Author name cluster

Piotr Koniusz

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

20 papers

2 author rows

AAAI Conference 2026 Conference Paper

Feature Hallucination for Self-supervised Action Recognition (Abstract Reprint)

Lei Wang
Piotr Koniusz

Understanding human actions in videos requires more than raw pixel analysis; it relies on high-level semantic reasoning and effective integration of multimodal features. We propose a deep translational action recognition framework that enhances recognition accuracy by jointly predicting action concepts and auxiliary features from RGB video frames. At test time, hallucination streams infer missing cues, enriching feature representations without increasing computational overhead. To focus on action-relevant regions beyond raw pixels, we introduce two novel domain-specific descriptors. Object Detection Features (ODF) aggregate outputs from multiple object detectors to capture contextual cues, while Saliency Detection Features (SDF) highlight spatial and intensity patterns crucial for action recognition. Our framework seamlessly integrates these descriptors with auxiliary modalities such as optical flow, Improved Dense Trajectories, skeleton data, and audio cues. It remains compatible with state-of-the-art architectures, including I3D, AssembleNet, Video Transformer Network, FASTER, and recent models like VideoMAE V2 and InternVideo2. To handle uncertainty in auxiliary features, we incorporate aleatoric uncertainty modeling in the hallucination step and introduce a robust loss function to mitigate feature noise. Our multimodal self-supervised action recognition framework achieves state-of-the-art performance on multiple benchmarks, including Kinetics-400, Kinetics-600, and Something-Something V2, demonstrating its effectiveness in capturing fine-grained action dynamics.

PDF Details DOI

AAAI Conference 2026 Conference Paper

Learning Time in Static Classifiers

Xi Ding
Lei Wang
Piotr Koniusz
Yongsheng Gao

Real-world visual data rarely presents as isolated, static instances. Instead, it often evolves gradually over time through variations in pose, lighting, object state, or scene context. However, conventional classifiers are typically trained under the assumption of temporal independence, limiting their ability to capture such dynamics. We propose a simple yet effective framework that equips standard feedforward classifiers with temporal reasoning, all without modifying model architectures or introducing recurrent modules. At the heart of our approach is a novel Support-Exemplar-Query (SEQ) learning paradigm, which structures training data into temporally coherent trajectories. These trajectories enable the model to learn class-specific temporal prototypes and align prediction sequences via a differentiable soft-DTW loss. A multi-term objective further promotes semantic consistency and temporal smoothness. By interpreting input sequences as evolving feature trajectories, our method introduces a strong temporal inductive bias through loss design alone. This proves highly effective in both static and temporal tasks: it enhances performance on fine-grained and ultra-fine-grained image classification, and delivers precise, temporally consistent predictions in video anomaly detection. Despite its simplicity, our approach bridges static and temporal learning in a modular and data-efficient manner, requiring only a simple classifier on top of pre-extracted features.

PDF Details DOI

NeurIPS Conference 2025 Conference Paper

Amortized Active Generation of Pareto Sets

Daniel Steinberg
Asiri Wijesinghe
Rafael Oliveira
Piotr Koniusz
Cheng Soon Ong
Edwin Bonilla

We introduce active generation of Pareto sets (A-GPS), a new framework for online discrete black-box multi-objective optimization (MOO). A-GPS learns a generative model of the Pareto set that supports a-posteriori conditioning on user preferences. The method employs a class probability estimator (CPE) to predict non-dominance relations and to condition the generative model toward high-performing regions of the search space. We also show that this non-dominance CPE implicitly estimates the probability of hypervolume improvement (PHVI). To incorporate subjective trade-offs, A-GPS introduces preference direction vectors that encode user-specified preferences in objective space. At each iteration, the model is updated using both Pareto membership and alignment with these preference directions, producing an amortized generative model capable of sampling across the Pareto front without retraining. The result is a simple yet powerful approach that achieves high-quality Pareto set approximations, avoids explicit hypervolume computation, and flexibly captures user preferences. Empirical results on synthetic benchmarks and protein design tasks demonstrate strong sample efficiency and effective preference incorporation.

