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Learning modular object-centric representations is crucial for systematic generalization. Existing methods show promising object-binding capabilities empirically, but theoretical identifiability guarantees remain relatively underdeveloped. Understanding when object-centric representations can theoretically be identified is crucial for scaling slot-based methods to high-dimensional images with correctness guarantees. To that end, we propose a probabilistic slot-attention algorithm that imposes an aggregate mixture prior over object-centric slot representations, thereby providing slot identifiability guarantees without supervision, up to an equivalence relation. We provide empirical verification of our theoretical identifiability result using both simple 2-dimensional data and high-resolution imaging datasets.

Modeling open hole failure of composites is a complex task, consisting in a highly nonlinear response with interacting failure modes. Numerical modeling of this phenomenon has traditionally been based on the finite element method, but requires to tradeoff between high fidelity and computational cost. To mitigate this shortcoming, recent work has leveraged machine learning to predict the strength of open hole composite specimens. Here, we also propose using data-based models but to tackle open hole composite failure from a classification point of view. More specifically, we show how to train surrogate models to learn the ultimate failure envelope of an open hole composite plate under in-plane loading. To achieve this, we solve the classification problem via support vector machine (SVM) and test different classifiers by changing the SVM kernel function. The flexibility of kernel-based SVM also allows us to integrate the recently developed quantum kernels in our algorithm and compare them with the standard radial basis function (RBF) kernel. Finally, thanks to kernel-target alignment optimization, we tune the free parameters of all kernels to best separate safe and failure-inducing loading states. The results show classification accuracies higher than 90% for RBF, especially after alignment, followed closely by the quantum kernel classifiers.

The vortex electromagnetic wave carried by multiple orthogonal orbital angular momentum (OAM) modes in the same frequency band can be applied to the field of wireless communications, which greatly increases the spectrum efficiency. The uniform circular array (UCA) is widely used to generate and receive vortex electromagnetic waves with multiple OAM-modes. However, the maximum number of orthogonal OAM-modes based on UCA is usually limited to the number of array-elements of the UCA antenna, leaving how to utilize more OAM-modes to achieve higher channel capacity with a fixed number of arrayelements as an intriguing question. In this paper, we propose an N-dimensional quasi-fractal UCA (ND QF-UCA) antenna structure in different fractal geometry layouts to break through the limits of array-elements number on OAM-modes number. We develop the N-dimensional OAM modulation (NOM) and demodulation (NOD) schemes for OAM multiplexing transmission with the OAM-modes number exceeding the array-elements number, which is beyond the traditional concept of multiple antenna based wireless communications. Then, we investigate different dimensional multiplexing transmission schemes based on the corresponding QF-UCA antenna structure with various array-element layouts and evaluate the optimal layout type and dimension to obtain the highest channel capacity with a fixed number of array-elements. Simulation results show that our proposed schemes can obtain a higher spectrum efficiency, surpassing those of alternative array-element layouts of QF-UCA and the traditional multiple antenna systems.

We present a domain decomposition strategy for developing structure-preserving finite element discretizations from data when exact governing equations are unknown. On subdomains, trainable Whitney form elements are used to identify structure-preserving models from data, providing a Dirichlet-to-Neumann map which may be used to globally construct a mortar method. The reduced-order local elements may be trained offline to reproduce high-fidelity Dirichlet data in cases where first principles model derivation is either intractable, unknown, or computationally prohibitive. In such cases, particular care must be taken to preserve structure on both local and mortar levels without knowledge of the governing equations, as well as to ensure well-posedness and stability of the resulting monolithic data-driven system. This strategy provides a flexible means of both scaling to large systems and treating complex geometries, and is particularly attractive for multiscale problems with complex microstructure geometry. While consistency is traditionally obtained in finite element methods via quasi-optimality results and the Bramble-Hilbert lemma as the local element diameter $h\rightarrow0$, our analysis establishes notions of accuracy and stability for finite h with accuracy coming from matching data. Numerical experiments and analysis establish properties for $H(\operatorname{div})$ problems in small data limits ($\mathcal{O}(1)$ reference solutions).

Consider a multi-class labelling problem, where the labels can take values in $[k]$, and a predictor predicts a distribution over the labels. In this work, we study the following foundational question: Are there notions of multi-class calibration that give strong guarantees of meaningful predictions and can be achieved in time and sample complexities polynomial in $k$? Prior notions of calibration exhibit a tradeoff between computational efficiency and expressivity: they either suffer from having sample complexity exponential in $k$, or needing to solve computationally intractable problems, or give rather weak guarantees. Our main contribution is a notion of calibration that achieves all these desiderata: we formulate a robust notion of projected smooth calibration for multi-class predictions, and give new recalibration algorithms for efficiently calibrating predictors under this definition with complexity polynomial in $k$. Projected smooth calibration gives strong guarantees for all downstream decision makers who want to use the predictor for binary classification problems of the form: does the label belong to a subset $T \subseteq [k]$: e.g. is this an image of an animal? It ensures that the probabilities predicted by summing the probabilities assigned to labels in $T$ are close to some perfectly calibrated binary predictor for that task. We also show that natural strengthenings of our definition are computationally hard to achieve: they run into information theoretic barriers or computational intractability. Underlying both our upper and lower bounds is a tight connection that we prove between multi-class calibration and the well-studied problem of agnostic learning in the (standard) binary prediction setting.

