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To assess the quality of a probabilistic prediction for stochastic dynamical systems (SDSs), scoring rules assign a numerical score based on the predictive distribution and the measured state. In this paper, we propose an $\epsilon$-logarithm score that generalizes the celebrated logarithm score by considering a neighborhood with radius $\epsilon$. We characterize the probabilistic predictability of an SDS by optimizing the expected score over the space of probability measures. We show how the probabilistic predictability is quantitatively determined by the neighborhood radius, the differential entropies of process noises, and the system dimension. Given any predictor, we provide approximations for the expected score with an error of scale $\mathcal{O}(\epsilon)$. In addition to the expected score, we also analyze the asymptotic behaviors of the score on individual trajectories. Specifically, we prove that the score on a trajectory can converge to the expected score when the process noises are independent and identically distributed. Moreover, the convergence speed against the trajectory length $T$ is of scale $\mathcal{O}(T^{-\frac{1}{2}})$ in the sense of probability. Finally, numerical examples are given to elaborate the results.

We introduce the concept of multiple temporal perspectives, a novel approach applicable to Recurrent Neural Network (RNN) architectures for enhancing their understanding of sequential data. This method involves maintaining diverse temporal views of previously encountered text, significantly enriching the language models' capacity to interpret context. To show the efficacy of this approach, we incorporate it into the Receptance Weighted Key Value (RWKV) architecture, addressing its inherent challenge of retaining all historical information within a single hidden state. Notably, this improvement is achieved with a minimal increase in the number of parameters --even as little as $0.04\%$ of the original number of parameters. Further, the additional parameters necessary for the multiple temporal perspectives are fine-tuned with minimal computational overhead, avoiding the need for a full pre-training. The resulting model maintains linear computational complexity during prompt inference, ensuring consistent efficiency across various sequence lengths. The empirical results and ablation studies included in our research validate the effectiveness of our approach, showcasing improved performance across multiple benchmarks. The code, model weights and datasets are open-sourced at: //github.com/RazvanDu/TemporalRNNs.

Motion modeling is critical in flow-based Video Frame Interpolation (VFI). Existing paradigms either consider linear combinations of bidirectional flows or directly predict bilateral flows for given timestamps without exploring favorable motion priors, thus lacking the capability of effectively modeling spatiotemporal dynamics in real-world videos. To address this limitation, in this study, we introduce Generalizable Implicit Motion Modeling (GIMM), a novel and effective approach to motion modeling for VFI. Specifically, to enable GIMM as an effective motion modeling paradigm, we design a motion encoding pipeline to model spatiotemporal motion latent from bidirectional flows extracted from pre-trained flow estimators, effectively representing input-specific motion priors. Then, we implicitly predict arbitrary-timestep optical flows within two adjacent input frames via an adaptive coordinate-based neural network, with spatiotemporal coordinates and motion latent as inputs. Our GIMM can be smoothly integrated with existing flow-based VFI works without further modifications. We show that GIMM performs better than the current state of the art on the VFI benchmarks.

Optimizing warehouse layouts is crucial due to its significant impact on efficiency and productivity. We present an AI-driven framework for automated warehouse layout generation. This framework employs constrained beam search to derive optimal layouts within given spatial parameters, adhering to all functional requirements. The feasibility of the generated layouts is verified based on criteria such as item accessibility, required minimum clearances, and aisle connectivity. A scoring function is then used to evaluate the feasible layouts considering the number of storage locations, access points, and accessibility costs. We demonstrate our method's ability to produce feasible, optimal layouts for a variety of warehouse dimensions and shapes, diverse door placements, and interconnections. This approach, currently being prepared for deployment, will enable human designers to rapidly explore and confirm options, facilitating the selection of the most appropriate layout for their use-case.

Visual Place Recognition (VPR) systems often have imperfect performance, which affects robot navigation decisions. This research introduces a novel Multi-Layer Perceptron (MLP) integrity monitor for VPR which demonstrates improved performance and generalizability over the previous state-of-the-art SVM approach, removing per-environment training and reducing manual tuning requirements. We test our proposed system in extensive real-world experiments, where we also present two real-time integrity-based VPR verification methods: an instantaneous rejection method for a robot navigating to a goal zone (Experiment 1); and a historical method that takes a best, verified, match from its recent trajectory and uses an odometer to extrapolate forwards to a current position estimate (Experiment 2). Noteworthy results for Experiment 1 include a decrease in aggregate mean along-track goal error from ~9.8m to ~3.1m in missions the robot pursued to completion, and an increase in the aggregate rate of successful mission completion from ~41% to ~55%. Experiment 2 showed a decrease in aggregate mean along-track localization error from ~2.0m to ~0.5m, and an increase in the aggregate precision of localization attempts from ~97% to ~99%. Overall, our results demonstrate the practical usefulness of a VPR integrity monitor in real-world robotics to improve VPR localization and consequent navigation performance.

Large Language Models (LLMs) have shown excellent generalization capabilities that have led to the development of numerous models. These models propose various new architectures, tweaking existing architectures with refined training strategies, increasing context length, using high-quality training data, and increasing training time to outperform baselines. Analyzing new developments is crucial for identifying changes that enhance training stability and improve generalization in LLMs. This survey paper comprehensively analyses the LLMs architectures and their categorization, training strategies, training datasets, and performance evaluations and discusses future research directions. Moreover, the paper also discusses the basic building blocks and concepts behind LLMs, followed by a complete overview of LLMs, including their important features and functions. Finally, the paper summarizes significant findings from LLM research and consolidates essential architectural and training strategies for developing advanced LLMs. Given the continuous advancements in LLMs, we intend to regularly update this paper by incorporating new sections and featuring the latest LLM models.

2D-based Industrial Anomaly Detection has been widely discussed, however, multimodal industrial anomaly detection based on 3D point clouds and RGB images still has many untouched fields. Existing multimodal industrial anomaly detection methods directly concatenate the multimodal features, which leads to a strong disturbance between features and harms the detection performance. In this paper, we propose Multi-3D-Memory (M3DM), a novel multimodal anomaly detection method with hybrid fusion scheme: firstly, we design an unsupervised feature fusion with patch-wise contrastive learning to encourage the interaction of different modal features; secondly, we use a decision layer fusion with multiple memory banks to avoid loss of information and additional novelty classifiers to make the final decision. We further propose a point feature alignment operation to better align the point cloud and RGB features. Extensive experiments show that our multimodal industrial anomaly detection model outperforms the state-of-the-art (SOTA) methods on both detection and segmentation precision on MVTec-3D AD dataset. Code is available at //github.com/nomewang/M3DM.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding generalization power of overparametrized neural networks, the role of depth in deep architectures, the apparent absence of the curse of dimensionality, the surprisingly successful optimization performance despite the non-convexity of the problem, understanding what features are learned, why deep architectures perform exceptionally well in physical problems, and which fine aspects of an architecture affect the behavior of a learning task in which way. We present an overview of modern approaches that yield partial answers to these questions. For selected approaches, we describe the main ideas in more detail.

Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features - which occur regularly in real-world input domains and within the hidden layers of GNNs - and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model. With this work, we hope to steer some of the GNN research towards new aggregation methods which we believe are essential in the search for powerful and robust models.