PDF Details

NeurIPS Conference 2025 Conference Paper

CrossSpectra: Exploiting Cross-Layer Smoothness for Parameter-Efficient Fine-Tuning

Yifei Zhang
Hao Zhu
Junhao Dong
Haoran Shi
Ziqiao Meng
Piotr Koniusz
Han Yu

Parameter-efficient fine-tuning (PEFT) is essential for adapting large foundation models without excessive storage cost. However, current approaches such as LoRA treat each layer’s adaptation independently, overlooking correlations across layers. This independence causes the number of trainable parameters to grow linearly with model depth. We provide theoretical and empirical evidence that skip connections in transformers create smooth gradient propagation across layers. This smoothness leads to weight adaptations that concentrate most of their energy in low-frequency spectral components, especially along the layer dimension. Empirical analysis confirms this effect, showing that most of adaptation energy lies in low frequencies. Building on this insight, we propose CrossSpectra, which parameterizes all attention-weight adaptations $(Q, K, V)$ across layers as a single 3D tensor and represents them with sparse spectral coefficients ($\kappa_1, \kappa_2$). Using $\kappa_{1}$ non-zero coefficients within each layer’s frequency space and truncating to $\kappa_{2}$ frequencies across layers, CrossSpectra requires $\mathcal{O}(\kappa_{1}\kappa_{2})$ parameters instead of LoRA’s $\mathcal{O}(Lrd)$, where $L$ is the number of layers and $r$ the rank. Across natural-language and vision benchmarks, \methodname{} matches or surpasses baseline performance while using fewer parameters than LoRA, achieving only $0. 36\%$ of LoRA’s parameter count when fine-tuning LLaMA-7B on instruction-following tasks. These results show that exploiting the \textbf{architectural smoothness of transformers} through spectral analysis yields major efficiency gains in PEFT.

PDF Details

NeurIPS Conference 2025 Conference Paper

Graph Your Own Prompt

Xi Ding
Lei Wang
Piotr Koniusz
Yongsheng Gao

We propose Graph Consistency Regularization (GCR), a novel framework that injects relational graph structures, derived from model predictions, into the learning process to promote class-aware, semantically meaningful feature representations. Functioning as a form of self-prompting, GCR enables the model to refine its internal structure using its own outputs. While deep networks learn rich representations, these often capture noisy inter-class similarities that contradict the model's predicted semantics. GCR addresses this issue by introducing parameter-free Graph Consistency Layers (GCLs) at arbitrary depths. Each GCL builds a batch-level feature similarity graph and aligns it with a global, class-aware masked prediction graph, derived by modulating softmax prediction similarities with intra-class indicators. This alignment enforces that feature-level relationships reflect class-consistent prediction behavior, acting as a semantic regularizer throughout the network. Unlike prior work, GCR introduces a multi-layer, cross-space graph alignment mechanism with adaptive weighting, where layer importance is learned from graph discrepancy magnitudes. This allows the model to prioritize semantically reliable layers and suppress noisy ones, enhancing feature quality without modifying the architecture or training procedure. GCR is model-agnostic, lightweight, and improves semantic structure across various networks and datasets. Experiments show that GCR promotes cleaner feature structure, stronger intra-class cohesion, and improved generalization, offering a new perspective on learning from prediction structure.

