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Researcher profile

Morteza Mardani

Morteza Mardani contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningComputer Visionmath.OCArtificial Intelligenceeess.IVphysics.ao-phComputation and LanguagePerformance

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Published work

10 published item(s)

preprint2026arXiv

Continuous Diffusion Scales Competitively with Discrete Diffusion for Language

While diffusion has drawn considerable recent attention from the language modeling community, continuous diffusion has appeared less scalable than discrete approaches. To challenge this belief we revisit Plaid, a likelihood-based continuous diffusion language model (DLM), and construct RePlaid by aligning the architecture of Plaid with modern discrete DLMs. In this unified setting, we establish the first scaling law for continuous DLMs that rivals discrete DLMs: RePlaid exhibits a compute gap of only $20\times$ compared to autoregressive models, outperforms Duo while using fewer parameters, and outperforms MDLM in the over-trained regime. We benchmark RePlaid against recent continuous DLMs: on OpenWebText, RePlaid achieves a new state-of-the-art PPL bound of $22.1$ among continuous DLMs and superior generation quality. These results suggest that continuous diffusion, when trained via likelihood, is a highly competitive and scalable alternative to discrete DLMs. Moreover, we offer theoretical insights to understand the advantage of likelihood-based training. We show that optimizing the noise schedule to minimize the ELBO's variance naturally yields linear cross-entropy (information loss) over time. This evenly distributes denoising difficulty without any case-specific time reparameterization. In addition, we find that optimizing embeddings via likelihood creates structured geometries and drives the most significant likelihood gain.

0 citations0 reviewsNo code linkedOpen access
preprint2024arXiv

AGG: Amortized Generative 3D Gaussians for Single Image to 3D

Given the growing need for automatic 3D content creation pipelines, various 3D representations have been studied to generate 3D objects from a single image. Due to its superior rendering efficiency, 3D Gaussian splatting-based models have recently excelled in both 3D reconstruction and generation. 3D Gaussian splatting approaches for image to 3D generation are often optimization-based, requiring many computationally expensive score-distillation steps. To overcome these challenges, we introduce an Amortized Generative 3D Gaussian framework (AGG) that instantly produces 3D Gaussians from a single image, eliminating the need for per-instance optimization. Utilizing an intermediate hybrid representation, AGG decomposes the generation of 3D Gaussian locations and other appearance attributes for joint optimization. Moreover, we propose a cascaded pipeline that first generates a coarse representation of the 3D data and later upsamples it with a 3D Gaussian super-resolution module. Our method is evaluated against existing optimization-based 3D Gaussian frameworks and sampling-based pipelines utilizing other 3D representations, where AGG showcases competitive generation abilities both qualitatively and quantitatively while being several orders of magnitude faster. Project page: https://ir1d.github.io/AGG/

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers

Vision transformers have delivered tremendous success in representation learning. This is primarily due to effective token mixing through self attention. However, this scales quadratically with the number of pixels, which becomes infeasible for high-resolution inputs. To cope with this challenge, we propose Adaptive Fourier Neural Operator (AFNO) as an efficient token mixer that learns to mix in the Fourier domain. AFNO is based on a principled foundation of operator learning which allows us to frame token mixing as a continuous global convolution without any dependence on the input resolution. This principle was previously used to design FNO, which solves global convolution efficiently in the Fourier domain and has shown promise in learning challenging PDEs. To handle challenges in visual representation learning such as discontinuities in images and high resolution inputs, we propose principled architectural modifications to FNO which results in memory and computational efficiency. This includes imposing a block-diagonal structure on the channel mixing weights, adaptively sharing weights across tokens, and sparsifying the frequency modes via soft-thresholding and shrinkage. The resulting model is highly parallel with a quasi-linear complexity and has linear memory in the sequence size. AFNO outperforms self-attention mechanisms for few-shot segmentation in terms of both efficiency and accuracy. For Cityscapes segmentation with the Segformer-B3 backbone, AFNO can handle a sequence size of 65k and outperforms other efficient self-attention mechanisms.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Demystifying Batch Normalization in ReLU Networks: Equivalent Convex Optimization Models and Implicit Regularization

