In recent years there has been a considerable amount of research on local post hoc explanations for neural networks. However, work on building interpretable neural architectures has been relatively sparse. In this paper, we present a novel neural architecture, CoFrNet, inspired by the form of continued fractions which are known to have many attractive properties in number theory, such as fast convergence of approximations to real numbers. We show that CoFrNets can be efficiently trained as well as interpreted leveraging their particular functional form. Moreover, we prove that such architectures are universal approximators based on a proof strategy that is different than the typical strategy used to prove universal approximation results for neural networks based on infinite width (or depth), which is likely to be of independent interest. We experiment on nonlinear synthetic functions and are able to accurately model as well as estimate feature attributions and even higher order terms in some cases, which is a testament to the representational power as well as interpretability of such architectures. To further showcase the power of CoFrNets, we experiment on seven real datasets spanning tabular, text and image modalities, and show that they are either comparable or significantly better than other interpretable models and multilayer perceptrons, sometimes approaching the accuracies of state-of-the-art models.

Speaker recognition models face challenges in multi-lingual settings due to the entanglement of linguistic information within speaker embeddings. The overlap between vocal traits such as accent, vocal anatomy, and a language's phonetic structure complicates separating linguistic and speaker information. Disentangling these components can significantly improve speaker recognition accuracy. To this end, we propose a novel disentanglement learning strategy that integrates joint learning through prefix-tuned cross-attention. This approach is particularly effective when speakers switch between languages. Experimental results show the model generalizes across monolingual and multi-lingual settings, including unseen languages. Notably, the proposed model improves the equal error rate across multiple datasets, highlighting its ability to separate language information from speaker embeddings and enhance recognition in diverse linguistic conditions.

The widespread deployment of neural networks in critical decision-making systems has created an urgent need for interpretable machine learning models. While these architectures demonstrate remarkable empirical success across diverse domains, their internal mechanisms remain largely opaque, earning them the notorious designation as "black boxes". This opacity originates from the confluence of several fundamental challenges: the high-dimensional nature of parameter spaces, the compositional complexity introduced by multiple layers of non-linear transformations, and the emergent behaviours that arise from the interplay between architecture and optimisation dynamics. In this work, we focus on Multilayer Perceptrons (MLPs), the foundational architecture underlying modern deep learning. Despite their apparent simplicity compared to contemporary architectures, MLPs remain ubiquitous as essential components in more complex models. They appear as dense layers in Convolutional Neural Networks (CNNs), as projection heads in Vision Transformers, and as feed-forward networks in Transformer blocks. Understanding the internal representations learned by MLPs thus provides a gateway to interpreting broader classes of neural architectures. Moreover, in safety-critical applications such as medical diagnosis, financial risk assessment, and autonomous systems, the ability to interpret MLP decisions is highly important. The challenge of neural network interpretability has two complementary research directions.

Finding the right initialisation for neural networks is crucial to ensure smooth training and good performance. In transformers, the wrong initialisation can lead to one of two failure modes of self-attention layers: rank collapse, where all tokens collapse into similar representations, and entropy collapse, where highly concentrated attention scores lead to training instability. While the right initialisation has been extensively studied in feed-forward networks, an exact description of signal propagation through a full transformer block has so far been lacking. Here, we provide an analytical theory of signal propagation through vanilla transformer blocks with self-attention layers, layer normalisation, skip connections and ReLU MLP. To treat the self-attention layer, we draw on a formal parallel with the Random Energy Model from statistical physics. We identify and characterise two regimes governed by the variance of the query and key initialisations: a low-variance regime, where we recover the known rank collapse behaviour; and a previously unexplored high-variance regime, where signal is preserved but \textit{entropy collapse} occurs. In the low-variance regime, we calculate the critical strength for the residual connection to ensure signal propagation. Our theory yields trainability diagrams that identify the correct choice of initialisation hyper-parameters for a given architecture. Experiments with BERT-style models trained on TinyStories validate our predictions. Our theoretical framework gives a unified perspective on the two failure modes of self-attention and gives quantitative predictions on the scale of both weights and residual connections that guarantees smooth training.

