We propose a Kolmogorov-Arnold Representation-based Hamiltonian Neural Network (KAR-HNN) that replaces the Multilayer Perceptrons (MLPs) with univariate transformations. While Hamiltonian Neural Networks (HNNs) ensure energy conservation by learning Hamiltonian functions directly from data, existing implementations, often relying on MLPs, cause hypersensitivity to the hyperparameters while exploring complex energy landscapes. Our approach exploits the localized function approximations to better capture high-frequency and multi-scale dynamics, reducing energy drift and improving long-term predictive stability. The networks preserve the symplectic form of Hamiltonian systems, and thus maintain interpretability and physical consistency. After assessing KAR-HNN on four benchmark problems including spring-mass, simple pendulum, two- and three-body problem, we foresee its effectiveness for accurate and stable modeling of realistic physical processes often at high dimensions and with few known parameters.

Classical machine learning (CML) has been extensively studied for malware classification. With the emergence of quantum computing, quantum machine learning (QML) presents a paradigm-shifting opportunity to improve malware detection, though its application in this domain remains largely unexplored. In this study, we investigate two hybrid quantum-classical models -- a Quantum Multilayer Perceptron (QMLP) and a Quantum Convolutional Neural Network (QCNN), for malware classification. Both models utilize angle embedding to encode malware features into quantum states. QMLP captures complex patterns through full qubit measurement and data re-uploading, while QCNN achieves faster training via quantum convolution and pooling layers that reduce active qubits. We evaluate both models on five widely used malware datasets -- API-Graph, EMBER-Domain, EMBER-Class, AZ-Domain, and AZ-Class, across binary and multiclass classification tasks. Our results show high accuracy for binary classification -- 95-96% on API-Graph, 91-92% on AZ-Domain, and 77% on EMBER-Domain. In multiclass settings, accuracy ranges from 91.6-95.7% on API-Graph, 41.7-93.6% on AZ-Class, and 60.7-88.1% on EMBER-Class. Overall, QMLP outperforms QCNN in complex multiclass tasks, while QCNN offers improved training efficiency at the cost of reduced accuracy.

Multimodal in-context learning (ICL) equips Large Vision-language Models (LVLMs) with the ability to adapt to new tasks via multiple user-provided demonstrations, without requiring any model parameter updates. However, its effectiveness is constrained by the token-intensive nature of multimodal inputs and the complexity of cross-modal few-shot reasoning, which together hinder LVLMs from extracting useful patterns from demonstrations. To address these challenges, we propose \textbf{M$^2$IV}, a novel representation engineering approach that replaces explicit token-level demonstrations with a set of learnable Multimodal In-context Vectors directly injected into the residual streams of LVLMs. By analyzing the distinct roles of multi-head attention (MHA) and multi-layer perceptrons (MLP) in the ICL process, we design a training strategy that enables M$^2$IV to perform fine-grained semantic distillation and robust cross-modal representation learning. M$^2$IV not only improves performance across diverse tasks and LVLMs but also significantly reduces token overhead, enabling graceful scaling to many-shot scenarios. To further enhance usability, we introduce \textbf{VLibrary}, a repository that stores trained M$^2$IVs for flexible retrieval and injection. With VLibrary, users can steer pre-trained LVLMs in a customized manner that meets diverse requirements. Extensive experiments demonstrate that M$^2$IV consistently outperforms vanilla ICL and prior representation engineering baselines, achieving an average accuracy gain of 3.74\% with substantial improvements in overall efficiency.

Learning is a physical process. Here, we aim to study a simple dynamical system composed of springs and sticks capable of arbitrarily approximating any continuous function. The main idea of our work is to use the sticks to mimic a piecewise-linear approximation of the given function, use the potential energy of springs to encode a desired mean squared error loss function, and converge to a minimum-energy configuration via dissipation. We apply the proposed simulation system to regression tasks and show that its performance is comparable to that of multi-layer perceptrons. In addition, we study the thermodynamic properties of the system and find a relation between the free energy change of the system and its ability to learn an underlying data distribution. We empirically find a \emph{thermodynamic learning barrier} for the system caused by the fluctuations of the environment, whereby the system cannot learn if its change in free energy hits such a barrier. We believe this simple model can help us better understand learning systems from a physical point of view.

