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We introduce the FRactional-Order graph Neural Dynamical network (FROND), a new continuous graph neural network (GNN) framework. Unlike traditional continuous GNNs that rely on integer-order differential equations, FROND employs the Caputo fractional derivative to leverage the non-local properties of fractional calculus. This approach enables the capture of long-term dependencies in feature updates, moving beyond the Markovian update mechanisms in conventional integer-order models and offering enhanced capabilities in graph representation learning. We offer an interpretation of the node feature updating process in FROND from a non-Markovian random walk perspective when the feature updating is particularly governed by a diffusion process. We demonstrate analytically that oversmoothing can be mitigated in this setting. Experimentally, we validate the FROND framework by comparing the fractional adaptations of various established integer-order continuous GNNs, demonstrating their consistently improved performance and underscoring the framework's potential as an effective extension to enhance traditional continuous GNNs. The code is available at \url{https://github.com/zknus/ICLR2024-FROND}., Comment: The Twelfth International Conference on Learning Representations

Point cloud registration is a fundamental technique in 3-D computer vision with applications in graphics, autonomous driving, and robotics. However, registration tasks under challenging conditions, under which noise or perturbations are prevalent, can be difficult. We propose a robust point cloud registration approach that leverages graph neural partial differential equations (PDEs) and heat kernel signatures. Our method first uses graph neural PDE modules to extract high dimensional features from point clouds by aggregating information from the 3-D point neighborhood, thereby enhancing the robustness of the feature representations. Then, we incorporate heat kernel signatures into an attention mechanism to efficiently obtain corresponding keypoints. Finally, a singular value decomposition (SVD) module with learnable weights is used to predict the transformation between two point clouds. Empirical experiments on a 3-D point cloud dataset demonstrate that our approach not only achieves state-of-the-art performance for point cloud registration but also exhibits better robustness to additive noise or 3-D shape perturbations., Comment: Accepted by IEEE Transactions on Geoscience and Remote Sensing

Chain-of-thought (CoT), tree-of-thought (ToT), and related techniques work surprisingly well in practice for some complex reasoning tasks with Large Language Models (LLMs), but why? This work seeks the underlying reasons by conducting experimental case studies and linking the performance benefits to well-established sample and computational complexity principles in machine learning. We experimented with 6 reasoning tasks, ranging from grade school math, air travel planning, ..., to Blocksworld. The results suggest that (i) both CoT and ToT benefit significantly from task decomposition, which breaks a complex reasoning task into a sequence of steps with low sample complexity and explicitly outlines the reasoning structure, and (ii) for computationally hard reasoning tasks, the more sophisticated tree structure of ToT outperforms the linear structure of CoT. These findings provide useful guidelines for the use of LLM in solving reasoning tasks in practice.

Motivated by applications to group synchronization and quadratic assignment on random data, we study a general problem of Bayesian inference of an unknown ``signal'' belonging to a high-dimensional compact group, given noisy pairwise observations of a featurization of this signal. We establish a quantitative comparison between the signal-observation mutual information in any such problem with that in a simpler model with linear observations, using interpolation methods. For group synchronization, our result proves a replica formula for the asymptotic mutual information and Bayes-optimal mean-squared-error. Via analyses of this replica formula, we show that the conjectural phase transition threshold for computationally-efficient weak recovery of the signal is determined by a classification of the real-irreducible components of the observed group representation(s), and we fully characterize the information-theoretic limits of estimation in the example of angular/phase synchronization over $SO(2)$/$U(1)$. For quadratic assignment, we study observations given by a kernel matrix of pairwise similarities and a randomly permutated and noisy counterpart, and we show in a bounded signal-to-noise regime that the asymptotic mutual information coincides with that in a Bayesian spiked model with i.i.d. signal prior.