Batch Normalization (BN) is a commonly used technique to accelerate and stabilize training of deep neural networks. Despite its empirical success, a full theoretical understanding of BN is yet to be developed. In this work, we analyze BN through the lens of convex optimization. We introduce an analytic framework based on convex duality to obtain exact convex representations of weight-decay regularized ReLU networks with BN, which can be trained in polynomial-time. Our analyses also show that optimal layer weights can be obtained as simple closed-form formulas in the high-dimensional and/or overparameterized regimes. Furthermore, we find that Gradient Descent provides an algorithmic bias effect on the standard non-convex BN network, and we design an approach to explicitly encode this implicit regularization into the convex objective. Experiments with CIFAR image classification highlight the effectiveness of this explicit regularization for mimicking and substantially improving the performance of standard BN networks.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators

FourCastNet, short for Fourier Forecasting Neural Network, is a global data-driven weather forecasting model that provides accurate short to medium-range global predictions at $0.25^{\circ}$ resolution. FourCastNet accurately forecasts high-resolution, fast-timescale variables such as the surface wind speed, precipitation, and atmospheric water vapor. It has important implications for planning wind energy resources, predicting extreme weather events such as tropical cyclones, extra-tropical cyclones, and atmospheric rivers. FourCastNet matches the forecasting accuracy of the ECMWF Integrated Forecasting System (IFS), a state-of-the-art Numerical Weather Prediction (NWP) model, at short lead times for large-scale variables, while outperforming IFS for variables with complex fine-scale structure, including precipitation. FourCastNet generates a week-long forecast in less than 2 seconds, orders of magnitude faster than IFS. The speed of FourCastNet enables the creation of rapid and inexpensive large-ensemble forecasts with thousands of ensemble-members for improving probabilistic forecasting. We discuss how data-driven deep learning models such as FourCastNet are a valuable addition to the meteorology toolkit to aid and augment NWP models.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operators

Extreme weather amplified by climate change is causing increasingly devastating impacts across the globe. The current use of physics-based numerical weather prediction (NWP) limits accuracy due to high computational cost and strict time-to-solution limits. We report that a data-driven deep learning Earth system emulator, FourCastNet, can predict global weather and generate medium-range forecasts five orders-of-magnitude faster than NWP while approaching state-of-the-art accuracy. FourCast-Net is optimized and scales efficiently on three supercomputing systems: Selene, Perlmutter, and JUWELS Booster up to 3,808 NVIDIA A100 GPUs, attaining 140.8 petaFLOPS in mixed precision (11.9%of peak at that scale). The time-to-solution for training FourCastNet measured on JUWELS Booster on 3,072GPUs is 67.4minutes, resulting in an 80,000times faster time-to-solution relative to state-of-the-art NWP, in inference. FourCastNet produces accurate instantaneous weather predictions for a week in advance, enables enormous ensembles that better capture weather extremes, and supports higher global forecast resolutions.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

