论文检索

Neuroscience, Cognitive Science

Yufei Guo, Yuanpei Chen, Zecheng Hao, Weihang Peng, Zhou Jie, Yuhan Zhang, Xiaode Liu, Zhe Ma

The Spiking Neural Network (SNN) is a biologically inspired neural network infrastructure that has recently garnered significant attention. It utilizes binary spike activations to transmit information, thereby replacing multiplications with additions and resulting in high energy efficiency. However, training an SNN directly poses a challenge due to the undefined gradient of the firing spike process. Although prior works have employed various surrogate gradient training methods that use an alternative function to replace the firing process during back-propagation, these approaches ignore an intrinsic problem: gradient vanishing. To address this issue, we propose a shortcut back-propagation method in the paper, which advocates for transmitting the gradient directly from the loss to the shallow layers. This enables us to present the gradient to the shallow layers directly, thereby significantly mitigating the gradient vanishing problem. Additionally, this method does not introduce any burden during the inference phase.To strike a balance between final accuracy and ease of training, we also propose an evolutionary training framework and implement it by inducing a balance coefficient that dynamically changes with the training epoch, which further improves the network's performance. Extensive experiments conducted over static and dynamic datasets using several popular network structures reveal that our method consistently outperforms state-of-the-art methods.

Theory · Active Learning and Interactive Learning

Felix Teufel, Carsten Stahlhut, Jesper Ferkinghoff-Borg

Bayesian optimization (BO) is an attractive machine learning framework for performing sample-efficient global optimization of black-box functions. The optimization process is guided by an acquisition function that selects points to acquire in each round of BO. In batched BO, when multiple points are acquired in parallel, commonly used acquisition functions are often high-dimensional and intractable, leading to the use of sampling-based alternatives. We propose a statistical physics inspired acquisition function that can natively handle batches. Batched Energy-Entropy acquisition for BO (BEEBO) enables tight control of the explore-exploit trade-off of the optimization process and generalizes to heteroskedastic black-box problems. We demonstrate the applicability of BEEBO on a range of problems, showing competitive performance to existing acquisition functions.

Generative Models

Tobias Schröder, Zijing Ou, Yingzhen Li, Andrew Duncan

Energy-based models (EBMs) offer a flexible framework for probabilistic modelling across various data domains. However, training EBMs on data in discrete or mixed state spaces poses significant challenges due to the lack of robust and fast sampling methods. In this work, we propose to train discrete EBMs with Energy Discrepancy, a loss function which only requires the evaluation of the energy function at data points and their perturbed counterparts, thus eliminating the need for Markov chain Monte Carlo. We introduce perturbations of the data distribution by simulating a diffusion process on the discrete state space endowed with a graph structure. This allows us to inform the choice of perturbation from the structure of the modelled discrete variable, while the continuous time parameter enables fine-grained control of the perturbation. Empirically, we demonstrate the efficacy of the proposed approaches in a wide range of applications, including the estimation of discrete densities with non-binary vocabulary and binary image modelling. We also introduce the first application of EBMs to tabular data sets with applications in synthetic data generation and calibrated classification.

Deep Learning · Everything Else

Yiyang Zhao, Yunzhuo Liu, Bo Jiang, Tian Guo

This work presents a novel approach to neural architecture search (NAS) that aims to increase carbon efficiency for the model design process. The proposed framework CE-NAS addresses the key challenge of high carbon cost associated with NAS by exploring the carbon emission variations of energy and energy differences of different NAS algorithms. At the high level, CE-NAS leverages a reinforcement-learning agent to dynamically adjust GPU resources based on carbon intensity, predicted by a time-series transformer, to balance energy-efficient sampling and energy-intensive evaluation tasks. Furthermore, CE-NAS leverages a recently proposed multi-objective optimizer to effectively reduce the NAS search space. We demonstrate the efficacy of CE-NAS in lowering carbon emissions while achieving SOTA results for both NAS datasets and open-domain NAS tasks. For example, on the HW-NasBench dataset, CE-NAS reduces carbon emissions by up to 7.22X while maintaining a search efficiency comparable to vanilla NAS. For open-domain NAS tasks, CE-NAS achieves SOTA results with 97.35% top-1 accuracy on CIFAR-10 with only 1.68M parameters and a carbon consumption of 38.53 lbs of CO2. On ImageNet, our searched model achieves 80.6% top-1 accuracy with a 0.78 ms TensorRT latency using FP16 on NVIDIA V100, consuming only 909.86 lbs of CO2, making it comparable to other one-shot-based NAS baselines. Our code is available at https://github.com/cake-lab/CE-NAS.

