The computational cost of softmax-based attention in transformers limits their applicability to long-context tasks. Adaptive sparsity, of which $\alpha$-entmax attention is an example, offers a flexible data-dependent alternative, but existing implementations are inefficient and do not leverage the sparsity to obtain runtime and memory gains. In this work, we propose AdaSplash, which combines the efficiency of GPU-optimized algorithms with the sparsity benefits of $\alpha$-entmax. We first introduce a hybrid Halley-bisection algorithm, resulting in a 7-fold reduction in the number of iterations needed to compute the $\alpha$-entmax transformation. Then, we implement custom Triton kernels to efficiently handle adaptive sparsity. Experiments with RoBERTa and ModernBERT for text classification and single-vector retrieval, along with GPT-2 for language modeling, show that our method achieves substantial improvements in runtime and memory efficiency compared to existing $\alpha$-entmax implementations. It approaches -- and in some cases surpasses -- the efficiency of highly optimized softmax implementations like FlashAttention-2, enabling long-context training while maintaining strong task performance.

Face morphing is one of the seminal problems in computer graphics, with numerous artistic and forensic applications. It is notoriously challenging due to pose, lighting, gender, and ethnicity variations. Generally, this task consists of a warping for feature alignment and a blending for a seamless transition between the warped images. We propose to leverage coordinate-based neural networks to represent such warpings and blendings of face images. During training, we exploit the smoothness and flexibility of such networks, by combining energy functionals employed in classical approaches without discretizations. Additionally, our method is time-dependent, allowing a continuous warping, and blending of the target images. During warping inference, we need both direct and inverse transformations of the time-dependent warping. The first is responsible for morphing the target image into the source image, while the inverse is used for morphing in the opposite direction. Our neural warping stores those maps in a single network due to its inversible property, dismissing the hard task of inverting them. The results of our experiments indicate that our method is competitive with both classical and data-based neural techniques under the lens of face-morphing detection approaches. Aesthetically, the resulting images present a seamless blending of diverse faces not yet usual in the literature.

In state-of-the-art deep learning for object recognition, SoftMax and Sigmoid functions are most commonly employed as the predictor outputs. Such layers often produce overconfident predictions rather than proper probabilistic scores, which can thus harm the decision-making of `critical' perception systems applied in autonomous driving and robotics. Given this, the experiments in this work propose a probabilistic approach based on distributions calculated out of the Logit layer scores of pre-trained networks. We demonstrate that Maximum Likelihood (ML) and Maximum a-Posteriori (MAP) functions are more suitable for probabilistic interpretations than SoftMax and Sigmoid-based predictions for object recognition. We explore distinct sensor modalities via RGB images and LiDARs (RV: range-view) data from the KITTI and Lyft Level-5 datasets, where our approach shows promising performance compared to the usual SoftMax and Sigmoid layers, with the benefit of enabling interpretable probabilistic predictions. Another advantage of the approach introduced in this paper is that the ML and MAP functions can be implemented in existing trained networks, that is, the approach benefits from the output of the Logit layer of pre-trained networks. Thus, there is no need to carry out a new training phase since the ML and MAP functions are used in the test/prediction phase.