.The code and samples are available at: https://anonymous.4open.science/r/multilingualTTS-BA4C.

Time series data are collected in temporal order and are widely used to train systems for prediction, modeling and classification to name a few. These systems require large amounts of data to improve generalization and prevent over-fitting. However there is a comparative lack of time series data due to operational constraints. This situation is alleviated by synthesizing data which have a suitable spread of features yet retain the distinctive features of the original data. These would be its basic statistical properties and overall shape which are important for short time series such as in rehabilitative applications or in quickly changing portions of lengthy data. In our earlier work synthesized surrogate time series were used to augment rehabilitative data. This gave good results in classification but the resulting waveforms did not preserve the original signal shape. To remedy this, we use singular spectrum analysis (SSA) to separate a signal into trends and cycles to describe the shape of the signal and low level components. In a novel way we subject the low level component to randomizing processes then recombine this with the original trend and cycle components to form a synthetic time series. We compare our approach with other methods, using statistical and shape measures and demonstrate its effectiveness in classification., Comment: This version of the paper under the same title, acknowledges the data source and the funding for current research using this data. arXiv admin note: substantial text overlap with arXiv:2404.14211

CHEOPS is a space telescope specifically designed to monitor transiting exoplanets orbiting bright stars. In September 2023, CHEOPS completed its nominal mission and remains in excellent operational conditions. The mission has been extended until the end of 2026. Scientific and instrumental data have been collected throughout in-orbit commissioning and nominal operations, enabling a comprehensive analysis of the mission's performance. In this article, we present the results of this analysis with a twofold goal. First, we aim to inform the scientific community about the present status of the mission and what can be expected as the instrument ages. Secondly, we intend for this publication to serve as a legacy document for future missions, providing insights and lessons learned from the successful operation of CHEOPS. To evaluate the instrument performance in flight, we developed a comprehensive monitoring and characterisation programme. It consists of dedicated observations that allow us to characterise the instrument's response. In addition to the standard collection of nominal science and housekeeping data, these observations provide input for detecting, modelling, and correcting instrument systematics, discovering and addressing anomalies, and comparing the instrument's actual performance with expectations. The precision of the CHEOPS measurements has enabled the mission objectives to be met and exceeded. Careful modelling of the instrumental systematics allows the data quality to be significantly improved during the light curve analysis phase, resulting in more precise scientific measurements. CHEOPS is compliant with the driving scientific requirements of the mission. Although visible, the ageing of the instrument has not affected the mission's performance., Comment: Accepted for publication in Astronomy and Astrophysics

Located at the bottom of the main sequence, ultracool dwarf stars are widespread in the solar neighbourhood. Nevertheless, their extremely low luminosity has left their planetary population largely unexplored, and only one of them, TRAPPIST-1, has so far been found to host a transiting planetary system. In this context, we present the SPECULOOS project's detection of an Earth-sized planet in a 17 h orbit around an ultracool dwarf of M6.5 spectral type located 16.8 pc away. The planet's high irradiation (16 times that of Earth) combined with the infrared luminosity and Jupiter-like size of its host star make it one of the most promising rocky exoplanet targets for detailed emission spectroscopy characterization with JWST. Indeed, our sensitivity study shows that just ten secondary eclipse observations with the Mid-InfraRed Instrument/Low-Resolution Spectrometer on board JWST should provide strong constraints on its atmospheric composition and/or surface mineralogy.

Effective ownership of software artifacts, particularly code, is crucial for accountability, knowledge sharing, and code quality enhancement. Researchers have proposed models linking ownership of software artifacts with developer performance and code quality. Our study aims to systematically examine various ownership models and provide a structured literature overview. Conducting a systematic literature review, we identified 79 relevant papers published between 2005 and 2022. We developed a taxonomy of ownership artifacts based on type, owners, and degree of ownership, along with compiling modeling variables and analytics types used in each study. Additionally, we assessed the replication status of each study. As a result, we identified nine distinct software artifacts whose ownership has been discussed in the literature, with "Code" being the most frequently analyzed artifact. We found that only three papers (3.79%) provided code and data, whereas nine papers (11.4%) provided only data. Using our systematic literature review results, we replicated experiments on nine priority projects at \texttt{Brightsquid}. The company aimed to compare its code quality against ownership factors in other teams, so we conducted a replication study using their data. Unlike prior studies, we found no strong correlation between minor contributors and bug numbers. Surprisingly, we found no strong link between the total number of developers modifying a file and bug counts, contrasting previous findings. However, we observed a significant correlation between major contributors and bug counts, diverging from earlier research., Comment: Pre-print an accepted paper for the ESE journal

