publications

2026

1. ICLR’26

   A Generalized Geometric Theoretical Framework of Centroid Discriminant Analysis for Linear Classification of Multi-dimensional Data

   Yue Wu, Jialin Zhao, and Carlo Vittorio Cannistraci^{^}

   ICLR’26: The Fourteenth International Conference on Learning Representations , 2026

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   With the advent of the neural network era, traditional machine learning methods have increasingly been overshadowed. Nevertheless, continuing research on the role of geometry for learning in data science is crucial to envision and understand new principles behind the design of efficient machine learning. Linear classifiers are favored in certain tasks due to their reduced susceptibility to overfitting and their ability to provide interpretable decision boundaries. However, achieving both scalability and high predictive performance in linear classification remains a persistent challenge. Here, we propose a theoretical framework named geometric discriminant analysis (GDA). GDA includes the family of linear classifiers that can be expressed as a function of a centroid discriminant basis (CDB0) - the connection line between two centroids - adjusted by geometric corrections under different constraints. We demonstrate that linear discriminant analysis (LDA) is a subcase of the GDA theoretical framework, and we show its convergence to CDB0 under certain conditions. Then, based on the GDA framework, we propose an efficient linear classifier named centroid discriminant analysis (CDA) which is defined as a special case of GDA under a 2D plane geometric constraint. CDA training is initialized starting from CDB0 and involves the iterative calculation of new adjusted centroid discriminant lines whose optimal rotations on the associated 2D planes are searched via Bayesian optimization. CDA has good scalability (quadratic time complexity) which is lower than LDA and support vector machine (SVM) (cubic complexity). Results on 27 real datasets across classification tasks of standard images, medical images and chemical properties, offer empirical evidence that CDA outperforms other linear methods such as LDA, SVM and logistic regression (LR) in terms of scalability, performance and stability. Furthermore, we show that linear CDA can be generalized to nonlinear CDA via kernel method, demonstrating improvements on the linear version with tests on three challenging datasets of images and chemical data. GDA’s general validity as a new theoretical framework may inspire the design of new classifiers under the definition of different geometric constraints, paving the way towards a deeper understanding of the role of geometry in learning from data.

2. ICLR’26

   Alignment-Enhanced Integration of Connectivity and Spectral Sparsity in Dynamic Sparse Training of LLM

   Wenjing Wu, Yingtao Zhang, Jialin Zhao, and Carlo Vittorio Cannistraci^{^}

   ICLR’26: The Fourteenth International Conference on Learning Representations , 2026

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   With the rapid development of large language models (LLMs), identifying efficient strategies for training such large-scale systems has become increasingly critical. Although LLMs have achieved remarkable success across diverse applications, the necessity of maintaining full dense matrices during pre-training has been questioned, giving rise to parameter-efficient sparse pre-training methods which retains parameter-efficiency in both training and inference. These methods can be further divided into connectivity sparse training and spectral sparse training, with dynamic connectivity sparse training and low-rank factorization emerging as representative approaches for the two branches. However, a unified framework that effectively combines the strengths of both has yet to be established. In this work, we observe that the cancellation effect between the sparse and low-rank branches may limit the expressivity of the model, manifesting as output conflicts when the two components are combined. To address this issue, we first quantify the cancellation effect using the overlap cancellation ratio (OCR) and then propose a novel scheme that integrates dynamic sparse training with low-rank training, introducing a simple yet effective alignment loss to mitigate the disagreement between the two branches and promote better collaboration. We validate this scheme by combining a representative dynamic sparse training method, CHTs, with low-rank training, resulting in a new parameter-efficient training approach termed CHTsL. The method is evaluated on LLaMA60M and LLaMA130M using the OpenWebText and C4 datasets, where only 10%, 20%, and 30% of the parameters are preserved compared to dense training. Experimental results demonstrate that our proposed scheme effectively alleviates the cancellation effect, especially in the Q and K matrices of the attention layers, and improves training stability and performance compared to the naive combination of sparse and low-rank components. Additionally, the new scheme enables CHTsL to consistently outperform other parameter-efficient sparse training methods under the same parameter budget, achieving performance closest to that of dense training.

