Miracle-dz/UniFAR-FTUs huggingface dataset:
Coarse-to-Fine Point Cloud Registration with SE(3)-Equivariant Representations

Point cloud registration is a crucial problem in computer vision and robotics. Existing methods either rely on matching local geometric features, which are sensitive to the pose differences, or leverage global shapes, which leads to inconsistency when facing distribution variances such as partial overlapping. Combining the advantages of both types of methods, we adopt a coarse-to-fine pipeline that concurrently handles both issues. We first reduce the pose differences between input point clouds by aligning global features; then we match the local features to further refine the inaccurate alignments resulting from distribution variances. As global feature alignment requires the features to preserve the poses of input point clouds and local feature matching expects the features to be invariant to these poses, we propose an SE(3)-equivariant feature extractor to simultaneously generate two types of features. In this feature extractor, representations that preserve the poses are first encoded by our novel SE(3)-equivariant network and then converted into pose-invariant ones by a pose-detaching module. Experiments demonstrate that our proposed method increases the recall rate by 20% compared to state-of-the-art methods when facing both pose differences and distribution variances.
Sperner systems with restricted differences

A BSTRACT . Let F be a family of subsets of [ n ] and L be a subset of [ n ] . We say F is an L differencing Sperner system if | A \ B | ∈ L for any distinct A, B ∈ F . Let p be a prime and q be a power of p . Frankl ﬁrst studied p -modular L -differencing Sperner systems and showed an upper bound of the form P | L | i =0 (cid:0) ni (cid:1) . In this paper, we obtain new upper bounds on q -modular L differencing Sperner systems using elementary p -adic analysis and polynomial method, extending and improving existing results substantially. Moreover, our techniques can be used to derive new upper bounds on subsets of the hypercube with restricted Hamming distances. One highlight of the paper is the ﬁrst analogue of the celebrated Snevily’s theorem in the q -modular setting, which results in several new upper bounds on q -modular L -avoiding L -intersecting systems. In particular, we improve a result of Felszeghy, Heged˝us, and R´onyai, and give a partial answer to a question posed by Babai, Frankl, Kutin, and ˇStefankoviˇc.
Decomposed Prompting: A Modular Approach for Solving Complex Tasks

Few-shot prompting is a surprisingly powerful way to use Large Language Models (LLMs) to solve various tasks. However, this approach struggles as the task complexity increases or when the individual reasoning steps of the task themselves are hard to learn, especially when embedded in more complex tasks. To address this, we propose Decomposed Prompting, a new approach to solve complex tasks by decomposing them (via prompting) into simpler sub-tasks that can be delegated to a library of prompting-based LLMs dedicated to these sub-tasks. This modular structure allows each prompt to be optimized for its specific sub-task, further decomposed if necessary, and even easily replaced with more effective prompts, trained models, or symbolic functions if desired. We show that the flexibility and modularity of Decomposed Prompting allows it to outperform prior work on few-shot prompting using GPT3. On symbolic reasoning tasks, we can further decompose sub-tasks that are hard for LLMs into even simpler solvable sub-tasks. When the complexity comes from the input length, we can recursively decompose the task into the same task but with smaller inputs. We also evaluate our approach on textual multi-step reasoning tasks: on long-context multi-hop QA task, we can more effectively teach the sub-tasks via our separate sub-tasks prompts; and on open-domain multi-hop QA, we can incorporate a symbolic information retrieval within our decomposition framework, leading to improved performance on both tasks. Datasets, Code and Prompts available at https://github.com/allenai/DecomP.
Medical Image Retrieval via Nearest Neighbor Search on Pre-trained Image Features