Band selection in hyperspectral imaging (HSI) is critical for optimising data processing and enhancing analytical accuracy. Traditional approaches have predominantly concentrated on analysing spectral and pixel characteristics within individual bands independently. These approaches overlook the potential benefits of integrating multiple data sources, such as Light Detection and Ranging (LiDAR), and is further challenged by the limited availability of labeled data in HSI processing, which represents a significant obstacle. To address these challenges, this paper introduces a novel unsupervised band selection framework that incorporates attention mechanisms and an Autoencoder for reconstruction-based band selection. Our methodology distinctively integrates HSI with LiDAR data through an attention score, using a convolutional Autoencoder to process the combined feature mask. This fusion effectively captures essential spatial and spectral features and reduces redundancy in hyperspectral datasets. A comprehensive comparative analysis of our innovative fused band selection approach is performed against existing unsupervised band selection and fusion models. We used data sets such as Houston 2013, Trento, and MUUFLE for our experiments. The results demonstrate that our method achieves superior classification accuracy and significantly outperforms existing models. This enhancement in HSI band selection, facilitated by the incorporation of LiDAR features, underscores the considerable advantages of integrating features from different sources., Comment: 13 pages, 13figures, 6 tables

The fusion of hyperspectral and LiDAR data has been an active research topic. Existing fusion methods have ignored the high-dimensionality and redundancy challenges in hyperspectral images, despite that band selection methods have been intensively studied for hyperspectral image (HSI) processing. This paper addresses this significant gap by introducing a cross-attention mechanism from the transformer architecture for the selection of HSI bands guided by LiDAR data. LiDAR provides high-resolution vertical structural information, which can be useful in distinguishing different types of land cover that may have similar spectral signatures but different structural profiles. In our approach, the LiDAR data are used as the "query" to search and identify the "key" from the HSI to choose the most pertinent bands for LiDAR. This method ensures that the selected HSI bands drastically reduce redundancy and computational requirements while working optimally with the LiDAR data. Extensive experiments have been undertaken on three paired HSI and LiDAR data sets: Houston 2013, Trento and MUUFL. The results highlight the superiority of the cross-attention mechanism, underlining the enhanced classification accuracy of the identified HSI bands when fused with the LiDAR features. The results also show that the use of fewer bands combined with LiDAR surpasses the performance of state-of-the-art fusion models., Comment: 15 pages, 13 figures

Continual learning, an important aspect of artificial intelligence and machine learning research, focuses on developing models that learn and adapt to new tasks while retaining previously acquired knowledge. Existing continual learning algorithms usually involve a small number of tasks with uniform sizes and may not accurately represent real-world learning scenarios. In this paper, we investigate the performance of continual learning algorithms with a large number of tasks drawn from a task distribution that is long-tail in terms of task sizes. We design one synthetic dataset and two real-world continual learning datasets to evaluate the performance of existing algorithms in such a setting. Moreover, we study an overlooked factor in continual learning, the optimizer states, e.g. first and second moments in the Adam optimizer, and investigate how it can be used to improve continual learning performance. We propose a method that reuses the optimizer states in Adam by maintaining a weighted average of the second moments from previous tasks. We demonstrate that our method, compatible with most existing continual learning algorithms, effectively reduces forgetting with only a small amount of additional computational or memory costs, and provides further improvements on existing continual learning algorithms, particularly in a long-tail task sequence.

This paper addresses the challenge of object-centric layout generation under spatial constraints, seen in multiple domains including floorplan design process. The design process typically involves specifying a set of spatial constraints that include object attributes like size and inter-object relations such as relative positioning. Existing works, which typically represent objects as single nodes, lack the granularity to accurately model complex interactions between objects. For instance, often only certain parts of an object, like a room's right wall, interact with adjacent objects. To address this gap, we introduce a factor graph based approach with four latent variable nodes for each room, and a factor node for each constraint. The factor nodes represent dependencies among the variables to which they are connected, effectively capturing constraints that are potentially of a higher order. We then develop message-passing on the bipartite graph, forming a factor graph neural network that is trained to produce a floorplan that aligns with the desired requirements. Our approach is simple and generates layouts faithful to the user requirements, demonstrated by a large improvement in IOU scores over existing methods. Additionally, our approach, being inferential and accurate, is well-suited to the practical human-in-the-loop design process where specifications evolve iteratively, offering a practical and powerful tool for AI-guided design., Comment: To be published at IEEE/CVF CVPR 2024

