Carlo Vittorio Cannistraci

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.

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.

Yan Ge, Philipp Rosendahl, Claudio Durán et al.

Despite fluorescent cell-labelling being widely employed in biomedical studies, some of its drawbacks are inevitable, with unsuitable fluorescent probes or probes inducing a functional change being the main limitations. Consequently, the demand for and development of label-free methodologies to classify cells is strong and its impact on precision medicine is relevant. Towards this end, high-throughput techniques for cell mechanical phenotyping have been proposed to get a multidimensional biophysical characterization of single cells. With this motivation, our goal here is to investigate the extent to which an unsupervised machine learning methodology, which is applied exclusively on morpho-rheological markers obtained by real-time deformability and fluorescence cytometry (RT-FDC), can address the difficult task of providing label-free discrimination of reticulocytes from mature red blood cells. We focused on this problem, since the characterization of reticulocytes (their percentage and cellular features) in the blood is vital in multiple human disease conditions, especially bone-marrow disorders such as anemia and leukemia. Our approach reports promising label-free results in the classification of reticulocytes from mature red blood cells, and it represents a step forward in the development of high-throughput morpho-rheological-based methodologies for the computational categorization of single cells. Besides, our methodology can be an alternative but also a complementary method to integrate with existing cell-labelling techniques.

A. Acevedo, S. Ciucci, MJ. Kuo et al.

Evaluating data separation in a geometrical space is fundamental for pattern recognition. A plethora of dimensionality reduction (DR) algorithms have been developed in order to reveal the emergence of geometrical patterns in a low dimensional visible representation space, in which high-dimensional samples similarities are approximated by geometrical distances. However, statistical measures to evaluate directly in the low dimensional geometrical space the sample group separability attaiend by these DR algorithms are missing. Certainly, these separability measures could be used both to compare algorithms performance and to tune algorithms parameters. Here, we propose three statistical measures (named as PSI-ROC, PSI-PR, and PSI-P) that have origin from the Projection Separability (PS) rationale introduced in this study, which is expressly designed to assess group separability of data samples in a geometrical space. Traditional cluster validity indices (CVIs) might be applied in this context but they show limitations because they are not specifically tailored for DR. Our PS measures are compared to six baseline cluster validity indices, using five non-linear datasets and six different DR algorithms. The results provide clear evidence that statistical-based measures based on PS rationale are more accurate than CVIs and can be adopted to control the tuning of parameter-dependent DR algorithms.

C. Duran, A. Acevedo, S. Ciucci et al.

The development of algorithms for unsupervised pattern recognition by nonlinear clustering is a notable problem in data science. Markov clustering (MCL) is a renowned algorithm that simulates stochastic flows on a network of sample similarities to detect the structural organization of clusters in the data, but it has never been generalized to deal with data nonlinearity. Minimum Curvilinearity (MC) is a principle that approximates nonlinear sample distances in the high-dimensional feature space by curvilinear distances, which are computed as transversal paths over their minimum spanning tree, and then stored in a kernel. Here we propose MC-MCL, which is the first nonlinear kernel extension of MCL and exploits Minimum Curvilinearity to enhance the performance of MCL in real and synthetic data with underlying nonlinear patterns. MC-MCL is compared with baseline clustering methods, including DBSCAN, K-means and affinity propagation. We find that Minimum Curvilinearity provides a valuable framework to estimate nonlinear distances also when its kernel is applied in combination with MCL. Indeed, MC-MCL overcomes classical MCL and even baseline clustering algorithms in different nonlinear datasets.

Alessandro Muscoloni, Carlo Vittorio Cannistraci

Analysis of 'big data' characterized by high-dimensionality such as word vectors and complex networks requires often their representation in a geometrical space by embedding. Recent developments in machine learning and network geometry have pointed out the hyperbolic space as a useful framework for the representation of this data derived by real complex physical systems. In the hyperbolic space, the radial coordinate of the nodes characterizes their hierarchy, whereas the angular distance between them represents their similarity. Several studies have highlighted the relationship between the angular coordinates of the nodes embedded in the hyperbolic space and the community metadata available. However, such analyses have been often limited to a visual or qualitative assessment. Here, we introduce the angular separation index (ASI), to quantitatively evaluate the separation of node network communities or data clusters over the angular coordinates of a geometrical space. ASI is particularly useful in the hyperbolic space - where it is extensively tested along this study - but can be used in general for any assessment of angular separation regardless of the adopted geometry. ASI is proposed together with an exact test statistic based on a uniformly random null model to assess the statistical significance of the separation. We show that ASI allows to discover two significant phenomena in network geometry. The first is that the increase of temperature in 2D hyperbolic network generative models, not only reduces the network clustering but also induces a 'dimensionality jump' of the network to dimensions higher than two. The second is that ASI can be successfully applied to detect the intrinsic dimensionality of network structures that grow in a hidden geometrical space.

Carlo Vittorio Cannistraci, Alessandro Muscoloni

Affinity propagation is one of the most effective unsupervised pattern recognition algorithms for data clustering in high-dimensional feature space. However, the numerous attempts to test its performance for community detection in complex networks have been attaining results very far from the state of the art methods such as Infomap and Louvain. Yet, all these studies agreed that the crucial problem is to convert the unweighted network topology in a 'smart-enough' node dissimilarity matrix that is able to properly address the message passing procedure behind affinity propagation clustering. Here we introduce a conceptual innovation and we discuss how to leverage network latent geometry notions in order to design dissimilarity matrices for affinity propagation community detection. Our results demonstrate that the latent geometry inspired dissimilarity measures we design bring affinity propagation to equal or outperform current state of the art methods for community detection. These findings are solidly proven considering both synthetic 'realistic' networks (with known ground-truth communities) and real networks (with community metadata), even when the data structure is corrupted by noise artificially induced by missing or spurious connectivity.

Josephine Maria Thomas, Alessandro Muscoloni, Sara Ciucci et al.

Complex network topologies and hyperbolic geometry seem specularly connected, and one of the most fascinating and challenging problems of recent complex network theory is to map a given network to its hyperbolic space. The Popularity Similarity Optimization (PSO) model represents - at the moment - the climax of this theory. It suggests that the trade-off between node popularity and similarity is a mechanism to explain how complex network topologies emerge - as discrete samples - from the continuous world of hyperbolic geometry. The hyperbolic space seems appropriate to represent real complex networks. In fact, it preserves many of their fundamental topological properties, and can be exploited for real applications such as, among others, link prediction and community detection. Here, we observe for the first time that a topological-based machine learning class of algorithms - for nonlinear unsupervised dimensionality reduction - can directly approximate the network's node angular coordinates of the hyperbolic model into a two-dimensional space, according to a similar topological organization that we named angular coalescence. On the basis of this phenomenon, we propose a new class of algorithms that offers fast and accurate coalescent embedding of networks in the hyperbolic space even for graphs with thousands of nodes.