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Mar 14

Scattering Vision Transformer: Spectral Mixing Matters

Vision transformers have gained significant attention and achieved state-of-the-art performance in various computer vision tasks, including image classification, instance segmentation, and object detection. However, challenges remain in addressing attention complexity and effectively capturing fine-grained information within images. Existing solutions often resort to down-sampling operations, such as pooling, to reduce computational cost. Unfortunately, such operations are non-invertible and can result in information loss. In this paper, we present a novel approach called Scattering Vision Transformer (SVT) to tackle these challenges. SVT incorporates a spectrally scattering network that enables the capture of intricate image details. SVT overcomes the invertibility issue associated with down-sampling operations by separating low-frequency and high-frequency components. Furthermore, SVT introduces a unique spectral gating network utilizing Einstein multiplication for token and channel mixing, effectively reducing complexity. We show that SVT achieves state-of-the-art performance on the ImageNet dataset with a significant reduction in a number of parameters and FLOPS. SVT shows 2\% improvement over LiTv2 and iFormer. SVT-H-S reaches 84.2\% top-1 accuracy, while SVT-H-B reaches 85.2\% (state-of-art for base versions) and SVT-H-L reaches 85.7\% (again state-of-art for large versions). SVT also shows comparable results in other vision tasks such as instance segmentation. SVT also outperforms other transformers in transfer learning on standard datasets such as CIFAR10, CIFAR100, Oxford Flower, and Stanford Car datasets. The project page is available on this webpage.https://badripatro.github.io/svt/.

Diffusion Probabilistic Model Made Slim

Despite the recent visually-pleasing results achieved, the massive computational cost has been a long-standing flaw for diffusion probabilistic models (DPMs), which, in turn, greatly limits their applications on resource-limited platforms. Prior methods towards efficient DPM, however, have largely focused on accelerating the testing yet overlooked their huge complexity and sizes. In this paper, we make a dedicated attempt to lighten DPM while striving to preserve its favourable performance. We start by training a small-sized latent diffusion model (LDM) from scratch, but observe a significant fidelity drop in the synthetic images. Through a thorough assessment, we find that DPM is intrinsically biased against high-frequency generation, and learns to recover different frequency components at different time-steps. These properties make compact networks unable to represent frequency dynamics with accurate high-frequency estimation. Towards this end, we introduce a customized design for slim DPM, which we term as Spectral Diffusion (SD), for light-weight image synthesis. SD incorporates wavelet gating in its architecture to enable frequency dynamic feature extraction at every reverse steps, and conducts spectrum-aware distillation to promote high-frequency recovery by inverse weighting the objective based on spectrum magni tudes. Experimental results demonstrate that, SD achieves 8-18x computational complexity reduction as compared to the latent diffusion models on a series of conditional and unconditional image generation tasks while retaining competitive image fidelity.

ViG: Linear-complexity Visual Sequence Learning with Gated Linear Attention

Recently, linear complexity sequence modeling networks have achieved modeling capabilities similar to Vision Transformers on a variety of computer vision tasks, while using fewer FLOPs and less memory. However, their advantage in terms of actual runtime speed is not significant. To address this issue, we introduce Gated Linear Attention (GLA) for vision, leveraging its superior hardware-awareness and efficiency. We propose direction-wise gating to capture 1D global context through bidirectional modeling and a 2D gating locality injection to adaptively inject 2D local details into 1D global context. Our hardware-aware implementation further merges forward and backward scanning into a single kernel, enhancing parallelism and reducing memory cost and latency. The proposed model, ViG, offers a favorable trade-off in accuracy, parameters, and FLOPs on ImageNet and downstream tasks, outperforming popular Transformer and CNN-based models. Notably, ViG-S matches DeiT-B's accuracy while using only 27% of the parameters and 20% of the FLOPs, running 2times faster on 224times224 images. At 1024times1024 resolution, ViG-T uses 5.2times fewer FLOPs, saves 90% GPU memory, runs 4.8times faster, and achieves 20.7% higher top-1 accuracy than DeiT-T. These results position ViG as an efficient and scalable solution for visual representation learning. Code is available at https://github.com/hustvl/ViG.

Jointly-Learned Exit and Inference for a Dynamic Neural Network : JEI-DNN

Large pretrained models, coupled with fine-tuning, are slowly becoming established as the dominant architecture in machine learning. Even though these models offer impressive performance, their practical application is often limited by the prohibitive amount of resources required for every inference. Early-exiting dynamic neural networks (EDNN) circumvent this issue by allowing a model to make some of its predictions from intermediate layers (i.e., early-exit). Training an EDNN architecture is challenging as it consists of two intertwined components: the gating mechanism (GM) that controls early-exiting decisions and the intermediate inference modules (IMs) that perform inference from intermediate representations. As a result, most existing approaches rely on thresholding confidence metrics for the gating mechanism and strive to improve the underlying backbone network and the inference modules. Although successful, this approach has two fundamental shortcomings: 1) the GMs and the IMs are decoupled during training, leading to a train-test mismatch; and 2) the thresholding gating mechanism introduces a positive bias into the predictive probabilities, making it difficult to readily extract uncertainty information. We propose a novel architecture that connects these two modules. This leads to significant performance improvements on classification datasets and enables better uncertainty characterization capabilities.

SpectralGPT: Spectral Foundation Model

The foundation model has recently garnered significant attention due to its potential to revolutionize the field of visual representation learning in a self-supervised manner. While most foundation models are tailored to effectively process RGB images for various visual tasks, there is a noticeable gap in research focused on spectral data, which offers valuable information for scene understanding, especially in remote sensing (RS) applications. To fill this gap, we created for the first time a universal RS foundation model, named SpectralGPT, which is purpose-built to handle spectral RS images using a novel 3D generative pretrained transformer (GPT). Compared to existing foundation models, SpectralGPT 1) accommodates input images with varying sizes, resolutions, time series, and regions in a progressive training fashion, enabling full utilization of extensive RS big data; 2) leverages 3D token generation for spatial-spectral coupling; 3) captures spectrally sequential patterns via multi-target reconstruction; 4) trains on one million spectral RS images, yielding models with over 600 million parameters. Our evaluation highlights significant performance improvements with pretrained SpectralGPT models, signifying substantial potential in advancing spectral RS big data applications within the field of geoscience across four downstream tasks: single/multi-label scene classification, semantic segmentation, and change detection.

Gated Linear Attention Transformers with Hardware-Efficient Training

Transformers with linear attention allow for efficient parallel training but can simultaneously be formulated as an RNN with 2D (matrix-valued) hidden states, thus enjoying linear (with respect to output length) inference complexity. Recent works such as RetNet (Sun et al., 2023) and TransNormerLLM (Qin et al., 2023a) observe that adding a global decay term to the additive RNN update rule greatly improves performance, sometimes outperforming standard Transformers with softmax attention when trained at scale. In this work we show that adding a data-dependent gating mechanism further improves performance. We derive a parallel form of this gated linear attention layer that enables efficient training. However, a straightforward, numerically stable implementation of this parallel form requires generalized matrix multiplications in log-space for numerical stability, and thus cannot take advantage of tensor cores on modern GPUs which are optimized for standard matrix multiplications. We develop a hardware-efficient version of the parallel form that can still make use of tensor cores through block-parallel computations over sequence chunks. Experiments on moderate-scale language modeling (340M-parameter models trained on 15B tokens, 1.3B-parameter models trained on 100B tokens) show that gated linear attention (GLA) Transformers perform competitively against a strong LLaMA-architecture Transformer baseline (Touvron et al., 2023) as well as Mamba (Gu & Dao, 2023), a recently introduced state-space model with a data-dependent state transition mechanism. For training speed, our Triton-based implementation performs comparably to CUDA-optimized FlashAttention-2 (Dao, 2023) under the regular 2048 training length setting, while outperforming FlashAttention-2 when training on longer sequences beyond 4096.

Solving High-Dimensional PDEs with Latent Spectral Models

Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored the multiscale architectures and various operator designs, they are limited to learning the operators as a whole in the coordinate space. In real physical science problems, PDEs are complex coupled equations with numerical solvers relying on discretization into high-dimensional coordinate space, which cannot be precisely approximated by a single operator nor efficiently learned due to the curse of dimensionality. We present Latent Spectral Models (LSM) toward an efficient and precise solver for high-dimensional PDEs. Going beyond the coordinate space, LSM enables an attention-based hierarchical projection network to reduce the high-dimensional data into a compact latent space in linear time. Inspired by classical spectral methods in numerical analysis, we design a neural spectral block to solve PDEs in the latent space that approximates complex input-output mappings via learning multiple basis operators, enjoying nice theoretical guarantees for convergence and approximation. Experimentally, LSM achieves consistent state-of-the-art and yields a relative gain of 11.5% averaged on seven benchmarks covering both solid and fluid physics. Code is available at https://github.com/thuml/Latent-Spectral-Models.

Is Temperature Sample Efficient for Softmax Gaussian Mixture of Experts?

Dense-to-sparse gating mixture of experts (MoE) has recently become an effective alternative to a well-known sparse MoE. Rather than fixing the number of activated experts as in the latter model, which could limit the investigation of potential experts, the former model utilizes the temperature to control the softmax weight distribution and the sparsity of the MoE during training in order to stabilize the expert specialization. Nevertheless, while there are previous attempts to theoretically comprehend the sparse MoE, a comprehensive analysis of the dense-to-sparse gating MoE has remained elusive. Therefore, we aim to explore the impacts of the dense-to-sparse gate on the maximum likelihood estimation under the Gaussian MoE in this paper. We demonstrate that due to interactions between the temperature and other model parameters via some partial differential equations, the convergence rates of parameter estimations are slower than any polynomial rates, and could be as slow as O(1/log(n)), where n denotes the sample size. To address this issue, we propose using a novel activation dense-to-sparse gate, which routes the output of a linear layer to an activation function before delivering them to the softmax function. By imposing linearly independence conditions on the activation function and its derivatives, we show that the parameter estimation rates are significantly improved to polynomial rates.