Classifying hyperspectral images is a difficult task in remote sensing, due to their complex high-dimensional data. To address this challenge, we propose HSIMamba, a novel framework that uses bidirectional reversed convolutional neural network pathways to extract spectral features more efficiently. Additionally, it incorporates a specialized block for spatial analysis. Our approach combines the operational efficiency of CNNs with the dynamic feature extraction capability of attention mechanisms found in Transformers. However, it avoids the associated high computational demands. HSIMamba is designed to process data bidirectionally, significantly enhancing the extraction of spectral features and integrating them with spatial information for comprehensive analysis. This approach improves classification accuracy beyond current benchmarks and addresses computational inefficiencies encountered with advanced models like Transformers. HSIMamba were tested against three widely recognized datasets Houston 2013, Indian Pines, and Pavia University and demonstrated exceptional performance, surpassing existing state-of-the-art models in HSI classification. This method highlights the methodological innovation of HSIMamba and its practical implications, which are particularly valuable in contexts where computational resources are limited. HSIMamba redefines the standards of efficiency and accuracy in HSI classification, thereby enhancing the capabilities of remote sensing applications. Hyperspectral imaging has become a crucial tool for environmental surveillance, agriculture, and other critical areas that require detailed analysis of the Earth surface. Please see our code in HSIMamba for more details., Comment: 11 pages, 2 figures, 8 tables

Knee osteoarthritis is a degenerative joint disease that induces chronic pain and disability. Bone morphological analysis is a promising tool to understand the mechanical aspect of this disorder. This study proposes a 2D bone morphological analysis using manually segmented bones to explore morphological features related to distinct pain conditions. Furthermore, six semantic segmentation algorithms are assessed for extracting femur and tibia bones from X-ray images. Our analysis reveals that the morphology of the femur undergoes significant changes in instances where pain worsens. Conversely, improvements in pain may not manifest pronounced alterations in bone shape. The few-shot-learning-based algorithm, UniverSeg, demonstrated superior segmentation results with Dice scores of 99.69% for femur and 99.60% for tibia. Regarding pain condition classification, the zero-shot-learning-based algorithm, CP-SAM, achieved the highest accuracy at 66% among all models. UniverSeg is recommended for automatic knee bone segmentation, while SAM models show potential with prompt encoder modifications for optimized outcomes. These findings highlight the effectiveness of few-shot learning for semantic segmentation and the potential of zero-shot learning in enhancing classification models for knee osteoarthritis diagnosis.

Survival analysis is essential for studying time-to-event outcomes and providing a dynamic understanding of the probability of an event occurring over time. Various survival analysis techniques, from traditional statistical models to state-of-the-art machine learning algorithms, support healthcare intervention and policy decisions. However, there remains ongoing discussion about their comparative performance. We conducted a comparative study of several survival analysis methods, including Cox proportional hazards (CoxPH), stepwise CoxPH, elastic net penalized Cox model, Random Survival Forests (RSF), Gradient Boosting machine (GBM) learning, AutoScore-Survival, DeepSurv, time-dependent Cox model based on neural network (CoxTime), and DeepHit survival neural network. We applied the concordance index (C-index) for model goodness-of-fit, and integral Brier scores (IBS) for calibration, and considered the model interpretability. As a case study, we performed a retrospective analysis of patients admitted through the emergency department of a tertiary hospital from 2017 to 2019, predicting 90-day all-cause mortality based on patient demographics, clinicopathological features, and historical data. The results of the C-index indicate that deep learning achieved comparable performance, with DeepSurv producing the best discrimination (DeepSurv: 0.893; CoxTime: 0.892; DeepHit: 0.891). The calibration of DeepSurv (IBS: 0.041) performed the best, followed by RSF (IBS: 0.042) and GBM (IBS: 0.0421), all using the full variables. Moreover, AutoScore-Survival, using a minimal variable subset, is easy to interpret, and can achieve good discrimination and calibration (C-index: 0.867; IBS: 0.044). While all models were satisfactory, DeepSurv exhibited the best discrimination and calibration. In addition, AutoScore-Survival offers a more parsimonious model and excellent interpretability.

