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In this paper we study a principal-agent problem in continuous time with multiple lump-sum payments (contracts) paid at different deterministic times. We reduce the non-zero sum Stackelberg game between the principal and agent to a standard stochastic optimal control problem. We apply our result to a benchmark model for which we investigate how different inputs (payment frequencies, payments' distribution, discounting factors, agent's reservation utility) affect the principal's value and agent's optimal compensations.

Seeking high-quality representations with latent variable models (LVMs) to reveal the intrinsic correlation between neural activity and behavior or sensory stimuli has attracted much interest. Most work has focused on analyzing motor neural activity that controls clear behavioral traces and has modeled neural temporal relationships in a way that does not conform to natural reality. For studies of visual brain regions, naturalistic visual stimuli are high-dimensional and time-dependent, making neural activity exhibit intricate dynamics. To cope with such conditions, we propose Time-Dependent Split VAE (TiDeSPL-VAE), a sequential LVM that decomposes visual neural activity into two latent representations while considering time dependence. We specify content latent representations corresponding to the component of neural activity driven by the current visual stimulus, and style latent representations corresponding to the neural dynamics influenced by the organism's internal state. To progressively generate the two latent representations over time, we introduce state factors to construct conditional distributions with time dependence and apply self-supervised contrastive learning to shape them. By this means, TiDeSPL-VAE can effectively analyze complex visual neural activity and model temporal relationships in a natural way. We compare our model with alternative approaches on synthetic data and neural data from the mouse visual cortex. The results show that our model not only yields the best decoding performance on naturalistic scenes/movies but also extracts explicit neural dynamics, demonstrating that it builds latent representations more relevant to visual stimuli.

Video action recognition (VAR) plays crucial roles in various domains such as surveillance, healthcare, and industrial automation, making it highly significant for the society. Consequently, it has long been a research spot in the computer vision field. As artificial neural networks (ANNs) are flourishing, convolution neural networks (CNNs), including 2D-CNNs and 3D-CNNs, as well as variants of the vision transformer (ViT), have shown impressive performance on VAR. However, they usually demand huge computational cost due to the large data volume and heavy information redundancy introduced by the temporal dimension. To address this challenge, some researchers have turned to brain-inspired spiking neural networks (SNNs), such as recurrent SNNs and ANN-converted SNNs, leveraging their inherent temporal dynamics and energy efficiency. Yet, current SNNs for VAR also encounter limitations, such as nontrivial input preprocessing, intricate network construction/training, and the need for repetitive processing of the same video clip, hindering their practical deployment. In this study, we innovatively propose the directly trained SVFormer (Spiking Video transFormer) for VAR. SVFormer integrates local feature extraction, global self-attention, and the intrinsic dynamics, sparsity, and spike-driven nature of SNNs, to efficiently and effectively extract spatio-temporal features. We evaluate SVFormer on two RGB datasets (UCF101, NTU-RGBD60) and one neuromorphic dataset (DVS128-Gesture), demonstrating comparable performance to the mainstream models in a more efficient way. Notably, SVFormer achieves a top-1 accuracy of 84.03% with ultra-low power consumption (21 mJ/video) on UCF101, which is state-of-the-art among directly trained deep SNNs, showcasing significant advantages over prior models., Comment: Accepted by IJCAI 2024 workshop - Human Brain and Artificial Intelligence

Spiking neural networks (SNNs) offer a promising energy-efficient alternative to artificial neural networks (ANNs), in virtue of their high biological plausibility, rich spatial-temporal dynamics, and event-driven computation. The direct training algorithms based on the surrogate gradient method provide sufficient flexibility to design novel SNN architectures and explore the spatial-temporal dynamics of SNNs. According to previous studies, the performance of models is highly dependent on their sizes. Recently, direct training deep SNNs have achieved great progress on both neuromorphic datasets and large-scale static datasets. Notably, transformer-based SNNs show comparable performance with their ANN counterparts. In this paper, we provide a new perspective to summarize the theories and methods for training deep SNNs with high performance in a systematic and comprehensive way, including theory fundamentals, spiking neuron models, advanced SNN models and residual architectures, software frameworks and neuromorphic hardware, applications, and future trends. The reviewed papers are collected at https://github.com/zhouchenlin2096/Awesome-Spiking-Neural-Networks, Comment: Accepted by Frontiers in Neuroscience

