However, many use cases of neural network verification require solving the inverse problem, or over-approximating the set of inputs that lead to certain outputs.

This paper presents a new mechanism to facilitate the training of mask transformers for efficient panoptic segmentation, democratizing its deployment. We observe that due to the high complexity in the training objective of panoptic segmentation, it will inevitably lead to much higher penalization on false positive.

In this paper we revisit the fixed-confidence identification of the Pareto optimal set in a multi-objective multi-armed bandit model.

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Furthermore, we show that the density modes can be obtained as byproducts of the assignment variables via simple maximum-value operations whose additional computational cost is linear in the number of data points.

Thus our heuristic relaxation does give valid upper bounds of the exact Lipschitz constant.

Gradient-based optimization with categorical variables typically relies on score-function estimators, which are unbiased but noisy, or on continuous relaxations that replace the discrete distribution with a smooth surrogate admitting a pathwise (reparameterized) gradient, at the cost of optimizing a biased, temperature-dependent objective. In this paper, we extend this family of relaxations by introducing a diffusion-based soft reparameterization for categorical distributions. For these distributions, the denoiser under a Gaussian noising process admits a closed form and can be computed efficiently, yielding a training-free diffusion sampler through which we can backpropagate. Our experiments show that the proposed reparameterization trick yields competitive or improved optimization performance on various benchmarks.

In Appendix B, we provide proofs of the theorems. In Table 6, we provide a list of oracle functions of three basic operation types, including affine transformation, unary nonlinear function, and binary nonlinear function. This lower bound can be used for training ReLU networks with loss fusion. Figure 4 compares the linear bounds in LiRP A and IBP respesctively. We refer readers to those existing works for details.