As COVID-19 enters its fifth year, it continues to pose a significant global health threat, with the constantly mutating SARS-CoV-2 virus challenging drug effectiveness. A comprehensive understanding of virus-drug interactions is essential for predicting and improving drug effectiveness, especially in combating drug resistance during the pandemic. In response, the Path Laplacian Transformer-based Prospective Analysis Framework (PLFormer-PAF) has been proposed, integrating historical data analysis and predictive modeling strategies. This dual-strategy approach utilizes path topology to transform protein-ligand complexes into topological sequences, enabling the use of advanced large language models for analyzing protein-ligand interactions and enhancing its reliability with factual insights garnered from historical data. It has shown unparalleled performance in predicting binding affinity tasks across various benchmarks, including specific evaluations related to SARS-CoV-2, and assesses the impact of virus mutations on drug efficacy, offering crucial insights into potential drug resistance. The predictions align with observed mutation patterns in SARS-CoV-2, indicating that the widespread use of the Pfizer drug has lead to viral evolution and reduced drug efficacy. PLFormer-PAF's capabilities extend beyond identifying drug-resistant strains, positioning it as a key tool in drug discovery research and the development of new therapeutic strategies against fast-mutating viruses like COVID-19.

Permutation invariance is among the most common symmetry that can be exploited to simplify complex problems in machine learning (ML). There has been a tremendous surge of research activities in building permutation invariant ML architectures. However, less attention is given to: (1) how to statistically test for permutation invariance of coordinates in a random vector where the dimension is allowed to grow with the sample size; (2) how to leverage permutation invariance in estimation problems and how does it help reduce dimensions. In this paper, we take a step back and examine these questions in several fundamental problems: (i) testing the assumption of permutation invariance of multivariate distributions; (ii) estimating permutation invariant densities; (iii) analyzing the metric entropy of permutation invariant function classes and compare them with their counterparts without imposing permutation invariance; (iv) deriving an embedding of permutation invariant reproducing kernel Hilbert spaces for efficient computation. In particular, our methods for (i) and (iv) are based on a sorting trick and (ii) is based on an averaging trick. These tricks substantially simplify the exploitation of permutation invariance., Comment: 27 pages, 2 figures, 4 Tables

This letter studies the performance of reconfigurable intelligent surface (RIS)-aided communications for a fluid antenna system (FAS) enabled receiver. Specifically, a fixed singleantenna base station (BS) transmits information through a RIS to a mobile user (MU) which is equipped with a planar fluid antenna in the absence of a direct link.We first analyze the spatial correlation structures among the positions (or ports) in the planar FAS, and then derive the joint distribution of the equivalent channel gain at the user by exploiting the central limit theorem. Furthermore, we obtain compact analytical expressions for the outage probability (OP) and delay outage rate (DOR). Numerical results illustrate that using FAS with only one activated port into the RIS-aided communication network can greatly enhance the performance, when compared to traditional antenna systems (TAS).

