Wide neural networks with random weights and biases are Gaussian processes, as observed by Neal (1995) for shallow networks, and more recently by Lee et al.~(2018) and Matthews et al.~(2018) for deep fully-connected networks, as well as by Novak et al.~(2019) and Garriga-Alonso et al.~(2019) for deep convolutional networks. We show that this Neural Network-Gaussian Process correspondence surprisingly extends to all modern feedforward or recurrent neural networks composed of multilayer perceptron, RNNs (e.g. LSTMs, GRUs), (nD or graph) convolution, pooling, skip connection, attention, batch normalization, and/or layer normalization. More generally, we introduce a language for expressing neural network computations, and our result encompasses all such expressible neural networks. This work serves as a tutorial on the \emph{tensor programs} technique formulated in Yang (2019) and elucidates the Gaussian Process results obtained there. We provide open-source implementations of the Gaussian Process kernels of simple RNN, GRU, transformer, and batchnorm+ReLU network at github.com/thegregyang/GP4A. Please see our arxiv version for the complete and up-to-date version of this paper.

The vulnerability of deep neural networks has been widely found in various models as well as tasks where slight perturbations on the inputs could lead to incorrect predictions. These perturbed inputs are known as adversarial examples and one of the intriguing properties of them is Adversarial Transfersability, i.e. the capability of adversarial examples to fool other models. Traditionally, this transferability is always regarded as a critical threat to the defense against adversarial attacks, however, we argue that the network robustness can be significantly boosted by utilizing adversarial transferability from a new perspective. In this work, we first discuss the influence of different popular normalization layers on the adversarial transferability, and then provide both empirical evidence and theoretical analysis to shed light on the relationship between normalization types and transferability. Based on our theoretical analysis, we propose a simple yet effective module named Random Normalization Aggregation (RNA) which replaces the batch normalization layers in the networks and aggregates different selected normalization types to form a huge random space. Specifically, a random path is sampled during each inference procedure so that the network itself can be treated as an ensemble of a wide range of different models. Since the entire random space is designed with low adversarial transferability, it is difficult to perform effective attacks even when the network parameters are accessible. We conduct extensive experiments on various models and datasets, and demonstrate the strong superiority of proposed algorithm.

Equilibrium systems are a powerful way to express neural computations. As special cases, they include models of great current interest in both neuroscience and machine learning, such as deep neural networks, equilibrium recurrent neural networks, deep equilibrium models, or meta-learning. Here, we present a new principle for learning such systems with a temporally-and spatially-local rule. Our principle casts learning as a \emph{least-control} problem, where we first introduce an optimal controller to lead the system towards a solution state, and then define learning as reducing the amount of control needed to reach such a state. We show that incorporating learning signals within a dynamics as an optimal control enables transmitting activity-dependent credit assignment information, avoids storing intermediate states in memory, and does not rely on infinitesimal learning signals. In practice, our principle leads to strong performance matching that of leading gradient-based learning methods when applied to an array of problems involving recurrent neural networks and meta-learning. Our results shed light on how the brain might learn and offer new ways of approaching a broad class of machine learning problems.

Previous works show global covariance pooling (GCP) has great potential to improve deep architectures especially on visual recognition tasks, where post-normalization of GCP plays a very important role in final performance. Although several post-normalization strategies have been studied, these methods pay more close attention to effect of normalization on covariance representations rather than the whole GCP networks, and their effectiveness requires further understanding. Meanwhile, existing effective post-normalization strategies (e.g., matrix power normalization) usually suffer from high computational complexity (e.g., $O(d^{3})$ for $d$-dimensional inputs). To handle above issues, this work first analyzes the effect of post-normalization from the perspective of training GCP networks. Particularly, we for the first time show that \textit{effective post-normalization can make a good trade-off between representation decorrelation and information preservation for GCP, which are crucial to alleviate over-fitting and increase representation ability of deep GCP networks, respectively}. Based on this finding, we can improve existing post-normalization methods with some small modifications, providing further support to our observation. Furthermore, this finding encourages us to propose a novel pre-normalization method for GCP (namely DropCov), which develops an adaptive channel dropout on features right before GCP, aiming to reach trade-off between representation decorrelation and information preservation in a more efficient way. Our DropCov only has a linear complexity of $O(d)$, while being free for inference. Extensive experiments on various benchmarks (i.e., ImageNet-1K, ImageNet-C, ImageNet-A, Stylized-ImageNet, and iNat2017) show our DropCov is superior to the counterparts in terms of efficiency and effectiveness, and provides a simple yet effective method to improve performance of deep architectures involving both deep convolutional neural networks (CNNs) and vision transformers (ViTs).