The paper discusses the capabilities of multilayer perceptron neural networks implementing metric recognition methods, for which the values of the weights are calculated analytically by formulas. Comparative experiments in training a neural network with pre-calculated weights and with random initialization of weights on different sizes of the MNIST training dataset are carried out. The results of the experiments show that a multilayer perceptron with pre-calculated weights can be trained much faster and is much more robust to the reduction of the training dataset.

--Under the nearing error-corrected era of quantum computing, it is necessary to understand the suitability of certain post-NISQ algorithms for practical problems. One of the most promising, applicable and yet difficult to implement in practical terms is the Harrow, Hassidim and Lloyd (HHL) algorithm for linear systems of equations. An enormous number of problems can be expressed as linear systems of equations, from Machine Learning to fluid dynamics. However, in most cases, HHL will not be able to provide a practical, reasonable solution to these problems. This paper's goal inquires about whether problems can be labeled using Machine Learning classifiers as suitable or unsuitable for HHL implementation when some numerical information about the problem is known beforehand. This work demonstrates that training on significantly representative data distributions is critical to achieve good classifications of the problems based on the numerical properties of the matrix representing the system of equations. Accurate classification is possible through Multi-Layer Perceptrons, although with careful design of the training data distribution and classifier parameters. The HHL algorithm by Harrow, Hassidim and Lloyd is a well known quantum algorithm for quantum-mechanically constructing the solution of a linear systems of equations [1]. HHL is one of those quantum algorithms that will only make sense under quantum error-corrected implementation. Although its depth (number of gate layers) varies depending on certain conditions as it will be shown, HHL results in deep quantum circuits. As we approach this new era of quantum computing, it is necessary to gain understanding of the actual implementability of certain algorithms. The linear system of equations problem can be defined as, given a matrix A and a vector b, find a vector xsuch that A x= b. In quantum notation, this is expressed as A | x = | b, where A is a Hermitian operator -- a workaround exists when A is not Hermitian-- and b has to be encoded in a quantum state |b and, hence, it has to be normalized.

Recent 3D Gaussian Splatting (3DGS) techniques for Visual Simultaneous Localization and Mapping (SLAM) have significantly progressed in tracking and high-fidelity mapping. However, their sequential optimization framework and sensitivity to dynamic objects limit real-time performance and robustness in real-world scenarios. We present UP-SLAM, a real-time RGB-D SLAM system for dynamic environments that decouples tracking and mapping through a parallelized framework. A probabilistic octree is employed to manage Gaussian primitives adaptively, enabling efficient initialization and pruning without hand-crafted thresholds. To robustly filter dynamic regions during tracking, we propose a training-free uncertainty estimator that fuses multi-modal residuals to estimate per-pixel motion uncertainty, achieving open-set dynamic object handling without reliance on semantic labels. Furthermore, a temporal encoder is designed to enhance rendering quality. Concurrently, low-dimensional features are efficiently transformed via a shallow multilayer perceptron to construct DINO features, which are then employed to enrich the Gaussian field and improve the robustness of uncertainty prediction. Extensive experiments on multiple challenging datasets suggest that UP-SLAM outperforms state-of-the-art methods in both localization accuracy (by 59.8%) and rendering quality (by 4.57 dB PSNR), while maintaining real-time performance and producing reusable, artifact-free static maps in dynamic environments.The project: https://aczheng-cai.github.io/up_slam.github.io/

The ability of a brain or a neural network to efficiently learn depends crucially on both the task structure and the learning rule.Previous works have analyzed the dynamical equations describing learning in the relatively simplified context of the perceptron under assumptions of a student-teacher framework or a linearized output. While these assumptions have facilitated theoretical understanding, they have precluded a detailed understanding of the roles of the nonlinearity and input-data distribution in determining the learning dynamics, limiting the applicability of the theories to real biological or artificial neural networks.Here, we use a stochastic-process approach to derive flow equations describing learning, applying this framework to the case of a nonlinear perceptron performing binary classification. We characterize the effects of the learning rule (supervised or reinforcement learning, SL/RL) and input-data distribution on the perceptron's learning curve and the forgetting curve as subsequent tasks are learned.In particular, we find that the input-data noise differently affects the learning speed under SL vs. RL, as well as determines how quickly learning of a task is overwritten by subsequent learning. Additionally, we verify our approach with real data using the MNIST dataset.This approach points a way toward analyzing learning dynamics for more-complex circuit architectures.

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.