Daily Papers

Tangent Model Composition (TMC) is a method to combine component models independently fine-tuned around a pre-trained point. Component models are tangent vectors to the pre-trained model that can be added, scaled, or subtracted to support incremental learning, ensembling, or unlearning. Component models are composed at inference time via scalar combination, reducing the cost of ensembling to that of a single model. TMC improves accuracy by 4.2% compared to ensembling non-linearly fine-tuned models at a 2.5x to 10x reduction of inference cost, growing linearly with the number of component models. Each component model can be forgotten at zero cost, with no residual effect on the resulting inference. When used for continual fine-tuning, TMC is not constrained by sequential bias and can be executed in parallel on federated data. TMC outperforms recently published continual fine-tuning methods almost uniformly on each setting -- task-incremental, class-incremental, and data-incremental -- on a total of 13 experiments across 3 benchmark datasets, despite not using any replay buffer. TMC is designed for composing models that are local to a pre-trained embedding, but could be extended to more general settings.

We introduce Tangent Attention Fine-Tuning (TAFT), a method for fine-tuning linearized transformers obtained by computing a First-order Taylor Expansion around a pre-trained initialization. We show that the Jacobian-Vector Product resulting from linearization can be computed efficiently in a single forward pass, reducing training and inference cost to the same order of magnitude as its original non-linear counterpart, while using the same number of parameters. Furthermore, we show that, when applied to various downstream visual classification tasks, the resulting Tangent Transformer fine-tuned with TAFT can perform comparably with fine-tuning the original non-linear network. Since Tangent Transformers are linear with respect to the new set of weights, and the resulting fine-tuning loss is convex, we show that TAFT enjoys several advantages compared to non-linear fine-tuning when it comes to model composition, parallel training, machine unlearning, and differential privacy.

We address the problem of performing backpropagation for computation graphs involving 3D transformation groups SO(3), SE(3), and Sim(3). 3D transformation groups are widely used in 3D vision and robotics, but they do not form vector spaces and instead lie on smooth manifolds. The standard backpropagation approach, which embeds 3D transformations in Euclidean spaces, suffers from numerical difficulties. We introduce a new library, which exploits the group structure of 3D transformations and performs backpropagation in the tangent spaces of manifolds. We show that our approach is numerically more stable, easier to implement, and beneficial to a diverse set of tasks. Our plug-and-play PyTorch library is available at https://github.com/princeton-vl/lietorch.

Recent diffusion models achieve the state-of-the-art performance in image generation, but often suffer from semantic inconsistencies or hallucinations. While various inference-time guidance methods can enhance generation, they often operate indirectly by relying on external signals or architectural modifications, which introduces additional computational overhead. In this paper, we propose Tangential Amplifying Guidance (TAG), a more efficient and direct guidance method that operates solely on trajectory signals without modifying the underlying diffusion model. TAG leverages an intermediate sample as a projection basis and amplifies the tangential components of the estimated scores with respect to this basis to correct the sampling trajectory. We formalize this guidance process by leveraging a first-order Taylor expansion, which demonstrates that amplifying the tangential component steers the state toward higher-probability regions, thereby reducing inconsistencies and enhancing sample quality. TAG is a plug-and-play, architecture-agnostic module that improves diffusion sampling fidelity with minimal computational addition, offering a new perspective on diffusion guidance.

At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit, thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: during gradient descent on the parameters of an ANN, the network function f_theta (which maps input vectors to output vectors) follows the kernel gradient of the functional cost (which is convex, in contrast to the parameter cost) w.r.t. a new kernel: the Neural Tangent Kernel (NTK). This kernel is central to describe the generalization features of ANNs. While the NTK is random at initialization and varies during training, in the infinite-width limit it converges to an explicit limiting kernel and it stays constant during training. This makes it possible to study the training of ANNs in function space instead of parameter space. Convergence of the training can then be related to the positive-definiteness of the limiting NTK. We prove the positive-definiteness of the limiting NTK when the data is supported on the sphere and the non-linearity is non-polynomial. We then focus on the setting of least-squares regression and show that in the infinite-width limit, the network function f_theta follows a linear differential equation during training. The convergence is fastest along the largest kernel principal components of the input data with respect to the NTK, hence suggesting a theoretical motivation for early stopping. Finally we study the NTK numerically, observe its behavior for wide networks, and compare it to the infinite-width limit.