This paper investigates the performance of physical layer security (PLS) in fluid antenna-aided communication systems under arbitrary correlated fading channels. In particular, it is considered that a single fixed-antenna transmitter aims to send confidential information to a legitimate receiver equipped with a planar fluid antenna system (FAS), while an eavesdropper, also taking advantage of a planar FAS, attempts to decode the desired message. For this scenario, we first present analytical expressions of the equivalent channel distributions at the legitimate user and eavesdropper by using copula, so that the obtained analytical results are valid for any arbitrarily correlated fading distributions. Then, with the help of Gauss-Laguerre quadrature, we derive compact analytical expressions for the average secrecy capacity (ASC), the secrecy outage probability (SOP), and the secrecy energy efficiency (SEE) for the FAS wiretap channel. Moreover, for exemplary purposes, we also obtain the compact expression of ASC, SOP, and SEE by utilizing the Gaussian copula under correlated Rayleigh fading channels as a special case. Eventually, numerical results indicate that applying the fluid antenna with only one activated port to PLS can guarantee more secure and reliable transmission, when compared to traditional antenna systems (TAS) exploiting maximal ratio combining (MRC) and antenna selection (AS) under selection combining (SC).

Message passing Graph Neural Networks (GNNs) are known to be limited in expressive power by the 1-WL color-refinement test for graph isomorphism. Other more expressive models either are computationally expensive or need preprocessing to extract structural features from the graph. In this work, we propose to make GNNs universal by guiding the learning process with exact isomorphism solver techniques which operate on the paradigm of Individualization and Refinement (IR), a method to artificially introduce asymmetry and further refine the coloring when 1-WL stops. Isomorphism solvers generate a search tree of colorings whose leaves uniquely identify the graph. However, the tree grows exponentially large and needs hand-crafted pruning techniques which are not desirable from a learning perspective. We take a probabilistic view and approximate the search tree of colorings (i.e. embeddings) by sampling multiple paths from root to leaves of the search tree. To learn more discriminative representations, we guide the sampling process with particle filter updates, a principled approach for sequential state estimation. Our algorithm is end-to-end differentiable, can be applied with any GNN as backbone and learns richer graph representations with only linear increase in runtime. Experimental evaluation shows that our approach consistently outperforms leading GNN models on both synthetic benchmarks for isomorphism detection as well as real-world datasets., Comment: Published as a conference paper at ICLR 2022

Simulation Based Calibration (SBC) is applied to analyse two commonly used, competing Markov chain Monte Carlo algorithms for estimating the posterior distribution of a stochastic volatility model. In particular, the bespoke 'off-set mixture approximation' algorithm proposed by Kim, Shephard, and Chib (1998) is explored together with a Hamiltonian Monte Carlo algorithm implemented through Stan. The SBC analysis involves a simulation study to assess whether each sampling algorithm has the capacity to produce valid inference for the correctly specified model, while also characterising statistical efficiency through the effective sample size. Results show that Stan's No-U-Turn sampler, an implementation of Hamiltonian Monte Carlo, produces a well-calibrated posterior estimate while the celebrated off-set mixture approach is less efficient and poorly calibrated, though model parameterisation also plays a role. Limitations and restrictions of generality are discussed., Comment: Masters thesis, 44 pages, 20 figures

The 2019 edition of Stack Overflow developer survey highlights that, for the first time, Python outperformed Java in terms of popularity. The gap between Python and Java further widened in the 2020 edition of the survey. Unfortunately, despite the rapid increase in Python's popularity, there are not many testing and debugging tools that are designed for Python. This is in stark contrast with the abundance of testing and debugging tools for Java. Thus, there is a need to push research on tools that can help Python developers. One factor that contributed to the rapid growth of Java testing and debugging tools is the availability of benchmarks. A popular benchmark is the Defects4J benchmark; its initial version contained 357 real bugs from 5 real-world Java programs. Each bug comes with a test suite that can expose the bug. Defects4J has been used by hundreds of testing and debugging studies and has helped to push the frontier of research in these directions. In this project, inspired by Defects4J, we create another benchmark database and tool that contain 493 real bugs from 17 real-world Python programs. We hope our benchmark can help catalyze future work on testing and debugging tools that work on Python programs.