Tycho van der Ouderaa, Mark van der Wilk, Pim de Haan

Symmetries have proven useful in machine learning models, improving generalisation and overall performance. At the same time, recent advancements in learning dynamical systems rely on modelling the underlying Hamiltonian to guarantee the conservation of energy.These approaches can be connected via a seminal result in mathematical physics: Noether's theorem, which states that symmetries in a dynamical system correspond to conserved quantities.This work uses Noether's theorem to parameterise symmetries as learnable conserved quantities. We then allow conserved quantities and associated symmetries to be learned directly from train data through approximate Bayesian model selection, jointly with the regular training procedure. As training objective, we derive a variational lower bound to the marginal likelihood. The objective automatically embodies an Occam's Razor effect that avoids collapse of conversation laws to the trivial constant, without the need to manually add and tune additional regularisers. We demonstrate a proof-of-principle on n-harmonic oscillators and n-body systems. We find that our method correctly identifies the correct conserved quantities and U(n) and SE(n) symmetry groups, improving overall performance and predictive accuracy on test data.

Applications

Wenjun Miao, Guansong Pang, Jin Zheng, Xiao Bai

One key challenge in Out-of-Distribution (OOD) detection is the absence of ground-truth OOD samples during training. One principled approach to address this issue is to use samples from external datasets as outliers ($\textit{i.e.}$, pseudo OOD samples) to train OOD detectors. However, we find empirically that the outlier samples often present a distribution shift compared to the true OOD samples, especially in Long-Tailed Recognition (LTR) scenarios, where ID classes are heavily imbalanced, $\textit{i.e.}$, the true OOD samples exhibit very different probability distribution to the head and tailed ID classes from the outliers. In this work, we propose a novel approach, namely $\textit{normalized outlier distribution adaptation}$ (AdaptOD), to tackle this distribution shift problem. One of its key components is $\textit{dynamic outlier distribution adaptation}$ that effectively adapts a vanilla outlier distribution based on the outlier samples to the true OOD distribution by utilizing the OOD knowledge in the predicted OOD samples during inference. Further, to obtain a more reliable set of predicted OOD samples on long-tailed ID data, a novel $\textit{dual-normalized energy loss}$ is introduced in AdaptOD, which leverages class- and sample-wise normalized energy to enforce a more balanced prediction energy on imbalanced ID samples. This helps avoid bias toward the head samples and learn a substantially better vanilla outlier distribution than existing energy losses during training. It also eliminates the need of manually tuning the sensitive margin hyperparameters in energy losses. Empirical results on three popular benchmarks for OOD detection in LTR show the superior performance of AdaptOD over state-of-the-art methods.Code is available at https://github.com/mala-lab/AdaptOD.

Physical Models · Physics

Timothy Nest, Maxence Ernoult

Power efficiency is plateauing in the standard digital electronics realm such that new hardware, models, and algorithms are needed to reduce the costs of AI training. The combination of energy-based analog circuits and the Equilibrium Propagation (EP) algorithm constitutes a compelling alternative compute paradigm for gradient-based optimization of neural nets. Existing analog hardware accelerators, however, typically incorporate digital circuitry to sustain auxiliary non-weight-stationary operations, mitigate analog device imperfections, and leverage existing digital platforms. Such heterogeneous hardware lacks a supporting theoretical framework. In this work, we introduce \emph{Feedforward-tied Energy-based Models} (ff-EBMs), a hybrid model comprised of feedforward and energy-based blocks housed on digital and analog circuits. We derive a novel algorithm to compute gradients end-to-end in ff-EBMs by backpropagating and ``eq-propagating'' through feedforward and energy-based parts respectively, enabling EP to be applied flexibly on realistic architectures. We experimentally demonstrate the effectiveness of this approach on ff-EBMs using Deep Hopfield Networks (DHNs) as energy-based blocks, and show that a standard DHN can be arbitrarily split into any uniform size while maintaining or improving performance with increases in simulation speed of up to four times. We then train ff-EBMs on ImageNet32 where we establish a new state-of-the-art performance for the EP literature (46 top-1 \%). Our approach offers a principled, scalable, and incremental roadmap for the gradual integration of self-trainable analog computational primitives into existing digital accelerators.