PDF Details

ICML Conference 2025 Conference Paper

Improving Zero-Shot Adversarial Robustness in Vision-Language Models by Closed-form Alignment of Adversarial Path Simplices

Junhao Dong 0001
Piotr Koniusz
Yifei Zhang
Hao Zhu 0010
Weiming Liu 0005
Xinghua Qu
Yew-Soon Ong

Vision-Language Models (VLMs) such as CLIP excel at zero-shot classification due to large-scale pre-training but are vulnerable to adversarial examples. Adversarial fine-tuning robustifies zero-shot models by aligning prediction scores of individual adversaries with their clean counterparts, which typically overlooks intermediate adversarial samples along the adversarial trajectory crossing the decision boundary. Such intermediate adversaries and their vicinity produce informative representations capturing the decision boundary in detail. They can be improved by sampling adversarial candidates from simplices formed by joining two consecutive vertices on the adversarial trajectory and their clean counterpart. However, sampling simplices for adversaries is very costly. To train robust VLM, we overcome these limitations by Taylor expansion and formulating an upper-bound of alignment loss that depends on the Jacobian/Hessian obtained at clean samples. As regions between clean and intermediate adversarial samples capture a larger decision landscape, we robustify VLM by plausible adversaries from simplices by our closed-form formulation equivalent to infinite uniform sampling of the simplex. We obtain state-of-the-art robustness across 15 datasets and diverse vision-language tasks.

Details

ICLR Conference 2025 Conference Paper

Learnable Expansion of Graph Operators for Multi-Modal Feature Fusion

Dexuan Ding
Lei Wang 0108
Liyun Zhu
Tom Gedeon
Piotr Koniusz

In computer vision tasks, features often come from diverse representations, domains (e.g., indoor and outdoor), and modalities (e.g., text, images, and videos). Effectively fusing these features is essential for robust performance, especially with the availability of powerful pre-trained models like vision-language models. However, common fusion methods, such as concatenation, element-wise operations, and non-linear techniques, often fail to capture structural relationships, deep feature interactions, and suffer from inefficiency or misalignment of features across domains or modalities. In this paper, we shift from high-dimensional feature space to a lower-dimensional, interpretable graph space by constructing relationship graphs that encode feature relationships at different levels, e.g., clip, frame, patch, token, etc. To capture deeper interactions, we expand graphs through iterative graph relationship updates and introduce a learnable graph fusion operator to integrate these expanded relationships for more effective fusion. Our approach is relationship-centric, operates in a homogeneous space, and is mathematically principled, resembling element-wise relationship score aggregation via multilinear polynomials. We demonstrate the effectiveness of our graph-based fusion method on video anomaly detection, showing strong performance across multi-representational, multi-modal, and multi-domain feature fusion tasks.

Details

NeurIPS Conference 2025 Conference Paper

Machine Unlearning via Task Simplex Arithmetic

Junhao Dong
Hao Zhu
Yifei Zhang
Xinghua Qu
Yew Soon Ong
Piotr Koniusz

As foundation Vision-Language Models (VLMs) unlock fine-tuning on smaller datasets while leveraging large-scale pre-training data, machine unlearning becomes critical in addressing privacy concerns and regulatory compliance. Task vector, representing the difference between parameters of models fine-tuned with and without specific data, is a popular retraining-free unlearning strategy. However, we observe that task vectors exhibit substantial sensitivity to various fine-tuning configurations, resulting in unstable unlearning effectiveness that correlates negatively with the prediction-level variance. While aggregating multiple functions (e. g. , VLM with classifier) whose parameters are represented by different task vectors reduces function variance and improves unlearning, the computational cost of obtaining numerous task vectors and aggregating functions is computationally high. Thus, in order to capture the space of task vectors induced by diverse fine-tuning strategies, we propose modeling it within the convex hull of $(Q-1)$-simplex whose vertices represent $Q$ task vectors. Although a function ensemble can be formed by sampling numerous task vectors from such a simplex, we derive a closed-form ensemble of an infinite number of functions whose parameters are uniformly sampled from the simplex, enabling efficient function-level task vector ensembling with enhanced unlearning performance. Extensive experiments and analyses across diverse datasets and scenarios demonstrate the efficacy of our method.