Spiking Transformers, which integrate Spiking Neural Networks (SNNs) with Transformer architectures, have attracted significant attention due to their potential for energy efficiency and high performance. However, existing models in this domain still suffer from suboptimal performance. We introduce several innovations to improve the performance: i) We propose a novel spike-form Q-K attention mechanism, tailored for SNNs, which efficiently models the importance of token or channel dimensions through binary vectors with linear complexity. ii) We incorporate the hierarchical structure, which significantly benefits the performance of both the brain and artificial neural networks, into spiking transformers to obtain multi-scale spiking representation. iii) We design a versatile and powerful patch embedding module with a deformed shortcut specifically for spiking transformers. Together, we develop QKFormer, a hierarchical spiking transformer based on Q-K attention with direct training. QKFormer shows significantly superior performance over existing state-of-the-art SNN models on various mainstream datasets. Notably, with comparable size to Spikformer (66.34 M, 74.81%), QKFormer (64.96 M) achieves a groundbreaking top-1 accuracy of 85.65% on ImageNet-1k, substantially outperforming Spikformer by 10.84%. To our best knowledge, this is the first time that directly training SNNs have exceeded 85% accuracy on ImageNet-1K. The code and models are publicly available at https://github.com/zhouchenlin2096/QKFormer, Comment: Accepted by NeurIPS 2024 (Spotlight). Code and Model: https://github.com/zhouchenlin2096/QKFormer

Spiking neural networks (SNNs) aim to realize brain-inspired intelligence on neuromorphic chips with high energy efficiency by introducing neural dynamics and spike properties. As the emerging spiking deep learning paradigm attracts increasing interest, traditional programming frameworks cannot meet the demands of the automatic differentiation, parallel computation acceleration, and high integration of processing neuromorphic datasets and deployment. In this work, we present the SpikingJelly framework to address the aforementioned dilemma. We contribute a full-stack toolkit for pre-processing neuromorphic datasets, building deep SNNs, optimizing their parameters, and deploying SNNs on neuromorphic chips. Compared to existing methods, the training of deep SNNs can be accelerated $11\times$, and the superior extensibility and flexibility of SpikingJelly enable users to accelerate custom models at low costs through multilevel inheritance and semiautomatic code generation. SpikingJelly paves the way for synthesizing truly energy-efficient SNN-based machine intelligence systems, which will enrich the ecology of neuromorphic computing., Comment: Accepted in Science Advances (https://www.science.org/doi/10.1126/sciadv.adi1480)

Deep neural networks (DNNs) are widely used models for investigating biological visual representations. However, existing DNNs are mostly designed to analyze neural responses to static images, relying on feedforward structures and lacking physiological neuronal mechanisms. There is limited insight into how the visual cortex represents natural movie stimuli that contain context-rich information. To address these problems, this work proposes the long-range feedback spiking network (LoRaFB-SNet), which mimics top-down connections between cortical regions and incorporates spike information processing mechanisms inherent to biological neurons. Taking into account the temporal dependence of representations under movie stimuli, we present Time-Series Representational Similarity Analysis (TSRSA) to measure the similarity between model representations and visual cortical representations of mice. LoRaFB-SNet exhibits the highest level of representational similarity, outperforming other well-known and leading alternatives across various experimental paradigms, especially when representing long movie stimuli. We further conduct experiments to quantify how temporal structures (dynamic information) and static textures (static information) of the movie stimuli influence representational similarity, suggesting that our model benefits from long-range feedback to encode context-dependent representations just like the brain. Altogether, LoRaFB-SNet is highly competent in capturing both dynamic and static representations of the mouse visual cortex and contributes to the understanding of movie processing mechanisms of the visual system. Our codes are available at https://github.com/Grasshlw/SNN-Neural-Similarity-Movie.

