ICLR 2024 Papers

International Conference on Learning Representations

Decision breakdown

2,260papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    863.8%
  • Spotlight
    36716.2%
  • Poster
    1,80780.0%

Browse all papers

On the generalization capacity of neural networks during generic multimodal reasoning

Takuya Ito, Soham Dan, Mattia Rigotti, James Kozloski, Murray Campbell

Expand abstract

The advent of the Transformer has led to the development of large language models (LLM), which appear to demonstrate human-like capabilities. To assess the generality of this class of models and a variety of other base neural network architectures to multimodal domains, we evaluated and compared their capacity for multimodal generalization. We introduce a multimodal question-answer benchmark to evaluate three specific types of out-of-distribution (OOD) generalization performance: distractor generalization (generalization in the presence of distractors), systematic compositional generalization (generalization to new task permutations), and productive compositional generalization (generalization to more complex tasks with deeper dependencies). While we found that most architectures faired poorly on most forms of generalization (e.g., RNNs and standard Transformers), models that leveraged cross-attention mechanisms between input domains, such as the Perceiver, fared better. Our positive results demonstrate that for multimodal distractor and systematic generalization, cross-attention is an important mechanism to integrate multiple sources of information. On the other hand, all architectures failed in productive generalization, suggesting fundamental limitations of existing architectures for specific types of multimodal OOD generalization. These results demonstrate the strengths and limitations of specific architectural components underlying modern neural models for multimodal reasoning. Finally, we provide *Generic COG* (gCOG), a configurable benchmark with several multimodal generalization splits, for future studies to explore.

Poster
Enhancing Small Medical Learners with Privacy-preserving Contextual Prompting

Xinlu Zhang, Shiyang Li, Xianjun Yang, Chenxin Tian, Yao Qin, Linda Ruth Petzold

Expand abstract

Large language models (LLMs) demonstrate remarkable medical expertise, but data privacy concerns impede their direct use in healthcare environments. Although offering improved data privacy protection, domain-specific small language models (SLMs) often underperform LLMs, emphasizing the need for methods that reduce this performance gap while alleviating privacy concerns. In this paper, we present a simple yet effective method that harnesses LLMs' medical proficiency to boost SLM performance in medical tasks under $privacy-restricted$ scenarios. Specifically, we mitigate patient privacy issues by extracting keywords from medical data and prompting the LLM to generate a medical knowledge-intensive context by simulating clinicians' thought processes. This context serves as additional input for SLMs, augmenting their decision-making capabilities. Our method significantly enhances performance in both few-shot and full training settings across three medical knowledge-intensive tasks, achieving up to a 22.57% increase in absolute accuracy compared to SLM fine-tuning without context, and sets new state-of-the-art results in two medical tasks within privacy-restricted scenarios. Further out-of-domain testing and experiments in two general domain datasets showcase its generalizability and broad applicability.

Poster
Fast and unified path gradient estimators for normalizing flows

Lorenz Vaitl, Ludwig Winkler, Lorenz Richter, Pan Kessel

Expand abstract

Recent work shows that path gradient estimators for normalizing flows have lower variance compared to standard estimators, resulting in improved training. However, they are often prohibitively more expensive from a computational point of view and cannot be applied to maximum likelihood training in a scalable manner, which severely hinders their widespread adoption. In this work, we overcome these crucial limitations. Specifically, we propose a fast path gradient estimator which works for all normalizing flow architectures of practical relevance for sampling from an unnormalized target distribution. We then show that this estimator can also be applied to maximum likelihood training and empirically establish its superior performance for several natural sciences applications.

Poster
Perceptual Scales Predicted by Fisher Information Metrics

Jonathan Vacher, Pascal Mamassian

Expand abstract

Perception is often viewed as a process that transforms physical variables, external to an observer, into internal psychological variables. Such a process can be modeled by a function coined *perceptual scale*. The *perceptual scale* can be deduced from psychophysical measurements that consist in comparing the relative differences between stimuli (i.e. difference scaling experiments). However, this approach is often overlooked by the modeling and experimentation communities. Here, we demonstrate the value of measuring the *perceptual scale* of classical (spatial frequency, orientation) and less classical physical variables (interpolation between textures) by embedding it in recent probabilistic modeling of perception. First, we show that the assumption that an observer has an internal representation of univariate parameters such as spatial frequency or orientation while stimuli are high-dimensional does not lead to contradictory predictions when following the theoretical framework. Second, we show that the measured *perceptual scale* corresponds to the transduction function hypothesized in this framework. In particular, we demonstrate that it is related to the Fisher information of the generative model that underlies perception and we test the predictions given by the generative model of different stimuli in a set a of difference scaling experiments. Our main conclusion is that the *perceptual scale* is mostly driven by the stimulus power spectrum. Finally, we propose that this measure of *perceptual scale* is a way to push further the notion of perceptual distances by estimating the perceptual geometry of images i.e. the path between images instead of simply the distance between those.

