Ankit Patel

Felix Abecassis, Anjulie Agrusa, Dong Ahn et al. · nvidia

Large Language Models (LLMs) today are powerful problem solvers across many domains, and they continue to get stronger as they scale in model size, training set size, and training set quality, as shown by extensive research and experimentation across the industry. Training a frontier model today requires on the order of tens to hundreds of yottaflops, which is a massive investment of time, compute, and energy. Improving pretraining efficiency is therefore essential to enable the next generation of even more capable LLMs. While 8-bit floating point (FP8) training is now widely adopted, transitioning to even narrower precision, such as 4-bit floating point (FP4), could unlock additional improvements in computational speed and resource utilization. However, quantization at this level poses challenges to training stability, convergence, and implementation, notably for large-scale models trained on long token horizons. In this study, we introduce a novel approach for stable and accurate training of large language models (LLMs) using the NVFP4 format. Our method integrates Random Hadamard transforms (RHT) to bound block-level outliers, employs a two-dimensional quantization scheme for consistent representations across both the forward and backward passes, utilizes stochastic rounding for unbiased gradient estimation, and incorporates selective high-precision layers. We validate our approach by training a 12-billion-parameter model on 10 trillion tokens -- the longest publicly documented training run in 4-bit precision to date. Our results show that the model trained with our NVFP4-based pretraining technique achieves training loss and downstream task accuracies comparable to an FP8 baseline. These findings highlight that NVFP4, when combined with our training approach, represents a major step forward in narrow-precision LLM training algorithms.

R. James Cotton, Emoonah McClerklin, Anthony Cimorelli et al.

Human pose estimation from monocular video is a rapidly advancing field that offers great promise to human movement science and rehabilitation. This potential is tempered by the smaller body of work ensuring the outputs are clinically meaningful and properly calibrated. Gait analysis, typically performed in a dedicated lab, produces precise measurements including kinematics and step timing. Using over 7000 monocular video from an instrumented gait analysis lab, we trained a neural network to map 3D joint trajectories and the height of individuals onto interpretable biomechanical outputs including gait cycle timing and sagittal plane joint kinematics and spatiotemporal trajectories. This task specific layer produces accurate estimates of the timing of foot contact and foot off events. After parsing the kinematic outputs into individual gait cycles, it also enables accurate cycle-by-cycle estimates of cadence, step time, double and single support time, walking speed and step length.

Justin Sahs, Ryan Pyle, Fabio Anselmi et al.

Despite classical statistical theory predicting severe overfitting, modern massively overparameterized neural networks still generalize well. This unexpected property is attributed to the network's so-called implicit bias, which describes its propensity to converge to solutions that generalize effectively, among the many possible that correctly label the training data. The aim of our research is to explore this bias from a new perspective, focusing on how non-linear activation functions contribute to shaping it. First, we introduce a reparameterization which removes a continuous weight rescaling symmetry. Second, in the kernel regime, we leverage this reparameterization to generalize recent findings that relate shallow Neural Networks to the Radon transform, deriving an explicit formula for the implicit bias induced by a broad class of activation functions. Specifically, by utilizing the connection between the Radon transform and the Fourier transform, we interpret the kernel regime's inductive bias as minimizing a spectral seminorm that penalizes high-frequency components, in a manner dependent on the activation function. Finally, in the adaptive regime, we demonstrate the existence of local dynamical attractors that facilitate the formation of clusters of hyperplanes where the input to a neuron's activation function is zero, yielding alignment between many neurons' response functions. We confirm these theoretical results with simulations. All together, our work provides a deeper understanding of the mechanisms underlying the generalization capabilities of overparameterized neural networks and its relation with the implicit bias, offering potential pathways for designing more efficient and robust models.

Justin Sahs, Ryan Pyle, Aneel Damaraju et al.