Most existing multi-object tracking methods typically learn visual tracking features via maximizing dis-similarities of different instances and minimizing similarities of the same instance. While such a feature learning scheme achieves promising performance, learning discriminative features solely based on visual information is challenging especially in case of environmental interference such as occlusion, blur and domain variance. In this work, we argue that multi-modal language-driven features provide complementary information to classical visual features, thereby aiding in improving the robustness to such environmental interference. To this end, we propose a new multi-object tracking framework, named LG-MOT, that explicitly leverages language information at different levels of granularity (scene-and instance-level) and combines it with standard visual features to obtain discriminative representations. To develop LG-MOT, we annotate existing MOT datasets with scene-and instance-level language descriptions. We then encode both instance-and scene-level language information into high-dimensional embeddings, which are utilized to guide the visual features during training. At inference, our LG-MOT uses the standard visual features without relying on annotated language descriptions. Extensive experiments on three benchmarks, MOT17, DanceTrack and SportsMOT, reveal the merits of the proposed contributions leading to state-of-the-art performance. On the DanceTrack test set, our LG-MOT achieves an absolute gain of 2.2\% in terms of target object association (IDF1 score), compared to the baseline using only visual features. Further, our LG-MOT exhibits strong cross-domain generalizability. The dataset and code will be available at ~\url{//github.com/WesLee88524/LG-MOT}.

Efficient numerical optimization methods can improve performance and reduce the environmental impact of computing in many applications. This work presents a proof-of-concept study combining primitive state representations and agent-environment interactions as first-order optimizers in the setting of budget-limited optimization. Through reinforcement learning (RL) over a set of training instances of an optimization problem class, optimal policies for sequential update selection of algorithmic iteration steps are approximated in generally formulated low-dimensional partial state representations that consider aspects of progress and resource use. For the investigated case studies, deployment of the trained agents to unseen instances of the quadratic optimization problem classes outperformed conventional optimal algorithms with optimized hyperparameters. The results show that elementary RL methods combined with succinct partial state representations can be used as heuristics to manage complexity in RL-based optimization, paving the way for agentic optimization approaches.

Today's distributed and pervasive computing addresses large-scale cyber-physical ecosystems, characterised by dense and large networks of devices capable of computation, communication and interaction with the environment and people. While most research focusses on treating these systems as "composites" (i.e., heterogeneous functional complexes), recent developments in fields such as self-organising systems and swarm robotics have opened up a complementary perspective: treating systems as "collectives" (i.e., uniform, collaborative, and self-organising groups of entities). This article explores the motivations, state of the art, and implications of this "collective computing paradigm" in software engineering, discusses its peculiar challenges, and outlines a path for future research, touching on aspects such as macroprogramming, collective intelligence, self-adaptive middleware, learning, synthesis, and experimentation of collective behaviour.

In-context learning (ICL) is becoming increasingly appealing to the AI community due to its flexibility, generality, sample efficiency, and exemption from artificial optimization skills. It is desirable to further enhance the generality and capability of ICL, which gives rise to the concept of general-purpose in-context learning (GPICL). We aim to extend ICL to address a broader range of tasks with an extended learning horizon and higher improvement potential, albeit with relatively limited zero-shot generalization. To this end, we introduce two lightweight but insightful benchmarks specifically crafted to train and evaluate GPICL functionalities. Each benchmark includes a vast number of tasks characterized by significant task variance, featuring minimal transferable knowledge among tasks. These tasks are designed to facilitate lifelong in-context learning through continuous generation and interaction. These features pose significant challenges for models that rely on context or interactions to improve their proficiency, including language models, decision models, and world models. Our experiments reveal that the scale of parameters alone may not be crucial for ICL or GPICL, suggesting alternative approaches such as increasing the scale of contexts and memory states.

Approaches based on deep neural networks have achieved striking performance when testing data and training data share similar distribution, but can significantly fail otherwise. Therefore, eliminating the impact of distribution shifts between training and testing data is crucial for building performance-promising deep models. Conventional methods assume either the known heterogeneity of training data (e.g. domain labels) or the approximately equal capacities of different domains. In this paper, we consider a more challenging case where neither of the above assumptions holds. We propose to address this problem by removing the dependencies between features via learning weights for training samples, which helps deep models get rid of spurious correlations and, in turn, concentrate more on the true connection between discriminative features and labels. Extensive experiments clearly demonstrate the effectiveness of our method on multiple distribution generalization benchmarks compared with state-of-the-art counterparts. Through extensive experiments on distribution generalization benchmarks including PACS, VLCS, MNIST-M, and NICO, we show the effectiveness of our method compared with state-of-the-art counterparts.