Poster
Emergent mechanisms for long timescales depend on training curriculum and affect performance in memory tasks

Sina Khajehabdollahi, Roxana Zeraati, Emmanouil Giannakakis, Tim Jakob Schäfer, Georg Martius, Anna Levina

Expand abstract

Recurrent neural networks (RNNs) in the brain and \emph{in silico} excel at solving tasks with intricate temporal dependencies. Long timescales required for solving such tasks can arise from properties of individual neurons (single-neuron timescale, $\tau$, e.g., membrane time constant in biological neurons) or recurrent interactions among them (network-mediated timescale, $\tau_\textrm{\small{net}}$). However, the contribution of each mechanism for optimally solving memory-dependent tasks remains poorly understood. Here, we train RNNs to solve $N$-parity and $N$-delayed match-to-sample tasks with increasing memory requirements controlled by $N$, by simultaneously optimizing recurrent weights and $\tau$s. We find that RNNs develop longer timescales with increasing $N$, but depending on the learning objective, they use different mechanisms. Two distinct curricula define learning objectives: sequential learning of a single-$N$ (single-head) or simultaneous learning of multiple $N$s (multi-head). Single-head networks increase their $\tau$ with $N$ and can solve large-$N$ tasks, but suffer from catastrophic forgetting. However, multi-head networks, which are explicitly required to hold multiple concurrent memories, keep $\tau$ constant and develop longer timescales through recurrent connectivity. We show that the multi-head curriculum increases training speed and stability to perturbations, and allows generalization to tasks beyond the training set. This curriculum also significantly improves training GRUs and LSTMs for large-$N$ tasks. Our results suggest that adapting timescales to task requirements via recurrent interactions allows learning more complex objectives and improves the RNN's performance.

Poster
Threaten Spiking Neural Networks through Combining Rate and Temporal Information

Zecheng Hao, Tong Bu, Xinyu Shi, Zihan Huang, Zhaofei Yu, Tiejun Huang

Expand abstract

Spiking Neural Networks (SNNs) have received widespread attention in academic communities due to their superior spatio-temporal processing capabilities and energy-efficient characteristics. With further in-depth application in various fields, the vulnerability of SNNs under adversarial attack has become a focus of concern. In this paper, we draw inspiration from two mainstream learning algorithms of SNNs and observe that SNN models reserve both rate and temporal information. To better understand the capabilities of these two types of information, we conduct a quantitative analysis separately for each. In addition, we note that the retention degree of temporal information is related to the parameters and input settings of spiking neurons. Building on these insights, we propose a hybrid adversarial attack based on rate and temporal information (HART), which allows for dynamic adjustment of the rate and temporal attributes. Experimental results demonstrate that compared to previous works, HART attack can achieve significant superiority under different attack scenarios, data types, network architecture, time-steps, and model hyper-parameters. These findings call for further exploration into how both types of information can be effectively utilized to enhance the reliability of SNNs. Code is available at [https://github.com/hzc1208/HART_Attack](https://github.com/hzc1208/HART_Attack).

Poster
Synaptic Weight Distributions Depend on the Geometry of Plasticity

Roman Pogodin, Jonathan Cornford, Arna Ghosh, Gauthier Gidel, Guillaume Lajoie, Blake Aaron Richards

Expand abstract

A growing literature in computational neuroscience leverages gradient descent and learning algorithms that approximate it to study synaptic plasticity in the brain. However, the vast majority of this work ignores a critical underlying assumption: the choice of distance for synaptic changes - i.e. the geometry of synaptic plasticity. Gradient descent assumes that the distance is Euclidean, but many other distances are possible, and there is no reason that biology necessarily uses Euclidean geometry. Here, using the theoretical tools provided by mirror descent, we show that the distribution of synaptic weights will depend on the geometry of synaptic plasticity. We use these results to show that experimentally-observed log-normal weight distributions found in several brain areas are not consistent with standard gradient descent (i.e. a Euclidean geometry), but rather with non-Euclidean distances. Finally, we show that it should be possible to experimentally test for different synaptic geometries by comparing synaptic weight distributions before and after learning. Overall, our work shows that the current paradigm in theoretical work on synaptic plasticity that assumes Euclidean synaptic geometry may be misguided and that it should be possible to experimentally determine the true geometry of synaptic plasticity in the brain.