Nearest neighbor search (NNS) aims to locate the points in high-dimensional space that is closest to the query point. The brute-force approach for finding the nearest neighbor becomes computationally infeasible when the number of points is large. The NNS has multiple applications in medicine, such as searching large medical imaging databases, disease classification, diagnosis, etc. With a focus on medical imaging, this paper proposes DenseLinkSearch an effective and efficient algorithm that searches and retrieves the relevant images from heterogeneous sources of medical images. Towards this, given a medical database, the proposed algorithm builds the index that consists of pre-computed links of each point in the database. The search algorithm utilizes the index to efficiently traverse the database in search of the nearest neighbor. We extensively tested the proposed NNS approach and compared the performance with state-of-the-art NNS approaches on benchmark datasets and our created medical image datasets. The proposed approach outperformed the existing approach in terms of retrieving accurate neighbors and retrieval speed. We also explore the role of medical image feature representation in content-based medical image retrieval tasks. We propose a Transformer-based feature representation technique that outperformed the existing pre-trained Transformer approach on CLEF 2011 medical image retrieval task. The source code of our experiments are available at https://github.com/deepaknlp/DLS.
Multi-task Self-supervised Graph Neural Networks Enable Stronger Task Generalization

Self-supervised learning (SSL) for graph neural networks (GNNs) has attracted increasing attention from the graph machine learning community in recent years, owing to its capability to learn performant node embeddings without costly label information. One weakness of conventional SSL frameworks for GNNs is that they learn through a single philosophy, such as mutual information maximization or generative reconstruction. When applied to various downstream tasks, these frameworks rarely perform equally well for every task, because one philosophy may not span the extensive knowledge required for all tasks. To enhance the task generalization across tasks, as an important first step forward in exploring fundamental graph models, we introduce PARETOGNN, a multi-task SSL framework for node representation learning over graphs. Specifically, PARETOGNN is self-supervised by manifold pretext tasks observing multiple philosophies. To reconcile different philosophies, we explore a multiple-gradient descent algorithm, such that PARETOGNN actively learns from every pretext task while minimizing potential conflicts. We conduct comprehensive experiments over four downstream tasks (i.e., node classification, node clustering, link prediction, and partition prediction), and our proposal achieves the best overall performance across tasks on 11 widely adopted benchmark datasets. Besides, we observe that learning from multiple philosophies enhances not only the task generalization but also the single task performances, demonstrating that PARETOGNN achieves better task generalization via the disjoint yet complementary knowledge learned from different philosophies. Our code is publicly available at https://github.com/jumxglhf/ParetoGNN.
Learning Signal Temporal Logic through Neural Network for Interpretable Classification

Machine learning techniques using neural networks have achieved promising success for time-series data classification. However, the models that they produce are challenging to verify and interpret. In this paper, we propose an explainable neural-symbolic framework for the classification of time-series behaviors. In particular, we use an expressive formal language, namely Signal Temporal Logic (STL), to constrain the search of the computation graph for a neural network. We design a novel time function and sparse softmax function to improve the soundness and precision of the neural-STL framework. As a result, we can efficiently learn a compact STL formula for the classification of time-series data through off-theshelf gradient-based tools. We demonstrate the computational efficiency, compactness, and interpretability of the proposed method through driving scenarios and naval surveillance case studies, compared with state-of-the-art baselines.
Prototype Design and Efficiency Analysis of a Novel Robot Drive Based on 3K-H-V Topology

Robot actuators directly affect the performance of robots, and robot drives directly affect the performance of robot actuators. With the development of robotics, robots have put higher requirements on robot drives, such as high stiffness, high accuracy, high loading, high efficiency, low backlash, compact size, and hollow structure. In order to meet the demand development of robot actuators, this research base proposes a new robot drive based on 3K-H-V topology using involute and cycloidal gear shapes, planetary cycloidal drive, from the perspective of drive topology and through the design idea of decoupling. In this study, the reduction ratio and the efficiency model of the 3K-H-V topology were analyzed, and a prototype planetary cycloidal actuator was designed. The feasibility of the drive is initially verified by experimentally concluding that the PCA has a hollow structure, compact size, and high torque density (69 Nm/kg).
Applicability of Hubbert model to global mining industry: Interpretations and insights

