Machine learning (ML) is rapidly transforming the way molecular dynamics simulations are performed and analyzed, from materials modeling to studies of protein folding and function. ML algorithms are often employed to learn low-dimensional representations of conformational landscapes and to cluster trajectories into relevant metastable states. Most of these algorithms require selecting a small number of features that describe the problem of interest. Although deep neural networks can tackle large numbers of input features, the training costs increase with input size, which makes the selection of a subset of features mandatory for most problems of practical interest. Here, we show that random nonlinear projections can be used to compress large feature spaces and make computations faster without substantial loss of information. We describe an efficient way to produce random projections and then exemplify the general procedure for protein folding. For our test cases NTL9 and the double-norleucin variant of the villin headpiece, we find that random compression retains the core static and dynamic information of the original high dimensional feature space and makes trajectory analysis more robust.

Large language models (LLMs) exhibit remarkable versatility in adopting diverse personas. In this study, we examine how assigning a persona influences a model's reasoning on an objective task. Using activation patching, we take a first step toward understanding how key components of the model encode persona-specific information. Our findings reveal that the early Multi-Layer Perceptron (MLP) layers attend not only to the syntactic structure of the input but also process its semantic content. These layers transform persona tokens into richer representations, which are then used by the middle Multi-Head Attention (MHA) layers to shape the model's output. Additionally, we identify specific attention heads that disproportionately attend to racial and color-based identities.

Transformer models achieve excellent scaling property, where the performance is improved with the increment of model capacity. However, large-scale model parameters lead to an unaffordable cost of computing and memory. We analyze popular transformer architectures and find that multilayer perceptron (MLP) modules take up the majority of model parameters. To this end, we focus on the recoverability of the compressed models and propose a Diversity-Guided MLP Reduction (DGMR) method to significantly reduce the parameters of large vision transformers with only negligible performance degradation. Specifically, we conduct a Gram-Schmidt weight pruning strategy to eliminate redundant neurons of MLP hidden layer, while preserving weight diversity for better performance recover during distillation. Compared to the model trained from scratch, our pruned model only requires 0.06\% data of LAION-2B (for the training of large vision transformers) without labels (ImageNet-1K) to recover the original performance. Experimental results on several state-of-the-art large vision transformers demonstrate that our method achieves a more than 57.0\% parameter and FLOPs reduction in a near lossless manner. Notably, for EVA-CLIP-E (4.4B), our method accomplishes a 71.5\% parameter and FLOPs reduction without performance degradation. The source code and trained weights are available at https://github.com/visresearch/DGMR.

Thanks to our geometric subdivision, we can integrate the neural network analytically, and use it as a control variate for Monte Carlo integration. The integral of the approximation provides a biased estimate (left), which is corrected by Monte Carlo integration of the residual integrand (center left), obtaining the final unbiased estimate (center right), which can achieve a lower error than vanilla Monte Carlo (right). Abstract Control variates are a variance-reduction technique for Monte Carlo integration. The principle involves approximating the integrand by a function that can be analytically integrated, and integrating using the Monte Carlo method only the residual difference between the integrand and the approximation, to obtain an unbiased estimate. Neural networks are universal approx-imators that could potentially be used as a control variate. However, the challenge lies in the analytic integration, which is not possible in general. In this manuscript, we study one of the simplest neural network models, the multilayered perceptron (MLP) with continuous piecewise linear activation functions, and its possible analytic integration. W e propose an integration method based on integration domain subdivision, employing techniques from computational geometry to solve this problem in 2D. W e demonstrate that an MLP can be used as a control variate in combination with our integration method, showing applications in the light transport simulation. 1. Introduction To synthesize photorealistic images, we need to solve notoriously complex integrals that model the underlying light transport. In general, these integrals do not have an analytic solution, and thus we employ tools of numerical integration to solve them. Among those, Monte Carlo integration is prominent, providing a general and robust solution, efficiently dealing with, for example, high dimensions or discontinuities that other numerical methods may struggle with. Monte Carlo converges to a correct solution with an increasing number of samples; however, it may require a large number of samples to suppress variance, that otherwise exhibits as high-frequency noise in the rendered images, under an acceptable threshold.

Diffusion models typically employ static or heuristic classifier-free guidance (CFG) schedules, which often fail to adapt across timesteps and noise conditions. In this work, we introduce a quantum reinforcement learning (QRL) controller that dynamically adjusts CFG at each denoising step. The controller adopts a hybrid quantum--classical actor--critic architecture: a shallow variational quantum circuit (VQC) with ring entanglement generates policy features, which are mapped by a compact multilayer perceptron (MLP) into Gaussian actions over $Δ$CFG, while a classical critic estimates value functions. The policy is optimized using Proximal Policy Optimization (PPO) with Generalized Advantage Estimation (GAE), guided by a reward that balances classification confidence, perceptual improvement, and action regularization. Experiments on CIFAR-10 demonstrate that our QRL policy improves perceptual quality (LPIPS, PSNR, SSIM) while reducing parameter count compared to classical RL actors and fixed schedules. Ablation studies on qubit number and circuit depth reveal trade-offs between accuracy and efficiency, and extended evaluations confirm robust generation under long diffusion schedules.