Deep learning weather models now match numerical weather prediction accuracy while running orders of magnitude faster, but produce deterministic forecasts without uncertainty estimates, a critical gap for high-stakes decisions during extreme weather events. This paper proposes Neural Tangent Kernel-based uncertainty quantification (NTK-UQ) using last-layer empirical features. Theoretical analysis predicts that UQ quality is architecture-dependent through two mechanisms. First, a variance collapse mechanism explains when UQ fails: when the eigenvalue truncation rank approaches the effective rank of the feature space, the GP correction term consumes nearly all prior variance, destroying discrimination between tropical cyclones and routine conditions; architectures with concentrated spectra (spectral operators) require aggressive truncation (k leq 10), while attention-based models tolerate full-rank computation. Second, decomposition performance depends on the non-Gaussian, heavy-tailed structure of extreme weather: Independent Component Analysis exploits higher-order statistics (kurtosis, negentropy) to isolate heavy-tailed extreme-event features, achieving higher discrimination than singular value decomposition, which captures only second-order variance. A data-driven selection rule chooses ICA or SVD from the feature eigenspectrum concentration ratio, correctly prescribing the superior decomposition for all four evaluated architectures. Compared to split conformal prediction (the natural post-hoc baseline), NTK-UQ achieves 31--37\% sharper prediction intervals at 90\% coverage, and uniquely produces adaptive intervals that scale with extreme event severity, which conformal prediction cannot achieve by construction. The framework requires no retraining; inference-time uncertainty requires only a single matrix-vector product per sample.

Neural tangent kernels (NTKs) are a powerful tool for analyzing deep, non-linear neural networks. In the infinite-width limit, NTKs can easily be computed for most common architectures, yielding full analytic control over the training dynamics. However, at infinite width, important properties of training such as NTK evolution or feature learning are absent. Nevertheless, finite width effects can be included by computing corrections to the Gaussian statistics at infinite width. We introduce Feynman diagrams for computing finite-width corrections to NTK statistics. These dramatically simplify the necessary algebraic manipulations and enable the computation of layer-wise recursion relations for arbitrary statistics involving preactivations, NTKs and certain higher-derivative tensors (dNTK and ddNTK) required to predict the training dynamics at leading order. We demonstrate the feasibility of our framework by extending stability results for deep networks from preactivations to NTKs and proving the absence of finite-width corrections for scale-invariant nonlinearities such as ReLU on the diagonal of the Gram matrix of the NTK. We numerically implement the complete set of equations necessary to compute the first-order corrections for arbitrary inputs and demonstrate that the results follow the statistics of sampled neural networks for widths ngtrsim 20.

World Action Models (WAM) improve robot policies by augmenting sparse action supervision with dense future prediction. However, much of the predictable future is dominated by appearance and scene persistence rather than action-dependent dynamics. We observe that several recent WAM designs, including optical flow, motion-centric representations, and latent actions, can be understood from a common perspective in which world supervision becomes more efficient as it contains a higher proportion of action-relevant variation. Based on this insight, we introduce Action Tangent Fields, which reformulate world supervision through a local Taylor expansion of how actions induce changes in future dynamics. We represent future dynamics in Residual-VAE space, where the future latent remains recoverable from the current latent and its residual, and use a strong action-conditioned world model (ACWM) to probe the local correspondence between action variations and residual-world variations. This local first-order structure is distilled into the WAM to guide its denoising supervision toward dynamics that are more tightly coupled to action, rather than merely predictable from appearance. Across LIBERO-Plus, RoboTwin, and RoboTwin2.0-Plus, our method consistently improves robustness to lighting, background, camera, layout, and other environmental perturbations. Despite using no large-scale embodied pretraining, it achieves stronger robustness under several distribution shifts than pretrained policies. We further distill multi-step VideoDiT denoising into a single step for efficient inference. Our results suggest that effective WAM supervision should remain information-rich while concentrating its predictive capacity on the directions along which actions change the future.