Flow and heat transfer in a compressor rotating disc cavity with axial throughflow is investigated using wall-modelled large-eddy simulations (WMLES). These are compared to measurements from recently published experiments and used to investigate high Reynolds number effects. The simulations use an open-source CFD solver with high parallel efficiency and employ the Boussinesq approximation for centrifugal buoyancy. Kinetic energy effects (characterised by Eckert number) are accounted for by scaling the thermal boundary conditions from static temperature to rotary stagnation temperature. The WMLES shows very encouraging agreement with experiments up to the highest Reynolds number tested, $Re_\phi=3.0\times10^6$. A further simulation at $Re_\phi=10^7$ extends the investigation to an operating condition more representative of aero engine high pressure compressors. The results support the scaling of shroud heat transfer found at lower $Re_\phi$, but disc heat transfer is higher than expected from a simple extrapolation of lower $Re_\phi$ results. This is associated with transition to turbulence in the disc Ekman layers and is consistent with the boundary layer Reynolds numbers at this condition. The introduction of swirl in the axial throughflow, as may occur at engine conditions, could reduce the boundary layer Reynolds numbers and delay the transition.

Deep learning has enabled breakthroughs in automated diagnosis from medical imaging, with many successful applications in ophthalmology. However, standard medical image classification approaches only assess disease presence at the time of acquisition, neglecting the common clinical setting of longitudinal imaging. For slow, progressive eye diseases like age-related macular degeneration (AMD) and primary open-angle glaucoma (POAG), patients undergo repeated imaging over time to track disease progression and forecasting the future risk of developing disease is critical to properly plan treatment. Our proposed Longitudinal Transformer for Survival Analysis (LTSA) enables dynamic disease prognosis from longitudinal medical imaging, modeling the time to disease from sequences of fundus photography images captured over long, irregular time periods. Using longitudinal imaging data from the Age-Related Eye Disease Study (AREDS) and Ocular Hypertension Treatment Study (OHTS), LTSA significantly outperformed a single-image baseline in 19/20 head-to-head comparisons on late AMD prognosis and 18/20 comparisons on POAG prognosis. A temporal attention analysis also suggested that, while the most recent image is typically the most influential, prior imaging still provides additional prognostic value., Comment: Accepted to npj Digital Medicine

Previously, a class of regular and asymptotically flat gravitating scalar solitons (scalarons) has been constructed in the Einstein--Klein--Gordon (EKG) theory by adopting a phantom field with Higgs-like potential where the kinetic term has the wrong sign and the scalaron possesses the negative Arnowitt--Deser--Misner (ADM) mass as a consequence. In this paper, we demonstrate that the use of the phantom field can be avoided by inverting the Higgs-like potential in the EKG system when the kinetic term has a proper sign, such that the corresponding gravitating scalaron can possess the positive ADM mass. We systematically study the basic properties of the gravitating scalaron, such as the ADM mass, the energy conditions, the geodesics of test particles, etc. Moreover, we find that it can be smoothly connected to the counterpart hairy black hole solutions from our recent work in the small horizon limit., Comment: 18 pages with 9 figures. Special Issue of the Universe (MDPI): Compact Objects (invited contribution)

We investigate scalarized black holes in the Einstein-minimally coupled scalar theory with a negative potential $V(\phi)=-\alpha^2\phi^6$. The tachyonic instability is absent from analyzing the linearized scalar equation, which could not allow for spontaneous scalarization. However, we obtain the black hole solutions with scalar hair by solving three full equations because this scalar potential violates the weak energy condition. This shows clearly that scalarized black holes can be obtained without introducing a non-minimal scalar coupling term. We perform the stability analysis for scalarized black holes by adopting radial perturbations, implying that all scalarized black holes belonging to a single branch are unstable., Comment: 18 pages with 8 figures (To match with the published version)

Time series (TS) data have consistently been in short supply, yet their demand remains high for training systems in prediction, modeling, classification, and various other applications. Synthesis can serve to expand the sample population, yet it is crucial to maintain the statistical characteristics between the synthesized and the original TS : this ensures consistent sampling of data for both training and testing purposes. However the time domain features of the data may not be maintained. This motivates for our work, the objective which is to preserve the following features in a synthesized TS: its fundamental statistical characteristics and important time domain features like its general shape and prominent transients. In a novel way, we first isolate important TS features into various components using a spectrogram and singular spectrum analysis. The residual signal is then randomized in a way that preserves its statistical properties. These components are then recombined for the synthetic time series. Using accelerometer data in a clinical setting, we use statistical and shape measures to compare our method to others. We show it has higher fidelity to the original signal features, has good diversity and performs better data classification in a deep learning application.