2025

1. Preprint

   Accelerating Attention with Basis Decomposition

   Jialin Zhao^{^}

   Preprint: Under review, 2025

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   Attention is a core operation in large language models (LLMs) and vision-language models (VLMs). We present BD Attention (BDA), the first lossless algorithmic reformulation of attention. BDA is enabled by a simple matrix identity from Basis Decomposition (BD), which restructures multi-head projections into a compact form while preserving exact outputs. Unlike I/O-aware system optimizations such as FlashAttention, BDA provides a mathematically guaranteed acceleration that is architecture-agnostic. On DeepSeek-V2-Lite (16B, FP16), BDA requires only 4s of offline preparation with no retraining required and, on modern GPUs, achieves 32% faster key/value projections and 25% smaller weights, while increasing end-to-end perplexity (PPL) by just 0.02% (FP16) or 0.0004% (FP32)—a negligible effect on model performance. These results position BDA as the first theoretically exact method for lossless attention acceleration that is complementary to existing engineering-level optimizations. Our code is available at https://github.com/abcbdf/basis-decomposition-official

2. ICML’25

   Pivoting Factorization: A Compact Meta Low-Rank Representation of Sparsity for Efficient Inference in Large Language Models

   Jialin Zhao^{^}, Yingtao Zhang, and Carlo Vittorio Cannistraci^{^}

   ICML’25: Forty-second International Conference on Machine Learning , 2025

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   The rapid growth of Large Language Models has driven demand for effective model compression techniques to reduce memory and computation costs. Low-rank pruning has gained attention for its GPU compatibility across all densities. However, low-rank pruning struggles to match the performance of semi-structured pruning, often doubling perplexity at similar densities. In this paper, we propose Pivoting Factorization (PIFA), a novel lossless meta low-rank representation that unsupervisedly learns a compact form of any low-rank representation, effectively eliminating redundant information. PIFA identifies pivot rows (linearly independent rows) and expresses non-pivot rows as linear combinations, achieving 24.2% additional memory savings and 24.6% faster inference over low-rank layers at rank = 50% of dimension. To mitigate the performance degradation caused by low-rank pruning, we introduce a novel, retraining-free reconstruction method that minimizes error accumulation (M). MPIFA, combining M and PIFA into an end-to-end framework, significantly outperforms existing low-rank pruning methods, and achieves performance comparable to semi-structured pruning, while surpassing it in GPU efficiency and compatibility. Our code is available at https://github.com/biomedical-cybernetics/pivoting-factorization.

3. ICML’25

   Sparse Spectral Training and Inference on Euclidean and Hyperbolic Neural Networks

   Jialin Zhao^{^}, Yingtao Zhang, Xinghang Li, Huaping Liu, and Carlo Vittorio Cannistraci^{^}

   ICML’25: Forty-second International Conference on Machine Learning , 2025

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   The growing demands on GPU memory posed by the increasing number of neural network parameters call for training approaches that are more memory-efficient. Previous memory reduction training techniques, such as Low-Rank Adaptation (LoRA) and ReLoRA, face challenges, with LoRA being constrained by its low-rank structure, particularly during intensive tasks like pre-training, and ReLoRA suffering from saddle point issues. In this paper, we propose Sparse Spectral Training (SST) to optimize memory usage for pre-training. SST updates all singular values and selectively updates singular vectors through a multinomial sampling method weighted by the magnitude of the singular values. Furthermore, SST employs singular value decomposition to initialize and periodically reinitialize low-rank parameters, reducing distortion relative to full-rank training compared to other low-rank methods. Through comprehensive testing on both Euclidean and hyperbolic neural networks across various tasks, SST demonstrates its ability to outperform existing memory reduction training methods and is comparable to full-rank training in various cases. On LLaMA-1.3B, with only 18.7% of the parameters trainable compared to full-rank training (using a rank equivalent to 6% of the embedding dimension), SST reduces the perplexity gap between other low-rank methods and full-rank training by 97.4%. This result highlights SST as an effective parameter-efficient technique for model pre-training.

4. NeurIPS’25

   Adaptive Cannistraci-Hebb Network Automata Modelling of Complex Networks for Path-based Link Prediction

   Jialin Zhao, Alessandro Muscoloni, Umberto Michieli, Yingtao Zhang, and Carlo Vittorio Cannistraci^{^}

   NeurIPS’25: Advances in neural information processing systems, 2025
5. NeurIPS’25

   Brain network science modelling of sparse neural networks enables Transformers and LLMs to perform as fully connected

   Yingtao Zhang, Diego Cerretti, Jialin Zhao, Wenjing Wu, Ziheng Liao, Umberto Michieli, and Carlo Vittorio Cannistraci^{^}

   NeurIPS’25: Advances in neural information processing systems, 2025

2024

1. ICLR’24

   Plug-and-Play: An Efficient Post-training Pruning Method for Large Language Models

   Yingtao Zhang^{^}, Haoli Bai, Haokun Lin, Jialin Zhao, Lu Hou, and Carlo Vittorio Cannistraci^{^}