Reinforcement Learning · Everything Else

Bhavya, Lenart Treven, Florian Dorfler, Stelian Coros, Andreas Krause

We study the problem of nonepisodic reinforcement learning (RL) for nonlinear dynamical systems, where the system dynamics are unknown and the RL agent has to learn from a single trajectory, i.e., without resets. We propose **N**on**e**pisodic **O**ptistmic **RL** (NeoRL), an approach based on the principle of optimism in the face of uncertainty. NeoRL uses well-calibrated probabilistic models and plans optimistically w.r.t. the epistemic uncertainty about the unknown dynamics. Under continuity and bounded energy assumptions on the system, weprovide a first-of-its-kind regret bound of $\mathcal{O}(\beta_T \sqrt{T \Gamma_T})$ for general nonlinear systems with Gaussian process dynamics. We compare NeoRL to other baselines on several deep RL environments and empirically demonstrate that NeoRL achieves the optimal average cost while incurring the least regret.

Graph Neural Networks

Li Sun, Zhenhao Huang, Qiqi Wan, Hao Peng, Philip S Yu

Graph neural networks (GNNs) have become the dominant solution for learning on graphs, the typical non-Euclidean structures. Conventional GNNs, constructed with the Artificial Neuron Network (ANN), have achieved impressive performance at the cost of high computation and energy consumption. In parallel, spiking GNNs with brain-like spiking neurons are drawing increasing research attention owing to the energy efficiency. So far, existing spiking GNNs consider graphs in Euclidean space, ignoring the structural geometry, and suffer from the high latency issue due to Back-Propagation-Through-Time (BPTT) with the surrogate gradient. In light of the aforementioned issues, we are devoted to exploring spiking GNN on Riemannian manifolds, and present a Manifold-valued Spiking GNN (MSG). In particular, we design a new spiking neuron on geodesically complete manifolds with the diffeomorphism, so that BPTT regarding the spikes is replaced by the proposed differentiation via manifold. Theoretically, we show that MSG approximates a solver of the manifold ordinary differential equation. Extensive experiments on common graphs show the proposed MSG achieves superior performance to previous spiking GNNs and energy efficiency to conventional GNNs.

Generative Models · Diffusion models

Sangwoong Yoon, Himchan Hwang, Dohyun Kwon, Yung-Kyun Noh, Frank Park

We present a maximum entropy inverse reinforcement learning (IRL) approach for improving the sample quality of diffusion generative models, especially when the number of generation time steps is small. Similar to how IRL trains a policy based on the reward function learned from expert demonstrations, we train (or fine-tune) a diffusion model using the log probability density estimated from training data. Since we employ an energy-based model (EBM) to represent the log density, our approach boils down to the joint training of a diffusion model and an EBM. Our IRL formulation, named Diffusion by Maximum Entropy IRL (DxMI), is a minimax problem that reaches equilibrium when both models converge to the data distribution. The entropy maximization plays a key role in DxMI, facilitating the exploration of the diffusion model and ensuring the convergence of the EBM. We also propose Diffusion by Dynamic Programming (DxDP), a novel reinforcement learning algorithm for diffusion models, as a subroutine in DxMI. DxDP makes the diffusion model update in DxMI efficient by transforming the original problem into an optimal control formulation where value functions replace back-propagation in time. Our empirical studies show that diffusion models fine-tuned using DxMI can generate high-quality samples in as few as 4 and 10 steps. Additionally, DxMI enables the training of an EBM without MCMC, stabilizing EBM training dynamics and enhancing anomaly detection performance.

Data-centric AI

Haowei Zhu, Ling Yang, Jun-Hai Yong, Hongzhi Yin, Jiawei Jiang, Meng Xiao, Wentao Zhang, Bin Wang