Spotlight
Adaptive deep spiking neural network with global-local learning via balanced excitatory and inhibitory mechanism

Tingting Jiang, Qi Xu, Xuming Ran, Jiangrong Shen, Pan Lv, Qiang Zhang, Gang Pan

Expand abstract

The training method of Spiking Neural Networks (SNNs) is an essential problem, and how to integrate local and global learning is a worthy research interest. However, the current integration methods do not consider the network conditions suitable for local and global learning, and thus fail to balance their advantages. In this paper, we propose an Excitation-Inhibition Mechanism-assisted Hybrid Learning(EIHL) algorithm that adjusts the network connectivity by using the excitation-inhibition mechanism and then switches between local and global learning according to the network connectivity. The experimental results on CIFAR10/100 and DVS-CIFAR10 demonstrate that the EIHL not only has better accuracy performance than other methods but also has excellent sparsity advantage. Especially, the Spiking VGG11 is trained by EIHL, STBP, and STDP on DVS_CIFAR10, respectively. The accuracy of the Spiking VGG11 model on EIHL is 62.45%, which is 4.35% higher than STBP and 11.40% higher than STDP, and the sparsity is 18.74%, which is 18.74% higher than the other two methods. Moreover, the excitation-inhibition mechanism used in our method also offers a new perspective on the field of SNN learning.

Poster
Towards LLM4QPE: Unsupervised Pretraining of Quantum Property Estimation and A Benchmark

Yehui Tang, Hao Xiong, Nianzu Yang, Tailong Xiao, Junchi Yan

Expand abstract

Estimating the properties of quantum systems such as quantum phase has been critical in addressing the essential quantum many-body problems in physics and chemistry. Deep learning models have been recently introduced to property estimation, surpassing conventional statistical approaches. However, these methods are tailored to the specific task and quantum data at hand. It remains an open and attractive question for devising a more universal task-agnostic pretraining model for quantum property estimation. In this paper, we propose LLM4QPE, a large language model style quantum task-agnostic pretraining and finetuning paradigm that 1) performs unsupervised pretraining on diverse quantum systems with different physical conditions; 2) uses the pretrained model for supervised finetuning and delivers high performance with limited training data, on downstream tasks. It mitigates the cost for quantum data collection and speeds up convergence. Extensive experiments show the promising efficacy of LLM4QPE in various tasks including classifying quantum phases of matter on Rydberg atom model and predicting two-body correlation function on anisotropic Heisenberg model.

Spotlight
Fine-Tuned Language Models Generate Stable Inorganic Materials as Text

Nate Gruver, Anuroop Sriram, Andrea Madotto, Andrew Gordon Wilson, C. Lawrence Zitnick, Zachary Ward Ulissi

Expand abstract

We propose fine-tuning large language models for generation of stable materials. While unorthodox, fine-tuning large language models on text-encoded atomistic data is simple to implement yet reliable, with around 90\% of sampled structures obeying physical constraints on atom positions and charges. Using energy above hull calculations from both learned ML potentials and gold-standard DFT calculations, we show that our strongest model (fine-tuned LLaMA-2 70B) can generate materials predicted to be metastable at about twice the rate (49\% vs 28\%) of CDVAE, a competing diffusion model. Because of text prompting's inherent flexibility, our models can simultaneously be used for unconditional generation of stable material, infilling of partial structures and text-conditional generation. Finally, we show that language models' ability to capture key symmetries of crystal structures improves with model scale, suggesting that the biases of pretrained LLMs are surprisingly well-suited for atomistic data.

Poster
The Expressive Leaky Memory Neuron: an Efficient and Expressive Phenomenological Neuron Model Can Solve Long-Horizon Tasks.