Dynamic Spectrum Mixer for Visual Recognition

Recently, MLP-based vision backbones have achieved promising performance in several visual recognition tasks. However, the existing MLP-based methods directly aggregate tokens with static weights, leaving the adaptability to different images untouched. Moreover, Recent research demonstrates that MLP-Transformer is great at creating long-range dependencies but ineffective at catching high frequencies that primarily transmit local information, which prevents it from applying to the downstream dense prediction tasks, such as semantic segmentation. To address these challenges, we propose a content-adaptive yet computationally efficient structure, dubbed Dynamic Spectrum Mixer (DSM). The DSM represents token interactions in the frequency domain by employing the Discrete Cosine Transform, which can learn long-term spatial dependencies with log-linear complexity. Furthermore, a dynamic spectrum weight generation layer is proposed as the spectrum bands selector, which could emphasize the informative frequency bands while diminishing others. To this end, the technique can efficiently learn detailed features from visual input that contains both high- and low-frequency information. Extensive experiments show that DSM is a powerful and adaptable backbone for a range of visual recognition tasks. Particularly, DSM outperforms previous transformer-based and MLP-based models, on image classification, object detection, and semantic segmentation tasks, such as 83.8 \% top-1 accuracy on ImageNet, and 49.9 \% mIoU on ADE20K.

Spatial-frequency channels, shape bias, and adversarial robustness

What spatial frequency information do humans and neural networks use to recognize objects? In neuroscience, critical band masking is an established tool that can reveal the frequency-selective filters used for object recognition. Critical band masking measures the sensitivity of recognition performance to noise added at each spatial frequency. Existing critical band masking studies show that humans recognize periodic patterns (gratings) and letters by means of a spatial-frequency filter (or "channel'') that has a frequency bandwidth of one octave (doubling of frequency). Here, we introduce critical band masking as a task for network-human comparison and test 14 humans and 76 neural networks on 16-way ImageNet categorization in the presence of narrowband noise. We find that humans recognize objects in natural images using the same one-octave-wide channel that they use for letters and gratings, making it a canonical feature of human object recognition. On the other hand, the neural network channel, across various architectures and training strategies, is 2-4 times as wide as the human channel. In other words, networks are vulnerable to high and low frequency noise that does not affect human performance. Adversarial and augmented-image training are commonly used to increase network robustness and shape bias. Does this training align network and human object recognition channels? Three network channel properties (bandwidth, center frequency, peak noise sensitivity) correlate strongly with shape bias (53% variance explained) and with robustness of adversarially-trained networks (74% variance explained). Adversarial training increases robustness but expands the channel bandwidth even further away from the human bandwidth. Thus, critical band masking reveals that the network channel is more than twice as wide as the human channel, and that adversarial training only increases this difference.

Robustifying State-space Models for Long Sequences via Approximate Diagonalization

State-space models (SSMs) have recently emerged as a framework for learning long-range sequence tasks. An example is the structured state-space sequence (S4) layer, which uses the diagonal-plus-low-rank structure of the HiPPO initialization framework. However, the complicated structure of the S4 layer poses challenges; and, in an effort to address these challenges, models such as S4D and S5 have considered a purely diagonal structure. This choice simplifies the implementation, improves computational efficiency, and allows channel communication. However, diagonalizing the HiPPO framework is itself an ill-posed problem. In this paper, we propose a general solution for this and related ill-posed diagonalization problems in machine learning. We introduce a generic, backward-stable "perturb-then-diagonalize" (PTD) methodology, which is based on the pseudospectral theory of non-normal operators, and which may be interpreted as the approximate diagonalization of the non-normal matrices defining SSMs. Based on this, we introduce the S4-PTD and S5-PTD models. Through theoretical analysis of the transfer functions of different initialization schemes, we demonstrate that the S4-PTD/S5-PTD initialization strongly converges to the HiPPO framework, while the S4D/S5 initialization only achieves weak convergences. As a result, our new models show resilience to Fourier-mode noise-perturbed inputs, a crucial property not achieved by the S4D/S5 models. In addition to improved robustness, our S5-PTD model averages 87.6% accuracy on the Long-Range Arena benchmark, demonstrating that the PTD methodology helps to improve the accuracy of deep learning models.

Rayleigh Quotient Graph Neural Networks for Graph-level Anomaly Detection

Graph-level anomaly detection has gained significant attention as it finds applications in various domains, such as cancer diagnosis and enzyme prediction. However, existing methods fail to capture the spectral properties of graph anomalies, resulting in unexplainable framework design and unsatisfying performance. In this paper, we re-investigate the spectral differences between anomalous and normal graphs. Our main observation shows a significant disparity in the accumulated spectral energy between these two classes. Moreover, we prove that the accumulated spectral energy of the graph signal can be represented by its Rayleigh Quotient, indicating that the Rayleigh Quotient is a driving factor behind the anomalous properties of graphs. Motivated by this, we propose Rayleigh Quotient Graph Neural Network (RQGNN), the first spectral GNN that explores the inherent spectral features of anomalous graphs for graph-level anomaly detection. Specifically, we introduce a novel framework with two components: the Rayleigh Quotient learning component (RQL) and Chebyshev Wavelet GNN with RQ-pooling (CWGNN-RQ). RQL explicitly captures the Rayleigh Quotient of graphs and CWGNN-RQ implicitly explores the spectral space of graphs. Extensive experiments on 10 real-world datasets show that RQGNN outperforms the best rival by 6.74% in Macro-F1 score and 1.44% in AUC, demonstrating the effectiveness of our framework. Our code is available at https://github.com/xydong127/RQGNN.

SpectFormer: Frequency and Attention is what you need in a Vision Transformer

Vision transformers have been applied successfully for image recognition tasks. There have been either multi-headed self-attention based (ViT dosovitskiy2020image, DeIT, touvron2021training) similar to the original work in textual models or more recently based on spectral layers (Fnetlee2021fnet, GFNetrao2021global, AFNOguibas2021efficient). We hypothesize that both spectral and multi-headed attention plays a major role. We investigate this hypothesis through this work and observe that indeed combining spectral and multi-headed attention layers provides a better transformer architecture. We thus propose the novel Spectformer architecture for transformers that combines spectral and multi-headed attention layers. We believe that the resulting representation allows the transformer to capture the feature representation appropriately and it yields improved performance over other transformer representations. For instance, it improves the top-1 accuracy by 2\% on ImageNet compared to both GFNet-H and LiT. SpectFormer-S reaches 84.25\% top-1 accuracy on ImageNet-1K (state of the art for small version). Further, Spectformer-L achieves 85.7\% that is the state of the art for the comparable base version of the transformers. We further ensure that we obtain reasonable results in other scenarios such as transfer learning on standard datasets such as CIFAR-10, CIFAR-100, Oxford-IIIT-flower, and Standford Car datasets. We then investigate its use in downstream tasks such of object detection and instance segmentation on the MS-COCO dataset and observe that Spectformer shows consistent performance that is comparable to the best backbones and can be further optimized and improved. Hence, we believe that combined spectral and attention layers are what are needed for vision transformers.

Statistical Perspective of Top-K Sparse Softmax Gating Mixture of Experts

Top-K sparse softmax gating mixture of experts has been widely used for scaling up massive deep-learning architectures without increasing the computational cost. Despite its popularity in real-world applications, the theoretical understanding of that gating function has remained an open problem. The main challenge comes from the structure of the top-K sparse softmax gating function, which partitions the input space into multiple regions with distinct behaviors. By focusing on a Gaussian mixture of experts, we establish theoretical results on the effects of the top-K sparse softmax gating function on both density and parameter estimations. Our results hinge upon defining novel loss functions among parameters to capture different behaviors of the input regions. When the true number of experts k_{ast} is known, we demonstrate that the convergence rates of density and parameter estimations are both parametric on the sample size. However, when k_{ast} becomes unknown and the true model is over-specified by a Gaussian mixture of k experts where k > k_{ast}, our findings suggest that the number of experts selected from the top-K sparse softmax gating function must exceed the total cardinality of a certain number of Voronoi cells associated with the true parameters to guarantee the convergence of the density estimation. Moreover, while the density estimation rate remains parametric under this setting, the parameter estimation rates become substantially slow due to an intrinsic interaction between the softmax gating and expert functions.

Outliers with Opposing Signals Have an Outsized Effect on Neural Network Optimization

We identify a new phenomenon in neural network optimization which arises from the interaction of depth and a particular heavy-tailed structure in natural data. Our result offers intuitive explanations for several previously reported observations about network training dynamics. In particular, it implies a conceptually new cause for progressive sharpening and the edge of stability; we also highlight connections to other concepts in optimization and generalization including grokking, simplicity bias, and Sharpness-Aware Minimization. Experimentally, we demonstrate the significant influence of paired groups of outliers in the training data with strong opposing signals: consistent, large magnitude features which dominate the network output throughout training and provide gradients which point in opposite directions. Due to these outliers, early optimization enters a narrow valley which carefully balances the opposing groups; subsequent sharpening causes their loss to rise rapidly, oscillating between high on one group and then the other, until the overall loss spikes. We describe how to identify these groups, explore what sets them apart, and carefully study their effect on the network's optimization and behavior. We complement these experiments with a mechanistic explanation on a toy example of opposing signals and a theoretical analysis of a two-layer linear network on a simple model. Our finding enables new qualitative predictions of training behavior which we confirm experimentally. It also provides a new lens through which to study and improve modern training practices for stochastic optimization, which we highlight via a case study of Adam versus SGD.