The scale and quality of a dataset significantly impact the performance of deep models. However, acquiring large-scale annotated datasets is both a costly and time-consuming endeavor. To address this challenge, dataset expansion technologies aim to automatically augment datasets, unlocking the full potential of deep models. Current data expansion techniques include image transformation and image synthesis methods. Transformation-based methods introduce only local variations, leading to limited diversity. In contrast, synthesis-based methods generate entirely new content, greatly enhancing informativeness. However, existing synthesis methods carry the risk of distribution deviations, potentially degrading model performance with out-of-distribution samples. In this paper, we propose DistDiff, a training-free data expansion framework based on the distribution-aware diffusion model. DistDiff constructs hierarchical prototypes to approximate the real data distribution, optimizing latent data points within diffusion models with hierarchical energy guidance. We demonstrate its capability to generate distribution-consistent samples, significantly improving data expansion tasks. DistDiff consistently enhances accuracy across a diverse range of datasets compared to models trained solely on original data. Furthermore, our approach consistently outperforms existing synthesis-based techniques and demonstrates compatibility with widely adopted transformation-based augmentation methods. Additionally, the expanded dataset exhibits robustness across various architectural frameworks.

Jiaxu Leng, Zhanjie Wu, Mingpi Tan, Yiran Liu, Ji Gan, Haosheng Chen, Xinbo Gao

While numerous Video Violence Detection (VVD) methods have focused on representation learning in Euclidean space, they struggle to learn sufficiently discriminative features, leading to weaknesses in recognizing normal events that are visually similar to violent events (i.e., ambiguous violence). In contrast, hyperbolic representation learning, renowned for its ability to model hierarchical and complex relationships between events, has the potential to amplify the discrimination between visually similar events. Inspired by these, we develop a novel Dual-Space Representation Learning (DSRL) method for weakly supervised VVD to utilize the strength of both Euclidean and hyperbolic geometries, capturing the visual features of events while also exploring the intrinsic relations between events, thereby enhancing the discriminative capacity of the features. DSRL employs a novel information aggregation strategy to progressively learn event context in hyperbolic spaces, which selects aggregation nodes through layer-sensitive hyperbolic association degrees constrained by hyperbolic Dirichlet energy. Furthermore, DSRL attempts to break the cyber-balkanization of different spaces, utilizing cross-space attention to facilitate information interactions between Euclidean and hyperbolic space to capture better discriminative features for final violence detection. Comprehensive experiments demonstrate the effectiveness of our proposed DSRL.

Neuroscience, Cognitive Science

Yufei Guo, Weihang Peng, Xiaode Liu, Yuanpei Chen, Yuhan Zhang, Xin Tong, Zhou Jie, Zhe Ma

Spiking neural networks (SNNs) have gained more and more interest as one of the energy-efficient alternatives of conventional artificial neural networks (ANNs). They exchange 0/1 spikes for processing information, thus most of the multiplications in networks can be replaced by additions. However, binary spike feature maps will limit the expressiveness of the SNN and result in unsatisfactory performance compared with ANNs. It is shown that a rich output feature representation, i.e., the feature vector before classifier) is beneficial to training an accurate model in ANNs for classification. We wonder if it also does for SNNs and how to improve the feature representation of the SNN.To this end, we materialize this idea in two special designed methods for SNNs.First, inspired by some ANN-SNN methods that directly copy-paste the weight parameters from trained ANN with light modification to homogeneous SNN can obtain a well-performed SNN, we use rich information of the weight parameters from the trained ANN counterpart to guide the feature representation learning of the SNN. In particular, we present the SNN's and ANN's feature representation from the same input to ANN's classifier to product SNN's and ANN's outputs respectively and then align the feature with the KL-divergence loss as in knowledge distillation methods, called L_ AF loss.It can be seen as a novel and effective knowledge distillation method specially designed for the SNN that comes from both the knowledge distillation and ANN-SNN methods. Various ablation study shows that the L_AF loss is more powerful than the vanilla knowledge distillation method.Second, we replace the last Leaky Integrate-and-Fire (LIF) activation layer as the ReLU activation layer to generate the output feature, thus a more powerful SNN with full-precision feature representation can be achieved but with only a little extra computation.Experimental results show that our method consistently outperforms the current state-of-the-art algorithms on both popular non-spiking static and neuromorphic datasets. We provide an extremely simple but effective way to train high-accuracy spiking neural networks.