Aaron Spieler, Nasim Rahaman, Georg Martius, Bernhard Schölkopf, Anna Levina

Expand abstract

Biological cortical neurons are remarkably sophisticated computational devices, temporally integrating their vast synaptic input over an intricate dendritic tree, subject to complex, nonlinearly interacting internal biological processes. A recent study proposed to characterize this complexity by fitting accurate surrogate models to replicate the input-output relationship of a detailed biophysical cortical pyramidal neuron model and discovered it needed temporal convolutional networks (TCN) with millions of parameters. Requiring these many parameters, however, could stem from a misalignment between the inductive biases of the TCN and cortical neuron's computations. In light of this, and to explore the computational implications of leaky memory units and nonlinear dendritic processing, we introduce the Expressive Leaky Memory (ELM) neuron model, a biologically inspired phenomenological model of a cortical neuron. Remarkably, by exploiting such slowly decaying memory-like hidden states and two-layered nonlinear integration of synaptic input, our ELM neuron can accurately match the aforementioned input-output relationship with under ten thousand trainable parameters. To further assess the computational ramifications of our neuron design, we evaluate it on various tasks with demanding temporal structures, including the Long Range Arena (LRA) datasets, as well as a novel neuromorphic dataset based on the Spiking Heidelberg Digits dataset (SHD-Adding). Leveraging a larger number of memory units with sufficiently long timescales, and correspondingly sophisticated synaptic integration, the ELM neuron displays substantial long-range processing capabilities, reliably outperforming the classic Transformer or Chrono-LSTM architectures on LRA, and even solving the Pathfinder-X task with over 70\% accuracy (16k context length). These findings raise further questions about the computational sophistication of individual cortical neurons and their role in extracting complex long-range temporal dependencies.

Poster
A Framework for Inference Inspired by Human Memory Mechanisms

Xiangyu Zeng, Jie Lin, Piao Hu, Ruizheng Huang, Zhicheng Zhang

Expand abstract

How humans and machines make sense of current inputs for relation reasoning and question-answering while putting the perceived information into context of our past memories, has been a challenging conundrum in cognitive science and artificial intelligence. Inspired by human brain's memory system and cognitive architectures, we propose a PMI framework that consists of perception, memory and inference components. Notably, the memory module comprises working and long-term memory, with the latter endowed with a higher-order structure to retain extensive and complex relational knowledge and experience. Through a differentiable competitive write access, current perceptions update working memory, which is later merged with long-term memory via outer product associations, reducing information conflicts and averting memory overflow. In the inference module, relevant information is retrieved from two separate memory origins and associatively integrated to attain a more comprehensive and precise interpretation of current perceptions. We exploratively apply our PMI to improve prevailing Transformers and CNN models on question-answering tasks like bAbI-20k and Sort-of-CLEVR datasets, as well as detecting equilateral triangles, language modeling and image classification tasks, and in each case, our PMI enhancements consistently outshine their original counterparts significantly. Visualization analyses reveal that relational memory consolidation, along with the interaction and integration of information from diverse memory sources, substantially contributes to the model effectiveness on inference tasks.

Poster
How connectivity structure shapes rich and lazy learning in neural circuits

Yuhan Helena Liu, Aristide Baratin, Jonathan Cornford, Stefan Mihalas, Eric Todd SheaBrown, Guillaume Lajoie

Expand abstract

In theoretical neuroscience, recent work leverages deep learning tools to explore how some network attributes critically influence its learning dynamics. Notably, initial weight distributions with small (resp. large) variance may yield a rich (resp. lazy) regime, where significant (resp. minor) changes to network states and representation are observed over the course of learning. However, in biology, neural circuit connectivity generally has a low-rank structure and therefore differs markedly from the random initializations generally used for these studies. As such, here we investigate how the structure of the initial weights — in particular their effective rank — influences the network learning regime. Through both empirical and theoretical analyses, we discover that high-rank initializations typically yield smaller network changes indicative of lazier learning, a finding we also confirm with experimentally-driven initial connectivity in recurrent neural networks. Conversely, low-rank initialization biases learning towards richer learning. Importantly, however, as an exception to this rule, we find lazier learning can still occur with a low-rank initialization that aligns with task and data statistics. Our research highlights the pivotal role of initial weight structures in shaping learning regimes, with implications for metabolic costs of plasticity and risks of catastrophic forgetting.

