With the growing interest in quantum machine learning, the perceptron -- a fundamental building block in traditional machine learning -- has emerged as a valuable model for exploring quantum advantages. Two quantum perceptron algorithms based on Grover's search, were developed in arXiv:1602.04799 to accelerate training and improve statistical efficiency in perceptron learning. This paper points out and corrects a mistake in the proof of Theorem 2 in arXiv:1602.04799. Specifically, we show that the probability of sampling from a normal distribution for a $D$-dimensional hyperplane that perfectly classifies the data scales as $\Omega(\gamma^{D})$ instead of $\Theta({\gamma})$, where $\gamma$ is the margin. We then revisit two well-established linear programming algorithms -- the ellipsoid method and the cutting plane random walk algorithm -- in the context of perceptron learning, and show how quantum search algorithms can be leveraged to enhance the overall complexity. Specifically, both algorithms gain a sub-linear speed-up $O(\sqrt{N})$ in the number of data points $N$ as a result of Grover's algorithm and an additional $O(D^{1.5})$ speed-up is possible for cutting plane random walk algorithm employing quantum walk search.

--Ensemble learning plays a crucial role in practical applications of online learning due to its enhanced classification performance and adaptable adjustment mechanisms. However, most weight allocation strategies in ensemble learning are heuristic, making it challenging to theoretically guarantee that the ensemble classifier outperforms its base classifiers. T o address this issue, a performance-bounded online ensemble learning method based on multi-armed bandits, named PB-OEL, is proposed in this paper . Specifically, multi-armed bandit with expert advice is incorporated into online ensemble learning, aiming to update the weights of base classifiers and make predictions. A theoretical framework is established to bound the performance of the ensemble classifier relative to base classifiers. By setting expert advice of bandits, the bound exceeds the performance of any base classifier when the length of data stream is sufficiently large. Additionally, performance bounds for scenarios with limited annotations are also derived. Numerous experiments on benchmark datasets and a dataset of real-time safety assessment tasks are conducted. The experimental results validate the theoretical bound to a certain extent and demonstrate that the proposed method outperforms existing state-of-the-art methods. Index T erms --Online ensemble learning, performance bound, multi-armed bandits, concept drift, real-time safety assessment. NLINE learning (OL) holds significant potential for handling continuous data and is widely applied across various domains, including industry, recommendation systems, finance, and control systems [1]-[5]. The objective of OL is to continuously learn and update models from new data, enabling adaptation to non-stationary environments for optimized predictions or decisions. One mainstream idea in OL relies on maintaining a set of vectors for decision, as exemplified by the perceptron algorithm [6], passive-aggressive algorithm [7], confidence weighted-based algorithm [8] and imbalanced class weighted-based algorithm [9].

We introduce KANITE, a framework leveraging Kolmogorov-Arnold Networks (KANs) for Individual Treatment Effect (ITE) estimation under multiple treatments setting in causal inference. By utilizing KAN's unique abilities to learn univariate activation functions as opposed to learning linear weights by Multi-Layer Perceptrons (MLPs), we improve the estimates of ITEs. The KANITE framework comprises two key architectures: 1.Integral Probability Metric (IPM) architecture: This employs an IPM loss in a specialized manner to effectively align towards ITE estimation across multiple treatments. 2. Entropy Balancing (EB) architecture: This uses weights for samples that are learned by optimizing entropy subject to balancing the covariates across treatment groups. Extensive evaluations on benchmark datasets demonstrate that KANITE outperforms state-of-the-art algorithms in both $\epsilon_{\text{PEHE}}$ and $\epsilon_{\text{ATE}}$ metrics. Our experiments highlight the advantages of KANITE in achieving improved causal estimates, emphasizing the potential of KANs to advance causal inference methodologies across diverse application areas.