How do neurons operate on sparse distributed representations? A mathematical theory of sparsity, neurons and active dendrites

We propose a formal mathematical model for sparse representations and active dendrites in neocortex. Our model is inspired by recent experimental findings on active dendritic processing and NMDA spikes in pyramidal neurons. These experimental and modeling studies suggest that the basic unit of pattern memory in the neocortex is instantiated by small clusters of synapses operated on by localized non-linear dendritic processes. We derive a number of scaling laws that characterize the accuracy of such dendrites in detecting activation patterns in a neuronal population under adverse conditions. We introduce the union property which shows that synapses for multiple patterns can be randomly mixed together within a segment and still lead to highly accurate recognition. We describe simulation results that provide further insight into sparse representations as well as two primary results. First we show that pattern recognition by a neuron with active dendrites can be extremely accurate and robust with high dimensional sparse inputs even when using a tiny number of synapses to recognize large patterns. Second, equations representing recognition accuracy of a dendrite predict optimal NMDA spiking thresholds under a generous set of assumptions. The prediction tightly matches NMDA spiking thresholds measured in the literature. Our model matches many of the known properties of pyramidal neurons. As such the theory provides a mathematical framework for understanding the benefits and limits of sparse representations in cortical networks.

Exemplar-free Continual Learning of Vision Transformers via Gated Class-Attention and Cascaded Feature Drift Compensation

We propose a new method for exemplar-free class incremental training of ViTs. The main challenge of exemplar-free continual learning is maintaining plasticity of the learner without causing catastrophic forgetting of previously learned tasks. This is often achieved via exemplar replay which can help recalibrate previous task classifiers to the feature drift which occurs when learning new tasks. Exemplar replay, however, comes at the cost of retaining samples from previous tasks which for many applications may not be possible. To address the problem of continual ViT training, we first propose gated class-attention to minimize the drift in the final ViT transformer block. This mask-based gating is applied to class-attention mechanism of the last transformer block and strongly regulates the weights crucial for previous tasks. Importantly, gated class-attention does not require the task-ID during inference, which distinguishes it from other parameter isolation methods. Secondly, we propose a new method of feature drift compensation that accommodates feature drift in the backbone when learning new tasks. The combination of gated class-attention and cascaded feature drift compensation allows for plasticity towards new tasks while limiting forgetting of previous ones. Extensive experiments performed on CIFAR-100, Tiny-ImageNet and ImageNet100 demonstrate that our exemplar-free method obtains competitive results when compared to rehearsal based ViT methods.

PGN: The RNN's New Successor is Effective for Long-Range Time Series Forecasting

Due to the recurrent structure of RNN, the long information propagation path poses limitations in capturing long-term dependencies, gradient explosion/vanishing issues, and inefficient sequential execution. Based on this, we propose a novel paradigm called Parallel Gated Network (PGN) as the new successor to RNN. PGN directly captures information from previous time steps through the designed Historical Information Extraction (HIE) layer and leverages gated mechanisms to select and fuse it with the current time step information. This reduces the information propagation path to O(1), effectively addressing the limitations of RNN. To enhance PGN's performance in long-range time series forecasting tasks, we propose a novel temporal modeling framework called Temporal PGN (TPGN). TPGN incorporates two branches to comprehensively capture the semantic information of time series. One branch utilizes PGN to capture long-term periodic patterns while preserving their local characteristics. The other branch employs patches to capture short-term information and aggregate the global representation of the series. TPGN achieves a theoretical complexity of O(L), ensuring efficiency in its operations. Experimental results on five benchmark datasets demonstrate the state-of-the-art (SOTA) performance and high efficiency of TPGN, further confirming the effectiveness of PGN as the new successor to RNN in long-range time series forecasting. The code is available in this repository: https://github.com/Water2sea/TPGN.

Fire Together Wire Together: A Dynamic Pruning Approach with Self-Supervised Mask Prediction

Dynamic model pruning is a recent direction that allows for the inference of a different sub-network for each input sample during deployment. However, current dynamic methods rely on learning a continuous channel gating through regularization by inducing sparsity loss. This formulation introduces complexity in balancing different losses (e.g task loss, regularization loss). In addition, regularization based methods lack transparent tradeoff hyperparameter selection to realize a computational budget. Our contribution is two-fold: 1) decoupled task and pruning losses. 2) Simple hyperparameter selection that enables FLOPs reduction estimation before training. Inspired by the Hebbian theory in Neuroscience: "neurons that fire together wire together", we propose to predict a mask to process k filters in a layer based on the activation of its previous layer. We pose the problem as a self-supervised binary classification problem. Each mask predictor module is trained to predict if the log-likelihood for each filter in the current layer belongs to the top-k activated filters. The value k is dynamically estimated for each input based on a novel criterion using the mass of heatmaps. We show experiments on several neural architectures, such as VGG, ResNet and MobileNet on CIFAR and ImageNet datasets. On CIFAR, we reach similar accuracy to SOTA methods with 15% and 24% higher FLOPs reduction. Similarly in ImageNet, we achieve lower drop in accuracy with up to 13% improvement in FLOPs reduction.

Learning Delays in Spiking Neural Networks using Dilated Convolutions with Learnable Spacings

Spiking Neural Networks (SNNs) are a promising research direction for building power-efficient information processing systems, especially for temporal tasks such as speech recognition. In SNNs, delays refer to the time needed for one spike to travel from one neuron to another. These delays matter because they influence the spike arrival times, and it is well-known that spiking neurons respond more strongly to coincident input spikes. More formally, it has been shown theoretically that plastic delays greatly increase the expressivity in SNNs. Yet, efficient algorithms to learn these delays have been lacking. Here, we propose a new discrete-time algorithm that addresses this issue in deep feedforward SNNs using backpropagation, in an offline manner. To simulate delays between consecutive layers, we use 1D convolutions across time. The kernels contain only a few non-zero weights - one per synapse - whose positions correspond to the delays. These positions are learned together with the weights using the recently proposed Dilated Convolution with Learnable Spacings (DCLS). We evaluated our method on three datasets: the Spiking Heidelberg Dataset (SHD), the Spiking Speech Commands (SSC) and its non-spiking version Google Speech Commands v0.02 (GSC) benchmarks, which require detecting temporal patterns. We used feedforward SNNs with two or three hidden fully connected layers, and vanilla leaky integrate-and-fire neurons. We showed that fixed random delays help and that learning them helps even more. Furthermore, our method outperformed the state-of-the-art in the three datasets without using recurrent connections and with substantially fewer parameters. Our work demonstrates the potential of delay learning in developing accurate and precise models for temporal data processing. Our code is based on PyTorch / SpikingJelly and available at: https://github.com/Thvnvtos/SNN-delays

Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEs

Generating realistic time series data is important for many engineering and scientific applications. Existing work tackles this problem using generative adversarial networks (GANs). However, GANs are often unstable during training, and they can suffer from mode collapse. While variational autoencoders (VAEs) are known to be more robust to these issues, they are (surprisingly) less often considered for time series generation. In this work, we introduce Koopman VAE (KVAE), a new generative framework that is based on a novel design for the model prior, and that can be optimized for either regular and irregular training data. Inspired by Koopman theory, we represent the latent conditional prior dynamics using a linear map. Our approach enhances generative modeling with two desired features: (i) incorporating domain knowledge can be achieved by leverageing spectral tools that prescribe constraints on the eigenvalues of the linear map; and (ii) studying the qualitative behavior and stablity of the system can be performed using tools from dynamical systems theory. Our results show that KVAE outperforms state-of-the-art GAN and VAE methods across several challenging synthetic and real-world time series generation benchmarks. Whether trained on regular or irregular data, KVAE generates time series that improve both discriminative and predictive metrics. We also present visual evidence suggesting that KVAE learns probability density functions that better approximate empirical ground truth distributions.

The Principles of Deep Learning Theory

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

FPGA: Fast Patch-Free Global Learning Framework for Fully End-to-End Hyperspectral Image Classification

Deep learning techniques have provided significant improvements in hyperspectral image (HSI) classification. The current deep learning based HSI classifiers follow a patch-based learning framework by dividing the image into overlapping patches. As such, these methods are local learning methods, which have a high computational cost. In this paper, a fast patch-free global learning (FPGA) framework is proposed for HSI classification. In FPGA, an encoder-decoder based FCN is utilized to consider the global spatial information by processing the whole image, which results in fast inference. However, it is difficult to directly utilize the encoder-decoder based FCN for HSI classification as it always fails to converge due to the insufficiently diverse gradients caused by the limited training samples. To solve the divergence problem and maintain the abilities of FCN of fast inference and global spatial information mining, a global stochastic stratified sampling strategy is first proposed by transforming all the training samples into a stochastic sequence of stratified samples. This strategy can obtain diverse gradients to guarantee the convergence of the FCN in the FPGA framework. For a better design of FCN architecture, FreeNet, which is a fully end-to-end network for HSI classification, is proposed to maximize the exploitation of the global spatial information and boost the performance via a spectral attention based encoder and a lightweight decoder. A lateral connection module is also designed to connect the encoder and decoder, fusing the spatial details in the encoder and the semantic features in the decoder. The experimental results obtained using three public benchmark datasets suggest that the FPGA framework is superior to the patch-based framework in both speed and accuracy for HSI classification. Code has been made available at: https://github.com/Z-Zheng/FreeNet.