Poster
Evaluating Representation Learning on the Protein Structure Universe

Arian Rokkum Jamasb, Alex Morehead, Chaitanya K. Joshi, Zuobai Zhang, Kieran Didi, Simon V Mathis, Charles Harris, Jian Tang, Jianlin Cheng, Pietro Lio, Tom Leon Blundell

Expand abstract

We introduce ProteinWorkshop, a comprehensive benchmark suite for representation learning on protein structures with Geometric Graph Neural Networks. We consider large-scale pre-training and downstream tasks on both experimental and predicted structures to enable the systematic evaluation of the quality of the learned structural representation and their usefulness in capturing functional relationships for downstream tasks. We find that: (1) large-scale pretraining on AlphaFold structures and auxiliary tasks consistently improve the performance of both rotation-invariant and equivariant GNNs, and (2) more expressive equivariant GNNs benefit from pretraining to a greater extent compared to invariant models. We aim to establish a common ground for the machine learning and computational biology communities to rigorously compare and advance protein structure representation learning. Our open-source codebase reduces the barrier to entry for working with large protein structure datasets by providing: (1) storage-efficient dataloaders for large-scale structural databases including AlphaFoldDB and ESM Atlas, as well as (2) utilities for constructing new tasks from the entire PDB. ProteinWorkshop is available at: github.com/a-r-j/ProteinWorkshop.

Poster
CAMIL: Context-Aware Multiple Instance Learning for Cancer Detection and Subtyping in Whole Slide Images

Olga Fourkioti, Matt De Vries, Chris Bakal

Expand abstract

The visual examination of tissue biopsy sections is fundamental for cancer diagnosis, with pathologists analyzing sections at multiple magnifications to discern tumor cells and their subtypes. However, existing attention-based multiple instance learning (MIL) models used for analyzing Whole Slide Images (WSIs) in cancer diagnostics often overlook the contextual information of tumor and neighboring tiles, leading to misclassifications. To address this, we propose the Context-Aware Multiple Instance Learning (CAMIL) architecture. CAMIL incorporates neighbor-constrained attention to consider dependencies among tiles within a WSI and integrates contextual constraints as prior knowledge into the MIL model. We evaluated CAMIL on subtyping non-small cell lung cancer (TCGA-NSCLC) and detecting lymph node (CAMELYON16 and CAMELYON17) metastasis, achieving test AUCs of 97.5\%, 95.9\%, and 88.1\%, respectively, outperforming other state-of-the-art methods. Additionally, CAMIL enhances model interpretability by identifying regions of high diagnostic value. Our code is available at https://github.com/olgarithmics/ICLR_CAMIL.

Spotlight
Intriguing Properties of Generative Classifiers

Priyank Jaini, Kevin Clark, Robert Geirhos

Expand abstract

What is the best paradigm to recognize objects---discriminative inference (fast but potentially prone to shortcut learning) or using a generative model (slow but potentially more robust)? We build on recent advances in generative modeling that turn text-to-image models into classifiers. This allows us to study their behavior and to compare them against discriminative models and human psychophysical data. We report four intriguing emergent properties of generative classifiers: they show a record-breaking human-like shape bias (99% for Imagen), near human-level out-of-distribution accuracy, state-of-the-art alignment with human classification errors, and they understand certain perceptual illusions. Our results indicate that while the current dominant paradigm for modeling human object recognition is discriminative inference, zero-shot generative models approximate human object recognition data surprisingly well.

Spotlight
Learning Thresholds with Latent Values and Censored Feedback

Jiahao Zhang, Tao Lin, Weiqiang Zheng, Zhe Feng, Yifeng Teng, Xiaotie Deng

Expand abstract

In this paper, we investigate a problem of *actively* learning threshold in latent space, where the *unknown* reward $g(\gamma, v)$ depends on the proposed threshold $\gamma$ and latent value $v$ and it can be $only$ achieved if the threshold is lower than or equal to the *unknown* latent value. This problem has broad applications in practical scenarios, e.g., reserve price optimization in online auctions, online task assignments in crowdsourcing, setting recruiting bars in hiring, etc. We first characterize the query complexity of learning a threshold with the expected reward at most $\epsilon$ smaller than the optimum and prove that the number of queries needed can be infinitely large even when $g(\gamma, v)$ is monotone with respect to both $\gamma$ and $v$. On the positive side, we provide a tight query complexity $\tilde{\Theta}(1/\epsilon^3)$ when $g$ is monotone and the CDF of value distribution is Lipschitz. Moreover, we show a tight $\tilde{\Theta}(1/\epsilon^3)$ query complexity can be achieved as long as $g$ satisfies one-sided Lipschitzness, which provides a complete characterization for this problem. Finally, we extend this model to an online learning setting and demonstrate a tight $\Theta(T^{2/3})$ regret bound using continuous-arm bandit techniques and the aforementioned query complexity results.