Diffusion models have achieved remarkable success in text-to-image synthesis, largely attributed to the use of classifier-free guidance (CFG), which enables high-quality, condition-aligned image generation. CFG combines the conditional score (e.g., text-conditioned) with the unconditional score to control the output. However, the unconditional score is in charge of estimating the transition between manifolds of adjacent timesteps from x_t to x_{t-1}, which may inadvertently interfere with the trajectory toward the specific condition. In this work, we introduce a novel approach that leverages a geometric perspective on the unconditional score to enhance CFG performance when conditional scores are available. Specifically, we propose a method that filters the singular vectors of both conditional and unconditional scores using singular value decomposition. This filtering process aligns the unconditional score with the conditional score, thereby refining the sampling trajectory to stay closer to the manifold. Our approach improves image quality with negligible additional computation. We provide deeper insights into the score function behavior in diffusion models and present a practical technique for achieving more accurate and contextually coherent image synthesis.

Graph neural networks (GNNs) achieve remarkable performance in graph machine learning tasks but can be hard to train on large-graph data, where their learning dynamics are not well understood. We investigate the training dynamics of large-graph GNNs using graph neural tangent kernels (GNTKs) and graphons. In the limit of large width, optimization of an overparametrized NN is equivalent to kernel regression on the NTK. Here, we investigate how the GNTK evolves as another independent dimension is varied: the graph size. We use graphons to define limit objects -- graphon NNs for GNNs, and graphon NTKs for GNTKs -- , and prove that, on a sequence of graphs, the GNTKs converge to the graphon NTK. We further prove that the spectrum of the GNTK, which is related to the directions of fastest learning which becomes relevant during early stopping, converges to the spectrum of the graphon NTK. This implies that in the large-graph limit, the GNTK fitted on a graph of moderate size can be used to solve the same task on the large graph, and to infer the learning dynamics of the large-graph GNN. These results are verified empirically on node regression and classification tasks.

Empirical neural tangent kernels (eNTKs) can provide a good understanding of a given network's representation: they are often far less expensive to compute and applicable more broadly than infinite width NTKs. For networks with O output units (e.g. an O-class classifier), however, the eNTK on N inputs is of size NO times NO, taking O((NO)^2) memory and up to O((NO)^3) computation. Most existing applications have therefore used one of a handful of approximations yielding N times N kernel matrices, saving orders of magnitude of computation, but with limited to no justification. We prove that one such approximation, which we call "sum of logits", converges to the true eNTK at initialization for any network with a wide final "readout" layer. Our experiments demonstrate the quality of this approximation for various uses across a range of settings.

We propose a novel theoretical framework of analysis for Generative Adversarial Networks (GANs). We reveal a fundamental flaw of previous analyses which, by incorrectly modeling GANs' training scheme, are subject to ill-defined discriminator gradients. We overcome this issue which impedes a principled study of GAN training, solving it within our framework by taking into account the discriminator's architecture. To this end, we leverage the theory of infinite-width neural networks for the discriminator via its Neural Tangent Kernel. We characterize the trained discriminator for a wide range of losses and establish general differentiability properties of the network. From this, we derive new insights about the convergence of the generated distribution, advancing our understanding of GANs' training dynamics. We empirically corroborate these results via an analysis toolkit based on our framework, unveiling intuitions that are consistent with GAN practice.

A recent trend in explainable AI research has focused on surrogate modeling, where neural networks are approximated as simpler ML algorithms such as kernel machines. A second trend has been to utilize kernel functions in various explain-by-example or data attribution tasks. In this work, we combine these two trends to analyze approximate empirical neural tangent kernels (eNTK) for data attribution. Approximation is critical for eNTK analysis due to the high computational cost to compute the eNTK. We define new approximate eNTK and perform novel analysis on how well the resulting kernel machine surrogate models correlate with the underlying neural network. We introduce two new random projection variants of approximate eNTK which allow users to tune the time and memory complexity of their calculation. We conclude that kernel machines using approximate neural tangent kernel as the kernel function are effective surrogate models, with the introduced trace NTK the most consistent performer. Open source software allowing users to efficiently calculate kernel functions in the PyTorch framework is available (https://github.com/pnnl/projection\_ntk).