SpectralEarth: Training Hyperspectral Foundation Models at Scale

Foundation models have triggered a paradigm shift in computer vision and are increasingly being adopted in remote sensing, particularly for multispectral imagery. Yet, their potential in hyperspectral imaging (HSI) remains untapped due to the absence of comprehensive and globally representative hyperspectral datasets. To close this gap, we introduce SpectralEarth, a large-scale multi-temporal dataset designed to pretrain hyperspectral foundation models leveraging data from the Environmental Mapping and Analysis Program (EnMAP). SpectralEarth comprises 538,974 image patches covering 415,153 unique locations from more than 11,636 globally distributed EnMAP scenes spanning two years of archive. Additionally, 17.5% of these locations include multiple timestamps, enabling multi-temporal HSI analysis. Utilizing state-of-the-art self-supervised learning (SSL) algorithms, we pretrain a series of foundation models on SpectralEarth. We integrate a spectral adapter into classical vision backbones to accommodate the unique characteristics of HSI. In tandem, we construct four downstream datasets for land-cover and crop-type mapping, providing benchmarks for model evaluation. Experimental results support the versatility of our models, showcasing their generalizability across different tasks and sensors. We also highlight computational efficiency during model fine-tuning. The dataset, models, and source code will be made publicly available.

ConnNet: A Long-Range Relation-Aware Pixel-Connectivity Network for Salient Segmentation

Salient segmentation aims to segment out attention-grabbing regions, a critical yet challenging task and the foundation of many high-level computer vision applications. It requires semantic-aware grouping of pixels into salient regions and benefits from the utilization of global multi-scale contexts to achieve good local reasoning. Previous works often address it as two-class segmentation problems utilizing complicated multi-step procedures including refinement networks and complex graphical models. We argue that semantic salient segmentation can instead be effectively resolved by reformulating it as a simple yet intuitive pixel-pair based connectivity prediction task. Following the intuition that salient objects can be naturally grouped via semantic-aware connectivity between neighboring pixels, we propose a pure Connectivity Net (ConnNet). ConnNet predicts connectivity probabilities of each pixel with its neighboring pixels by leveraging multi-level cascade contexts embedded in the image and long-range pixel relations. We investigate our approach on two tasks, namely salient object segmentation and salient instance-level segmentation, and illustrate that consistent improvements can be obtained by modeling these tasks as connectivity instead of binary segmentation tasks for a variety of network architectures. We achieve state-of-the-art performance, outperforming or being comparable to existing approaches while reducing inference time due to our less complex approach.

ESSAformer: Efficient Transformer for Hyperspectral Image Super-resolution

Single hyperspectral image super-resolution (single-HSI-SR) aims to restore a high-resolution hyperspectral image from a low-resolution observation. However, the prevailing CNN-based approaches have shown limitations in building long-range dependencies and capturing interaction information between spectral features. This results in inadequate utilization of spectral information and artifacts after upsampling. To address this issue, we propose ESSAformer, an ESSA attention-embedded Transformer network for single-HSI-SR with an iterative refining structure. Specifically, we first introduce a robust and spectral-friendly similarity metric, \ie, the spectral correlation coefficient of the spectrum (SCC), to replace the original attention matrix and incorporates inductive biases into the model to facilitate training. Built upon it, we further utilize the kernelizable attention technique with theoretical support to form a novel efficient SCC-kernel-based self-attention (ESSA) and reduce attention computation to linear complexity. ESSA enlarges the receptive field for features after upsampling without bringing much computation and allows the model to effectively utilize spatial-spectral information from different scales, resulting in the generation of more natural high-resolution images. Without the need for pretraining on large-scale datasets, our experiments demonstrate ESSA's effectiveness in both visual quality and quantitative results.

Learning to Segment from Scribbles using Multi-scale Adversarial Attention Gates

Large, fine-grained image segmentation datasets, annotated at pixel-level, are difficult to obtain, particularly in medical imaging, where annotations also require expert knowledge. Weakly-supervised learning can train models by relying on weaker forms of annotation, such as scribbles. Here, we learn to segment using scribble annotations in an adversarial game. With unpaired segmentation masks, we train a multi-scale GAN to generate realistic segmentation masks at multiple resolutions, while we use scribbles to learn their correct position in the image. Central to the model's success is a novel attention gating mechanism, which we condition with adversarial signals to act as a shape prior, resulting in better object localization at multiple scales. Subject to adversarial conditioning, the segmentor learns attention maps that are semantic, suppress the noisy activations outside the objects, and reduce the vanishing gradient problem in the deeper layers of the segmentor. We evaluated our model on several medical (ACDC, LVSC, CHAOS) and non-medical (PPSS) datasets, and we report performance levels matching those achieved by models trained with fully annotated segmentation masks. We also demonstrate extensions in a variety of settings: semi-supervised learning; combining multiple scribble sources (a crowdsourcing scenario) and multi-task learning (combining scribble and mask supervision). We release expert-made scribble annotations for the ACDC dataset, and the code used for the experiments, at https://vios-s.github.io/multiscale-adversarial-attention-gates

SpikeGPT: Generative Pre-trained Language Model with Spiking Neural Networks

As the size of large language models continue to scale, so does the computational resources required to run it. Spiking Neural Networks (SNNs) have emerged as an energy-efficient approach to deep learning that leverage sparse and event-driven activations to reduce the computational overhead associated with model inference. While they have become competitive with non-spiking models on many computer vision tasks, SNNs have also proven to be more challenging to train. As a result, their performance lags behind modern deep learning, and we are yet to see the effectiveness of SNNs in language generation. In this paper, inspired by the Receptance Weighted Key Value (RWKV) language model, we successfully implement `SpikeGPT', a generative language model with binary, event-driven spiking activation units. We train the proposed model on two model variants: 45M and 216M parameters. To the best of our knowledge, SpikeGPT is the largest backpropagation-trained SNN model to date, rendering it suitable for both the generation and comprehension of natural language. We achieve this by modifying the transformer block to replace multi-head self attention to reduce quadratic computational complexity O(N^2) to linear complexity O(N) with increasing sequence length. Input tokens are instead streamed in sequentially to our attention mechanism (as with typical SNNs). Our preliminary experiments show that SpikeGPT remains competitive with non-spiking models on tested benchmarks, while maintaining 20x fewer operations when processed on neuromorphic hardware that can leverage sparse, event-driven activations. Our code implementation is available at https://github.com/ridgerchu/SpikeGPT.

Unleashing the Potential of Spiking Neural Networks by Dynamic Confidence

This paper presents a new methodology to alleviate the fundamental trade-off between accuracy and latency in spiking neural networks (SNNs). The approach involves decoding confidence information over time from the SNN outputs and using it to develop a decision-making agent that can dynamically determine when to terminate each inference. The proposed method, Dynamic Confidence, provides several significant benefits to SNNs. 1. It can effectively optimize latency dynamically at runtime, setting it apart from many existing low-latency SNN algorithms. Our experiments on CIFAR-10 and ImageNet datasets have demonstrated an average 40% speedup across eight different settings after applying Dynamic Confidence. 2. The decision-making agent in Dynamic Confidence is straightforward to construct and highly robust in parameter space, making it extremely easy to implement. 3. The proposed method enables visualizing the potential of any given SNN, which sets a target for current SNNs to approach. For instance, if an SNN can terminate at the most appropriate time point for each input sample, a ResNet-50 SNN can achieve an accuracy as high as 82.47% on ImageNet within just 4.71 time steps on average. Unlocking the potential of SNNs needs a highly-reliable decision-making agent to be constructed and fed with a high-quality estimation of ground truth. In this regard, Dynamic Confidence represents a meaningful step toward realizing the potential of SNNs.

A Generative Self-Supervised Framework using Functional Connectivity in fMRI Data

Deep neural networks trained on Functional Connectivity (FC) networks extracted from functional Magnetic Resonance Imaging (fMRI) data have gained popularity due to the increasing availability of data and advances in model architectures, including Graph Neural Network (GNN). Recent research on the application of GNN to FC suggests that exploiting the time-varying properties of the FC could significantly improve the accuracy and interpretability of the model prediction. However, the high cost of acquiring high-quality fMRI data and corresponding phenotypic labels poses a hurdle to their application in real-world settings, such that a model na\"ively trained in a supervised fashion can suffer from insufficient performance or a lack of generalization on a small number of data. In addition, most Self-Supervised Learning (SSL) approaches for GNNs to date adopt a contrastive strategy, which tends to lose appropriate semantic information when the graph structure is perturbed or does not leverage both spatial and temporal information simultaneously. In light of these challenges, we propose a generative SSL approach that is tailored to effectively harness spatio-temporal information within dynamic FC. Our empirical results, experimented with large-scale (>50,000) fMRI datasets, demonstrate that our approach learns valuable representations and enables the construction of accurate and robust models when fine-tuned for downstream tasks.

