We introduce a use of the \(M\)-cover (or \(M\)-layer) transform for machine learning. The method replicates a model \(M\) times, but instead of coupling the copies through parameter averaging or an explicit attractive force, as in replicated SGD or Elastic SGD, it rewires the contexts in which local learning messages are computed. Each local loss is evaluated on a routed model whose parameters are drawn from different copies according to permutations sampled from a structured mixing kernel \(Q\). Training then uses the original local update rule, while the resulting learning messages are redistributed across the copies through these routed computational paths. Thus \(Q\) defines a topology for message transport and controls the long-loop structure of the lifted factor graph. We formulate this construction for perceptrons, committee machines, and multilayer perceptrons, showing that the same principle applies from discrete models to differentiable neural networks. The resulting framework provides a mechanism for improving generalization through structured message sharing rather than replica collapse or parameter-space coupling.

The transformer architecture [52], which underlies present-day Large Language Models, has been one of the main drivers of recent advances in machine learning and artificial intelligence. At each layer, the hidden state of the network is updated by sequentially applying two distinct operations: attention modules [3], which capture long-range interactions in the input sequence, and classical MultiLayer Perceptrons (MLPs), acting separately on each element of that sequence. Despite their empirical success, the mechanisms governing information propagation through depth, and the way attention and MLP blocks jointly shape internal representations, remain only partially understood from a theoretical viewpoint. Recent progress has come from viewing transformers in suitable scaling limits as deterministic mean-field interacting particle systems modeling the evolution of N tokens1 through the layers of the neural network architecture (the so-called residual stream dynamics), see, among others, [46, 26, 27, 45]. In these descriptions, depth plays the role of a continuous time variable, and, in the large-context regime (N), the evolution of token representations is encoded by a PDE for their empirical distribution. This viewpoint is closely connected to the literature on scaling laws, where the effect of various scaling exponents controlling the relative size of the network's hyperparameters (e.g., depth, width, context length) on the effective dynamics of the model

Multilayer-perceptrons (MLP) are known to struggle with learning functions of high-frequencies, and in particular cases with wide frequency bands. We present a spatially adaptive progressive encoding (SAPE) scheme for input signals of MLP networks, which enables them to better fit a wide range of frequencies without sacrificing training stability or requiring any domain specific preprocessing. SAPE gradually unmasks signal components with increasing frequencies as a function of time and space. The progressive exposure of frequencies is monitored by a feedback loop throughout the neural optimization process, allowing changes to propagate at different rates among local spatial portions of the signal space. We demonstrate the advantage of SAPE on a variety of domains and applications, including regression of low dimensional signals and images, representation learning of occupancy networks, and a geometric task of mesh transfer between 3D shapes.

Machine learning models of chemical bioactivity are increasingly used for prioritizing a small number of compounds in virtual screening libraries for experimental follow-up. In these applications, assessing model accuracy by early hit enrichment such as Positive Predicted Value (PPV) calculated for top N hits (PPV@N) is more appropriate and actionable than traditional global metrics such as AUC. We present KANEL, an ensemble workflow that combines interpretable Kolmogorov-Arnold Networks (KANs) with XGBoost, random forest, and multilayer perceptron models trained on complementary molecular representations (LillyMol descriptors, RDKit-derived descriptors, and Morgan fingerprints). Across five public PubChem BioAssay datasets (AIDs 485314, 485341, 504466, 624202, and 651820), Optuna-optimized weighted ensembles consistently outperformed the best single model in PPV@128 by 0.06-0.12

Graph Neural Networks (GNNs) have shown superior performance in node classification. However, GNNs perform poorly in the Few-Shot Node Classification (FSNC) task that requires robust generalization to make accurate predictions for unseen classes with limited labels. To tackle the challenge, we propose the integration of Sharpness-Aware Minimization (SAM)--a technique designed to enhance model generalization by finding a flat minimum of the loss landscape--into GNN training. The standard SAM approach, however, consists of two forward-backward steps in each training iteration, doubling the computational cost compared to the base optimizer (e.g., Adam). To mitigate this drawback, we introduce a novel algorithm, Fast Graph Sharpness-Aware Minimization (FGSAM), that integrates the rapid training of Multi-Layer Perceptrons (MLPs) with the superior performance of GNNs. Specifically, we utilize GNNs for parameter perturbation while employing MLPs to minimize the perturbed loss so that we can find a flat minimum with good generalization more efficiently.

