We introduce FAEclust, a novel functional autoencoder framework for cluster analysis of multi-dimensional functional data, data that are random realizations of vector-valued random functions. Our framework features a universal-approximator encoder that captures complex nonlinear interdependencies among component functions, and a universal-approximator decoder capable of accurately reconstructing both Euclidean and manifold-valued functional data. Stability and robustness are enhanced through innovative regularization strategies applied to functional weights and biases. Additionally, we incorporate a clustering loss into the network's training objective, promoting the learning of latent representations that are conducive to effective clustering. A key innovation is our shape-informed clustering objective, ensuring that the clustering results are resistant to phase variations in the functions. We establish the universal approximation property of our non-linear decoder and validate the effectiveness of our model through extensive experiments.

In explainable AI, DNN gradients are used to interpret the prediction; in safetycritical control systems, gradients could encode safety constraints; in scientificcomputing applications, gradients could encode physical invariants. While recent work on provable editing of DNNs has focused on input-output constraints, the problem of enforcing hard constraints on DNN gradients remains unaddressed. We present ProGrad, the first efficient approach for editing the parameters of a DNN to provably enforce hard constraints on the DNN gradients.

Diffusion models have gained increasing attention for their impressive generation abilities but currently struggle with rendering accurate and coherent text. To address this issue, we introduce TextDiffuser, focusing on generating images with visually appealing text that is coherent with backgrounds. TextDiffuser consists of two stages: first, a Transformer model generates the layout of keywords extracted from text prompts, and then diffusion models generate images conditioned on the text prompt and the generated layout. Additionally, we contribute the first large-scale text images dataset with OCR annotations, MARIO-10M, containing 10 million image-text pairs with text recognition, detection, and character-level segmentation annotations. We further collect the MARIO-Eval benchmark to serve as a comprehensive tool for evaluating text rendering quality.

Unlike MI, some GEMINIs do not require regularisations when training.

TextDiffuser consists of two stages: first, a Transformer model generates the layout of keywords extracted from text prompts, and then diffusion models generate images conditioned on the text prompt and the generated layout.

Boltzmann machines are powerful distributions that have been shown to be an effective prior over binary latent variables in variational autoencoders (VAEs).

Giventextual explanations, our proposed framework uses agenerative model conditioned on textual input to create data points representing the explanations. Bycomparing theneuron'sresponse tothese generated data points and control data points, we can estimate the quality of the explanation.

That is, thestrong (s( )= k k1) andweakinstantiations (s( )= sum( )) coincideforone-layerneural networks.

Our algorithm is based on the semidefinite program (SDP) relaxation of the non-convexl1-regularized PCA problem.

Inthis experiment, we only quantize the weights, not the activations, to compare the performance degradation as weight bit-width decreases. The mean squared errors (MSE) of the weights across different bit-widths are also reported. The name of the layer and the number of parameters in parenthesis are shown in the column. All numbers are results of the last epoch. Table A3: ResNet-32 trained with Adam on the CIFAR-100 dataset.