Training for temporal sparsity in deep neural networks, application in video processing

Activation sparsity improves compute efficiency and resource utilization in sparsity-aware neural network accelerators. As the predominant operation in DNNs is multiply-accumulate (MAC) of activations with weights to compute inner products, skipping operations where (at least) one of the two operands is zero can make inference more efficient in terms of latency and power. Spatial sparsification of activations is a popular topic in DNN literature and several methods have already been established to bias a DNN for it. On the other hand, temporal sparsity is an inherent feature of bio-inspired spiking neural networks (SNNs), which neuromorphic processing exploits for hardware efficiency. Introducing and exploiting spatio-temporal sparsity, is a topic much less explored in DNN literature, but in perfect resonance with the trend in DNN, to shift from static signal processing to more streaming signal processing. Towards this goal, in this paper we introduce a new DNN layer (called Delta Activation Layer), whose sole purpose is to promote temporal sparsity of activations during training. A Delta Activation Layer casts temporal sparsity into spatial activation sparsity to be exploited when performing sparse tensor multiplications in hardware. By employing delta inference and ``the usual'' spatial sparsification heuristics during training, the resulting model learns to exploit not only spatial but also temporal activation sparsity (for a given input data distribution). One may use the Delta Activation Layer either during vanilla training or during a refinement phase. We have implemented Delta Activation Layer as an extension of the standard Tensoflow-Keras library, and applied it to train deep neural networks on the Human Action Recognition (UCF101) dataset. We report an almost 3x improvement of activation sparsity, with recoverable loss of model accuracy after longer training.

A Closer Look at Fourier Spectrum Discrepancies for CNN-generated Images Detection

CNN-based generative modelling has evolved to produce synthetic images indistinguishable from real images in the RGB pixel space. Recent works have observed that CNN-generated images share a systematic shortcoming in replicating high frequency Fourier spectrum decay attributes. Furthermore, these works have successfully exploited this systematic shortcoming to detect CNN-generated images reporting up to 99% accuracy across multiple state-of-the-art GAN models. In this work, we investigate the validity of assertions claiming that CNN-generated images are unable to achieve high frequency spectral decay consistency. We meticulously construct a counterexample space of high frequency spectral decay consistent CNN-generated images emerging from our handcrafted experiments using DCGAN, LSGAN, WGAN-GP and StarGAN, where we empirically show that this frequency discrepancy can be avoided by a minor architecture change in the last upsampling operation. We subsequently use images from this counterexample space to successfully bypass the recently proposed forensics detector which leverages on high frequency Fourier spectrum decay attributes for CNN-generated image detection. Through this study, we show that high frequency Fourier spectrum decay discrepancies are not inherent characteristics for existing CNN-based generative models--contrary to the belief of some existing work--, and such features are not robust to perform synthetic image detection. Our results prompt re-thinking of using high frequency Fourier spectrum decay attributes for CNN-generated image detection. Code and models are available at https://keshik6.github.io/Fourier-Discrepancies-CNN-Detection/

Forecasting Trajectory and Behavior of Road-Agents Using Spectral Clustering in Graph-LSTMs

We present a novel approach for traffic forecasting in urban traffic scenarios using a combination of spectral graph analysis and deep learning. We predict both the low-level information (future trajectories) as well as the high-level information (road-agent behavior) from the extracted trajectory of each road-agent. Our formulation represents the proximity between the road agents using a weighted dynamic geometric graph (DGG). We use a two-stream graph-LSTM network to perform traffic forecasting using these weighted DGGs. The first stream predicts the spatial coordinates of road-agents, while the second stream predicts whether a road-agent is going to exhibit overspeeding, underspeeding, or neutral behavior by modeling spatial interactions between road-agents. Additionally, we propose a new regularization algorithm based on spectral clustering to reduce the error margin in long-term prediction (3-5 seconds) and improve the accuracy of the predicted trajectories. Moreover, we prove a theoretical upper bound on the regularized prediction error. We evaluate our approach on the Argoverse, Lyft, Apolloscape, and NGSIM datasets and highlight the benefits over prior trajectory prediction methods. In practice, our approach reduces the average prediction error by approximately 75% over prior algorithms and achieves a weighted average accuracy of 91.2% for behavior prediction. Additionally, our spectral regularization improves long-term prediction by up to 70%.

Coordinate-Aware Modulation for Neural Fields

Neural fields, mapping low-dimensional input coordinates to corresponding signals, have shown promising results in representing various signals. Numerous methodologies have been proposed, and techniques employing MLPs and grid representations have achieved substantial success. MLPs allow compact and high expressibility, yet often suffer from spectral bias and slow convergence speed. On the other hand, methods using grids are free from spectral bias and achieve fast training speed, however, at the expense of high spatial complexity. In this work, we propose a novel way for exploiting both MLPs and grid representations in neural fields. Unlike the prevalent methods that combine them sequentially (extract features from the grids first and feed them to the MLP), we inject spectral bias-free grid representations into the intermediate features in the MLP. More specifically, we suggest a Coordinate-Aware Modulation (CAM), which modulates the intermediate features using scale and shift parameters extracted from the grid representations. This can maintain the strengths of MLPs while mitigating any remaining potential biases, facilitating the rapid learning of high-frequency components. In addition, we empirically found that the feature normalizations, which have not been successful in neural filed literature, proved to be effective when applied in conjunction with the proposed CAM. Experimental results demonstrate that CAM enhances the performance of neural representation and improves learning stability across a range of signals. Especially in the novel view synthesis task, we achieved state-of-the-art performance with the least number of parameters and fast training speed for dynamic scenes and the best performance under 1MB memory for static scenes. CAM also outperforms the best-performing video compression methods using neural fields by a large margin.

Hebbian Learning based Orthogonal Projection for Continual Learning of Spiking Neural Networks

Neuromorphic computing with spiking neural networks is promising for energy-efficient artificial intelligence (AI) applications. However, different from humans who continually learn different tasks in a lifetime, neural network models suffer from catastrophic forgetting. How could neuronal operations solve this problem is an important question for AI and neuroscience. Many previous studies draw inspiration from observed neuroscience phenomena and propose episodic replay or synaptic metaplasticity, but they are not guaranteed to explicitly preserve knowledge for neuron populations. Other works focus on machine learning methods with more mathematical grounding, e.g., orthogonal projection on high dimensional spaces, but there is no neural correspondence for neuromorphic computing. In this work, we develop a new method with neuronal operations based on lateral connections and Hebbian learning, which can protect knowledge by projecting activity traces of neurons into an orthogonal subspace so that synaptic weight update will not interfere with old tasks. We show that Hebbian and anti-Hebbian learning on recurrent lateral connections can effectively extract the principal subspace of neural activities and enable orthogonal projection. This provides new insights into how neural circuits and Hebbian learning can help continual learning, and also how the concept of orthogonal projection can be realized in neuronal systems. Our method is also flexible to utilize arbitrary training methods based on presynaptic activities/traces. Experiments show that our method consistently solves forgetting for spiking neural networks with nearly zero forgetting under various supervised training methods with different error propagation approaches, and outperforms previous approaches under various settings. Our method can pave a solid path for building continual neuromorphic computing systems.

Graph Mamba: Towards Learning on Graphs with State Space Models

Graph Neural Networks (GNNs) have shown promising potential in graph representation learning. The majority of GNNs define a local message-passing mechanism, propagating information over the graph by stacking multiple layers. These methods, however, are known to suffer from two major limitations: over-squashing and poor capturing of long-range dependencies. Recently, Graph Transformers (GTs) emerged as a powerful alternative to Message-Passing Neural Networks (MPNNs). GTs, however, have quadratic computational cost, lack inductive biases on graph structures, and rely on complex Positional/Structural Encodings (SE/PE). In this paper, we show that while Transformers, complex message-passing, and SE/PE are sufficient for good performance in practice, neither is necessary. Motivated by the recent success of State Space Models (SSMs), such as Mamba, we present Graph Mamba Networks (GMNs), a general framework for a new class of GNNs based on selective SSMs. We discuss and categorize the new challenges when adopting SSMs to graph-structured data, and present four required and one optional steps to design GMNs, where we choose (1) Neighborhood Tokenization, (2) Token Ordering, (3) Architecture of Bidirectional Selective SSM Encoder, (4) Local Encoding, and dispensable (5) PE and SE. We further provide theoretical justification for the power of GMNs. Experiments demonstrate that despite much less computational cost, GMNs attain an outstanding performance in long-range, small-scale, large-scale, and heterophilic benchmark datasets.

Towards Deeper Graph Neural Networks

Graph neural networks have shown significant success in the field of graph representation learning. Graph convolutions perform neighborhood aggregation and represent one of the most important graph operations. Nevertheless, one layer of these neighborhood aggregation methods only consider immediate neighbors, and the performance decreases when going deeper to enable larger receptive fields. Several recent studies attribute this performance deterioration to the over-smoothing issue, which states that repeated propagation makes node representations of different classes indistinguishable. In this work, we study this observation systematically and develop new insights towards deeper graph neural networks. First, we provide a systematical analysis on this issue and argue that the key factor compromising the performance significantly is the entanglement of representation transformation and propagation in current graph convolution operations. After decoupling these two operations, deeper graph neural networks can be used to learn graph node representations from larger receptive fields. We further provide a theoretical analysis of the above observation when building very deep models, which can serve as a rigorous and gentle description of the over-smoothing issue. Based on our theoretical and empirical analysis, we propose Deep Adaptive Graph Neural Network (DAGNN) to adaptively incorporate information from large receptive fields. A set of experiments on citation, co-authorship, and co-purchase datasets have confirmed our analysis and insights and demonstrated the superiority of our proposed methods.

