This study investigates whether second-order geometric cues - planar curvature magnitude, curvature sign, and gradient orientation - are sufficient on their own to drive a multilayer perceptron (MLP) classifier for handwritten character recognition (HCR), offering an alternative to convolutional neural networks (CNNs). Using these three handcrafted feature maps as inputs, our curvature-orientation MLP achieves 97 percent accuracy on MNIST digits and 89 percent on EMNIST letters. These results underscore the discriminative power of curvature-based representations for handwritten character images and demonstrate that the advantages of deep learning can be realized even with interpretable, hand-engineered features.

We introduce CosmoCore, a neuroscience-inspired reinforcement learning (RL) architecture that integrates affective signals to enhance code generation in large language models (LLMs). Motivated by human and animal learning where embarrassment from mistakes drives rapid correction, as observed in training a puppy to avoid repeating errors after a single scolding CosmoCore tags code generation trajectories with valence and surprise using a lightweight multi-layer perceptron (MLP). High-negative valence (cringe) episodes, such as buggy code outputs, are prioritized in a Dream Queue for five-fold replay during off-policy updates, while low-surprise successes are pruned to prevent overconfidence and buffer bloat. Evaluated on code generation benchmarks like HumanEval and BigCodeBench, alongside simulations with a custom data pipeline environment, CosmoCore reduces hallucinated code (e.g., syntax errors or logical bugs) by 48\% and accelerates self-correction by 45\%. Local experiments using Hugging Face models in a PySpark environment validate these gains, with code snippets provided for replication. Ablations confirm valence tagging boosts curiosity in exploration, and pruning mitigates inefficiency. This framework extends RL from human feedback (RLHF) for more emotionally aware code assistants, with applications in IDEs and data pipelines. Code and the custom mini-world simulation are released.

Estimating heterogeneous treatment effects (HTEs) in time-varying settings is particularly challenging, as the probability of observing certain treatment sequences decreases exponentially with longer prediction horizons. Thus, the observed data contain little support for many plausible treatment sequences, which creates severe overlap problems. Existing meta-learners for the time-varying setting typically assume adequate treatment overlap, and thus suffer from exploding estimation variance when the overlap is low. To address this problem, we introduce a novel overlap-weighted orthogonal (WO) meta-learner for estimating HTEs that targets regions in the observed data with high probability of receiving the interventional treatment sequences. This offers a fully data-driven approach through which our WO-learner can counteract instabilities as in existing meta-learners and thus obtain more reliable HTE estimates. Methodologically, we develop a novel Neyman-orthogonal population risk function that minimizes the overlap-weighted oracle risk. We show that our WO-learner has the favorable property of Neyman-orthogonality, meaning that it is robust against misspecification in the nuisance functions. Further, our WO-learner is fully model-agnostic and can be applied to any machine learning model. Through extensive experiments with both transformer and LSTM backbones, we demonstrate the benefits of our novel WO-learner.

Zero-shot learning, which aims to recognize new categories that are not included in the training set, has gained popularity owing to its potential ability in the real-word applications. Zero-shot learning models rely on learning an embedding space, where both semantic descriptions of classes and visual features of instances can be embedded for nearest neighbor search. Recently, most of the existing works consider the visual space formulated by deep visual features as an ideal choice of the embedding space. However, the discrete distribution of instances in the visual space makes the data structure unremarkable. We argue that optimizing the visual space is crucial as it allows semantic vectors to be embedded into the visual space more effectively. In this work, we propose two strategies to accomplish this purpose. One is the visual prototype based method, which learns a visual prototype for each visual class, so that, in the visual space, a class can be represented by a prototype feature instead of a series of discrete visual features. The other is to optimize the visual feature structure in an intermediate embedding space, and in this method we successfully devise a multilayer perceptron framework based algorithm that is able to learn the common intermediate embedding space and meanwhile to make the visual data structure more distinctive. Through extensive experimental evaluation on four benchmark datasets, we demonstrate that optimizing visual space is beneficial for zero-shot learning. Besides, the proposed prototype based method achieves the new state-of-the-art performance.

As AI systems enter high-stakes domains, evaluation must extend beyond predictive accuracy to include explainability, fairness, robustness, and sustainability. We introduce RAISE (Responsible AI Scoring and Evaluation), a unified framework that quantifies model performance across these four dimensions and aggregates them into a single, holistic Responsibility Score. We evaluated three deep learning models: a Multilayer Perceptron (MLP), a Tabular ResNet, and a Feature Tokenizer Transformer, on structured datasets from finance, healthcare, and socioeconomics. Our findings reveal critical trade-offs: the MLP demonstrated strong sustainability and robustness, the Transformer excelled in explainability and fairness at a very high environmental cost, and the Tabular ResNet offered a balanced profile. These results underscore that no single model dominates across all responsibility criteria, highlighting the necessity of multi-dimensional evaluation for responsible model selection. Our implementation is available at: https://github.com/raise-framework/raise.