Poster
Solving High Frequency and Multi-Scale PDEs with Gaussian Processes

Shikai Fang, Madison Cooley, Da Long, Shibo Li, Mike Kirby, Shandian Zhe

Expand abstract

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and multi-scale PDEs, which can be due to spectral bias during neural network training. To address this problem, we resort to the Gaussian process (GP) framework. To flexibly capture the dominant frequencies, we model the power spectrum of the PDE solution with a student $t$ mixture or Gaussian mixture. We apply the inverse Fourier transform to obtain the covariance function (by Wiener-Khinchin theorem). The covariance derived from the Gaussian mixture spectrum corresponds to the known spectral mixture kernel. Next, we estimate the mixture weights in the log domain, which we show is equivalent to placing a Jeffreys prior. It automatically induces sparsity, prunes excessive frequencies, and adjusts the remaining toward the ground truth. Third, to enable efficient and scalable computation on massive collocation points, which are critical to capture high frequencies, we place the collocation points on a grid, and multiply our covariance function at each input dimension. We use the GP conditional mean to predict the solution and its derivatives so as to fit the boundary condition and the equation itself. As a result, we can derive a Kronecker product structure in the covariance matrix. We use Kronecker product properties and multilinear algebra to promote computational efficiency and scalability, without low-rank approximations. We show the advantage of our method in systematic experiments. The code is released at {https://github.com/xuangu-fang/Gaussian-Process-Slover-for-High-Freq-PDE}.

Poster
Traveling Waves Encode The Recent Past and Enhance Sequence Learning

T. Anderson Keller, Lyle Muller, Terrence Sejnowski, Max Welling

Expand abstract

Traveling waves of neural activity have been observed throughout the brain at a diversity of regions and scales; however, their precise computational role is still debated. One physically inspired hypothesis suggests that the cortical sheet may act like a wave-propagating system capable of invertibly storing a short-term memory of sequential stimuli through induced waves traveling across the cortical surface, and indeed many experimental results from neuroscience correlate wave activity with memory tasks. To date, however, the computational implications of this idea have remained hypothetical due to the lack of a simple recurrent neural network architecture capable of exhibiting such waves. In this work, we introduce a model to fill this gap, which we denote the Wave-RNN (wRNN), and demonstrate how such an architecture indeed efficiently encodes the recent past through a suite of synthetic memory tasks where wRNNs learn faster and reach significantly lower error than wave-free counterparts. We further explore the implications of this memory storage system on more complex sequence modeling tasks such as sequential image classification and find that wave-based models not only again outperform comparable wave-free RNNs while using significantly fewer parameters, but additionally perform comparably to more complex gated architectures such as LSTMs and GRUs.

Poster
A Lie Group Approach to Riemannian Batch Normalization

Ziheng Chen, Yue Song, Yunmei Liu, Nicu Sebe

Expand abstract

Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and concomitantly, normalization techniques have also been adapted to several manifolds, referred to as Riemannian normalization. Nonetheless, most of the existing Riemannian normalization methods have been derived in an ad hoc manner and only apply to specific manifolds. This paper establishes a unified framework for Riemannian Batch Normalization (RBN) techniques on Lie groups. Our framework offers the theoretical guarantee of controlling both the Riemannian mean and variance. Empirically, we focus on Symmetric Positive Definite (SPD) manifolds, which possess three distinct types of Lie group structures. Using the deformation concept, we generalize the existing Lie groups on SPD manifolds into three families of parameterized Lie groups. Specific normalization layers induced by these Lie groups are then proposed for SPD neural networks. We demonstrate the effectiveness of our approach through three sets of experiments: radar recognition, human action recognition, and electroencephalography (EEG) classification. The code is available at https://github.com/GitZH-Chen/LieBN.git.

Poster