Learned Low Precision Graph Neural Networks

Deep Graph Neural Networks (GNNs) show promising performance on a range of graph tasks, yet at present are costly to run and lack many of the optimisations applied to DNNs. We show, for the first time, how to systematically quantise GNNs with minimal or no loss in performance using Network Architecture Search (NAS). We define the possible quantisation search space of GNNs. The proposed novel NAS mechanism, named Low Precision Graph NAS (LPGNAS), constrains both architecture and quantisation choices to be differentiable. LPGNAS learns the optimal architecture coupled with the best quantisation strategy for different components in the GNN automatically using back-propagation in a single search round. On eight different datasets, solving the task of classifying unseen nodes in a graph, LPGNAS generates quantised models with significant reductions in both model and buffer sizes but with similar accuracy to manually designed networks and other NAS results. In particular, on the Pubmed dataset, LPGNAS shows a better size-accuracy Pareto frontier compared to seven other manual and searched baselines, offering a 2.3 times reduction in model size but a 0.4% increase in accuracy when compared to the best NAS competitor. Finally, from our collected quantisation statistics on a wide range of datasets, we suggest a W4A8 (4-bit weights, 8-bit activations) quantisation strategy might be the bottleneck for naive GNN quantisations.

Redesigning Multi-Scale Neural Network for Crowd Counting

Perspective distortions and crowd variations make crowd counting a challenging task in computer vision. To tackle it, many previous works have used multi-scale architecture in deep neural networks (DNNs). Multi-scale branches can be either directly merged (e.g. by concatenation) or merged through the guidance of proxies (e.g. attentions) in the DNNs. Despite their prevalence, these combination methods are not sophisticated enough to deal with the per-pixel performance discrepancy over multi-scale density maps. In this work, we redesign the multi-scale neural network by introducing a hierarchical mixture of density experts, which hierarchically merges multi-scale density maps for crowd counting. Within the hierarchical structure, an expert competition and collaboration scheme is presented to encourage contributions from all scales; pixel-wise soft gating nets are introduced to provide pixel-wise soft weights for scale combinations in different hierarchies. The network is optimized using both the crowd density map and the local counting map, where the latter is obtained by local integration on the former. Optimizing both can be problematic because of their potential conflicts. We introduce a new relative local counting loss based on relative count differences among hard-predicted local regions in an image, which proves to be complementary to the conventional absolute error loss on the density map. Experiments show that our method achieves the state-of-the-art performance on five public datasets, i.e. ShanghaiTech, UCF_CC_50, JHU-CROWD++, NWPU-Crowd and Trancos.

PIGEON: Optimizing CUDA Code Generator for End-to-End Training and Inference of Relational Graph Neural Networks

Relational graph neural networks (RGNNs) are graph neural networks (GNNs) with dedicated structures for modeling the different types of nodes and/or edges in heterogeneous graphs. While RGNNs have been increasingly adopted in many real-world applications due to their versatility and accuracy, they pose performance and system design challenges due to their inherent computation patterns, gap between the programming interface and kernel APIs, and heavy programming efforts in optimizing kernels caused by their coupling with data layout and heterogeneity. To systematically address these challenges, we propose Pigeon, a novel two-level intermediate representation (IR) and its code generator framework, that (a) represents the key properties of the RGNN models to bridge the gap between the programming interface and kernel APIs, (b) decouples model semantics, data layout, and operators-specific optimization from each other to reduce programming efforts, (c) expresses and leverages optimization opportunities in inter-operator transforms, data layout, and operator-specific schedules. By building on one general matrix multiply (GEMM) template and a node/edge traversal template, Pigeon achieves up to 7.8x speed-up in inference and 5.6x speed-up in training compared with the state-of-the-art public systems in select models, i.e., RGCN, RGAT, HGT, when running heterogeneous graphs provided by Deep Graph Library (DGL) and Open Graph Benchmark (OGB). Pigeon also triggers fewer out-of-memory (OOM) errors. In addition, we propose linear operator fusion and compact materialization to further accelerate the system by up to 2.2x.

SeerAttention: Learning Intrinsic Sparse Attention in Your LLMs

Attention is the cornerstone of modern Large Language Models (LLMs). Yet its quadratic complexity limits the efficiency and scalability of LLMs, especially for those with a long-context window. A promising approach addressing this limitation is to leverage the sparsity in attention. However, existing sparsity-based solutions predominantly rely on predefined patterns or heuristics to approximate sparsity. This practice falls short to fully capture the dynamic nature of attention sparsity in language-based tasks. This paper argues that attention sparsity should be learned rather than predefined. To this end, we design SeerAttention, a new Attention mechanism that augments the conventional attention with a learnable gate that adaptively selects significant blocks in an attention map and deems the rest blocks sparse. Such block-level sparsity effectively balances accuracy and speedup. To enable efficient learning of the gating network, we develop a customized FlashAttention implementation that extracts the block-level ground truth of attention map with minimum overhead. SeerAttention not only applies to post-training, but also excels in long-context fine-tuning. Our results show that at post-training stages, SeerAttention significantly outperforms state-of-the-art static or heuristic-based sparse attention methods, while also being more versatile and flexible to adapt to varying context lengths and sparsity ratios. When applied to long-context fine-tuning with YaRN, SeerAttention can achieve a remarkable 90% sparsity ratio at a 32k context length with minimal perplexity loss, offering a 5.67x speedup over FlashAttention-2.

Hybrid Spectral Denoising Transformer with Guided Attention

In this paper, we present a Hybrid Spectral Denoising Transformer (HSDT) for hyperspectral image denoising. Challenges in adapting transformer for HSI arise from the capabilities to tackle existing limitations of CNN-based methods in capturing the global and local spatial-spectral correlations while maintaining efficiency and flexibility. To address these issues, we introduce a hybrid approach that combines the advantages of both models with a Spatial-Spectral Separable Convolution (S3Conv), Guided Spectral Self-Attention (GSSA), and Self-Modulated Feed-Forward Network (SM-FFN). Our S3Conv works as a lightweight alternative to 3D convolution, which extracts more spatial-spectral correlated features while keeping the flexibility to tackle HSIs with an arbitrary number of bands. These features are then adaptively processed by GSSA which per-forms 3D self-attention across the spectral bands, guided by a set of learnable queries that encode the spectral signatures. This not only enriches our model with powerful capabilities for identifying global spectral correlations but also maintains linear complexity. Moreover, our SM-FFN proposes the self-modulation that intensifies the activations of more informative regions, which further strengthens the aggregated features. Extensive experiments are conducted on various datasets under both simulated and real-world noise, and it shows that our HSDT significantly outperforms the existing state-of-the-art methods while maintaining low computational overhead. Code is at https: //github.com/Zeqiang-Lai/HSDT.

Parallel Learning by Multitasking Neural Networks

A modern challenge of Artificial Intelligence is learning multiple patterns at once (i.e.parallel learning). While this can not be accomplished by standard Hebbian associative neural networks, in this paper we show how the Multitasking Hebbian Network (a variation on theme of the Hopfield model working on sparse data-sets) is naturally able to perform this complex task. We focus on systems processing in parallel a finite (up to logarithmic growth in the size of the network) amount of patterns, mirroring the low-storage level of standard associative neural networks at work with pattern recognition. For mild dilution in the patterns, the network handles them hierarchically, distributing the amplitudes of their signals as power-laws w.r.t. their information content (hierarchical regime), while, for strong dilution, all the signals pertaining to all the patterns are raised with the same strength (parallel regime). Further, confined to the low-storage setting (i.e., far from the spin glass limit), the presence of a teacher neither alters the multitasking performances nor changes the thresholds for learning: the latter are the same whatever the training protocol is supervised or unsupervised. Results obtained through statistical mechanics, signal-to-noise technique and Monte Carlo simulations are overall in perfect agreement and carry interesting insights on multiple learning at once: for instance, whenever the cost-function of the model is minimized in parallel on several patterns (in its description via Statistical Mechanics), the same happens to the standard sum-squared error Loss function (typically used in Machine Learning).

Resistive memory-based zero-shot liquid state machine for multimodal event data learning

The human brain is a complex spiking neural network (SNN) that learns multimodal signals in a zero-shot manner by generalizing existing knowledge. Remarkably, the brain achieves this with minimal power consumption, using event-based signals that propagate within its structure. However, mimicking the human brain in neuromorphic hardware presents both hardware and software challenges. Hardware limitations, such as the slowdown of Moore's law and the von Neumann bottleneck, hinder the efficiency of digital computers. On the software side, SNNs are known for their difficult training, especially when learning multimodal signals. To overcome these challenges, we propose a hardware-software co-design that combines a fixed and random liquid state machine (LSM) SNN encoder with trainable artificial neural network (ANN) projections. The LSM is physically implemented using analogue resistive memory, leveraging the inherent stochasticity of resistive switching to generate random weights. This highly efficient and nanoscale in-memory computing approach effectively addresses the von Neumann bottleneck and the slowdown of Moore's law. The ANN projections are implemented digitally, allowing for easy optimization using contrastive loss, which helps to overcome the difficulties associated with SNN training. We experimentally implement this co-design on a 40nm 256Kb in-memory computing macro. We first demonstrate LSM-based event encoding through supervised classification and linear probing on the N-MNIST and N-TIDIGITS datasets.