PDF Details

ICML Conference 2025 Conference Paper

Primitive Vision: Improving Diagram Understanding in MLLMs

Shan Zhang 0002
Aotian Chen
Yanpeng Sun
Jindong Gu
Yi-Yu Zheng
Piotr Koniusz
Kai Zou
Anton van den Hengel

Mathematical diagrams have a distinctive structure. Standard feature transforms designed for natural images (e. g. , CLIP) fail to process them effectively, limiting their utility in multimodal large language models (MLLMs). Current efforts to improve MLLMs have primarily focused on scaling mathematical visual instruction datasets and strengthening LLM backbones, yet fine-grained visual recognition errors remain unaddressed. Our systematic evaluation on the visual grounding capabilities of state-of-the-art MLLMs highlights that fine-grained visual understanding remains a crucial bottleneck in visual mathematical reasoning (GPT-4o exhibits a 70% grounding error rate, and correcting these errors improves reasoning accuracy by 12%). We thus propose a novel approach featuring a geometrically-grounded vision encoder and a feature router that dynamically selects between hierarchical visual feature maps. Our model accurately recognizes visual primitives and generates precise visual prompts aligned with the language model’s reasoning needs. In experiments, PRIMITIVE-Qwen2. 5-7B outperforms other 7B models by 12% on MathVerse and is on par with GPT-4V on MathVista. Our findings highlight the need for better fine-grained visual integration in MLLMs. Code is available at github. com/AI4Math-ShanZhang/SVE-Math.

Details

NeurIPS Conference 2025 Conference Paper

Robust SuperAlignment: Weak-to-Strong Robustness Generalization for Vision-Language Models

Junhao Dong
Cong Zhang
Xinghua Qu
Zejun Ma
Piotr Koniusz
Yew Soon Ong

Numerous well-established studies have demonstrated the superhuman capabilities of modern Vision-Language Models (VLMs) across a wide range of tasks. However, growing is the doubt about the continuing availability of reliable high-quality labeling (supervision) from human annotators, leading to stagnation of the model's performance. To address this challenge, ``superalignment'' employs the so-called weak-to-strong generalization paradigm, where the supervision from a weak model can provide generalizable knowledge for a strong model. While effective in aligning knowledge for clean samples between the strong and weak models, the standard weak-to-strong approach typically fails to capture adversarial robustness, exposing strong VLMs to adversarial attacks. This inability to transfer adversarial robustness is because adversarial samples are normally missing in the superalignment stage. To this end, we are the first to propose the weak-to-strong (adversarial) robustness generalization method to elicit zero-shot robustness in large-scale models by an unsupervised scheme, mitigating the unreliable information source for alignment from two perspectives: alignment re-weighting and source guidance refinement. We analyze settings under which robustness generalization is possible. Extensive experiments across various vision-language benchmarks validate the effectiveness of our method in numerous scenarios, demonstrating its plug-and-play applicability to large-scale VLMs.

PDF Details

AAAI Conference 2024 Conference Paper

Detect Any Keypoints: An Efficient Light-Weight Few-Shot Keypoint Detector

Changsheng Lu
Piotr Koniusz

Recently the prompt-based models have become popular across various language and vision tasks. Following that trend, we perform few-shot keypoint detection (FSKD) by detecting any keypoints in a query image, given the prompts formed by support images and keypoints. FSKD can be applied to detecting keypoints and poses of diverse animal species. In order to maintain flexibility of detecting varying number of keypoints, existing FSKD approaches modulate query feature map per support keypoint, then detect the corresponding keypoint from each modulated feature via a detection head. Such a separation of modulation-detection makes model heavy and slow when the number of keypoints increases. To overcome this issue, we design a novel light-weight detector which combines modulation and detection into one step, with the goal of reducing the computational cost without the drop of performance. Moreover, to bridge the large domain shift of keypoints between seen and unseen species, we further improve our model with mean feature based contrastive learning to align keypoint distributions, resulting in better keypoint representations for FSKD. Compared to the state of the art, our light-weight detector reduces the number of parameters by 50%, training/test time by 50%, and achieves 5.62% accuracy gain on 1-shot novel keypoint detection in the Animal pose dataset. Our model is also robust to the number of keypoints and saves memory when evaluating a large number of keypoints (e.g., 1000) per episode.