In Neural Architecture Search (NAS), reducing the cost of architecture evaluation remains one of the most crucial challenges. Among a plethora of efforts to bypass training of each candidate architecture to convergence for evaluation, the Neural Tangent Kernel (NTK) is emerging as a promising theoretical framework that can be utilized to estimate the performance of a neural architecture at initialization. In this work, we revisit several at-initialization metrics that can be derived from the NTK and reveal their key shortcomings. Then, through the empirical analysis of the time evolution of NTK, we deduce that modern neural architectures exhibit highly non-linear characteristics, making the NTK-based metrics incapable of reliably estimating the performance of an architecture without some amount of training. To take such non-linear characteristics into account, we introduce Label-Gradient Alignment (LGA), a novel NTK-based metric whose inherent formulation allows it to capture the large amount of non-linear advantage present in modern neural architectures. With minimal amount of training, LGA obtains a meaningful level of rank correlation with the post-training test accuracy of an architecture. Lastly, we demonstrate that LGA, complemented with few epochs of training, successfully guides existing search algorithms to achieve competitive search performances with significantly less search cost. The code is available at: https://github.com/nutellamok/DemystifyingNTK.

Task arithmetic has recently emerged as a cost-effective and scalable approach to edit pre-trained models directly in weight space: By adding the fine-tuned weights of different tasks, the model's performance can be improved on these tasks, while negating them leads to task forgetting. Yet, our understanding of the effectiveness of task arithmetic and its underlying principles remains limited. We present a comprehensive study of task arithmetic in vision-language models and show that weight disentanglement is the crucial factor that makes it effective. This property arises during pre-training and manifests when distinct directions in weight space govern separate, localized regions in function space associated with the tasks. Notably, we show that fine-tuning models in their tangent space by linearizing them amplifies weight disentanglement. This leads to substantial performance improvements across multiple task arithmetic benchmarks and diverse models. Building on these findings, we provide theoretical and empirical analyses of the neural tangent kernel (NTK) of these models and establish a compelling link between task arithmetic and the spatial localization of the NTK eigenfunctions. Overall, our work uncovers novel insights into the fundamental mechanisms of task arithmetic and offers a more reliable and effective approach to edit pre-trained models through the NTK linearization.

With diffusion and flow matching models achieving state-of-the-art generating performance, the interest of the community now turned to reducing the inference time without sacrificing sample quality. Consistency Models (CMs), which are trained to be consistent on diffusion or probability flow ordinary differential equation (PF-ODE) trajectories, enable one or two-step flow or diffusion sampling. However, CMs typically require prolonged training with large batch sizes to obtain competitive sample quality. In this paper, we examine the training dynamics of CMs near convergence and discover that CM tangents -- CM output update directions -- are quite oscillatory, in the sense that they move parallel to the data manifold, not towards the manifold. To mitigate oscillatory tangents, we propose a new loss function, called the manifold feature distance (MFD), which provides manifold-aligned tangents that point toward the data manifold. Consequently, our method -- dubbed Align Your Tangent (AYT) -- can accelerate CM training by orders of magnitude and even out-perform the learned perceptual image patch similarity metric (LPIPS). Furthermore, we find that our loss enables training with extremely small batch sizes without compromising sample quality. Code: https://github.com/1202kbs/AYT

The neural tangent kernel is a kernel function defined over the parameter distribution of an infinite width neural network. Despite the impracticality of this limit, the neural tangent kernel has allowed for a more direct study of neural networks and a gaze through the veil of their black box. More recently, it has been shown theoretically that the Laplace kernel and neural tangent kernel share the same reproducing kernel Hilbert space in the space of S^{d-1} alluding to their equivalence. In this work, we analyze the practical equivalence of the two kernels. We first do so by matching the kernels exactly and then by matching posteriors of a Gaussian process. Moreover, we analyze the kernels in R^d and experiment with them in the task of regression.