Understanding the learning dynamics and inductive bias of neural networks (NNs) is hindered by the opacity of the relationship between NN parameters and the function represented. We propose reparametrizing ReLU NNs as continuous piecewise linear splines. Using this spline lens, we study learning dynamics in shallow univariate ReLU NNs, finding unexpected insights and explanations for several perplexing phenomena. We develop a surprisingly simple and transparent view of the structure of the loss surface, including its critical and fixed points, Hessian, and Hessian spectrum. We also show that standard weight initializations yield very flat functions, and that this flatness, together with overparametrization and the initial weight scale, is responsible for the strength and type of implicit regularization, consistent with recent work arXiv:1906.05827. Our implicit regularization results are complementary to recent work arXiv:1906.07842, done independently, which showed that initialization scale critically controls implicit regularization via a kernel-based argument. Our spline-based approach reproduces their key implicit regularization results but in a far more intuitive and transparent manner. Going forward, our spline-based approach is likely to extend naturally to the multivariate and deep settings, and will play a foundational role in efforts to understand neural networks. Videos of learning dynamics using a spline-based visualization are available at http://shorturl.at/tFWZ2.

Josue Ortega Caro, Yilong Ju, Ryan Pyle et al.

Adversarial Attacks are still a significant challenge for neural networks. Recent work has shown that adversarial perturbations typically contain high-frequency features, but the root cause of this phenomenon remains unknown. Inspired by theoretical work on linear full-width convolutional models, we hypothesize that the local (i.e. bounded-width) convolutional operations commonly used in current neural networks are implicitly biased to learn high frequency features, and that this is one of the root causes of high frequency adversarial examples. To test this hypothesis, we analyzed the impact of different choices of linear and nonlinear architectures on the implicit bias of the learned features and the adversarial perturbations, in both spatial and frequency domains. We find that the high-frequency adversarial perturbations are critically dependent on the convolution operation because the spatially-limited nature of local convolutions induces an implicit bias towards high frequency features. The explanation for the latter involves the Fourier Uncertainty Principle: a spatially-limited (local in the space domain) filter cannot also be frequency-limited (local in the frequency domain). Furthermore, using larger convolution kernel sizes or avoiding convolutions (e.g. by using Vision Transformers architecture) significantly reduces this high frequency bias, but not the overall susceptibility to attacks. Looking forward, our work strongly suggests that understanding and controlling the implicit bias of architectures will be essential for achieving adversarial robustness.

Tan Nguyen, Nhat Ho, Ankit Patel et al.

Inspired by the success of Convolutional Neural Networks (CNNs) for supervised prediction in images, we design the Deconvolutional Generative Model (DGM), a new probabilistic generative model whose inference calculations correspond to those in a given CNN architecture. The DGM uses a CNN to design the prior distribution in the probabilistic model. Furthermore, the DGM generates images from coarse to finer scales. It introduces a small set of latent variables at each scale, and enforces dependencies among all the latent variables via a conjugate prior distribution. This conjugate prior yields a new regularizer based on paths rendered in the generative model for training CNNs-the Rendering Path Normalization (RPN). We demonstrate that this regularizer improves generalization, both in theory and in practice. In addition, likelihood estimation in the DGM yields training losses for CNNs, and inspired by this, we design a new loss termed as the Max-Min cross entropy which outperforms the traditional cross-entropy loss for object classification. The Max-Min cross entropy suggests a new deep network architecture, namely the Max-Min network, which can learn from less labeled data while maintaining good prediction performance. Our experiments demonstrate that the DGM with the RPN and the Max-Min architecture exceeds or matches the-state-of-art on benchmarks including SVHN, CIFAR10, and CIFAR100 for semi-supervised and supervised learning tasks.