PDF Details DOI

NeurIPS Conference 2024 Conference Paper

PACE: Marrying generalization in PArameter-efficient fine-tuning with Consistency rEgularization

Yao Ni
Shan Zhang
Piotr Koniusz

Parameter-Efficient Fine-Tuning (PEFT) effectively adapts pre-trained transformers to downstream tasks. However, the optimization of tasks performance often comes at the cost of generalizability in fine-tuned models. To address this issue, we theoretically connect smaller weight gradient norms during training and larger datasets to the improvements in model generalization. Motivated by this connection, we propose reducing gradient norms for enhanced generalization and aligning fine-tuned model with the pre-trained counterpart to retain knowledge from large-scale pre-training data. Yet, naive alignment does not guarantee gradient reduction and can potentially cause gradient explosion, complicating efforts to manage gradients. To address such an issue, we propose PACE, marrying generalization of PArameter-efficient fine-tuning with Consistency rEgularization. We perturb features learned from the adapter with the multiplicative noise and ensure the fine-tuned model remains consistent for same sample under different perturbations. Theoretical analysis shows that PACE not only implicitly regularizes gradients for enhanced generalization, but also implicitly aligns the fine-tuned and pre-trained models to retain knowledge. Experimental evidence supports our theories. PACE surpasses existing PEFT methods in visual adaptation tasks (VTAB-1k, FGVC, few-shot learning, domain adaptation) showcasing its potential for resource-efficient fine-tuning. It also improves LoRA in text classification (GLUE) and mathematical reasoning (GSM-8K).

PDF Details DOI

ICLR Conference 2024 Conference Paper

Pre-training with Random Orthogonal Projection Image Modeling

Maryam Haghighat
Peyman Moghadam
Shaheer Mohamed
Piotr Koniusz

Masked Image Modeling (MIM) is a powerful self-supervised strategy for visual pre-training without the use of labels. MIM applies random crops to input images, processes them with an encoder, and then recovers the masked inputs with a decoder, which encourages the network to capture and learn structural information about objects and scenes. The intermediate feature representations obtained from MIM are suitable for fine-tuning on downstream tasks. In this paper, we propose an Image Modeling framework based on random orthogonal projection instead of binary masking as in MIM. Our proposed Random Orthogonal Projection Image Modeling (ROPIM) reduces spatially-wise token information under guaranteed bound on the noise variance and can be considered as masking entire spatial image area under locally varying masking degrees. Since ROPIM uses a random subspace for the projection that realizes the masking step, the readily available complement of the subspace can be used during unmasking to promote recovery of removed information. In this paper, we show that using random orthogonal projection leads to superior performance compared to crop-based masking. We demonstrate state-of-the-art results on several popular benchmarks.

Details

NeurIPS Conference 2023 Conference Paper

Mitigating the Popularity Bias of Graph Collaborative Filtering: A Dimensional Collapse Perspective

Yifei Zhang
Hao Zhu
Yankai Chen
Zixing Song
Piotr Koniusz
Irwin King

Graph-based Collaborative Filtering (GCF) is widely used in personalized recommendation systems. However, GCF suffers from a fundamental problem where features tend to occupy the embedding space inefficiently (by spanning only a low-dimensional subspace). Such an effect is characterized in GCF by the embedding space being dominated by a few of popular items with the user embeddings highly concentrated around them. This enhances the so-called Matthew effect of the popularity bias where popular items are highly recommend whereas remaining items are ignored. In this paper, we analyze the above effect in GCF and reveal that the simplified graph convolution operation (typically used in GCF) shrinks the singular space of the feature matrix. As typical approaches (i. e. , optimizing the uniformity term) fail to prevent the embedding space degradation, we propose a decorrelation-enhanced GCF objective that promotes feature diversity by leveraging the so-called principle of redundancy reduction in embeddings. However, unlike conventional methods that use the Euclidean geometry to relax hard constraints for decorrelation, we exploit non-Euclidean geometry. Such a choice helps maintain the range space of the matrix and obtain small condition number, which prevents the embedding space degradation. Our method outperforms contrastive-based GCF models on several benchmark datasets and improves the performance for unpopular items.

