Ensemble simulations of high-dimensional flow models (e.g., Navier-Stokes-type PDEs) are computationally prohibitive for real-time appli cations. Neural operators enable fast inference but are limited by costly data req uirements and poor generalization to 3D flows. We present a data-free operator n etwork for the Navier-Stokes equations that eliminates the need for paire d solution data and enables robust, real-time inference for large ensemble for ecasting. The physics-grounded architecture takes initial and boundary conditio ns as well as forcing functions, yielding solutions robust to high variability a nd perturbations. Across 2D benchmarks and 3D test cases, the method surpasses prior n eural operators in accuracy and, for ensembles, achieves greater efficie ncy than conventional numerical solvers. Notably, it delivers accurate solutions of the three-dimensional Navier-Stokes equations--a regime not previously demonstr ated for data-free neural operators. By uniting a numerically grounded archit ecture with the scalability of machine learning, this approach establishes a pra ctical pathway toward data-free, high-fidelity PDE surrogates for end-to-end sci entific simulation and prediction. Solving PDEs efficiently and accurately is one of the central interests for scienc e and engineering. In addition, when dealing with various boundary conditions, initial con ditions, or external forcing terms of PDEs in fields such as fluid mechanics [1-3], materials science [4, 5], weather forecasting [6, 7], and design optimization [8, 9], P DEs are often required to be solved repeatedly. However, conventional numeric al solvers become prohibitively expensive in such settings, particularly for three-dimensional incompressible Navier-Stokes equations (NSEs) [10, 11]. This is because these s olvers rely on spatial-temporal discretization and iterative treatment of nonline ar terms, while performing time marching that demands substantial memory and computation. Moreover, they are not well suited for solving large ensembles of scenarios simu ltaneously, such as those required for uncertainty quantification or design explora tion. The resulting computational time, coupled with the need for extensive sampling in e nsemble or probabilistic simulations, constitutes a critical bottleneck [7, 12].

Long-range sequence modeling is a crucial aspect of natural language processing and time series analysis. However, traditional models like Recurrent Neural Networks (RNNs) and Transformers suffer from computational and memory inefficiencies, especially when dealing with long sequences. This paper introduces Logarithmic Memory Networks (LMNs), a novel architecture that leverages a hierarchical logarithmic tree structure to efficiently store and retrieve past information. LMNs dynamically summarize historical context, significantly reducing the memory footprint and computational complexity of attention mechanisms from O(n2) to O(log(n)). The model employs a single-vector, targeted attention mechanism to access stored information, and the memory block construction worker (summarizer) layer operates in two modes: a parallel execution mode during training for efficient processing of hierarchical tree structures and a sequential execution mode during inference, which acts as a memory management system. It also implicitly encodes positional information, eliminating the need for explicit positional encodings. These features make LMNs a robust and scalable solution for processing long-range sequences in resource-constrained environments, offering practical improvements in efficiency and scalability. The code is publicly available under the MIT License on GitHub: https://github.com/AhmedBoin/LogarithmicMemory.

Complicated first principles modelling and controller synthesis can be prohibitively slow and expensive for high-mix, low-volume products such as hydraulic excavators. Instead, in a data-driven approach, recorded trajectories from the real system can be used to train local model networks (LMNs), for which feedforward controllers are derived via feedback linearization. However, previous works required LMNs without zero dynamics for feedback linearization, which restricts the model structure and thus modelling capacity of LMNs. In this paper, we overcome this restriction by providing a criterion for when feedback linearization of LMNs with zero dynamics yields a valid controller. As a criterion we propose the bounded-input bounded-output stability of the resulting controller. In two additional contributions, we extend this approach to consider measured disturbance signals and multiple inputs and outputs. We illustrate the effectiveness of our contributions in a hydraulic excavator control application with hardware experiments. To this end, we train LMNs from recorded, noisy data and derive feedforward controllers used as part of a leveling assistance system on the excavator. In our experiments, incorporating disturbance signals and multiple inputs and outputs enhances tracking performance of the learned controller. A video of our experiments is available at https://youtu.be/lrrWBx2ASaE.

We attribute grokking, the phenomenon where generalization is much delayed after memorization, to compression. To do so, we define linear mapping number (LMN) to measure network complexity, which is a generalized version of linear region number for ReLU networks. LMN can nicely characterize neural network compression before generalization. Although the $L_2$ norm has been a popular choice for characterizing model complexity, we argue in favor of LMN for a number of reasons: (1) LMN can be naturally interpreted as information/computation, while $L_2$ cannot. (2) In the compression phase, LMN has linear relations with test losses, while $L_2$ is correlated with test losses in a complicated nonlinear way. (3) LMN also reveals an intriguing phenomenon of the XOR network switching between two generalization solutions, while $L_2$ does not. Besides explaining grokking, we argue that LMN is a promising candidate as the neural network version of the Kolmogorov complexity since it explicitly considers local or conditioned linear computations aligned with the nature of modern artificial neural networks.

Accurate lane detection under various road conditions is a critical function for autonomous driving. Generally, when detected lane lines from a front camera image are projected into a birds-eye view (BEV) for motion planning, the resulting lane lines are often distorted. And convolutional neural network (CNN)-based feature extractors often lose resolution when increasing the receptive field to detect global features such as lane lines. However, Lidar point cloud has little image distortion in the BEV-projection. Since lane lines are thin and stretch over entire BEV image while occupying only a small portion, lane lines should be detected as a global feature with high resolution. In this paper, we propose Lane Mixer Network (LMN) that extracts local features from Lidar point cloud, recognizes global features, and detects lane lines using a BEV encoder, a Mixer-based global feature extractor, and a detection head, respectively. In addition, we provide a world-first large urban lane dataset for Lidar, K-Lane, which has maximum 6 lanes under various urban road conditions. We demonstrate that the proposed LMN achieves the state-of-the-art performance, an F1 score of 91.67%, with K-Lane. The K-Lane, LMN training code, pre-trained models, and total dataset development platform are available at github.

