Proposition 1. Membrane potentials without spike reset are computed as a convolution Ṽ We proceed our proof in two steps. In step 1, we unroll the discretized LIF difference equation (without reset) in time and in step 2, we show how this is equivalent to the proposed convolution. This implies equivalence between Equations 1 and 2 for t = k + 1 assuming equivalence between Equations 1 and 2 holds true for t = k. By the principle of induction, equivalence is established given that both the base case and inductive step hold true. This is identical to Equation 2 and (by step 1) identical to Equation 1.

The adaptive leaky integrate-and-fire (ALIF) model is fundamental within computational neuroscience and has been instrumental in studying our brains in silico. Due to the sequential nature of simulating these neural models, a commonly faced issue is the speed-accuracy trade-off: either accurately simulate a neuron using a small discretisation time-step (DT), which is slow, or more quickly simulate a neuron using a larger DT and incur a loss in simulation accuracy. Here we provide a solution to this dilemma, by algorithmically reinterpreting the ALIF model, reducing the sequential simulation complexity and permitting a more efficient parallelisation on GPUs. We computationally validate our implementation to obtain over a 50 training speedup using small DTs on synthetic benchmarks. We also obtained a comparable performance to the standard ALIF implementation on different supervised classification tasks - yet in a fraction of the training time. Lastly, we showcase how our model makes it possible to quickly and accurately fit real electrophysiological recordings of cortical neurons, where very fine sub-millisecond DTs are crucial for capturing exact spike timing.

The human visual perception system demonstrates exceptional capabilities in learning without explicit supervision and understanding the part-to-whole composition of objects. Drawing inspiration from these two abilities, we propose Hierarchical Adaptive Self-Supervised Object Detection (HASSOD), a novel approach that learns to detect objects and understand their compositions without human supervision. HASSOD employs a hierarchical adaptive clustering strategy to group regions into object masks based on self-supervised visual representations, adaptively determining the number of objects per image. Furthermore, HASSOD identifies the hierarchical levels of objects in terms of composition, by analyzing coverage relations between masks and constructing tree structures. This additional selfsupervised learning task leads to improved detection performance and enhanced interpretability. Lastly, we abandon the inefficient multi-round self-training process utilized in prior methods and instead adapt the Mean Teacher framework from semi-supervised learning, which leads to a smoother and more efficient training process. Through extensive experiments on prevalent image datasets, we demonstrate the superiority of HASSOD over existing methods, thereby advancing the state of the art in self-supervised object detection. Notably, we improve Mask AR from 20.2 to 22.5 on LVIS, and from 17.0 to 26.0 on SA-1B.

Here we prove the correctness of path-based reasoning with A* algorithm. Second, we demonstrate that Eqn. 7 can be solved by Eqn. 8 if paths with the same length and the A.3, we merge paths by their length and stop nodes, A.3 Reasoning with A* Algorithm Finally, we prove that the A* iteration (Eqn. In order to prove Thm. A.4, we first prove a lemma for the analytic form of A.5 and Eqn. 5, it is Specifically, padding-free operations construct IDs for each sample in the batch, such that we can distinguish different samples when we apply operations to the whole batch. Alg. 2 provides the pseudo code for padding-free topk in PyTorch. Dataset statistics for transductive and inductive knowledge graph reasoning is summarized in Tab.

We consider a novel dynamic pricing and learning setting where in addition to setting prices of products in sequential rounds, the seller also ex-ante commits to'advertising schemes'. That is, in the beginning of each round the seller can decide what kind of signal they will provide to the buyer about the product's quality upon realization. Using the popular Bayesian persuasion framework to model the effect of these signals on the buyers' valuation and purchase responses, we formulate the problem of finding an optimal design of the advertising scheme along with a pricing scheme that maximizes the seller's expected revenue. Without any apriori knowledge of the buyers' demand function, our goal is to design an online algorithm that can use past purchase responses to adaptively learn the optimal pricing and advertising strategy. We study the regret of the algorithm when compared to the optimal clairvoyant price and advertising scheme.

Serialization-based methods, which serialize the 3D voxels and group them into multiple sequences before inputting to Transformers, have demonstrated their effectiveness in 3D object detection. However, serializing 3D voxels into 1D sequences will inevitably sacrifice the voxel spatial proximity. Such an issue is hard to be addressed by enlarging the group size with existing serializationbased methods due to the quadratic complexity of Transformers with feature sizes. Inspired by the recent advances of state space models (SSMs), we present a Voxel SSM, termed as Voxel Mamba, which employs a group-free strategy to serialize the whole space of voxels into a single sequence. The linear complexity of SSMs encourages our group-free design, alleviating the loss of spatial proximity of voxels. To further enhance the spatial proximity, we propose a Dual-scale SSM Block to establish a hierarchical structure, enabling a larger receptive field in the 1D serialization curve, as well as more complete local regions in 3D space. Moreover, we implicitly apply window partition under the group-free framework by positional encoding, which further enhances spatial proximity by encoding voxel positional information. Our experiments on Waymo Open Dataset and nuScenes dataset show that Voxel Mamba not only achieves higher accuracy than state-of-the-art methods, but also demonstrates significant advantages in computational efficiency.

Designing and deriving effective model-based reinforcement learning (MBRL) algorithms with a performance improvement guarantee is challenging, mainly attributed to the high coupling between model learning and policy optimization. Many prior methods that rely on return discrepancy to guide model learning ignore the impacts of model shift, which can lead to performance deterioration due to excessive model updates. Other methods use performance difference bound to explicitly consider model shift. However, these methods rely on a fixed threshold to constrain model shift, resulting in a heavy dependence on the threshold and a lack of adaptability during the training process. In this paper, we theoretically derive an optimization objective that can unify model shift and model bias and then formulate a fine-tuning process. This process adaptively adjusts the model updates to get a performance improvement guarantee while avoiding model overfitting.

Previous research has provided many intriguing insights into model robustness through the lens of frequency spectrum for the Deep Learning (DL) community. Many of these studies attempted to elucidate the connection between model sensitivity and frequency components. A commonly-held hypothesis is that the utilization of high-frequency components leads to a decrease in model robustnessWang et al. [2020]. Recent research has improved model robustness through a variety of methods, guided by this hypothesis. For example, Addepalli et al. [2022] applies regularization terms to high-frequency components to enhance model robustness.