Understanding disease similarity is critical for advancing diagnostics, drug discovery, and personalized treatment strategies. We present PhenoGnet, a novel graph-based contrastive learning framework designed to predict disease similarity by integrating gene functional interaction networks with the Human Phenotype Ontology (HPO). PhenoGnet comprises two key components: an intra-view model that separately encodes gene and phenotype graphs using Graph Convolutional Networks (GCNs) and Graph Attention Networks (GATs), and a cross view model implemented as a shared weight multilayer perceptron (MLP) that aligns gene and phenotype embeddings through contrastive learning. The model is trained using known gene phenotype associations as positive pairs and randomly sampled unrelated pairs as negatives. Diseases are represented by the mean embeddings of their associated genes and/or phenotypes, and pairwise similarity is computed via cosine similarity. Evaluation on a curated benchmark of 1,100 similar and 866 dissimilar disease pairs demonstrates strong performance, with gene based embeddings achieving an AUCPR of 0.9012 and AUROC of 0.8764, outperforming existing state of the art methods. Notably, PhenoGnet captures latent biological relationships beyond direct overlap, offering a scalable and interpretable solution for disease similarity prediction. These results underscore its potential for enabling downstream applications in rare disease research and precision medicine.

Variational quantum circuits (VQCs) are central to quantum machine learning, while recent progress in Kolmogorov-Arnold networks (KANs) highlights the power of learnable activation functions. We unify these directions by introducing quantum variational activation functions (QVAFs), realized through single-qubit data re-uploading circuits called DatA Re-Uploading ActivatioNs (DARUANs). We show that DARUAN with trainable weights in data pre-processing possesses an exponentially growing frequency spectrum with data repetitions, enabling an exponential reduction in parameter size compared with Fourier-based activations without loss of expressivity. Embedding DARUAN into KANs yields quantum-inspired KANs (QKANs), which retain the interpretability of KANs while improving their parameter efficiency, expressivity, and generalization. We further introduce two novel techniques to enhance scalability, feasibility and computational efficiency, such as layer extension and hybrid QKANs (HQKANs) as drop-in replacements of multi-layer perceptrons (MLPs) for feed-forward networks in large-scale models. We provide theoretical analysis and extensive experiments on function regression, image classification, and autoregressive generative language modeling, demonstrating the efficiency and scalability of QKANs. DARUANs and QKANs offer a promising direction for advancing quantum machine learning on both noisy intermediate-scale quantum (NISQ) hardware and classical quantum simulators.

Large language models (LLMs) demonstrate proficiency across numerous computational tasks, yet their inner workings remain unclear. In theory, the combination of causal self-attention and multilayer perceptron layers allows every token to access and compute information based on all preceding tokens. In practice, to what extent are such operations present? In this paper, on mental math tasks (i.e., direct math calculation via next-token prediction without explicit reasoning), we investigate this question in three steps: inhibiting input-specific token computations in the initial layers, restricting the routes of information transfer across token positions in the next few layers, and forcing all computation to happen at the last token in the remaining layers. With two proposed techniques, Context-Aware Mean Ablation (CAMA) and Attention-Based Peeking (ABP), we identify an All-for-One subgraph (AF1) with high accuracy on a wide variety of mental math tasks, where meaningful computation occurs very late (in terms of layer depth) and only at the last token, which receives information of other tokens in few specific middle layers. Experiments on a variety of models and arithmetic expressions show that this subgraph is sufficient and necessary for high model performance, transfers across different models, and works on a variety of input styles. Ablations on different CAMA and ABP alternatives reveal their unique advantages over other methods, which may be of independent interest.

Implicit neural representations have recently been extended to represent convolutional neural network weights via neural representation for neural networks, offering promising parameter compression benefits. However, standard multi-layer perceptrons used in neural representation for neural networks exhibit a pronounced spectral bias, hampering their ability to reconstruct high-frequency details effectively. In this paper, we propose SBS, a parameter-efficient enhancement to neural representation for neural networks that suppresses spectral bias using two techniques: (1) a unidirectional ordering-based smoothing that improves kernel smoothness in the output space, and (2) unidirectional ordering-based smoothing aware random fourier features that adaptively modulate the frequency bandwidth of input encodings based on layer-wise parameter count. Extensive evaluations on various ResNet models with datasets CIFAR-10, CIFAR-100, and ImageNet, demonstrate that SBS achieves significantly better reconstruction accuracy with less parameters compared to SOTA.

Gradient-based neural network training traditionally enforces symmetry between forward and backward propagation, requiring activation functions to be differentiable (or sub-differentiable) and strictly monotonic in certain regions to prevent flat gradient areas. This symmetry, linking forward activations closely to backward gradients, significantly restricts the selection of activation functions, particularly excluding those with substantial flat or non-differentiable regions. In this paper, we challenge this assumption through mathematical analysis, demonstrating that precise gradient magnitudes derived from activation functions are largely redundant, provided the gradient direction is preserved. Empirical experiments conducted on foundational architectures - such as Multi-Layer Perceptrons (MLPs), Convolutional Neural Networks (CNNs), and Binary Neural Networks (BNNs) - confirm that relaxing forward-backward symmetry and substituting traditional gradients with simpler or stochastic alternatives does not impair learning and may even enhance training stability and efficiency. We explicitly demonstrate that neural networks with flat or non-differentiable activation functions, such as the Heaviside step function, can be effectively trained, thereby expanding design flexibility and computational efficiency. Further empirical validation with more complex architectures remains a valuable direction for future research.