Weili Nie, Ankit Patel

Generative adversarial networks (GANs) are notoriously difficult to train and the reasons underlying their (non-)convergence behaviors are still not completely understood. By first considering a simple yet representative GAN example, we mathematically analyze its local convergence behavior in a non-asymptotic way. Furthermore, the analysis is extended to general GANs under certain assumptions. We find that in order to ensure a good convergence rate, two factors of the Jacobian in the GAN training dynamics should be simultaneously avoided, which are (i) the Phase Factor, i.e., the Jacobian has complex eigenvalues with a large imaginary-to-real ratio, and (ii) the Conditioning Factor, i.e., the Jacobian is ill-conditioned. Previous methods of regularizing the Jacobian can only alleviate one of these two factors, while making the other more severe. Thus we propose a new JAcobian REgularization (JARE) for GANs, which simultaneously addresses both factors by construction. Finally, we conduct experiments that confirm our theoretical analysis and demonstrate the advantages of JARE over previous methods in stabilizing GANs.

Weili Nie, Yang Zhang, Ankit Patel

Backpropagation-based visualizations have been proposed to interpret convolutional neural networks (CNNs), however a theory is missing to justify their behaviors: Guided backpropagation (GBP) and deconvolutional network (DeconvNet) generate more human-interpretable but less class-sensitive visualizations than saliency map. Motivated by this, we develop a theoretical explanation revealing that GBP and DeconvNet are essentially doing (partial) image recovery which is unrelated to the network decisions. Specifically, our analysis shows that the backward ReLU introduced by GBP and DeconvNet, and the local connections in CNNs are the two main causes of compelling visualizations. Extensive experiments are provided that support the theoretical analysis.

Wanjia Liu, Huaijin Chen, Rishab Goel et al.

Good temporal representations are crucial for video understanding, and the state-of-the-art video recognition framework is based on two-stream networks. In such framework, besides the regular ConvNets responsible for RGB frame inputs, a second network is introduced to handle the temporal representation, usually the optical flow (OF). However, OF or other task-oriented flow is computationally costly, and is thus typically pre-computed. Critically, this prevents the two-stream approach from being applied to reinforcement learning (RL) applications such as video game playing, where the next state depends on current state and action choices. Inspired by the early vision systems of mammals and insects, we propose a fast event-driven representation (EDR) that models several major properties of early retinal circuits: (1) logarithmic input response, (2) multi-timescale temporal smoothing to filter noise, and (3) bipolar (ON/OFF) pathways for primitive event detection[12]. Trading off the directional information for fast speed (> 9000 fps), EDR en-ables fast real-time inference/learning in video applications that require interaction between an agent and the world such as game-playing, virtual robotics, and domain adaptation. In this vein, we use EDR to demonstrate performance improvements over state-of-the-art reinforcement learning algorithms for Atari games, something that has not been possible with pre-computed OF. Moreover, with UCF-101 video action recognition experiments, we show that EDR performs near state-of-the-art in accuracy while achieving a 1,500x speedup in input representation processing, as compared to optical flow.

Romain Cosentino, Randall Balestriero, Richard Baraniuk et al.

In this work, we derive a generic overcomplete frame thresholding scheme based on risk minimization. Overcomplete frames being favored for analysis tasks such as classification, regression or anomaly detection, we provide a way to leverage those optimal representations in real-world applications through the use of thresholding. We validate the method on a large scale bird activity detection task via the scattering network architecture performed by means of continuous wavelets, known for being an adequate dictionary in audio environments.

Gavin Taylor, Ryan Burmeister, Zheng Xu et al.

With the growing importance of large network models and enormous training datasets, GPUs have become increasingly necessary to train neural networks. This is largely because conventional optimization algorithms rely on stochastic gradient methods that don't scale well to large numbers of cores in a cluster setting. Furthermore, the convergence of all gradient methods, including batch methods, suffers from common problems like saturation effects, poor conditioning, and saddle points. This paper explores an unconventional training method that uses alternating direction methods and Bregman iteration to train networks without gradient descent steps. The proposed method reduces the network training problem to a sequence of minimization sub-steps that can each be solved globally in closed form. The proposed method is advantageous because it avoids many of the caveats that make gradient methods slow on highly non-convex problems. The method exhibits strong scaling in the distributed setting, yielding linear speedups even when split over thousands of cores.