GLEAM: Greedy Learning for Large-Scale Accelerated MRI Reconstruction

Unrolled neural networks have recently achieved state-of-the-art accelerated MRI reconstruction. These networks unroll iterative optimization algorithms by alternating between physics-based consistency and neural-network based regularization. However, they require several iterations of a large neural network to handle high-dimensional imaging tasks such as 3D MRI. This limits traditional training algorithms based on backpropagation due to prohibitively large memory and compute requirements for calculating gradients and storing intermediate activations. To address this challenge, we propose Greedy LEarning for Accelerated MRI (GLEAM) reconstruction, an efficient training strategy for high-dimensional imaging settings. GLEAM splits the end-to-end network into decoupled network modules. Each module is optimized in a greedy manner with decoupled gradient updates, reducing the memory footprint during training. We show that the decoupled gradient updates can be performed in parallel on multiple graphical processing units (GPUs) to further reduce training time. We present experiments with 2D and 3D datasets including multi-coil knee, brain, and dynamic cardiac cine MRI. We observe that: i) GLEAM generalizes as well as state-of-the-art memory-efficient baselines such as gradient checkpointing and invertible networks with the same memory footprint, but with 1.3x faster training; ii) for the same memory footprint, GLEAM yields 1.1dB PSNR gain in 2D and 1.8 dB in 3D over end-to-end baselines.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Hidden Convexity of Wasserstein GANs: Interpretable Generative Models with Closed-Form Solutions

Generative Adversarial Networks (GANs) are commonly used for modeling complex distributions of data. Both the generators and discriminators of GANs are often modeled by neural networks, posing a non-transparent optimization problem which is non-convex and non-concave over the generator and discriminator, respectively. Such networks are often heuristically optimized with gradient descent-ascent (GDA), but it is unclear whether the optimization problem contains any saddle points, or whether heuristic methods can find them in practice. In this work, we analyze the training of Wasserstein GANs with two-layer neural network discriminators through the lens of convex duality, and for a variety of generators expose the conditions under which Wasserstein GANs can be solved exactly with convex optimization approaches, or can be represented as convex-concave games. Using this convex duality interpretation, we further demonstrate the impact of different activation functions of the discriminator. Our observations are verified with numerical results demonstrating the power of the convex interpretation, with applications in progressive training of convex architectures corresponding to linear generators and quadratic-activation discriminators for CelebA image generation. The code for our experiments is available at https://github.com/ardasahiner/ProCoGAN.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Unraveling Attention via Convex Duality: Analysis and Interpretations of Vision Transformers

Vision transformers using self-attention or its proposed alternatives have demonstrated promising results in many image related tasks. However, the underpinning inductive bias of attention is not well understood. To address this issue, this paper analyzes attention through the lens of convex duality. For the non-linear dot-product self-attention, and alternative mechanisms such as MLP-mixer and Fourier Neural Operator (FNO), we derive equivalent finite-dimensional convex problems that are interpretable and solvable to global optimality. The convex programs lead to {\it block nuclear-norm regularization} that promotes low rank in the latent feature and token dimensions. In particular, we show how self-attention networks implicitly clusters the tokens, based on their latent similarity. We conduct experiments for transferring a pre-trained transformer backbone for CIFAR-100 classification by fine-tuning a variety of convex attention heads. The results indicate the merits of the bias induced by attention compared with the existing MLP or linear heads.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Uncertainty Quantification in Deep MRI Reconstruction

Reliable MRI is crucial for accurate interpretation in therapeutic and diagnostic tasks. However, undersampling during MRI acquisition as well as the overparameterized and non-transparent nature of deep learning (DL) leaves substantial uncertainty about the accuracy of DL reconstruction. With this in mind, this study aims to quantify the uncertainty in image recovery with DL models. To this end, we first leverage variational autoencoders (VAEs) to develop a probabilistic reconstruction scheme that maps out (low-quality) short scans with aliasing artifacts to the diagnostic-quality ones. The VAE encodes the acquisition uncertainty in a latent code and naturally offers a posterior of the image from which one can generate pixel variance maps using Monte-Carlo sampling. Accurately predicting risk requires knowledge of the bias as well, for which we leverage Stein's Unbiased Risk Estimator (SURE) as a proxy for mean-squared-error (MSE). Extensive empirical experiments are performed for Knee MRI reconstruction under different training losses (adversarial and pixel-wise) and unrolled recurrent network architectures. Our key observations indicate that: 1) adversarial losses introduce more uncertainty; and 2) recurrent unrolled nets reduce the prediction uncertainty and risk.

0 citations0 reviewsNo code linkedOpen access