The Hubert’s model has been introduced in 1956 as a phenomenological description of the time evolution of US and world oil fields production. It has since then acquired a vast notoriety as a conceptual approach to resource depletion. It is often invoked nowadays in the context of the energy transition to question the limitations induced by the finitude of mineral stocks. Yet, its validity is often controversial despite its popularity. This paper offers a pedagogical introduction to the model, assesses its ability to describe the current evolution of 20 mining elements, and discusses the nature and robustness of conclusions drawn from Hubbert’s model considered either as a forecast or as a foresight tool. We also propose a novel way to represent graphically these conclusions as a “Hubbert’s map” which offers direct visualization of their main features.
GMMSeg: Gaussian Mixture based Generative Semantic Segmentation Models

Prevalent semantic segmentation solutions are, in essence, a dense discriminative classifier of p(class|pixel feature). Though straightforward, this de facto paradigm neglects the underlying data distribution p(pixel feature|class), and struggles to identify out-of-distribution data. Going beyond this, we propose GMMSeg, a new family of segmentation models that rely on a dense generative classifier for the joint distribution p(pixel feature,class). For each class, GMMSeg builds Gaussian Mixture Models (GMMs) via Expectation-Maximization (EM), so as to capture class-conditional densities. Meanwhile, the deep dense representation is end-to-end trained in a discriminative manner, i.e., maximizing p(class|pixel feature). This endows GMMSeg with the strengths of both generative and discriminative models. With a variety of segmentation architectures and backbones, GMMSeg outperforms the discriminative counterparts on three closed-set datasets. More impressively, without any modification, GMMSeg even performs well on open-world datasets. We believe this work brings fundamental insights into the related fields.
FQDet: Fast-converging Query-based Detector

Recently, two-stage Deformable DETR introduced the query-based two-stage head, a new type of two-stage head different from the region-based two-stage heads of classical detectors as Faster R-CNN. In query-based two-stage heads, the second stage selects one feature per detection processed by a transformer, called the query, as opposed to pooling a rectangular grid of features processed by CNNs as in region-based detectors. In this work, we improve the query-based head by improving the prior of the cross-attention operation with anchors, significantly speeding up the convergence while increasing its performance. Additionally, we empirically show that by improving the cross-attention prior, auxiliary losses and iterative bounding box mechanisms typically used by DETR-based detectors are no longer needed. By combining the best of both the classical and the DETR-based detectors, our FQDet head peaks at 45.4 AP on the 2017 COCO validation set when using a ResNet-50+TPN backbone, only after training for 12 epochs using the 1x schedule. We outperform other high-performing two-stage heads such as e.g. Cascade R-CNN, while using the same backbone and while being computationally cheaper. Additionally, when using the large ResNeXt-101-DCN+TPN backbone and multi-scale testing, our FQDet head achieves 52.9 AP on the 2017 COCO test-dev set after only 12 epochs of training. Code is released at https://github.com/CedricPicron/FQDet .
Inference in Near Singular Regression

This paper considers stationary regression models with near-collinear regressors. Limit theory is developed for regression estimates and test statistics in cases where the signal matrix is nearly singular in finite samples and is asymptotically degenerate. Examples include models that involve evaporating trends in the regressors that arise in conditions such as growth convergence. Structural equation models are also considered and limit theory is derived for the corresponding instrumental variable estimator, Wald test statistic, and overidentification test when the regressors are endogenous.
Holomorphic representation of quantum computations