This work introduces Probabilistic Kolmogorov-Arnold Network (P-KAN), a novel probabilistic extension of Kolmogorov-Arnold Networks (KANs) for time series forecasting. By replacing scalar weights with spline-based functional connections and directly parameterizing predictive distributions, P-KANs offer expressive yet parameter-efficient models capable of capturing nonlinear and heavy-tailed dynamics. We evaluate P-KANs on satellite traffic forecasting, where uncertainty-aware predictions enable dynamic thresholding for resource allocation. Results show that P-KANs consistently outperform Multi Layer Perceptron (MLP) baselines in both accuracy and calibration, achieving superior efficiency-risk trade-offs while using significantly fewer parameters. We build up P-KANs on two distributions, namely Gaussian and Student-t distributions. The Gaussian variant provides robust, conservative forecasts suitable for safety-critical scenarios, whereas the Student-t variant yields sharper distributions that improve efficiency under stable demand. These findings establish P-KANs as a powerful framework for probabilistic forecasting with direct applicability to satellite communications and other resource-constrained domains.

The fusion of Synthetic Aperture Radar (SAR) and RGB imagery for land cover classification remains challenging due to modality heterogeneity and underexploited spectral complementarity. Existing approaches often fail to decouple shared structural features from modality-complementary radiometric attributes, resulting in feature conflicts and information loss. To address this, we propose Phase-Amplitude Decoupling (PAD), a frequency-aware framework that separates phase (modality-shared) and amplitude (modality-complementary) components in the Fourier domain. This design reinforces shared structures while preserving complementary characteristics, thereby enhancing fusion quality. Unlike previous methods that overlook the distinct physical properties encoded in frequency spectra, PAD explicitly introduces amplitude-phase decoupling for multi-modal fusion. Specifically, PAD comprises two key components: 1) Phase Spectrum Correction (PSC), which aligns cross-modal phase features via convolution-guided scaling to improve geometric consistency; and 2) Amplitude Spectrum Fusion (ASF), which dynamically integrates high- and low-frequency patterns using frequency-adaptive multilayer perceptrons, effectively exploiting SAR's morphological sensitivity and RGB's spectral richness. Extensive experiments on WHU-OPT-SAR and DDHR-SK demonstrate state-of-the-art performance. This work establishes a new paradigm for physics-aware multi-modal fusion in remote sensing. The code will be available at https://github.com/RanFeng2/PAD.

We revisit the Universal Approximation Theorem(UAT) through the lens of the tropical geometry of neural networks and introduce a constructive, geometry-aware initialization for sigmoidal multi-layer perceptrons (MLPs). Tropical geometry shows that Rectified Linear Unit (ReLU) networks admit decision functions with a combinatorial structure often described as a tropical rational, namely a difference of tropical polynomials. Focusing on planar binary classification, we design purely sigmoidal MLPs that adhere to the finite-sum format of UAT: a finite linear combination of shifted and scaled sigmoids of affine functions. The resulting models yield decision boundaries that already align with prescribed shapes at initialization and can be refined by standard training if desired. This provides a practical bridge between the tropical perspective and smooth MLPs, enabling interpretable, shape-driven initialization without resorting to ReLU architectures. We focus on the construction and empirical demonstrations in two dimensions; theoretical analysis and higher-dimensional extensions are left for future work.

Analysing how information flows along the layers of a multilayer perceptron is a topic of paramount importance in the field of artificial neural networks. After framing the problem from the point of view of information theory, in this position article a specific investigation is conducted on the way information is processed, with particular reference to the requirements imposed by supervised learning. To this end, the concept of information matrix is devised and then used as formal framework for understanding the aetiology of optimisation strategies and for studying the information flow. The underlying research for this article has also produced several key outcomes: i) the definition of a parametric optimisation strategy, ii) the finding that the optimisation strategy proposed in the information bottleneck framework shares strong similarities with the one derived from the information matrix, and iii) the insight that a multilayer perceptron serves as a kind of "adaptor", meant to process the input according to the given objective.

The training of deep neural networks predominantly relies on a combination of gradient-based optimisation and back-propagation for the computation of the gradient. While incredibly successful, this approach faces challenges such as vanishing or exploding gradients, difficulties with non-smooth activations, and an inherently sequential structure that limits parallelisation. Lifted training methods offer an alternative by reformulating the nested optimisation problem into a higher-dimensional, constrained optimisation problem where the constraints are no longer enforced directly but penalised with penalty terms. This chapter introduces a unified framework that encapsulates various lifted training strategies--including the Method of Auxiliary Coordinates (MAC), Fenchel Lifted Networks, and Lifted Bregman Training--and demonstrates how diverse architectures, such as Multi-Layer Perceptrons (MLPs), Residual Neural Networks (ResNets), and Proximal Neural Networks (PNNs), fit within this structure. By leveraging tools from convex optimisation, particularly Bregman distances, the framework facilitates distributed optimisation, accommodates non-differentiable proximal activations, and can improve the conditioning of the training landscape. We discuss the implementation of these methods using block-coordinate descent (BCD) strategies--including deterministic implementations enhanced by accelerated (e.g., Nesterov, Heavyball) and adaptive (e.g., Adam) optimisation techniques--as well as implicit stochastic gradient methods (ISGM). Furthermore, we explore the application of this framework to inverse problems, detailing methodologies for both the training of specialised networks (e.g., unrolled architectures) and the stable inversion of pre-trained networks. Numerical results on standard imaging tasks validate the effectiveness and stability of the lifted Bregman approach compared to conventional training, particularly for architectures employing proximal activations.