Pre-Layer Normalization (Pre-LN) is the de facto choice for large language models (LLMs) and is crucial for stable pretraining and effective transfer learning. However, Pre-LN is inefficient due to repeated statistical calculations and suffers from the curse of depth. As layers grow, the magnitude and variance of the hidden state escalate, destabilizing training. Efficiency-oriented normalization-free methods such as Dynamic Tanh (DyT) improve speed but remain fragile at depth. To jointly address stability and efficiency, we propose Bounded Hyperbolic Tanh (BHyT), a drop-in replacement for Pre-LN. BHyT couples a tanh nonlinearity with explicit, data-driven input bounding to keep activations within a non-saturating range. It prevents depth-wise growth in activation magnitude and variance and comes with a theoretical stability guarantee. For efficiency, BHyT computes exact statistics once per block and replaces a second normalization with a lightweight variance approximation, enhancing efficiency. Empirically, BHyT demonstrates improved stability and efficiency during pretraining, achieving an average of 15.8% faster training and an average of 4.2% higher token generation throughput compared to RMSNorm., while matching or surpassing its inference performance and robustness across language understanding and reasoning benchmarks. Our code is available at: https://anonymous.4open.science/r/BHyT

State-of-the-art neural network training methods depend on the gradient of the network function. Therefore, they cannot be applied to networks whose activation functions do not have useful derivatives, such as binary and discrete-time spiking neural networks. To overcome this problem, the activation function's derivative is commonly substituted with a surrogate derivative, giving rise to surrogate gradient learning (SGL). This method works well in practice but lacks theoretical foundation. The neural tangent kernel (NTK) has proven successful in the analysis of gradient descent. Here, we provide a generalization of the NTK, which we call the surrogate gradient NTK, that enables the analysis of SGL. First, we study a naive extension of the NTK to activation functions with jumps, demonstrating that gradient descent for such activation functions is also ill-posed in the infinite-width limit. To address this problem, we generalize the NTK to gradient descent with surrogate derivatives, i.e., SGL. We carefully define this generalization and expand the existing key theorems on the NTK with mathematical rigor. Further, we illustrate our findings with numerical experiments. Finally, we numerically compare SGL in networks with sign activation function and finite width to kernel regression with the surrogate gradient NTK; the results confirm that the surrogate gradient NTK provides a good characterization of SGL.

In this paper, we establish a Lojasiewicz inequality for the pointed W-entropy in the Ricci flow, under the assumption that the geometry near the base point is close to a standard cylinder R^k times S^{n-k} or the quotient thereof. As an application, we prove the strong uniqueness of the cylindrical tangent flow at the first singular time of the Ricci flow. Specifically, we show that the modified Ricci flow near the singularity converges to the cylindrical model under a fixed gauge.

A quantum neural network (QNN) is a parameterized mapping efficiently implementable on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. It can be used for supervised learning when combined with classical gradient-based optimizers. Despite the existing empirical and theoretical investigations, the convergence of QNN training is not fully understood. Inspired by the success of the neural tangent kernels (NTKs) in probing into the dynamics of classical neural networks, a recent line of works proposes to study over-parameterized QNNs by examining a quantum version of tangent kernels. In this work, we study the dynamics of QNNs and show that contrary to popular belief it is qualitatively different from that of any kernel regression: due to the unitarity of quantum operations, there is a non-negligible deviation from the tangent kernel regression derived at the random initialization. As a result of the deviation, we prove the at-most sublinear convergence for QNNs with Pauli measurements, which is beyond the explanatory power of any kernel regression dynamics. We then present the actual dynamics of QNNs in the limit of over-parameterization. The new dynamics capture the change of convergence rate during training and implies that the range of measurements is crucial to the fast QNN convergence.

Selecting hyperparameters in deep learning greatly impacts its effectiveness but requires manual effort and expertise. Recent works show that Bayesian model selection with Laplace approximations can allow to optimize such hyperparameters just like standard neural network parameters using gradients and on the training data. However, estimating a single hyperparameter gradient requires a pass through the entire dataset, limiting the scalability of such algorithms. In this work, we overcome this issue by introducing lower bounds to the linearized Laplace approximation of the marginal likelihood. In contrast to previous estimators, these bounds are amenable to stochastic-gradient-based optimization and allow to trade off estimation accuracy against computational complexity. We derive them using the function-space form of the linearized Laplace, which can be estimated using the neural tangent kernel. Experimentally, we show that the estimators can significantly accelerate gradient-based hyperparameter optimization.