This paper investigates a perceptron, a simple neural network model, with ReLU activation and a ridge-regularized mean squared error (RR-MSE). Our approach leverages the fact that the RR-MSE for ReLU perceptron is piecewise polynomial, enabling a systematic analysis using tools from computational algebra. In particular, we develop a Divide-Enumerate-Merge strategy that exhaustively enumerates all local minima of the RR-MSE. By virtue of the algebraic formulation, our approach can identify not only the typical zero-dimensional minima (i.e., isolated points) obtained by numerical optimization, but also higher-dimensional minima (i.e., connected sets such as curves, surfaces, or hypersurfaces). Although computational algebraic methods are computationally very intensive for perceptrons of practical size, as a proof of concept, we apply the proposed approach in practice to minimal perceptrons with a few hidden units.

Large Vision-Language Models (LVLMs) commonly follow a paradigm that projects visual features and then concatenates them with text tokens to form a unified sequence input for Large Language Models (LLMs). However, this paradigm leads to a significant increase in the length of the input sequence, resulting in substantial computational overhead. Existing methods attempt to fuse visual information into the intermediate layers of LLMs, which alleviate the sequence length issue but often neglect the hierarchical semantic representations within the model and the fine-grained visual information available in the shallower visual encoding layers. To address this limitation, we propose DEHVF, an efficient vision-language fine-tuning method based on dynamic embedding and fusion of hierarchical visual features. Its core lies in leveraging the inherent hierarchical representation characteristics of visual encoders and language models. Through a lightweight hierarchical visual fuser, it dynamically selects and fuses hierarchical features corresponding to semantic granularity based on the internal representations of each layer in LLMs. The fused layer-related visual features are then projected and aligned before being directly embedded into the Feed-Forward Network (FFN) of the corresponding layer in LLMs. This approach not only avoids sequence expansion but also dynamically fuses multi-layer visual information. By fine-tuning only a small number of parameters, DEHVF achieves precise alignment and complementarity of cross-modal information at the same semantic granularity. We conducted experiments across various VL benchmarks, including visual question answering on ScienceQA and image captioning on COCO Captions. The results demonstrate that DEHVF achieves higher accuracy than existing parameter-efficient fine-tuning (PEFT) baselines while maintaining efficient training and inference.

We found that the ability of a network to learn symmetries generalizes over a range of architectures.

The performance of Deep Q-Networks (DQN) is critically dependent on the ability of its underlying neural network to accurately approximate the action-value function. Standard function approximators, such as multi-layer perceptrons, may struggle to efficiently represent the complex value landscapes inherent in many reinforcement learning problems. This paper introduces a novel architecture, the Chebyshev-DQN (Ch-DQN), which integrates a Chebyshev polynomial basis into the DQN framework to create a more effective feature representation. By leveraging the powerful function approximation properties of Chebyshev polynomials, we hypothesize that the Ch-DQN can learn more efficiently and achieve higher performance. We evaluate our proposed model on the CartPole-v1 benchmark and compare it against a standard DQN with a comparable number of parameters. Our results demonstrate that the Ch-DQN with a moderate polynomial degree (N=4) achieves significantly better asymptotic performance, outperforming the baseline by approximately 39\%. However, we also find that the choice of polynomial degree is a critical hyperparameter, as a high degree (N=8) can be detrimental to learning. This work validates the potential of using orthogonal polynomial bases in deep reinforcement learning while also highlighting the trade-offs involved in model complexity.

This paper proposes PreSem-Surf, an optimized method based on the Neural Radiance Field (NeRF) framework, capable of reconstructing high-quality scene surfaces from RGB-D sequences in a short time. The method integrates RGB, depth, and semantic information to improve reconstruction performance. Specifically, a novel SG-MLP sampling structure combined with PR-MLP (Preconditioning Multilayer Perceptron) is introduced for voxel pre-rendering, allowing the model to capture scene-related information earlier and better distinguish noise from local details. Furthermore, progressive semantic modeling is adopted to extract semantic information at increasing levels of precision, reducing training time while enhancing scene understanding. Experiments on seven synthetic scenes with six evaluation metrics show that PreSem-Surf achieves the best performance in C-L1, F-score, and IoU, while maintaining competitive results in NC, Accuracy, and Completeness, demonstrating its effectiveness and practical applicability.

We modify Kanerva's model and demonstrate a simple way to design a kernel memory network