We study bosonic quantum computations using the Segal-Bargmann representation of quantum states. We argue that this holomorphic representation is a natural one which not only gives a canonical description of bosonic quantum computing using basic elements of complex analysis but also provides a unifying picture which delineates the boundary between discrete- and continuous-variable quantum information theory. Using this representation, we show that the evolution of a single bosonic mode under a Gaussian Hamiltonian can be described as an integrable dynamical system of classical Calogero-Moser particles corresponding to the zeros of the holomorphic function, together with a conformal evolution of Gaussian parameters. We explain that the Calogero-Moser dynamics is due to unique features of bosonic Hilbert spaces such as squeezing. We then generalize the properties of this holomorphic representation to the multimode case, deriving a non-Gaussian hierarchy of quantum states and relating entanglement to factorization properties of holomorphic functions. Finally, we apply this formalism to discrete- and continuous- variable quantum measurements and obtain a classification of subuniversal models that are generalizations of Boson Sampling and Gaussian quantum computing.
Holographic magnetic phase transition

We study four-dimensional interacting fermions in a strong magnetic field, using the holographic Sakai-Sugimoto model of intersecting D4- and D8-branes in the deconfined, chiral-symmetric parallel phase. We find that as the magnetic field is varied, while staying in the parallel phase, the fermions exhibit a first-order phase transition in which their magnetization jumps discontinuously. Properties of this transition are consistent with a picture in which some of the fermions jump to the lowest Landau level. Similarities to known magnetic phase transitions are discussed.
Comment on ‘First accuracy evaluation of NIST-F2’

We discuss the treatment of the systematic frequency shifts due to microwave lensing and distributed cavity phase in Heavner et al 2014 Metrologia 51 174–82. We explain that the microwave lensing frequency shift is generally non-zero and finite in the limit of no applied microwave field. This systematic error was incorrectly treated and we find that it contributes a significant frequency offset. Accounting for this shift implies that the measured microwave amplitude dependence (e.g. due to microwave leakage) is comparable to the total reported inaccuracy. We also discuss the importance of vertically aligning the fountain perpendicular to the axis of the cavity feeds, when the cavity has only two independent feeds. Finally, we note that background gas collisions have a different behavior for cold clock atoms than for clock atoms at room-temperature, and therefore room temperature measurements do not directly apply to laser-cooled clocks.
Denotational semantics of general store and polymorphism

We contribute the first denotational semantics of polymorphic dependent type theory extended by an equational theory for general (higher-order) reference types and recursive types, based on a combination of guarded recursion and impredicative polymorphism; because our model is based on recursively defined semantic worlds, it is compatible with polymorphism and relational reasoning about stateful abstract datatypes. We then extend our language with modal constructs for proof-relevant relational reasoning based on the"logical relations as types"principle, in which equivalences between imperative abstract datatypes can be established synthetically. What is new in relation to prior typed denotational models of higher-order store is that our Kripke worlds need not be syntactically definable, and are thus compatible with relational reasoning in the heap. Our work combines recent advances in the operational semantics of state with the purely denotational viewpoint of synthetic guarded domain theory.
Counting cycles in planar triangulations

We investigate the minimum number of cycles of specified lengths in planar $n$-vertex triangulations $G$. It is proven that this number is $\Omega(n)$ for any cycle length at most $3 + \max \{ {\rm rad}(G^*), \lceil (\frac{n-3}{2})^{\log_32} \rceil \}$, where ${\rm rad}(G^*)$ denotes the radius of the triangulation's dual, which is at least logarithmic but can be linear in the order of the triangulation. We also show that there exist planar hamiltonian $n$-vertex triangulations containing $O(n)$ many $k$-cycles for any $k \in \{ \lceil n - \sqrt[5]{n} \rceil, \ldots, n \}$. Furthermore, we prove that planar 4-connected $n$-vertex triangulations contain $\Omega(n)$ many $k$-cycles for every $k \in \{ 3, \ldots, n \}$, and that, under certain additional conditions, they contain $\Omega(n^2)$ $k$-cycles for many values of $k$, including $n$.
Finite temperature field theory on the Moyal plane