   ICLR’24: The Twelfth International Conference on Learning Representations , 2024

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   With the rapid growth of large language models (LLMs), there is increasing demand for memory and computation in LLMs. Recent efforts on post-training pruning of LLMs aim to reduce the model size and computation requirements, yet the performance is still sub-optimal. In this paper, we present a plug-and-play solution for post-training pruning of LLMs. The proposed solution has two innovative components: 1) Relative Importance and Activations (RIA), a new pruning metric that jointly considers the weight and activations efficiently on LLMs, and 2) Channel Permutation, a new approach to maximally preserves important weights under N:M sparsity. The two proposed components can be readily combined to further enhance the N:M semi-structured pruning of LLMs. Our empirical experiments show that RIA alone can already surpass all existing post-training pruning methods on prevalent LLMs, e.g., LLaMA ranging from 7B to 65B. Furthermore, N:M semi-structured pruning with channel permutation can even outperform the original LLaMA2-70B on zero-shot tasks, together with practical speed-up on specific hardware. Our code is available at: https://github.com/biomedical-cybernetics/Relative-importance-and-activation-pruning

2. ICLR’24

   Epitopological learning and Cannistraci-Hebb network shape intelligence brain-Inspired theory for ultra-sparse advantage in deep learning

   Yingtao Zhang, Jialin Zhao, Wenjing Wu, Alessandro Muscoloni, and Carlo Vittorio Cannistraci^{^}

   ICLR’24: The Twelfth International Conference on Learning Representations , 2024

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   Sparse training (ST) aims to ameliorate deep learning by replacing fully connected artificial neural networks (ANNs) with sparse or ultra-sparse ones, such as brain networks are, therefore it might benefit to borrow brain-inspired learning paradigms from complex network intelligence theory. Here, we launch the ultra-sparse advantage challenge, whose goal is to offer evidence on the extent to which ultra-sparse (around 1% connection retained) topologies can achieve any leaning advantage against fully connected. Epitopological learning is a field of network science and complex network intelligence that studies how to implement learning on complex networks by changing the shape of their connectivity structure (epitopological plasticity). One way to implement Epitopological (epi- means new) Learning is via link prediction: predicting the likelihood of non-observed links to appear in the network. Cannistraci-Hebb learning theory inspired the CH3-L3 network automata rule for link prediction which is effective for general-purpose link prediction. Here, starting from CH3-L3 we propose Epitopological Sparse Meta-deep Learning (ESML) to apply Epitopological Learning to sparse training. In empirical experiments, we find that ESML learns ANNs with ultra-sparse hyperbolic (epi-)topology in which emerges a community layer organization that is meta-deep (meaning that each layer also has an internal depth due to power-law node hierarchy). Furthermore, we discover that ESML can in many cases automatically sparse the neurons during training (arriving even to 30% neurons left in hidden layers), this process of node dynamic removal is called percolation. Starting from this network science evidence, we design Cannistraci-Hebb training (CHT), a 4-step training methodology that puts ESML at its heart. We conduct experiments on 7 datasets and 5 network structures comparing CHT to dynamic sparse training SOTA algorithms and the fully connected counterparts. The results indicate that, with a mere 1% of links retained during training, CHT surpasses fully connected networks on VGG16, GoogLeNet, ResNet50, and ResNet152. This key finding is an evidence for ultra-sparse advantage and signs a milestone in deep learning. CHT acts akin to a gradient-free oracle that adopts CH3-L3-based epitopological learning to guide the placement of new links in the ultra-sparse network topology to facilitate sparse-weight gradient learning, and this in turn reduces the convergence time of ultra-sparse training. Finally, CHT offers the first examples of parsimony dynamic sparse training because, in many datasets, it can retain network performance by percolating and significantly reducing the node network size. Our code is available at: https://github.com/biomedical-cybernetics/Cannistraci-Hebb-training

2021

1. NeurIPS’21

   Adaptive Cannistraci-Hebb Network Automata Modelling of Complex Networks for Path-based Link Prediction

   Jialin Zhao, Yuxiao Dong, Ming Ding, Evgeny Kharlamov, and Jie Tang^{^}

   NeurIPS’21: Advances in neural information processing systems, 2021

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   The success of graph neural networks (GNNs) largely relies on the process of aggregating information from neighbors defined by the input graph structures. Notably, message passing based GNNs, e.g., graph convolutional networks, leverage the immediate neighbors of each node during the aggregation process, and recently, graph diffusion convolution (GDC) is proposed to expand the propagation neighborhood by leveraging generalized graph diffusion. However, the neighborhood size in GDC is manually tuned for each graph by conducting grid search over the validation set, making its generalization practically limited. To address this issue, we propose the adaptive diffusion convolution (ADC) strategy to automatically learn the optimal neighborhood size from the data. Furthermore, we break the conventional assumption that all GNN layers and feature channels (dimensions) should use the same neighborhood for propagation. We design strategies to enable ADC to learn a dedicated propagation neighborhood for each GNN layer and each feature channel, making the GNN architecture fully coupled with graph structures—the unique property that differs GNNs from traditional neural networks. By directly plugging ADC into existing GNNs, we observe consistent and significant outperformance over both GDC and their vanilla versions across various datasets, demonstrating the improved model capacity brought by automatically learning unique neighborhood size per layer and per channel in GNNs.