For safety and robustness of AI systems, we introduce as a theoretical and computational tool that compares a trained model to a reference dataset to determine whether they have similar multiscale geometric structure. Our proofs and examples show that this geometric similarity between dataset and model is essential to trustworthy interpolation and perturbation, and we conjecture that this new concept will add value to the current debate regarding the unclear relationship between overfitting' and generalization'' in applications of deep-learning. In typical deep-learning applications, an explicit geometric description of the model isimpossible, but parallax can estimate topological features (components, cycles, voids, etc.)in the model by examining the effect on the Rips complex of geodesic distortions using the reference dataset.Thus, parallax indicates whether the model shares similar multiscale geometric features with the dataset.Parallax presents theoretically via topological data analysis [TDA] as a bi-filtered persistence module,and the key properties of this module are stable under perturbation of the reference dataset.

We study a deep learning inspired formulation for the blind demodulation problem, which is the task of recovering two unknown vectors from their entrywise multiplication.

Neural networks are becoming more and more popular for the analysis of physiological time-series. The most successful deep learning systems in this domain combine convolutional and recurrent layers to extract useful features to model temporal relations. Unfortunately, these recurrent models are difficult to tune and optimize. In our experience, they often require task-specific modifications, which makes them challenging to use for non-experts. We propose U-Time, a fully feed-forward deep learning approach to physiological time series segmentation developed for the analysis of sleep data.

AI Wrapped: The 14 AI terms you couldn't avoid in 2025 From "superintelligence" to "slop," here are the words and phrases that defined another year of AI craziness. If the past 12 months have taught us anything, it's that the AI hype train is showing no signs of slowing. It's hard to believe that at the beginning of the year, DeepSeek had yet to turn the entire industry on its head, Meta was better known for trying (and failing) to make the metaverse cool than for its relentless quest to dominate superintelligence, and vibe coding wasn't a thing. If that's left you feeling a little confused, fear not. As we near the end of 2025, our writers have taken a look back over the AI terms that dominated the year, for better or worse. Make sure you take the time to brace yourself for what promises to be another bonkers year.

Homomorphic Encryption (HE) is one of the most promising security solutions to emerging Machine Learning as a Service (MLaaS). Several Leveled-HE (LHE)-enabled Convolutional Neural Networks (LHECNNs) are proposed to implement MLaaS to avoid the large bootstrapping overhead. However, prior LHECNNs have to pay significant computational overhead but achieve only low inference accuracy, due to their polynomial approximation activations and poolings. Stacking many polynomial approximation activation layers in a network greatly reduces the inference accuracy, since the polynomial approximation activation errors lead to a low distortion of the output distribution of the next batch normalization layer. So the polynomial approximation activations and poolings have become the obstacle to a fast and accurate LHECNN model.

Existing deep learning based facial landmark detection methods have achieved excellent performance. These methods, however, do not explicitly embed the structural dependencies among landmark points. They hence cannot preserve the geometric relationships between landmark points or generalize well to challenging conditions or unseen data. This paper proposes a method for deep structured facial landmark detection based on combining a deep Convolutional Network with a Conditional Random Field. We demonstrate its superior performance to existing state-of-the-art techniques in facial landmark detection, especially a better generalization ability on challenging datasets that include large pose and occlusion.