Laser Additive Manufacturing (LAM) presents unparalleled opportunities for fabricating complex, high-performance structures and components with unique material properties. Despite these advancements, achieving consistent part quality and process repeatability remains challenging. This paper provides a comprehensive review of various state-of-the-art in-situ process monitoring techniques, including optical-based monitoring, acoustic-based sensing, laser line scanning, and operando X-ray monitoring. These techniques are evaluated for their capabilities and limitations in detecting defects within Laser Powder Bed Fusion (LPBF) and Laser Directed Energy Deposition (LDED) processes. Furthermore, the review discusses emerging multisensor monitoring and machine learning (ML)-assisted defect detection methods, benchmarking ML models tailored for in-situ defect detection. The paper also discusses in-situ adaptive defect remediation strategies that advance LAM towards zero-defect autonomous operations, focusing on real-time closed-loop feedback control and defect correction methods. Research gaps such as the need for standardization, improved reliability and sensitivity, and decision-making strategies beyond early stopping are highlighted. Future directions are proposed, with an emphasis on multimodal sensor fusion for multiscale defect prediction and fault diagnosis, ultimately enabling self-adaptation in LAM processes. This paper aims to equip researchers and industry professionals with a holistic understanding of the current capabilities, limitations, and future directions in in-situ process monitoring and adaptive quality enhancement in LAM., Comment: 107 Pages, 29 Figures. Paper Accepted At Journal of Manufacturing Systems

Small planets transiting bright nearby stars are essential to our understanding of the formation and evolution of exoplanetary systems. However, few constitute prime targets for atmospheric characterization, and even fewer are part of multiple star systems. This work aims to validate TOI-4336 A b, a sub-Neptune-sized exoplanet candidate identified by the TESS space-based transit survey around a nearby M-dwarf. We validate the planetary nature of TOI-4336 A b through the global analysis of TESS and follow-up multi-band high-precision photometric data from ground-based telescopes, medium- and high-resolution spectroscopy of the host star, high-resolution speckle imaging, and archival images. The newly discovered exoplanet TOI-4336 A b has a radius of 2.1$\pm$0.1R$_{\oplus}$. Its host star is an M3.5-dwarf star of mass 0.33$\pm$0.01M$_{\odot}$ and radius 0.33$\pm$0.02R$_{\odot}$ member of a hierarchical triple M-dwarf system 22 pc away from the Sun. The planet's orbital period of 16.3 days places it at the inner edge of the Habitable Zone of its host star, the brightest of the inner binary pair. The parameters of the system make TOI-4336 A b an extremely promising target for the detailed atmospheric characterization of a temperate sub-Neptune by transit transmission spectroscopy with JWST., Comment: 27 pages, 19 figures, 7 tables. Accepted for publication in A&A

We propose an end-to-end approach for gaze target detection: predicting a head-target connection between individuals and the target image regions they are looking at. Most of the existing methods use independent components such as off-the-shelf head detectors or have problems in establishing associations between heads and gaze targets. In contrast, we investigate an end-to-end multi-person Gaze target detection framework with Heads and Targets Association (GazeHTA), which predicts multiple head-target instances based solely on input scene image. GazeHTA addresses challenges in gaze target detection by (1) leveraging a pre-trained diffusion model to extract scene features for rich semantic understanding, (2) re-injecting a head feature to enhance the head priors for improved head understanding, and (3) learning a connection map as the explicit visual associations between heads and gaze targets. Our extensive experimental results demonstrate that GazeHTA outperforms state-of-the-art gaze target detection methods and two adapted diffusion-based baselines on two standard datasets.

Integrating intelligent systems, such as robots, into dynamic group settings poses challenges due to the mutual influence of human behaviors and internal states. A robust representation of social interaction dynamics is essential for effective human-robot collaboration. Existing approaches often narrow their focus to facial expressions or speech, overlooking the broader context. We propose employing an adapted Temporal Graph Networks to comprehensively represent social interaction dynamics while enabling its practical implementation. Our method incorporates temporal multi-modal behavioral data including gaze interaction, voice activity and environmental context. This representation of social interaction dynamics is trained as a link prediction problem using annotated gaze interaction data. The F1-score outperformed the baseline model by 37.0%. This improvement is consistent for a secondary task of next speaker prediction which achieves an improvement of 29.0%. Our contributions are two-fold, including a model to representing social interaction dynamics which can be used for many downstream human-robot interaction tasks like human state inference and next speaker prediction. More importantly, this is achieved using a more concise yet efficient message passing method, significantly reducing it from 768 to 14 elements, while outperforming the baseline model., Comment: 7 pages, 4 figures