PDF Details

NeurIPS Conference 2023 Conference Paper

NICE: NoIse-modulated Consistency rEgularization for Data-Efficient GANs

Yao Ni
Piotr Koniusz

Generative Adversarial Networks (GANs) are powerful tools for image synthesis. However, they require access to vast amounts of training data, which is often costly and prohibitive. Limited data affects GANs, leading to discriminator overfitting and training instability. In this paper, we present a novel approach called NoIse-modulated Consistency rEgularization (NICE) to overcome these challenges. To this end, we introduce an adaptive multiplicative noise into the discriminator to modulate its latent features. We demonstrate the effectiveness of such a modulation in preventing discriminator overfitting by adaptively reducing the Rademacher complexity of the discriminator. However, this modulation leads to an unintended consequence of increased gradient norm, which can undermine the stability of GAN training. To mitigate this undesirable effect, we impose a constraint on the discriminator, ensuring its consistency for the same inputs under different noise modulations. The constraint effectively penalizes the first and second-order gradients of latent features, enhancing GAN stability. Experimental evidence aligns with our theoretical analysis, demonstrating the reduction of generalization error and gradient penalization of NICE. This substantiates the efficacy of NICE in reducing discriminator overfitting and improving stability of GAN training. NICE achieves state-of-the-art results on CIFAR-10, CIFAR-100, ImageNet and FFHQ datasets when trained with limited data, as well as in low-shot generation tasks.

PDF Details

AAAI Conference 2023 Conference Paper

Spectral Feature Augmentation for Graph Contrastive Learning and Beyond

Yifei Zhang
Hao Zhu
Zixing Song
Piotr Koniusz
Irwin King

Although augmentations (e.g., perturbation of graph edges, image crops) boost the efficiency of Contrastive Learning (CL), feature level augmentation is another plausible, complementary yet not well researched strategy. Thus, we present a novel spectral feature argumentation for contrastive learning on graphs (and images). To this end, for each data view, we estimate a low-rank approximation per feature map and subtract that approximation from the map to obtain its complement. This is achieved by the proposed herein incomplete power iteration, a non-standard power iteration regime which enjoys two valuable byproducts (under mere one or two iterations): (i) it partially balances spectrum of the feature map, and (ii) it injects the noise into rebalanced singular values of the feature map (spectral augmentation). For two views, we align these rebalanced feature maps as such an improved alignment step can focus more on less dominant singular values of matrices of both views, whereas the spectral augmentation does not affect the spectral angle alignment (singular vectors are not perturbed). We derive the analytical form for: (i) the incomplete power iteration to capture its spectrum-balancing effect, and (ii) the variance of singular values augmented implicitly by the noise. We also show that the spectral augmentation improves the generalization bound. Experiments on graph/image datasets show that our spectral feature augmentation outperforms baselines, and is complementary with other augmentation strategies and compatible with various contrastive losses.

PDF Details DOI

NeurIPS Conference 2022 Conference Paper

Generalized Laplacian Eigenmaps

Hao Zhu
Piotr Koniusz

Graph contrastive learning attracts/disperses node representations for similar/dissimilar node pairs under some notion of similarity. It may be combined with a low-dimensional embedding of nodes to preserve intrinsic and structural properties of a graph. COLES, a recent graph contrastive method combines traditional graph embedding and negative sampling into one framework. COLES in fact minimizes the trace difference between the within-class scatter matrix encapsulating the graph connectivity and the total scatter matrix encapsulating negative sampling. In this paper, we propose a more essential framework for graph embedding, called Generalized Laplacian EigeNmaps (GLEN), which learns a graph representation by maximizing the rank difference between the total scatter matrix and the within-class scatter matrix, resulting in the minimum class separation guarantee. However, the rank difference minimization is an NP-hard problem. Thus, we replace the trace difference that corresponds to the difference of nuclear norms by the difference of LogDet expressions, which we argue is a more accurate surrogate for the NP-hard rank difference than the trace difference. While enjoying a lesser computational cost, the difference of LogDet terms is lower-bounded by the Affine-invariant Riemannian metric (AIRM) and Jesen-Bregman the LogDet Divergence (JBLD), and upper-bounded by AIRM scaled by the factor of $\sqrt{m}$. We show that GLEN offers favourable accuracy/scalability compared to state-of-the-art baselines.