Acquiring an accurate world model online for model-based reinforcement learning (MBRL) is challenging due to data nonstationarity, which typically causes catastrophic forgetting for neural networks (NNs). From the online learning perspective, a Follow-The-Leader (FTL) world model is desirable, which optimally fits all previous experiences at each round. Unfortunately, NN-based models need re-training on all accumulated data at every interaction step to achieve FTL, which is computationally expensive for lifelong agents. In this paper, we revisit models that can achieve FTL with incremental updates. Specifically, our world model is a linear regression model supported by nonlinear random features. The linear part ensures efficient FTL update while the nonlinear random feature empowers the fitting of complex environments. To best trade off model capacity and computation efficiency, we introduce a locality sensitive sparse encoding, which allows us to conduct efficient sparse updates even with very high dimensional nonlinear features. We validate the representation power of our encoding and verify that it allows efficient online learning under data covariate shift. We also show, in the Dyna MBRL setting, that our world models learned online using a single pass of trajectory data either surpass or match the performance of deep world models trained with replay and other continual learning methods., Comment: ICLR 2024

In decision-making problems with limited training data, policy functions approximated using deep neural networks often exhibit suboptimal performance. An alternative approach involves learning a world model from the limited data and determining actions through online search. However, the performance is adversely affected by compounding errors arising from inaccuracies in the learned world model. While methods like TreeQN have attempted to address these inaccuracies by incorporating algorithmic inductive biases into the neural network architectures, the biases they introduce are often weak and insufficient for complex decision-making tasks. In this work, we introduce Differentiable Tree Search Network (D-TSN), a novel neural network architecture that significantly strengthens the inductive bias by embedding the algorithmic structure of a best-first online search algorithm. D-TSN employs a learned world model to conduct a fully differentiable online search. The world model is jointly optimized with the search algorithm, enabling the learning of a robust world model and mitigating the effect of prediction inaccuracies. Further, we note that a naive incorporation of best-first search could lead to a discontinuous loss function in the parameter space. We address this issue by adopting a stochastic tree expansion policy, formulating search tree expansion as another decision-making task, and introducing an effective variance reduction technique for the gradient computation. We evaluate D-TSN in an offline-RL setting with a limited training data scenario on Procgen games and grid navigation task, and demonstrate that D-TSN outperforms popular model-free and model-based baselines.

Training of modern large neural networks (NN) requires a combination of parallelization strategies encompassing data, model, or optimizer sharding. When strategies increase in complexity, it becomes necessary for partitioning tools to be 1) expressive, allowing the composition of simpler strategies, and 2) predictable to estimate performance analytically. We present PartIR, our design for a NN partitioning system. PartIR is focused on an incremental approach to rewriting and is hardware-and-runtime agnostic. We present a simple but powerful API for composing sharding strategies and a simulator to validate them. The process is driven by high-level programmer-issued partitioning tactics, which can be both manual and automatic. Importantly, the tactics are specified separately from the model code, making them easy to change. We evaluate PartIR on several different models to demonstrate its predictability, expressibility, and ability to reach peak performance..

We have integrated Easy JavaScript Simulation (EJSS) Data Analytics into the national Learning Management System for Singapore schools, known as the Singapore Student Learning Space (SLS). EJSS Data Analytics enhances the teaching and learning experience for educators and students by enabling educators to monitor and evaluate students interactions with interactive computer simulations. The data analytics and visualisation capabilities are delivered using the Moodle platform and version 1.3 of the specifications for Learning Tools Interoperability (LTI). In this paper, we showcase the potential for EJSS Data Analytics to identify students learning difficulties and misconceptions. Four examples of EJSS Data Analytics applications are provided to illustrate insights on aspects that include understanding a students sequential actions leading to specific task outcomes, the frequency of task attempts by each student, and the ratio of students achieving correct versus incorrect task completions. We identify five key considerations for designing the EJSS teacher dashboard. These considerations relate to Student Thought Process, Student Behaviour, Student Engagement, Student Choice, and Teacher Feedback. These five facets provide a framework for aligning our design efforts with the needs of students and teachers, also drawing upon research in data analytics for education., Comment: 10 pages, 13 figures, 26th International Conference on Multimedia in Physics Teaching and Learning (MPTL'26)