Based on Grossi and Modgil's recent work [1], this paper considers some issues on extension-based semantics for abstract argumentation framework (AAF, for short). First, an alternative fundamental lemma is given, which generalizes the corresponding result obtained in [1]. This lemma plays a central role in constructing some special extensions in terms of iterations of the defense function. Applying this lemma, some flaws in [1] are corrected and a number of structural properties of various extensionbased semantics are given. Second, the operator so-called reduced meet modulo an ultrafilter is presented. A number of fundamental semantics for AAF, including conflictfree, admissible, complete and stable semantics, are shown to be closed under this operator. Based on this fact, we provide a concise and uniform proof method to establish the universal definability of a family of range related semantics. Thirdly, using model-theoretical tools, we characterize the class of extension-based semantics that is closed under reduced meet modulo any ultrafilter, which brings us a metatheorem concerning the universal definability of range related semantics. Finally, in addition to range related semantics, some graded variants of traditional semantics of AAF are also considered in this paper, e.g., ideal semantics, eager semantics, etc. Keywords: Abstract argumentation framework, Graded extension-based semantics, Range related semantics, Universal definability.

Learning to solve sequential tasks with recurrent models requires the ability to memorize long sequences and to extract task-relevant features from them. In this paper, we study the memorization subtask from the point of view of the design and training of recurrent neural networks. We propose a new model, the Linear Memory Network, which features an encoding-based memorization component built with a linear autoencoder for sequences. We extend the memorization component with a modular memory that encodes the hidden state sequence at different sampling frequencies. Additionally, we provide a specialized training algorithm that initializes the memory to efficiently encode the hidden activations of the network. The experimental results on synthetic and real-world datasets show that specializing the training algorithm to train the memorization component always improves the final performance whenever the memorization of long sequences is necessary to solve the problem.

The paper develops a formal theory of the degree of justification of arguments, which relies solely on the structure of an argumentation framework, and which can be successfully interfaced with approaches to instantiated argumentation. The theory is developed in three steps. First, the paper introduces a graded generalization of the two key notions underpinning Dung's semantics: self-defense and conflict-freeness. This leads to a natural generalization of Dung's semantics, whereby standard extensions are weakened or strengthened depending on the level of self-defense and conflict-freeness they meet. The paper investigates the fixpoint theory of these semantics, establishing existence results for them. Second, the paper shows how graded semantics readily provide an approach to argument rankings, offering a novel contribution to the recently growing research programme on ranking-based semantics. Third, this novel approach to argument ranking is applied and studied in the context of instantiated argumentation frameworks, and in so doing is shown to account for a simple form of accrual of arguments within the Dung paradigm. Finally, the theory is compared in detail with existing approaches.

Movies provide us with a mass of visual content as well as attracting stories. Existing methods have illustrated that understanding movie stories through only visual content is still a hard problem. In this paper, for answering questions about movies, we put forward a Layered Memory Network (LMN) that represents frame-level and clip-level movie content by the Static Word Memory module and the Dynamic Subtitle Memory module, respectively. Particularly, we firstly extract words and sentences from the training movie subtitles. Then the hierarchically formed movie representations, which are learned from LMN, not only encode the correspondence between words and visual content inside frames, but also encode the temporal alignment between sentences and frames inside movie clips. We also extend our LMN model into three variant frameworks to illustrate the good extendable capabilities. We conduct extensive experiments on the MovieQA dataset. With only visual content as inputs, LMN with frame-level representation obtains a large performance improvement. When incorporating subtitles into LMN to form the clip-level representation, we achieve the state-of-the-art performance on the online evaluation task of 'Video+Subtitles'. The good performance successfully demonstrates that the proposed framework of LMN is effective and the hierarchically formed movie representations have good potential for the applications of movie question answering.

Augmenting a neural network with memory that can grow without growing the number of trained parameters is a recent powerful concept with many exciting applications. In this paper, we establish their potential in online adapting a batch trained neural network to domain-relevant labeled data at deployment time. We present the design of Labeled Memory Network (LMN), a new memory augmented neural network (MANN) for fast online model adaptation. We highlight three key features of LMNs. First, LMNs treat memory as a second boosted stage following the trained network thereby allowing the memory and network to play complementary roles. Unlike all existing MANNs that write to memory at every cycle, LMNs provide better memory utilization by writing only labeled data with non-zero loss. Second, LMNs organize the memory with the discrete class label as the primary key unlike existing MANNs where key is a real vector derived from the input. This simple, yet surprisingly unexplored alternative organization, safeguards against catastrophic forgetting of rare labels that current LRU based MANNs are subject to. Finally, LMNs model the evolving expertise of memory and network using a RNN, to determine online their respective weights we evaluate online model adaptation strategies on five sequence prediction tasks, an image classification task, and two language modeling tasks. We show that LMNs are better than other MANNs designed for meta-learning. We also found them to be more accurate and faster than state-of-the-art methods of retuning model parameters for adapting to domain-specific labeled data.