We present a method for 3D reconstruction only using calibrated multi-view surface azimuth maps. Our method, multi-view azimuth stereo, is effective for textureless or specular surfaces, which are difficult for conventional multi-view stereo methods. We introduce the concept of tangent space consistency: Multi-view azimuth observations of a surface point should be lifted to the same tangent space. Leveraging this consistency, we recover the shape by optimizing a neural implicit surface representation. Our method harnesses the robust azimuth estimation capabilities of photometric stereo methods or polarization imaging while bypassing potentially complex zenith angle estimation. Experiments using azimuth maps from various sources validate the accurate shape recovery with our method, even without zenith angles.

Modern deep learning requires large volumes of data, which could contain sensitive or private information that cannot be leaked. Recent work has shown for homogeneous neural networks a large portion of this training data could be reconstructed with only access to the trained network parameters. While the attack was shown to work empirically, there exists little formal understanding of its effective regime which datapoints are susceptible to reconstruction. In this work, we first build a stronger version of the dataset reconstruction attack and show how it can provably recover the entire training set in the infinite width regime. We then empirically study the characteristics of this attack on two-layer networks and reveal that its success heavily depends on deviations from the frozen infinite-width Neural Tangent Kernel limit. Next, we study the nature of easily-reconstructed images. We show that both theoretically and empirically, reconstructed images tend to "outliers" in the dataset, and that these reconstruction attacks can be used for dataset distillation, that is, we can retrain on reconstructed images and obtain high predictive accuracy.

We introduce torchNTK, a python library to calculate the empirical neural tangent kernel (NTK) of neural network models in the PyTorch framework. We provide an efficient method to calculate the NTK of multilayer perceptrons. We compare the explicit differentiation implementation against autodifferentiation implementations, which have the benefit of extending the utility of the library to any architecture supported by PyTorch, such as convolutional networks. A feature of the library is that we expose the user to layerwise NTK components, and show that in some regimes a layerwise calculation is more memory efficient. We conduct preliminary experiments to demonstrate use cases for the software and probe the NTK.

State-of-the-art federated learning methods can perform far worse than their centralized counterparts when clients have dissimilar data distributions. For neural networks, even when centralized SGD easily finds a solution that is simultaneously performant for all clients, current federated optimization methods fail to converge to a comparable solution. We show that this performance disparity can largely be attributed to optimization challenges presented by nonconvexity. Specifically, we find that the early layers of the network do learn useful features, but the final layers fail to make use of them. That is, federated optimization applied to this non-convex problem distorts the learning of the final layers. Leveraging this observation, we propose a Train-Convexify-Train (TCT) procedure to sidestep this issue: first, learn features using off-the-shelf methods (e.g., FedAvg); then, optimize a convexified problem obtained from the network's empirical neural tangent kernel approximation. Our technique yields accuracy improvements of up to +36% on FMNIST and +37% on CIFAR10 when clients have dissimilar data.

A natural strategy for continual learning is to weigh a Bayesian ensemble of fixed functions. This suggests that if a (single) neural network could be interpreted as an ensemble, one could design effective algorithms that learn without forgetting. To realize this possibility, we observe that a neural network classifier with N parameters can be interpreted as a weighted ensemble of N classifiers, and that in the lazy regime limit these classifiers are fixed throughout learning. We call these classifiers the neural tangent experts and show they output valid probability distributions over the labels. We then derive the likelihood and posterior probability of each expert given past data. Surprisingly, the posterior updates for these experts are equivalent to a scaled and projected form of stochastic gradient descent (SGD) over the network weights. Away from the lazy regime, networks can be seen as ensembles of adaptive experts which improve over time. These results offer a new interpretation of neural networks as Bayesian ensembles of experts, providing a principled framework for understanding and mitigating catastrophic forgetting in continual learning settings.