One Timestep is All You Need: Training Spiking Neural Networks with Ultra Low Latency

Spiking Neural Networks (SNNs) are energy efficient alternatives to commonly used deep neural networks (DNNs). Through event-driven information processing, SNNs can reduce the expensive compute requirements of DNNs considerably, while achieving comparable performance. However, high inference latency is a significant hindrance to the edge deployment of deep SNNs. Computation over multiple timesteps not only increases latency as well as overall energy budget due to higher number of operations, but also incurs memory access overhead of fetching membrane potentials, both of which lessen the energy benefits of SNNs. To overcome this bottleneck and leverage the full potential of SNNs, we propose an Iterative Initialization and Retraining method for SNNs (IIR-SNN) to perform single shot inference in the temporal axis. The method starts with an SNN trained with T timesteps (T>1). Then at each stage of latency reduction, the network trained at previous stage with higher timestep is utilized as initialization for subsequent training with lower timestep. This acts as a compression method, as the network is gradually shrunk in the temporal domain. In this paper, we use direct input encoding and choose T=5, since as per literature, it is the minimum required latency to achieve satisfactory performance on ImageNet. The proposed scheme allows us to obtain SNNs with up to unit latency, requiring a single forward pass during inference. We achieve top-1 accuracy of 93.05%, 70.15% and 67.71% on CIFAR-10, CIFAR-100 and ImageNet, respectively using VGG16, with just 1 timestep. In addition, IIR-SNNs perform inference with 5-2500X reduced latency compared to other state-of-the-art SNNs, maintaining comparable or even better accuracy. Furthermore, in comparison with standard DNNs, the proposed IIR-SNNs provide25-33X higher energy efficiency, while being comparable to them in classification performance.

Galaxy Spectra neural Network (GaSNet). II. Using Deep Learning for Spectral Classification and Redshift Predictions

Large sky spectroscopic surveys have reached the scale of photometric surveys in terms of sample sizes and data complexity. These huge datasets require efficient, accurate, and flexible automated tools for data analysis and science exploitation. We present the Galaxy Spectra Network/GaSNet-II, a supervised multi-network deep learning tool for spectra classification and redshift prediction. GaSNet-II can be trained to identify a customized number of classes and optimize the redshift predictions for classified objects in each of them. It also provides redshift errors, using a network-of-networks that reproduces a Monte Carlo test on each spectrum, by randomizing their weight initialization. As a demonstration of the capability of the deep learning pipeline, we use 260k Sloan Digital Sky Survey spectra from Data Release 16, separated into 13 classes including 140k galactic, and 120k extragalactic objects. GaSNet-II achieves 92.4% average classification accuracy over the 13 classes (larger than 90% for the majority of them), and an average redshift error of approximately 0.23% for galaxies and 2.1% for quasars. We further train/test the same pipeline to classify spectra and predict redshifts for a sample of 200k 4MOST mock spectra and 21k publicly released DESI spectra. On 4MOST mock data, we reach 93.4% accuracy in 10-class classification and an average redshift error of 0.55% for galaxies and 0.3% for active galactic nuclei. On DESI data, we reach 96% accuracy in (star/galaxy/quasar only) classification and an average redshift error of 2.8% for galaxies and 4.8% for quasars, despite the small sample size available. GaSNet-II can process ~40k spectra in less than one minute, on a normal Desktop GPU. This makes the pipeline particularly suitable for real-time analyses of Stage-IV survey observations and an ideal tool for feedback loops aimed at night-by-night survey strategy optimization.

MAXIM: Multi-Axis MLP for Image Processing

Recent progress on Transformers and multi-layer perceptron (MLP) models provide new network architectural designs for computer vision tasks. Although these models proved to be effective in many vision tasks such as image recognition, there remain challenges in adapting them for low-level vision. The inflexibility to support high-resolution images and limitations of local attention are perhaps the main bottlenecks. In this work, we present a multi-axis MLP based architecture called MAXIM, that can serve as an efficient and flexible general-purpose vision backbone for image processing tasks. MAXIM uses a UNet-shaped hierarchical structure and supports long-range interactions enabled by spatially-gated MLPs. Specifically, MAXIM contains two MLP-based building blocks: a multi-axis gated MLP that allows for efficient and scalable spatial mixing of local and global visual cues, and a cross-gating block, an alternative to cross-attention, which accounts for cross-feature conditioning. Both these modules are exclusively based on MLPs, but also benefit from being both global and `fully-convolutional', two properties that are desirable for image processing. Our extensive experimental results show that the proposed MAXIM model achieves state-of-the-art performance on more than ten benchmarks across a range of image processing tasks, including denoising, deblurring, deraining, dehazing, and enhancement while requiring fewer or comparable numbers of parameters and FLOPs than competitive models. The source code and trained models will be available at https://github.com/google-research/maxim.

Quantized Spike-driven Transformer

Spiking neural networks are emerging as a promising energy-efficient alternative to traditional artificial neural networks due to their spike-driven paradigm. However, recent research in the SNN domain has mainly focused on enhancing accuracy by designing large-scale Transformer structures, which typically rely on substantial computational resources, limiting their deployment on resource-constrained devices. To overcome this challenge, we propose a quantized spike-driven Transformer baseline (QSD-Transformer), which achieves reduced resource demands by utilizing a low bit-width parameter. Regrettably, the QSD-Transformer often suffers from severe performance degradation. In this paper, we first conduct empirical analysis and find that the bimodal distribution of quantized spike-driven self-attention (Q-SDSA) leads to spike information distortion (SID) during quantization, causing significant performance degradation. To mitigate this issue, we take inspiration from mutual information entropy and propose a bi-level optimization strategy to rectify the information distribution in Q-SDSA. Specifically, at the lower level, we introduce an information-enhanced LIF to rectify the information distribution in Q-SDSA. At the upper level, we propose a fine-grained distillation scheme for the QSD-Transformer to align the distribution in Q-SDSA with that in the counterpart ANN. By integrating the bi-level optimization strategy, the QSD-Transformer can attain enhanced energy efficiency without sacrificing its high-performance advantage.For instance, when compared to the prior SNN benchmark on ImageNet, the QSD-Transformer achieves 80.3% top-1 accuracy, accompanied by significant reductions of 6.0times and 8.1times in power consumption and model size, respectively. Code is available at https://github.com/bollossom/QSD-Transformer.

Revisiting Graph Neural Networks on Graph-level Tasks: Comprehensive Experiments, Analysis, and Improvements

Graphs are essential data structures for modeling complex interactions in domains such as social networks, molecular structures, and biological systems. Graph-level tasks, which predict properties or classes for the entire graph, are critical for applications, such as molecular property prediction and subgraph counting. Graph Neural Networks (GNNs) have shown promise in these tasks, but their evaluations are often limited to narrow datasets, tasks, and inconsistent experimental setups, restricting their generalizability. To address these limitations, we propose a unified evaluation framework for graph-level GNNs. This framework provides a standardized setting to evaluate GNNs across diverse datasets, various graph tasks (e.g., graph classification and regression), and challenging scenarios, including noisy, imbalanced, and few-shot graphs. Additionally, we propose a novel GNN model with enhanced expressivity and generalization capabilities. Specifically, we enhance the expressivity of GNNs through a k-path rooted subgraph approach, enabling the model to effectively count subgraphs (e.g., paths and cycles). Moreover, we introduce a unified graph contrastive learning algorithm for graphs across diverse domains, which adaptively removes unimportant edges to augment graphs, thereby significantly improving generalization performance. Extensive experiments demonstrate that our model achieves superior performance against fourteen effective baselines across twenty-seven graph datasets, establishing it as a robust and generalizable model for graph-level tasks.

Generalized Domain Conditioned Adaptation Network

Domain Adaptation (DA) attempts to transfer knowledge learned in the labeled source domain to the unlabeled but related target domain without requiring large amounts of target supervision. Recent advances in DA mainly proceed by aligning the source and target distributions. Despite the significant success, the adaptation performance still degrades accordingly when the source and target domains encounter a large distribution discrepancy. We consider this limitation may attribute to the insufficient exploration of domain-specialized features because most studies merely concentrate on domain-general feature learning in task-specific layers and integrate totally-shared convolutional networks (convnets) to generate common features for both domains. In this paper, we relax the completely-shared convnets assumption adopted by previous DA methods and propose Domain Conditioned Adaptation Network (DCAN), which introduces domain conditioned channel attention module with a multi-path structure to separately excite channel activation for each domain. Such a partially-shared convnets module allows domain-specialized features in low-level to be explored appropriately. Further, given the knowledge transferability varying along with convolutional layers, we develop Generalized Domain Conditioned Adaptation Network (GDCAN) to automatically determine whether domain channel activations should be separately modeled in each attention module. Afterward, the critical domain-specialized knowledge could be adaptively extracted according to the domain statistic gaps. As far as we know, this is the first work to explore the domain-wise convolutional channel activations separately for deep DA networks. Additionally, to effectively match high-level feature distributions across domains, we consider deploying feature adaptation blocks after task-specific layers, which can explicitly mitigate the domain discrepancy.

Exploiting the Brain's Network Structure for Automatic Identification of ADHD Subjects

Attention Deficit Hyperactive Disorder (ADHD) is a common behavioral problem affecting children. In this work, we investigate the automatic classification of ADHD subjects using the resting state Functional Magnetic Resonance Imaging (fMRI) sequences of the brain. We show that the brain can be modeled as a functional network, and certain properties of the networks differ in ADHD subjects from control subjects. We compute the pairwise correlation of brain voxels' activity over the time frame of the experimental protocol which helps to model the function of a brain as a network. Different network features are computed for each of the voxels constructing the network. The concatenation of the network features of all the voxels in a brain serves as the feature vector. Feature vectors from a set of subjects are then used to train a PCA-LDA (principal component analysis-linear discriminant analysis) based classifier. We hypothesized that ADHD-related differences lie in some specific regions of the brain and using features only from those regions is sufficient to discriminate ADHD and control subjects. We propose a method to create a brain mask that includes the useful regions only and demonstrate that using the feature from the masked regions improves classification accuracy on the test data set. We train our classifier with 776 subjects and test on 171 subjects provided by The Neuro Bureau for the ADHD-200 challenge. We demonstrate the utility of graph-motif features, specifically the maps that represent the frequency of participation of voxels in network cycles of length 3. The best classification performance (69.59%) is achieved using 3-cycle map features with masking. Our proposed approach holds promise in being able to diagnose and understand the disorder.

