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Discretization Effects in Spiking Neural Networks

Spiking neural networks (SNNs) are inspired by the continuous-time dynamics of biological neurons, yet their practical implementations typically rely on discrete-time approximations to accommodate digital hardware and time-stepped neuromorphic systems. This discretization, while necessary, introduces numerical errors that may affect training dynamics and model performance, especially in systems where precise spike timing encodes critical information. Recent work has proposed gradient-based training methods that treat spike times as differentiable continuous variables, enabling temporally precise learning. However, the impact of discretizing these spike times during deployment remains poorly understood. In this paper, we systematically investigate the effects of spike time discretization using a representative multi-spike model as a case study. We propose a causal discretization scheme and analyze its quantization error both theoretically and empirically. Our results show that this error depends not only on the time step size Δt but also on the temporal structure of the input. We demonstrate that certain structured inputs can produce local minima in discretization error, and we explore whether such minima correspond to optimal choices of Δt for real datasets. Experiments on MNIST, Fashion MNIST, and EMNIST reveal that discretization can influence both classification accuracy and network sparsity. Finally, we compare training and evaluation under mismatched and aligned time regimes, examining how consistency in spike time discretization affects performance and sparsity in spike-timing-based SNNs. ...
Journal article (2024) - Zimin Xia, Olaf Booij, Julian F.P. Kooij
We propose a novel end-to-end method for cross-view pose estimation. Given a ground-level query image and an aerial image that covers the query's local neighborhood, the 3 Degrees-of-Freedom camera pose of the query is estimated by matching its image descriptor to descriptors of local regions within the aerial image. The orientation-aware descriptors are obtained by using a translationally equivariant convolutional ground image encoder and contrastive learning. The Localization Decoder produces a dense probability distribution in a coarse-to-fine manner with a novel Localization Matching Upsampling module. A smaller Orientation Decoder produces a vector field to condition the orientation estimate on the localization. Our method is validated on the VIGOR and KITTI datasets, where it surpasses the state-of-the-art baseline by 72% and 36% in median localization error for comparable orientation estimation accuracy. The predicted probability distribution can represent localization ambiguity, and enables rejecting possible erroneous predictions. Without re-training, the model can infer on ground images with different field of views and utilize orientation priors if available. On the Oxford RobotCar dataset, our method can reliably estimate the ego-vehicle's pose over time, achieving a median localization error under 1 meter and a median orientation error of around 1 degree at 14 FPS. ...

Video object detection by single-frame object location anticipation

Conference paper (2023) - Xin Liu, Jan C. van Gemert, Fatemeh Karimi Nejadasl, Olaf Booij, Silvia L. Pintea
Objects in videos are typically characterized by continuous smooth motion. We exploit continuous smooth motion in three ways. 1) Improved accuracy by using object motion as an additional source of supervision, which we obtain by anticipating object locations from a static keyframe. 2) Improved efficiency by only doing the expensive feature computations on a small subset of all frames. Because neighboring video frames are often redundant, we only compute features for a single static keyframe and predict object locations in subsequent frames. 3) Reduced annotation cost, where we only annotate the keyframe and use smooth pseudo-motion between keyframes. We demonstrate computational efficiency, annotation efficiency, and improved mean average precision compared to the state-of-the-art on four datasets: ImageNet VID, EPIC KITCHENS-55, YouTube-BoundingBoxes and Waymo Open dataset. Our source code is available at https://github.com/L-KID/Video-object-detection-by-location-anticipation. ...