Neuroscience, Cognitive Science

Matthias Tangemann, Matthias Kümmerer, Matthias Bethge

Humans excel at detecting and segmenting moving objects according to the {\it Gestalt} principle of “common fate”. Remarkably, previous works have shown that human perception generalizes this principle in a zero-shot fashion to unseen textures or random dots. In this work, we seek to better understand the computational basis for this capability by evaluating a broad range of optical flow models and a neuroscience inspired motion energy model for zero-shot figure-ground segmentation of random dot stimuli. Specifically, we use the extensively validated motion energy model proposed by Simoncelli and Heeger in 1998 which is fitted to neural recordings in cortex area MT. We find that a cross section of 40 deep optical flow models trained on different datasets struggle to estimate motion patterns in random dot videos, resulting in poor figure-ground segmentation performance. Conversely, the neuroscience-inspired model significantly outperforms all optical flow models on this task. For a direct comparison to human perception, we conduct a psychophysical study using a shape identification task as a proxy to measure human segmentation performance. All state-of-the-art optical flow models fall short of human performance, but only the motion energy model matches human capability. This neuroscience-inspired model successfully addresses the lack of human-like zero-shot generalization to random dot stimuli in current computer vision models, and thus establishes a compelling link between the Gestalt psychology of human object perception and cortical motion processing in the brain.Code, models and datasets are available at https://github.com/mtangemann/motion_energy_segmentation

Computer Vision

Chau Tran, Duy M. H. Nguyen, Manh-Duy Nguyen, TrungTin Nguyen, Ngan Le, Pengtao Xie, Daniel Sonntag, James Zou, Binh Nguyen, Mathias Niepert

Increasing the throughput of the Transformer architecture, a foundational component used in numerous state-of-the-art models for vision and language tasks (e.g., GPT, LLaVa), is an important problem in machine learning. One recent and effective strategy is to merge token representations within Transformer models, aiming to reduce computational and memory requirements while maintaining accuracy. Prior work has proposed algorithms based on Bipartite Soft Matching (BSM), which divides tokens into distinct sets and merges the top $k$ similar tokens. However, these methods have significant drawbacks, such as sensitivity to token-splitting strategies and damage to informative tokens in later layers. This paper presents a novel paradigm called PiToMe, which prioritizes the preservation of informative tokens using an additional metric termed the \textit{energy score}. This score identifies large clusters of similar tokens as high-energy, indicating potential candidates for merging, while smaller (unique and isolated) clusters are considered as low-energy and preserved. Experimental findings demonstrate that PiToMe saved from 40-60\% FLOPs of the base models while exhibiting superior off-the-shelf performance on image classification (0.5\% average performance drop of ViT-MAEH compared to 2.6\% as baselines), image-text retrieval (0.3\% average performance drop of Clip on Flick30k compared to 4.5\% as others), and analogously in visual questions answering with LLaVa-7B. Furthermore, PiToMe is theoretically shown to preserve intrinsic spectral properties to the original token space under mild conditions.

Multimodal Models

Mingrui Wu, Xinyue Cai, Jiayi Ji, Jiale Li, Oucheng Huang, Gen Luo, Hao Fei, GUANNAN JIANG, Xiaoshuai Sun, Rongrong Ji

In this work, we propose a training-free method to inject visual prompts into Multimodal Large Language Models (MLLMs) through learnable latent variable optimization. We observe that attention, as the core module of MLLMs, connects text prompt tokens and visual tokens, ultimately determining the final results. Our approach involves adjusting visual tokens from the MLP output during inference, controlling the attention response to ensure text prompt tokens attend to visual tokens in referring regions. We optimize a learnable latent variable based on an energy function, enhancing the strength of referring regions in the attention map. This enables detailed region description and reasoning without the need for substantial training costs or model retraining. Our method offers a promising direction for integrating referring abilities into MLLMs, and supports referring with box, mask, scribble and point. The results demonstrate that our method exhibits out-of-domain generalization and interpretability.

Generative Models

Alexander Kolesov, Petr Mokrov, Igor Udovichenko, Milena Gazdieva, Gudmund Pammer, Anastasis Kratsios, Evgeny Burnaev, Aleksandr Korotin

Optimal transport (OT) barycenters are a mathematically grounded way of averaging probability distributions while capturing their geometric properties. In short, the barycenter task is to take the average of a collection of probability distributions w.r.t. given OT discrepancies. We propose a novel algorithm for approximating the continuous Entropic OT (EOT) barycenter for arbitrary OT cost functions. Our approach is built upon the dual reformulation of the EOT problem based on weak OT, which has recently gained the attention of the ML community. Beyond its novelty, our method enjoys several advantageous properties: (i) we establish quality bounds for the recovered solution; (ii) this approach seamlessly interconnects with the Energy-Based Models (EBMs) learning procedure enabling the use of well-tuned algorithms for the problem of interest; (iii) it provides an intuitive optimization scheme avoiding min-max, reinforce and other intricate technical tricks. For validation, we consider several low-dimensional scenarios and image-space setups, including *non-Euclidean* cost functions. Furthermore, we investigate the practical task of learning the barycenter on an image manifold generated by a pretrained generative model, opening up new directions for real-world applications. Our code is available at https://github.com/justkolesov/EnergyGuidedBarycenters.