On the Stability of Expressive Positional Encodings for Graph Neural Networks

Designing effective positional encodings for graphs is key to building powerful graph transformers and enhancing message-passing graph neural networks. Although widespread, using Laplacian eigenvectors as positional encodings faces two fundamental challenges: (1) Non-uniqueness: there are many different eigendecompositions of the same Laplacian, and (2) Instability: small perturbations to the Laplacian could result in completely different eigenspaces, leading to unpredictable changes in positional encoding. Despite many attempts to address non-uniqueness, most methods overlook stability, leading to poor generalization on unseen graph structures. We identify the cause of instability to be a "hard partition" of eigenspaces. Hence, we introduce Stable and Expressive Positional Encodings (SPE), an architecture for processing eigenvectors that uses eigenvalues to "softly partition" eigenspaces. SPE is the first architecture that is (1) provably stable, and (2) universally expressive for basis invariant functions whilst respecting all symmetries of eigenvectors. Besides guaranteed stability, we prove that SPE is at least as expressive as existing methods, and highly capable of counting graph structures. Finally, we evaluate the effectiveness of our method on molecular property prediction, and out-of-distribution generalization tasks, finding improved generalization compared to existing positional encoding methods.

One-hot Generalized Linear Model for Switching Brain State Discovery

Exposing meaningful and interpretable neural interactions is critical to understanding neural circuits. Inferred neural interactions from neural signals primarily reflect functional interactions. In a long experiment, subject animals may experience different stages defined by the experiment, stimuli, or behavioral states, and hence functional interactions can change over time. To model dynamically changing functional interactions, prior work employs state-switching generalized linear models with hidden Markov models (i.e., HMM-GLMs). However, we argue they lack biological plausibility, as functional interactions are shaped and confined by the underlying anatomical connectome. Here, we propose a novel prior-informed state-switching GLM. We introduce both a Gaussian prior and a one-hot prior over the GLM in each state. The priors are learnable. We will show that the learned prior should capture the state-constant interaction, shedding light on the underlying anatomical connectome and revealing more likely physical neuron interactions. The state-dependent interaction modeled by each GLM offers traceability to capture functional variations across multiple brain states. Our methods effectively recover true interaction structures in simulated data, achieve the highest predictive likelihood with real neural datasets, and render interaction structures and hidden states more interpretable when applied to real neural data.

When to Pre-Train Graph Neural Networks? From Data Generation Perspective!

In recent years, graph pre-training has gained significant attention, focusing on acquiring transferable knowledge from unlabeled graph data to improve downstream performance. Despite these recent endeavors, the problem of negative transfer remains a major concern when utilizing graph pre-trained models to downstream tasks. Previous studies made great efforts on the issue of what to pre-train and how to pre-train by designing a variety of graph pre-training and fine-tuning strategies. However, there are cases where even the most advanced "pre-train and fine-tune" paradigms fail to yield distinct benefits. This paper introduces a generic framework W2PGNN to answer the crucial question of when to pre-train (i.e., in what situations could we take advantage of graph pre-training) before performing effortful pre-training or fine-tuning. We start from a new perspective to explore the complex generative mechanisms from the pre-training data to downstream data. In particular, W2PGNN first fits the pre-training data into graphon bases, each element of graphon basis (i.e., a graphon) identifies a fundamental transferable pattern shared by a collection of pre-training graphs. All convex combinations of graphon bases give rise to a generator space, from which graphs generated form the solution space for those downstream data that can benefit from pre-training. In this manner, the feasibility of pre-training can be quantified as the generation probability of the downstream data from any generator in the generator space. W2PGNN offers three broad applications: providing the application scope of graph pre-trained models, quantifying the feasibility of pre-training, and assistance in selecting pre-training data to enhance downstream performance. We provide a theoretically sound solution for the first application and extensive empirical justifications for the latter two applications.

Du-IN: Discrete units-guided mask modeling for decoding speech from Intracranial Neural signals

Invasive brain-computer interfaces have garnered significant attention due to their high performance. The current intracranial stereoElectroEncephaloGraphy (sEEG) foundation models typically build univariate representations based on a single channel. Some of them further use Transformer to model the relationship among channels. However, due to the locality and specificity of brain computation, their performance on more difficult tasks, e.g., speech decoding, which demands intricate processing in specific brain regions, is yet to be fully investigated. We hypothesize that building multi-variate representations within certain brain regions can better capture the specific neural processing. To explore this hypothesis, we collect a well-annotated Chinese word-reading sEEG dataset, targeting language-related brain networks, over 12 subjects. Leveraging this benchmark dataset, we developed the Du-IN model that can extract contextual embeddings from specific brain regions through discrete codebook-guided mask modeling. Our model achieves SOTA performance on the downstream 61-word classification task, surpassing all baseline models. Model comparison and ablation analysis reveal that our design choices, including (i) multi-variate representation by fusing channels in vSMC and STG regions and (ii) self-supervision by discrete codebook-guided mask modeling, significantly contribute to these performances. Collectively, our approach, inspired by neuroscience findings, capitalizing on multi-variate neural representation from specific brain regions, is suitable for invasive brain modeling. It marks a promising neuro-inspired AI approach in BCI.

Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes

Despite the recent successes of vanilla Graph Neural Networks (GNNs) on many tasks, their foundation on pairwise interaction networks inherently limits their capacity to discern latent higher-order interactions in complex systems. To bridge this capability gap, we propose a novel approach exploiting the rich mathematical theory of simplicial complexes (SCs) - a robust tool for modeling higher-order interactions. Current SC-based GNNs are burdened by high complexity and rigidity, and quantifying higher-order interaction strengths remains challenging. Innovatively, we present a higher-order Flower-Petals (FP) model, incorporating FP Laplacians into SCs. Further, we introduce a Higher-order Graph Convolutional Network (HiGCN) grounded in FP Laplacians, capable of discerning intrinsic features across varying topological scales. By employing learnable graph filters, a parameter group within each FP Laplacian domain, we can identify diverse patterns where the filters' weights serve as a quantifiable measure of higher-order interaction strengths. The theoretical underpinnings of HiGCN's advanced expressiveness are rigorously demonstrated. Additionally, our empirical investigations reveal that the proposed model accomplishes state-of-the-art (SOTA) performance on a range of graph tasks and provides a scalable and flexible solution to explore higher-order interactions in graphs.

Forward Learning of Graph Neural Networks

Graph neural networks (GNNs) have achieved remarkable success across a wide range of applications, such as recommendation, drug discovery, and question answering. Behind the success of GNNs lies the backpropagation (BP) algorithm, which is the de facto standard for training deep neural networks (NNs). However, despite its effectiveness, BP imposes several constraints, which are not only biologically implausible, but also limit the scalability, parallelism, and flexibility in learning NNs. Examples of such constraints include storage of neural activities computed in the forward pass for use in the subsequent backward pass, and the dependence of parameter updates on non-local signals. To address these limitations, the forward-forward algorithm (FF) was recently proposed as an alternative to BP in the image classification domain, which trains NNs by performing two forward passes over positive and negative data. Inspired by this advance, we propose ForwardGNN in this work, a new forward learning procedure for GNNs, which avoids the constraints imposed by BP via an effective layer-wise local forward training. ForwardGNN extends the original FF to deal with graph data and GNNs, and makes it possible to operate without generating negative inputs (hence no longer forward-forward). Further, ForwardGNN enables each layer to learn from both the bottom-up and top-down signals without relying on the backpropagation of errors. Extensive experiments on real-world datasets show the effectiveness and generality of the proposed forward graph learning framework. We release our code at https://github.com/facebookresearch/forwardgnn.

PanFlowNet: A Flow-Based Deep Network for Pan-sharpening

Pan-sharpening aims to generate a high-resolution multispectral (HRMS) image by integrating the spectral information of a low-resolution multispectral (LRMS) image with the texture details of a high-resolution panchromatic (PAN) image. It essentially inherits the ill-posed nature of the super-resolution (SR) task that diverse HRMS images can degrade into an LRMS image. However, existing deep learning-based methods recover only one HRMS image from the LRMS image and PAN image using a deterministic mapping, thus ignoring the diversity of the HRMS image. In this paper, to alleviate this ill-posed issue, we propose a flow-based pan-sharpening network (PanFlowNet) to directly learn the conditional distribution of HRMS image given LRMS image and PAN image instead of learning a deterministic mapping. Specifically, we first transform this unknown conditional distribution into a given Gaussian distribution by an invertible network, and the conditional distribution can thus be explicitly defined. Then, we design an invertible Conditional Affine Coupling Block (CACB) and further build the architecture of PanFlowNet by stacking a series of CACBs. Finally, the PanFlowNet is trained by maximizing the log-likelihood of the conditional distribution given a training set and can then be used to predict diverse HRMS images. The experimental results verify that the proposed PanFlowNet can generate various HRMS images given an LRMS image and a PAN image. Additionally, the experimental results on different kinds of satellite datasets also demonstrate the superiority of our PanFlowNet compared with other state-of-the-art methods both visually and quantitatively.