PDF Details

ICLR Conference 2021 Conference Paper

Simple Spectral Graph Convolution

Hao Zhu 0010
Piotr Koniusz

Graph Convolutional Networks (GCNs) are leading methods for learning graph representations. However, without specially designed architectures, the performance of GCNs degrades quickly with increased depth. As the aggregated neighborhood size and neural network depth are two completely orthogonal aspects of graph representation, several methods focus on summarizing the neighborhood by aggregating K-hop neighborhoods of nodes while using shallow neural networks. However, these methods still encounter oversmoothing, and suffer from high computation and storage costs. In this paper, we use a modified Markov Diffusion Kernel to derive a variant of GCN called Simple Spectral Graph Convolution (SSGC). Our spectral analysis shows that our simple spectral graph convolution used in SSGC is a trade-off of low- and high-pass filter bands which capture the global and local contexts of each node. We provide two theoretical claims which demonstrate that we can aggregate over a sequence of increasingly larger neighborhoods compared to competitors while limiting severe oversmoothing. Our experimental evaluations show that SSGC with a linear learner is competitive in text and node classification tasks. Moreover, SSGC is comparable to other state-of-the-art methods for node clustering and community prediction tasks.

Details

UAI Conference 2019 Conference Paper

Fisher-Bures Adversary Graph Convolutional Networks

Ke Sun 0001
Piotr Koniusz
Z. Jane Wang 0001

In a graph convolutional network, we assume that the graph $G$ is generated wrt some observation noise. During learning, we make small random perturbations $\Delta{}G$ of the graph and try to improve generalization. Based on quantum information geometry, $\Delta{}G$ can be characterized by the eigendecomposition of the graph Laplacian matrix. We try to minimize the loss wrt the perturbed $G+\Delta{G}$ while making $\Delta{G}$ to be effective in terms of the Fisher information of the neural network. Our proposed model can consistently improve graph convolutional networks on semi-supervised node classification tasks with reasonable computational overhead. We present three different geometries on the manifold of graphs: the intrinsic geometry measures the information theoretic dynamics of a graph; the extrinsic geometry characterizes how such dynamics can affect externally a graph neural network; the embedding geometry is for measuring node embeddings. These new analytical tools are useful in developing a good understanding of graph neural networks and fostering new techniques.

Details

NeurIPS Conference 2014 Conference Paper

Convolutional Kernel Networks

Julien Mairal
Piotr Koniusz
Zaid Harchaoui
Cordelia Schmid

An important goal in visual recognition is to devise image representations that are invariant to particular transformations. In this paper, we address this goal with a new type of convolutional neural network (CNN) whose invariance is encoded by a reproducing kernel. Unlike traditional approaches where neural networks are learned either to represent data or for solving a classification task, our network learns to approximate the kernel feature map on training data. Such an approach enjoys several benefits over classical ones. First, by teaching CNNs to be invariant, we obtain simple network architectures that achieve a similar accuracy to more complex ones, while being easy to train and robust to overfitting. Second, we bridge a gap between the neural network literature and kernels, which are natural tools to model invariance. We evaluate our methodology on visual recognition tasks where CNNs have proven to perform well, e. g. , digit recognition with the MNIST dataset, and the more challenging CIFAR-10 and STL-10 datasets, where our accuracy is competitive with the state of the art.

PDF Details