Supernet training of LLMs is of great interest in industrial applications as it confers the ability to produce a palette of smaller models at constant cost, regardless of the number of models (of different size / latency) produced. We propose a new method called Multistage Low-rank Fine-tuning of Super-transformers (MLFS) for parameter-efficient supernet training. We show that it is possible to obtain high-quality encoder models that are suitable for commercial edge applications, and that while decoder-only models are resistant to a comparable degree of compression, decoders can be effectively sliced for a significant reduction in training time., Comment: This paper has been accepted for publication in NAACL 2024 (Industry Track)

Explainability models are now prevalent within machine learning to address the black-box nature of neural networks. The question now is which explainability model is most effective. Probabilistic Lipschitzness has demonstrated that the smoothness of a neural network is fundamentally linked to the quality of post hoc explanations. In this work, we prove theoretical lower bounds on the probabilistic Lipschitzness of Integrated Gradients, LIME and SmoothGrad. We propose a novel metric using probabilistic Lipschitzness, normalised astuteness, to compare the robustness of explainability models. Further, we prove a link between the local Lipschitz constant of a neural network and its stable rank. We then demonstrate that the stable rank of a neural network provides a heuristic for the robustness of explainability models.

The representation of subgrid-scale orography is a challenge in the physical parameterization of orographic gravity-wave sources in weather forecasting. A significant hurdle is encoding as much physical information with as simple a representation as possible. Other issues include scale awareness, i.e., the orographic representation has to change according to the grid cell size and usability on unstructured geodesic grids with non-quadrilateral grid cells. This work introduces a novel spectral analysis method approximating a scale-aware spectrum of subgrid-scale orography on unstructured geodesic grids. The dimension of the physical orographic data is reduced by more than two orders of magnitude in its spectral representation. Simultaneously, the power of the approximated spectrum is close to the physical value. The method is based on well-known least-squares spectral analyses. However, it is robust to the choice of the free parameters, and tuning the algorithm is generally unnecessary. Numerical experiments involving an idealized setup show that this novel spectral analysis performs significantly better than a straightforward least-squares spectral analysis in representing the physical energy of a spectrum. Studies involving real-world topographic data are conducted, and reasonable error scores within $\pm 10\%$ error relative to the maximum physical quantity of interest are achieved across different grid sizes and background wind speeds. The deterministic behavior of the method is investigated along with its principal capabilities and potential biases, and it is shown that the error scores can be iteratively improved if an optimization target is known. Discussions on the method's limitations and broader applicability conclude this work., Comment: 37 pages, 19 figures

We present a novel method for global motion planning of robotic systems that interact with the environment through contacts. Our method directly handles the hybrid nature of such tasks using tools from convex optimization. We formulate the motion-planning problem as a shortest-path problem in a graph of convex sets, where a path in the graph corresponds to a contact sequence and a convex set models the quasi-static dynamics within a fixed contact mode. For each contact mode, we use semidefinite programming to relax the nonconvex dynamics that results from the simultaneous optimization of the object's pose, contact locations, and contact forces. The result is a tight convex relaxation of the overall planning problem, that can be efficiently solved and quickly rounded to find a feasible contact-rich trajectory. As an initial application for evaluating our method, we apply it on the task of planar pushing. Exhaustive experiments show that our convex-optimization method generates plans that are consistently within a small percentage of the global optimum, without relying on an initial guess, and that our method succeeds in finding trajectories where a state-of-the-art baseline for contact-rich planning usually fails. We demonstrate the quality of these plans on a real robotic system.

Parity reasoning is challenging for Conflict-Driven Clause Learning (CDCL) SAT solvers. This has been observed even for simple formulas encoding two contradictory parity constraints with different variable orders (Chew and Heule 2020). We provide an analytical explanation for their hardness by showing that they require exponential resolution refutations with high probability when the variable order is chosen at random. We obtain this result by proving that these formulas, which are known to be Tseitin formulas, have Tseitin graphs of linear treewidth with high probability. Since such Tseitin formulas require exponential resolution proofs, our result follows. We generalize this argument to a new class of formulas that capture a basic form of parity reasoning involving a sum of two random parity constraints with random orders. Even when the variable order for the sum is chosen favorably, these formulas remain hard for resolution. In contrast, we prove that they have short DRAT refutations. We show experimentally that the running time of CDCL SAT solvers on both classes of formulas grows exponentially with their treewidth.