Travel demand modeling has shifted from aggregated trip-based models to behavior-oriented activity-based models because daily trips are essentially driven by human activities. To analyze the sequential activity-travel decisions, deep inverse reinforcement learning (DIRL) has proven effective in learning the decision mechanisms by approximating a reward function to represent preferences and a policy function to replicate observed behavior using deep neural networks (DNNs). However, most existing research has focused on using DIRL to enhance only prediction accuracy, with limited exploration into interpreting the underlying decision mechanisms guiding sequential decision-making. To address this gap, we introduce an interpretable DIRL framework for analyzing activity-travel decision processes, bridging the gap between data-driven machine learning and theory-driven behavioral models. Our proposed framework adapts an adversarial IRL approach to infer the reward and policy functions of activity-travel behavior. The policy function is interpreted through a surrogate interpretable model based on choice probabilities from the policy function, while the reward function is interpreted by deriving both short-term rewards and long-term returns for various activity-travel patterns. Our analysis of real-world travel survey data reveals promising results in two key areas: (i) behavioral pattern insights from the policy function, highlighting critical factors in decision-making and variations among socio-demographic groups, and (ii) behavioral preference insights from the reward function, indicating the utility individuals gain from specific activity sequences.

Studies in reward shaping for reinforcement learning (RL) have flourished in recent years due to its ability to speed up training. Our previous work proposed an adaptive potential function (APF) and showed that APF can accelerate the Q-learning with a Multi-layer Perceptron algorithm in the low-dimensional domain. This paper proposes to extend APF with an encoder (APF+) for RL state representation, allowing applying APF to the pixel-based Atari games using a state-encoding method that projects high-dimensional game's pixel frames to low-dimensional embeddings. We approach by designing the state-representation encoder as a W-shaped network (W-Net), by using which we are able to encode both the background as well as the moving entities in the game frames. Specifically, the embeddings derived from the pre-trained W-Net consist of two latent vectors: One represents the input state, and the other represents the deviation of the input state's representation from itself. We then incorporate W-Net into APF to train a downstream Dueling Deep Q-Network (DDQN), obtain the APF-WNet-DDQN, and demonstrate its effectiveness in Atari game-playing tasks. To evaluate the APF+W-Net module in such high-dimensional tasks, we compare with two types of baseline methods: (i) the basic DDQN; and (ii) two encoder-replaced APF-DDQN methods where we replace W-Net by (a) an unsupervised state representation method called Spatiotemporal Deep Infomax (ST-DIM) and (b) a ground truth state representation provided by the Atari Annotated RAM Interface (ARI). The experiment results show that out of 20 Atari games, APF-WNet-DDQN outperforms DDQN (14/20 games) and APF-STDIM-DDQN (13/20 games) significantly. In comparison against the APF-ARI-DDQN which employs embeddings directly of the detailed game-internal state information, the APF-WNet-DDQN achieves a comparable performance.

The human-like reasoning capabilities exhibited by Large Language Models (LLMs) challenge the traditional neural network theory's understanding of the flexibility of fixed-parameter systems. This paper proposes the "Cognitive Activation" theory, revealing the essence of LLMs' reasoning mechanisms from the perspective of dynamic systems: the model's reasoning ability stems from a chaotic process of dynamic information extraction in the parameter space. By introducing the Quasi-Lyapunov Exponent (QLE), we quantitatively analyze the chaotic characteristics of the model at different layers. Experiments show that the model's information accumulation follows a nonlinear exponential law, and the Multilayer Perceptron (MLP) accounts for a higher proportion in the final output than the attention mechanism. Further experiments indicate that minor initial value perturbations will have a substantial impact on the model's reasoning ability, confirming the theoretical analysis that large language models are chaotic systems. This research provides a chaos theory framework for the interpretability of LLMs' reasoning and reveals potential pathways for balancing creativity and reliability in model design.

