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  1. Current Deep Network (DN) visualization and inter-pretability methods rely heavily on data space visualizations such as scoring which dimensions of the data are responsible for their associated prediction or generating new data features or samples that best match a given DN unit or representation. In this paper, we go one step further by developing the first provably exact method for computing the geometry of a DN's mapping - including its decision boundary - over a specified region of the data space. By lever-aging the theory of Continuous Piece- Wise Linear (CPWL) spline DNs, SplineCam exactly computes a DN's geometry without resorting to approximations such as sampling or architecture simplification. SplineCam applies to any DN architecture based on CPWL activation nonlinearities, including (leaky) ReLU, absolute value, maxout, and max-pooling and can also be applied to regression DNs such as implicit neural representations. Beyond decision boundary visualization and characterization, SplineCam enables one to compare architectures, measure generalizability, and sample from the decision boundary on or off the data manifold. Project website: 
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    Free, publicly-accessible full text available June 1, 2024
  2. We present Polarity Sampling, a theoretically justified plug-and-play method for controlling the generation quality and diversity of any pre-trained deep generative network (DGN). Leveraging the fact that DGNs are, or can be approximated by, continuous piecewise affine splines, we derive the analytical DGN output space distribution as a function of the product of the DGN's Jacobian singular values raised to a power rho. We dub rho the polarity parameter and prove that rho focuses the DGN sampling on the modes (rho< 0) or anti-modes (rho> 0) of the DGN output space probability distribution. We demonstrate that nonzero polarity values achieve a better precision-recall (quality-diversity) Pareto frontier than standard methods, such as truncation, for a number of state-of-the-art DGNs. We also present quantitative and qualitative results on the improvement of overall generation quality (eg, in terms of the Frechet Inception Distance) for a number of state-of-the-art DGNs, including StyleGAN3, BigGAN-deep, NVAE, for different conditional and unconditional image generation tasks. In particular, Polarity Sampling redefines the state-of-the-art for StyleGAN2 on the FFHQ Dataset to FID 2.57, StyleGAN2 on the LSUN Car Dataset to FID 2.27 and StyleGAN3 on the AFHQv2 Dataset to FID 3.95. Colab Demo: bit. ly/polarity-samp 
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  3. Deep Generative Networks (DGNs) are extensively employed in Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and their variants to approximate the data manifold and distribution. However, training samples are often distributed non-uniformly on the manifold, due to the cost or convenience of collection. For example, the CelebA dataset contains a large fraction of smiling faces. These inconsistencies will be reproduced when sampling from the trained DGN, which is not always preferred, e.g., for fairness or data augmentation. In response, we develop MaGNET, a novel and theoretically motivated latent space sampler for any pre-trained DGN that produces samples uniformly distributed on the learned manifold. We perform a range of experiments on several datasets and DGNs, e.g., for the state-of-the-art StyleGAN2 trained on the FFHQ dataset, uniform sampling via MaGNET increases distribution precision by 4.1% and recall by 3.0% and decreases gender bias by 41.2%, without requiring labels or retraining. Since uniform sample distribution does not imply uniform semantic distribution, we also explore how semantic attributes of generated samples vary under MaGNET sampling. Colab and codes at 
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