Over the last decades, progress in modal analysis has enabled increasingly routine use of modal parameters, including those extracted from in-situ measurements, for applications such as structural health monitoring and finite element model updating. For output-only identification, or Operational Modal Analysis (OMA), widely adopted approaches include Stochastic Subspace Identification (SSI) methods and the Natural Excitation Technique combined with the Eigensystem Realization Algorithm (NExT-ERA). Nevertheless, SSI-based techniques may become cumbersome on large systems, while NExT-ERA fitting can struggle when measurements are contaminated by noise. To alleviate these, this work investigates an OMA frequency-domain formulation for aeronautical structures by coupling the Loewner Framework (LF) with NExT, yielding the proposed NExT-LF method. The method exploits the computational efficiency of LF together with the impulse response function retrieval enabled by NExT. NExT-LF is assessed on two experimental benchmarks: the eXperimental BeaRDS 2 high-aspect-ratio wing main spar and an Airbus Helicopters H135 bearingless main rotor blade. The identified modal parameters are compared against available experimental references and results obtained via SSI with Canonical Variate Analysis and NExT-ERA. The results show that the modes identified by NExT-LF correlate well with benchmark data, particularly for high-amplitude tests and in the low-frequency range.

A biological neural network in the cortex forms a neural field. Neurons in the field have their own receptive fields, and connection weights between two neurons are random but highly correlated when they are in close proximity in receptive fields. In this paper, we investigate such neural fields in a multilayer architecture to investigate the supervised learning of the fields. We empirically compare the performances of our field model with those of randomly connected deep networks. The behavior of a randomly connected network is investigated on the basis of the key idea of the neural tangent kernel regime, a recent development in the machine learning theory of over-parameterized networks; for most randomly connected neural networks, it is shown that global minima always exist in their small neighborhoods. We numerically show that this claim also holds for our neural fields. In more detail, our model has two structures: i) each neuron in a field has a continuously distributed receptive field, and ii) the initial connection weights are random but not independent, having correlations when the positions of neurons are close in each layer. We show that such a multilayer neural field is more robust than conventional models when input patterns are deformed by noise disturbances. Moreover, its generalization ability can be slightly superior to that of conventional models.

Machine learning models are vulnerable to adversarial perturbations, and a thought-provoking paper by Bubeck and Sellke has analyzed this phenomenon through the lens of over-parameterization: interpolating smoothly the data requires significantly more parameters than simply memorizing it. However, this "universal" law provides only a necessary condition for robustness, and it is unable to discriminate between models. In this paper, we address these gaps by focusing on empirical risk minimization in two prototypical settings, namely, random features and the neural tangent kernel (NTK). We prove that, for random features, the model is not robust for any degree of over-parameterization, even when the necessary condition coming from the universal law of robustness is satisfied. In contrast, for even activations, the NTK model meets the universal lower bound, and it is robust as soon as the necessary condition on over-parameterization is fulfilled. This also addresses a conjecture in prior work by Bubeck, Li and Nagaraj. Our analysis decouples the effect of the kernel of the model from an "interaction matrix", which describes the interaction with the test data and captures the effect of the activation. Our theoretical results are corroborated by numerical evidence on both synthetic and standard datasets (MNIST, CIFAR-10).

Several recent trends in machine learning theory and practice, from the design of state-of-the-art Gaussian Process to the convergence analysis of deep neural nets (DNNs) under stochastic gradient descent (SGD), have found it fruitful to study wide random neural networks. Central to these approaches are certain scaling limits of such networks. We unify these results by introducing a notion of a straightline tensor program that can express most neural network computations, and we characterize its scaling limit when its tensors are large and randomized. From our framework follows (1) the convergence of random neural networks to Gaussian processes for architectures such as recurrent neural networks, convolutional neural networks, residual networks, attention, and any combination thereof, with or without batch normalization; (2) conditions under which the gradient independence assumption -- that weights in backpropagation can be assumed to be independent from weights in the forward pass -- leads to correct computation of gradient dynamics, and corrections when it does not; (3) the convergence of the Neural Tangent Kernel, a recently proposed kernel used to predict training dynamics of neural networks under gradient descent, at initialization for all architectures in (1) without batch normalization. Mathematically, our framework is general enough to rederive classical random matrix results such as the semicircle and the Marchenko-Pastur laws, as well as recent results in neural network Jacobian singular values. We hope our work opens a way toward design of even stronger Gaussian Processes, initialization schemes to avoid gradient explosion/vanishing, and deeper understanding of SGD dynamics in modern architectures.