Spiking Neural Networks (SNNs) have been studied over decades to incorporate their biological plausibility and leverage their promising energy efficiency.

We study the slice-matching scheme, an efficient iterative method for distribution matching based on sliced optimal transport. We investigate convergence to the target distribution and derive quantitative non-asymptotic rates. To this end, we establish __ojasiewicz-type inequalities for the Sliced-Wasserstein objective. A key challenge is to control along the trajectory the constants in these inequalities. We show that this becomes tractable for Gaussian distributions. Specifically, eigenvalues are controlled when matching along random orthonormal bases at each iteration. We complement our theory with numerical experiments and illustrate the predicted dependence on dimension and step-size, as well as the stabilizing effect of orthonormal-basis sampling.

Distributed multi-task learning provides significant advantages in multi-agent networkswithheterogeneous datasources where agents aimtolearndistinctbut correlated models simultaneously. However, distributed algorithms for learning relatedness among tasks arenotresilient inthepresence ofByzantine agents. In this paper, we present an approach for Byzantine resilient distributed multi-task learning. We propose an efficient online weight assignment rule by measuring the accumulated loss using an agent's data and its neighbors' models. A small accumulated loss indicates a large similarity between the two tasks.

Algorithmic stability is a key characteristic of an algorithm regarding its sensitivity to perturbations of input samples. In this paper,we propose an innovativeunsupervised feature selection algorithm attaining this stability with provable guarantees.

Inspired by biology, spiking neural networks (SNNs) process information via discrete spikes over time, offering an energy-efficient alternative to the classical computing paradigm and classical artificial neural networks (ANNs). In this work, we analyze the representational power of SNNs by viewing them as sequence-to-sequence processors of spikes, i.e., systems that transform a stream of input spikes into a stream of output spikes. We establish the universal representation property for a natural class of spike train functions. Our results are fully quantitative, constructive, and near-optimal in the number of required weights and neurons. The analysis reveals that SNNs are particularly well-suited to represent functions with few inputs, low temporal complexity, or compositions of such functions. The latter is of particular interest, as it indicates that deep SNNs can efficiently capture composite functions via a modular design. As an application of our results, we discuss spike train classification. Overall, these results contribute to a rigorous foundation for understanding the capabilities and limitations of spike-based neuromorphic systems.

Multi-bit spiking neural networks (SNNs) have recently become a heated research spot, pursuing energy-efficient and high-accurate AI. However, with more bits involved, the associated memory and computation demands escalate to the point where the performance improvements become disproportionate. Based on the insight that different layers demonstrate different importance and extra bits could be wasted and interfering, this paper presents an adaptive bit allocation strategy for direct-trained SNNs, achieving fine-grained layer-wise allocation of memory and computation resources. Thus, SNN's efficiency and accuracy can be improved. Specifically, we parametrize the temporal lengths and the bit widths of weights and spikes, and make them learnable and controllable through gradients. To address the challenges caused by changeable bit widths and temporal lengths, we propose the refined spiking neuron, which can handle different temporal lengths, enable the derivation of gradients for temporal lengths, and suit spike quantization better. In addition, we theoretically formulate the step-size mismatch problem of learnable bit widths, which may incur severe quantization errors to SNN, and accordingly propose the step-size renewal mechanism to alleviate this issue. Experiments on various datasets, including the static CIFAR and ImageNet datasets and the dynamic CIFAR-DVS and DVS-GESTURE datasets, demonstrate that our methods can reduce the overall memory and computation cost while achieving higher accuracy. Particularly, our SEWResNet-34 can achieve a 2.69\% accuracy gain and 4.16$\times$ lower bit budgets over the advanced baseline work on ImageNet. This work is open-sourced at \href{https://github.com/Ikarosy/Towards-Efficient-and-Accurate-Spiking-Neural-Networks-via-Adaptive-Bit-Allocation}{this link}.

Federated learning must address heterogeneity, strict communication and computation limits, and privacy while ensuring performance. We propose an operator-theoretic framework that maps the $L^2$-optimal solution into a reproducing kernel Hilbert space (RKHS) via a forward operator, approximates it using available data, and maps back with the inverse operator, yielding a gradient-free scheme. Finite-sample bounds are derived using concentration inequalities over operator norms, and the framework identifies a data-dependent hypothesis space with guarantees on risk, error, robustness, and approximation. Within this space we design efficient kernel machines leveraging the space folding property of Kernel Affine Hull Machines. Clients transfer knowledge via a scalar space folding measure, reducing communication and enabling a simple differentially private protocol: summaries are computed from noise-perturbed data matrices in one step, avoiding per-round clipping and privacy accounting. The induced global rule requires only integer minimum and equality-comparison operations per test point, making it compatible with fully homomorphic encryption (FHE). Across four benchmarks, the gradient-free FL method with fixed encoder embeddings matches or outperforms strong gradient-based fine-tuning, with gains up to 23.7 points. In differentially private experiments, kernel smoothing mitigates accuracy loss in high-privacy regimes. The global rule admits an FHE realization using $Q \times C$ encrypted minimum and $C$ equality-comparison operations per test point, with operation-level benchmarks showing practical latencies. Overall, the framework provides provable guarantees with low communication, supports private knowledge transfer via scalar summaries, and yields an FHE-compatible prediction rule offering a mathematically grounded alternative to gradient-based federated learning under heterogeneity.