Kolmogorov-Arnold networks (KANs) are a remarkable innovation consisting of learnable activation functions with the potential to capture more complex relationships from data. Although KANs are useful in finding symbolic representations and continual learning of one-dimensional functions, their effectiveness in diverse machine learning (ML) tasks, such as vision, remains questionable. Presently, KANs are deployed by replacing multilayer perceptrons (MLPs) in deep network architectures, including advanced architectures such as vision Transformers (ViTs). In this paper, we are the first to design a general learnable Kolmogorov-Arnold Attention (KArAt) for vanilla ViTs that can operate on any choice of basis. However, the computing and memory costs of training them motivated us to propose a more modular version, and we designed particular learnable attention, called Fourier-KArAt. Fourier-KArAt and its variants either outperform their ViT counterparts or show comparable performance on CIFAR-10, CIFAR-100, and ImageNet-1K datasets. We dissect these architectures' performance and generalization capacity by analyzing their loss landscapes, weight distributions, optimizer path, attention visualization, and spectral behavior, and contrast them with vanilla ViTs. The goal of this paper is not to produce parameter- and compute-efficient attention, but to encourage the community to explore KANs in conjunction with more advanced architectures that require a careful understanding of learnable activations. Our open-source code and implementation details are available on: https://subhajitmaity.me/KArAt

Vision foundation models (VFMs) such as DINO have led to a paradigm shift in 2D camera-based perception towards extracting generalized features to support many downstream tasks. Recent works introduce self-supervised cross-modal knowledge distillation (KD) as a way to transfer these powerful generalization capabilities into 3D LiDAR-based models. However, they either rely on highly complex distillation losses, pseudo-semantic maps, or limit KD to features useful for semantic segmentation only. In this work, we propose CleverDistiller, a self-supervised, cross-modal 2D-to-3D KD framework introducing a set of simple yet effective design choices: Unlike contrastive approaches relying on complex loss design choices, our method employs a direct feature similarity loss in combination with a multi layer perceptron (MLP) projection head to allow the 3D network to learn complex semantic dependencies throughout the projection. Crucially, our approach does not depend on pseudo-semantic maps, allowing for direct knowledge transfer from a VFM without explicit semantic supervision. Additionally, we introduce the auxiliary self-supervised spatial task of occupancy prediction to enhance the semantic knowledge, obtained from a VFM through KD, with 3D spatial reasoning capabilities. Experiments on standard autonomous driving benchmarks for 2D-to-3D KD demonstrate that CleverDistiller achieves state-of-the-art performance in both semantic segmentation and 3D object detection (3DOD) by up to 10% mIoU, especially when fine tuning on really low data amounts, showing the effectiveness of our simple yet powerful KD strategy

Weight space learning is an emerging paradigm in the deep learning community. The primary goal of weight space learning is to extract informative features from a set of parameters using specially designed neural networks, often referred to as metanetworks. However, it remains unclear how these metanetworks learn solely from parameters. To address this, we take the first step toward understanding representations of metanetworks, specifically graph metanetworks (GMNs), which achieve state-of-the-art results in this field, using centered kernel alignment (CKA). Through various experiments, we reveal that GMNs and general neural networks (e.g., multi-layer perceptrons (MLPs) and convolutional neural networks (CNNs)) differ in terms of their representation space. The field of weight space learning has gained a lot of attention these days.

Accurate quantification of both aleatoric and epistemic uncertainties is essential when deploying Graph Neural Networks (GNNs) in high-stakes applications such as drug discovery and financial fraud detection, where reliable predictions are critical. Although Evidential Deep Learning (EDL) efficiently quantifies uncertainty using a Dirichlet distribution over predictive probabilities, existing EDL-based GNN (EGNN) models require modifications to the network architecture and retraining, failing to take advantage of pre-trained models. We propose a plug-and-play framework for uncertainty quantification in GNNs that works with pre-trained models without the need for retraining. Our Evidential Probing Network (EPN) uses a lightweight Multi-Layer-Perceptron (MLP) head to extract evidence from learned representations, allowing efficient integration with various GNN architectures. We further introduce evidence-based regularization techniques, referred to as EPN-reg, to enhance the estimation of epistemic uncertainty with theoretical justifications. Extensive experiments demonstrate that the proposed EPN-reg achieves state-of-the-art performance in accurate and efficient uncertainty quantification, making it suitable for real-world deployment.