The remarkable capabilities of modern large language models are rooted in their vast repositories of knowledge encoded within their parameters, enabling them to perceive the world and engage in reasoning. The inner workings of how these models store knowledge have long been a subject of intense interest and investigation among researchers. To date, most studies have concentrated on isolated components within these models, such as the Multilayer Perceptrons and attention head. In this paper, we delve into the computation graph of the language model to uncover the knowledge circuits that are instrumental in articulating specific knowledge. The experiments, conducted with GPT2 and TinyLLAMA, has allowed us to observe how certain information heads, relation heads, and Multilayer Perceptrons collaboratively encode knowledge within the model. Moreover, we evaluate the impact of current knowledge editing techniques on these knowledge circuits, providing deeper insights into the functioning and constraints of these editing methodologies. Finally, we utilize knowledge circuits to analyze and interpret language model behaviors such as hallucinations and in-context learning. We believe the knowledge circuit holds potential for advancing our understanding of Transformers and guiding the improved design of knowledge editing.

Fourier Neural Operators (FNOs) have shown promise for solving partial differential equations (PDEs).Typically, FNOs employ separate parameters for different frequency modes to specify tunable kernel integrals in Fourier space, which, yet, results in an undesirably large number of parameters when solving high-dimensional PDEs. A workaround is to abandon the frequency modes exceeding a predefined threshold, but this limits the FNOs' ability to represent high-frequency details and poses non-trivial challenges for hyper-parameter specification. To address these, we propose AMortized Fourier Neural Operator (AM-FNO), where an amortized neural parameterization of the kernel function is deployed to accommodate arbitrarily many frequency modes using a fixed number of parameters. We introduce two implementations of AM-FNO, based on the recently developed, appealing Kolmogorov-Arnold Network (KAN) and Multi-Layer Perceptrons (MLPs) equipped with orthogonal embedding functions respectively. We extensively evaluate our method on diverse datasets from various domains and observe up to 31\% average improvement compared to competing neural operator baselines.

Despite its widespread use in neural networks, error backpropagation has faced criticism for its lack of biological plausibility, suffering from issues such as the backward locking problem and the weight transport problem. These limitations have motivated researchers to explore more biologically plausible learning algorithms that could potentially shed light on how biological neural systems adapt and learn. Inspired by the counter-current exchange mechanisms observed in biological systems, we propose counter-current learning (CCL), a biologically plausible framework for credit assignment in deep learning. This framework employs a feedforward network to process input data and a feedback network to process targets, with each network enhancing the other through anti-parallel signal propagation. By leveraging the more informative signals from the bottom layer of the feedback network to guide the updates of the top layer of the feedforward network and vice versa, CCL enables the simultaneous transformation of source inputs to target outputs and the dynamic mutual influence of these transformations.Experimental results on MNIST, FashionMNIST, CIFAR10, CIFAR100, and STL-10 datasets using multi-layer perceptrons and convolutional neural networks demonstrate that CCL achieves comparable performance to other biological plausible algorithms while offering a more biologically realistic learning mechanism. Furthermore, we showcase the applicability of our approach to an autoencoder task, underscoring its potential for unsupervised representation learning.Our work presents a promising direction for biologically inspired and plausible learning algorithms, offering insights into the mechanisms of learning and adaptation in neural networks.

In this paper, we question if well pre-trained vision transformer (ViT) models could be used as teachers that exhibit scalable properties to advance cross architecture knowledge distillation research, in the context of adopting mainstream large-scale visual recognition datasets for evaluation. To make this possible, our analysis underlines the importance of seeking effective strategies to align (1) feature computing paradigm differences, (2) model scale differences, and (3) knowledge density differences. By combining three closely coupled components namely *cross attention projector*, *dual-view feature mimicking* and *teacher parameter perception* tailored to address the alignment problems stated above, we present a simple and effective knowledge distillation method, called *ScaleKD*. Our method can train student backbones that span across a variety of convolutional neural network (CNN), multi-layer perceptron (MLP), and ViT architectures on image classification datasets, achieving state-of-the-art knowledge distillation performance.