Deep artificial neural networks (ANNs) play a major role in modeling the visual pathways of primate and rodent. However, they highly simplify the computational properties of neurons compared to their biological counterparts. Instead, Spiking Neural Networks (SNNs) are more biologically plausible models since spiking neurons encode information with time sequences of spikes, just like biological neurons do. However, there is a lack of studies on visual pathways with deep SNNs models. In this study, we model the visual cortex with deep SNNs for the first time, and also with a wide range of state-of-the-art deep CNNs and ViTs for comparison. Using three similarity metrics, we conduct neural representation similarity experiments on three neural datasets collected from two species under three types of stimuli. Based on extensive similarity analyses, we further investigate the functional hierarchy and mechanisms across species. Almost all similarity scores of SNNs are higher than their counterparts of CNNs with an average of 6.6%. Depths of the layers with the highest similarity scores exhibit little differences across mouse cortical regions, but vary significantly across macaque regions, suggesting that the visual processing structure of mice is more regionally homogeneous than that of macaques. Besides, the multi-branch structures observed in some top mouse brain-like neural networks provide computational evidence of parallel processing streams in mice, and the different performance in fitting macaque neural representations under different stimuli exhibits the functional specialization of information processing in macaques. Taken together, our study demonstrates that SNNs could serve as promising candidates to better model and explain the functional hierarchy and mechanisms of the visual system., Comment: Accepted by Proceedings of the 37th AAAI Conference on Artificial Intelligence (AAAI-23)

Most of the existing deep learning-based sequential recommendation approaches utilize the recurrent neural network architecture or self-attention to model the sequential patterns and temporal influence among a user's historical behavior and learn the user's preference at a specific time. However, these methods have two main drawbacks. First, they focus on modeling users' dynamic states from a user-centric perspective and always neglect the dynamics of items over time. Second, most of them deal with only the first-order user-item interactions and do not consider the high-order connectivity between users and items, which has recently been proved helpful for the sequential recommendation. To address the above problems, in this article, we attempt to model user-item interactions by a bipartite graph structure and propose a new recommendation approach based on a Position-enhanced and Time-aware Graph Convolutional Network (PTGCN) for the sequential recommendation. PTGCN models the sequential patterns and temporal dynamics between user-item interactions by defining a position-enhanced and time-aware graph convolution operation and learning the dynamic representations of users and items simultaneously on the bipartite graph with a self-attention aggregator. Also, it realizes the high-order connectivity between users and items by stacking multi-layer graph convolutions. To demonstrate the effectiveness of PTGCN, we carried out a comprehensive evaluation of PTGCN on three real-world datasets of different sizes compared with a few competitive baselines. Experimental results indicate that PTGCN outperforms several state-of-the-art models in terms of two commonly-used evaluation metrics for ranking., Comment: 33 pages, 7 figures, 8 tables

Next (or successive) point-of-interest (POI) recommendation has attracted increasing attention in recent years. Most of the previous studies attempted to incorporate the spatiotemporal information and sequential patterns of user check-ins into recommendation models to predict the target user's next move. However, none of these approaches utilized the social influence of each user's friends. In this study, we discuss a new topic of next POI recommendation and present a deep attentive network for social-aware next POI recommendation called DAN-SNR. In particular, the DAN-SNR makes use of the self-attention mechanism instead of the architecture of recurrent neural networks to model sequential influence and social influence in a unified manner. Moreover, we design and implement two parallel channels to capture short-term user preference and long-term user preference as well as social influence, respectively. By leveraging multi-head self-attention, the DAN-SNR can model long-range dependencies between any two historical check-ins efficiently and weigh their contributions to the next destination adaptively. Also, we carried out a comprehensive evaluation using large-scale real-world datasets collected from two popular location-based social networks, namely Gowalla and Brightkite. Experimental results indicate that the DAN-SNR outperforms seven competitive baseline approaches regarding recommendation performance and is of high efficiency among six neural-network- and attention-based methods., Comment: 25 pages, 7 figures, and 6 tables