Generative Models

Peter Holderrieth, Yilun Xu, Tommi Jaakkola

Classical Hamiltonian mechanics has been widely used in machine learning in the form of Hamiltonian Monte Carlo for applications with predetermined force fields. In this paper, we explore the potential of deliberately designing force fields for Hamiltonian systems, introducing Hamiltonian velocity predictors (HVPs) as a core tool for constructing energy-based and generative models. We present two innovations: Hamiltonian Score Matching (HSM), which utilizes score functions to augment data by simulating Hamiltonian trajectories, and Hamiltonian Generative Flows (HGFs), a novel generative model that encompasses diffusion models and OT-flow matching as HGFs with zero force fields. We showcase the extended design space of force fields by introducing Oscillation HGFs, a generative model inspired by harmonic oscillators. Our experiments demonstrate that HSM and HGFs rival leading score-matching and generative modeling techniques. Overall, our work systematically elucidates the synergy between Hamiltonian dynamics, force fields, and generative models, thereby opening new avenues for applications of machine learning in physical sciences and dynamical systems.

Optimization · Large Scale, Parallel and Distributed

Shima Adeli, Mojtaba Tefagh, Gourav Jhanwar, Masoud Zarepisheh

Radiation therapy, treating over half of all cancer patients, involves using specialized machines to direct high-energy beams at tumors, aiming to damage cancer cells while minimizing harm to nearby healthy tissues. Customizing the shape and intensity of radiation beams for each patient leads to solving large-scale constrained optimization problems that need to be solved within tight clinical time-frame. At the core of these challenges is a large matrix that is commonly sparsified for computational efficiency by neglecting small elements. Such a crude approximation can degrade the quality of treatment, potentially causing unnecessary radiation exposure to healthy tissues—this may lead to significant radiation-induced side effects—or delivering inadequate radiation to the tumor, which is crucial for effective tumor treatment. In this work, we demonstrate, for the first time, that randomized sketch tools can effectively sparsify this matrix without sacrificing treatment quality. We also develop a novel randomized sketch method with desirable theoretical guarantees that outperforms existing techniques in practical application. Beyond developing a novel randomized sketch method, this work emphasizes the potential of harnessing scientific computing tools, crucial in today's big data analysis, to tackle computationally intensive challenges in healthcare. The application of these tools could have a profound impact on the lives of numerous cancer patients. Code and sample data available at https://github.com/PortPy-Project/CompressRTP

Neuroscience, Cognitive Science

Zecheng Hao, Xinyu Shi, Yujia Liu, Zhaofei Yu, Tiejun Huang

Compared to traditional Artificial Neural Network (ANN), Spiking Neural Network (SNN) has garnered widespread academic interest for its intrinsic ability to transmit information in a more energy-efficient manner. However, despite previous efforts to optimize the learning algorithm of SNNs through various methods, SNNs still lag behind ANNs in terms of performance. The recently proposed multi-threshold model provides more possibilities for further enhancing the learning capability of SNNs. In this paper, we rigorously analyze the relationship among the multi-threshold model, vanilla spiking model and quantized ANNs from a mathematical perspective, then propose a novel LM-HT model, which is an equidistant multi-threshold model that can dynamically regulate the global input current and membrane potential leakage on the time dimension. The LM-HT model can also be transformed into a vanilla single threshold model through reparameterization, thereby achieving more flexible hardware deployment. In addition, we note that the LM-HT model can seamlessly integrate with ANN-SNN Conversion framework under special initialization. This novel hybrid learning framework can effectively improve the relatively poor performance of converted SNNs under low time latency. Extensive experimental results have demonstrated that our model can outperform previous state-of-the-art works on various types of datasets, which promote SNNs to achieve a brand-new level of performance comparable to quantized ANNs. Code is available at https://github.com/hzc1208/LMHT_SNN.