In an earlier paper of the authors, a general family of instances of the relative Langlands duality of Ben-Zvi-Sakellaridis-Venkatesh [BZSV] were proposed and studied in the setting of branching problems for smooth representations. In this paper, we show the numerical conjectures of [BZSV] for the local Plancherel density, as well as an application to their conjectures on global periods, for this general family of instances.

In this work, we rigorously investigate the robustness of graph neural fractional-order differential equation (FDE) models. This framework extends beyond traditional graph neural (integer-order) ordinary differential equation (ODE) models by implementing the time-fractional Caputo derivative. Utilizing fractional calculus allows our model to consider long-term memory during the feature updating process, diverging from the memoryless Markovian updates seen in traditional graph neural ODE models. The superiority of graph neural FDE models over graph neural ODE models has been established in environments free from attacks or perturbations. While traditional graph neural ODE models have been verified to possess a degree of stability and resilience in the presence of adversarial attacks in existing literature, the robustness of graph neural FDE models, especially under adversarial conditions, remains largely unexplored. This paper undertakes a detailed assessment of the robustness of graph neural FDE models. We establish a theoretical foundation outlining the robustness characteristics of graph neural FDE models, highlighting that they maintain more stringent output perturbation bounds in the face of input and graph topology disturbances, compared to their integer-order counterparts. Our empirical evaluations further confirm the enhanced robustness of graph neural FDE models, highlighting their potential in adversarially robust applications., Comment: in Proc. AAAI Conference on Artificial Intelligence, Vancouver, Canada, Feb. 2024

Point cloud registration is a crucial technique in 3D computer vision with a wide range of applications. However, this task can be challenging, particularly in large fields of view with dynamic objects, environmental noise, or other perturbations. To address this challenge, we propose a model called PosDiffNet. Our approach performs hierarchical registration based on window-level, patch-level, and point-level correspondence. We leverage a graph neural partial differential equation (PDE) based on Beltrami flow to obtain high-dimensional features and position embeddings for point clouds. We incorporate position embeddings into a Transformer module based on a neural ordinary differential equation (ODE) to efficiently represent patches within points. We employ the multi-level correspondence derived from the high feature similarity scores to facilitate alignment between point clouds. Subsequently, we use registration methods such as SVD-based algorithms to predict the transformation using corresponding point pairs. We evaluate PosDiffNet on several 3D point cloud datasets, verifying that it achieves state-of-the-art (SOTA) performance for point cloud registration in large fields of view with perturbations. The implementation code of experiments is available at https://github.com/AI-IT-AVs/PosDiffNet.

Rydberg excitons (analogues of Rydberg atoms in condensed matter systems) are highly excited bound electron-hole states with large Bohr radii. The interaction between them as well as exciton coupling to light may lead to strong optical nonlinearity, with applications in sensing and quantum information processing. Here, we achieve strong effective photon-photon interactions (Kerr-like optical nonlinearity) via the Rydberg blockade phenomenon and the hybridisation of excitons and photons forming polaritons in a Cu$_2$O-filled microresonators. Under pulsed resonant excitation polariton resonance frequencies are renormalised due to the reduction of the photon-exciton coupling with increasing exciton density. Theoretical analysis shows that the Rydberg blockade plays a major role in the experimentally observed scaling of the polariton nonlinearity coefficient as $\propto n^{4.4 \pm 1.8}$ for principal quantum numbers up to n = 7. Such high principal quantum numbers studied in a polariton system for the first time are essential for realisation of high Rydberg optical nonlinearities, which paves the way towards quantum optical applications and fundamental studies of strongly-correlated photonic (polaritonic) states in a solid state system.