Jialin Zhao

Jialin Zhao, Yingtao Zhang, Carlo Vittorio Cannistraci

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.

Jialin Zhao

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.

Yingtao Zhang, Diego Cerretti, Jialin Zhao et al.

Dynamic sparse training (DST) can reduce the computational demands in ANNs, but faces difficulties in keeping peak performance at high sparsity levels. The Cannistraci-Hebb training (CHT) is a brain-inspired method for growing connectivity in DST. CHT leverages a gradient-free, topology-driven link regrowth, which has shown ultra-sparse (less than 1% connectivity) advantage across various tasks compared to fully connected networks. Yet, CHT suffers two main drawbacks: (i) its time complexity is $O(Nd^3)$ - N node network size, d node degree - restricting it to ultra-sparse regimes. (ii) it selects top link prediction scores, which is inappropriate for the early training epochs, when the network presents unreliable connections. Here, we design the first brain-inspired network model - termed bipartite receptive field (BRF) - to initialize the connectivity of sparse artificial neural networks. We further introduce a GPU-friendly matrix-based approximation of CH link prediction, reducing complexity to $O(N^3)$. We introduce the Cannistraci-Hebb training soft rule (CHTs), which adopts a flexible strategy for sampling connections in both link removal and regrowth, balancing the exploration and exploitation of network topology. Additionally, we integrate CHTs with a sigmoid gradual density decay (CHTss). Empirical results show that BRF offers performance advantages over previous network science models. Using 1% of connections, CHTs outperforms fully connected networks in MLP architectures on image classification tasks, compressing some networks to less than 30% of the nodes. Using 5% of the connections, CHTss outperforms fully connected networks in two Transformer-based machine translation tasks. Finally, at 30% connectivity, both CHTs and CHTss outperform other DST methods in language modeling and even exceed fully connected baselines in zero-shot tasks.

Jialin Zhao, Yingtao Zhang, Xinghang Li et al.

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.