In this paper, we initiate the study of finite temperature quantum field theories on the Moyal plane. Such theories violate causality which influences the properties of these theories. In particular, causality influences the fluctuation-dissipation theorem: as we show, a disturbance in a space-time region M{sub 1} creates a response in a space-time region M{sub 2} spacelike with respect to M{sub 1} (M{sub 1}xM{sub 2}). The relativistic Kubo formula with and without noncommutativity is discussed in detail, and the modified properties of relaxation time and the dependence of mean square fluctuations on time are derived. In particular, the Sinha-Sorkin result [Phys. Rev. B 45, 8123 (1992)] on the logarithmic time dependence of the mean square fluctuations is discussed in our context. We derive an exact formula for the noncommutative susceptibility in terms of the susceptibility for the corresponding commutative case. It shows that noncommutative corrections in the four-momentum space have remarkable periodicity properties as a function of the four-momentum k. They have direction dependence as well and vanish for certain directions of the spatial momentum. These are striking observable signals for noncommutativity. The Lehmann representation is also generalized to any value of the noncommutativity parameter {theta}{sup {mu}}{sup {nu}} and finite temperatures.
FedMT: Federated Learning with Mixed-type Labels

In federated learning (FL), classifiers (e.g., deep networks) are trained on datasets from multiple data centers without exchanging data across them, which improves the sample efficiency. However, the conventional FL setting assumes the same labeling criterion in all data centers involved, thus limiting its practical utility. This limitation becomes particularly notable in domains like disease diagnosis, where different clinical centers may adhere to different standards, making traditional FL methods unsuitable. This paper addresses this important yet under-explored setting of FL, namely FL with mixed-type labels, where the allowance of different labeling criteria introduces inter-center label space differences. To address this challenge effectively and efficiently, we introduce a model-agnostic approach called FedMT, which estimates label space correspondences and projects classification scores to construct loss functions. The proposed FedMT is versatile and integrates seamlessly with various FL methods, such as FedAvg. Experimental results on benchmark and medical datasets highlight the substantial improvement in classification accuracy achieved by FedMT in the presence of mixed-type labels.
Low-Light Image Restoration Based on Retina Model using Neural Networks

—We report the possibility of using a simple neural network for effortless restoration of low-light images inspired by the retina model, which mimics the neurophysiological principles and dynamics of various types of optical neurons. The proposed neural network model saves the cost of computational overhead in contrast with traditional signal-processing models, and generates results comparable with complicated deep learning models from the subjective perceptual perspective. This work shows that to directly simulate the functionalities of retinal neurons using neural networks not only avoids the manually seeking for the optimal parameters, but also paves the way to build corresponding artificial versions for certain neurobiological organizations.
Methods of modern mathematical physics. III. Scattering theory

Topics covered include: overview; classical particle scattering; principles of scattering in Hilbert space; quantum scattering; long range potentials; optical and acoustical scattering; the linear Boltzmann equation; nonlinear wave equations; spin wave scattering; quantum field scattering; and phase space analysis of scattering and spectral theory. (GHT)
Regression-Based Elastic Metric Learning on Shape Spaces of Elastic Curves

We propose a metric learning paradigm, Regression-based Elastic Metric Learning (REML), which optimizes the elastic metric for geodesic regression on the manifold of discrete curves. Geodesic regression is most accurate when the chosen metric models the data trajectory close to a geodesic on the discrete curve manifold. When tested on cell shape trajectories, regression with REML's learned metric has better predictive power than with the conventionally used square-root-velocity (SRV) metric.
Feature Importance for Time Series Data: Improving KernelSHAP

Feature importance techniques have enjoyed widespread attention in the explainable AI literature as a means of determining how trained machine learning models make their predictions. We consider Shapley value based approaches to feature importance, applied in the context of time series data. We present closed form solutions for the SHAP values of a number of time series models, including VARMAX. We also show how KernelSHAP can be applied to time series tasks, and how the feature importances that come from this technique can be combined to perform"event detection". Finally, we explore the use of Time Consistent Shapley values for feature importance.