Predicting signed interactions in biological networks is crucial for understanding drug mechanisms and facilitating drug repurposing. While deep graph models have demonstrated success in modeling complex biological systems, existing approaches often fail to distinguish between positive and negative interactions, limiting their utility for precise pharmacological predictions. In this study, we propose a novel deep graph model, \textbf{RGCNTD} (Relational Graph Convolutional Network with Tensor Decomposition), designed to predict both polar (e.g., activation, inhibition) and non-polar (e.g., binding, affect) chemical-gene interactions. Our model integrates graph convolutional networks with tensor decomposition to enhance feature representation and incorporates a conflict-aware sampling strategy to resolve polarity ambiguities. We introduce new evaluation metrics, \textit{AUC\textsubscript{polarity}} and \textit{CP@500}, to assess the model's ability to differentiate interaction types. Experimental results demonstrate that \textbf{RGCNTD} outperforms baseline models, achieving superior classification accuracy and improved discrimination of polar edges. Furthermore, we analyze the impact of subgraph components on predictive performance, revealing that additional network structures do not always enhance accuracy. These findings highlight the importance of polarity-aware modeling in drug discovery and network pharmacology, providing a robust framework for predicting complex biological interactions.
We introduce MIGS (Multi-Identity Gaussian Splatting), a novel method that learns a single neural representation for multiple identities, using only monocular videos. Recent 3D Gaussian Splatting (3DGS) approaches for human avatars require per-identity optimization. However, learning a multi-identity representation presents advantages in robustly animating humans under arbitrary poses. We propose to construct a high-order tensor that combines all the learnable 3DGS parameters for all the training identities. By assuming a low-rank structure and factorizing the tensor, we model the complex rigid and non-rigid deformations of multiple subjects in a unified network, significantly reducing the total number of parameters. Our proposed approach leverages information from all the training identities and enables robust animation under challenging unseen poses, outperforming existing approaches. It can also be extended to learn unseen identities.
Linear causal disentanglement is a recent method in causal representation learning to describe a collection of observed variables via latent variables with causal dependencies between them. It can be viewed as a generalization of both independent component analysis and linear structural equation models. We study the identifiability of linear causal disentanglement, assuming access to data under multiple contexts, each given by an intervention on a latent variable. We show that one perfect intervention on each latent variable is sufficient and in the worst case necessary to recover parameters under perfect interventions, generalizing previous work to allow more latent than observed variables. We give a constructive proof that computes parameters via a coupled tensor decomposition. For soft interventions, we find the equivalence class of latent graphs and parameters that are consistent with observed data, via the study of a system of polynomial equations. Our results hold assuming the existence of non-zero higher-order cumulants, which implies non-Gaussianity of variables.
In recent years, there has been growing interest in jointly analyzing a foreground dataset, representing an experimental group, and a background dataset, representing a control group. The goal of such contrastive investigations is to identify salient features in the experimental group relative to the control. Independent component analysis (ICA) is a powerful tool for learning independent patterns in a dataset. We generalize it to contrastive ICA (cICA). For this purpose, we devise a new linear algebra based tensor decomposition algorithm, which is more expressive but just as efficient and identifiable as other linear algebra based algorithms. We establish the identifiability of cICA and demonstrate its performance in finding patterns and visualizing data, using synthetic, semi-synthetic, and real-world datasets, comparing the approach to existing methods.
The (efficient and parsimonious) decomposition of higher-order tensors is a fundamental problem with numerous applications in a variety of fields. Several methods have been proposed in the literature to that end, with the Tucker and PARAFAC decompositions being the most prominent ones. Inspired by the latter, in this work we propose a multi-resolution low-rank tensor decomposition to describe (approximate) a tensor in a hierarchical fashion. The central idea of the decomposition is to recast the tensor into \emph{multiple} lower-dimensional tensors to exploit the structure at different levels of resolution. The method is first explained, an alternating least squares algorithm is discussed, and preliminary simulations illustrating the potential practical relevance are provided.
Recent research has shown that pruning large-scale language models for inference is an effective approach to improving model efficiency, significantly reducing model weights with minimal impact on performance. Interestingly, pruning can sometimes even enhance accuracy by removing noise that accumulates during training, particularly through matrix decompositions. However, recent work has primarily focused on single matrix decompositions or lower precision techniques, which may fail to fully capture structural patterns. To address these limitations, we introduce TRAWL (Tensor Reduced and Approximated Weights for Large Language Models), a technique that applies tensor decomposition across multiple weight matrices to effectively denoise LLMs by capturing global structural patterns. Our experiments show that TRAWL improves model performance by up to 16% over baseline models on benchmark datasets, without requiring additional data, training, or fine-tuning.
The unsourced random access (URA) has emerged as a viable scheme for supporting the massive machine-type communications (mMTC) in the sixth generation (6G) wireless networks. Notably, the tensor-based URA (TURA), with its inherent tensor structure, stands out by simultaneously enhancing performance and reducing computational complexity for the multi-user separation, especially in mMTC networks with a large numer of active devices. However, current TURA scheme lacks the soft decoder, thus precluding the incorporation of existing advanced coding techniques. In order to fully explore the potential of the TURA, this paper investigates the Polarcoded TURA (PTURA) scheme and develops the corresponding iterative Bayesian receiver with feedback (IBR-FB). Specifically, in the IBR-FB, we propose the Grassmannian modulation-aided Bayesian tensor decomposition (GM-BTD) algorithm under the variational Bayesian learning (VBL) framework, which leverages the property of the Grassmannian modulation to facilitate the convergence of the VBL process, and has the ability to generate the required soft information without the knowledge of the number of active devices. Furthermore, based on the soft information produced by the GM-BTD, we design the soft Grassmannian demodulator in the IBR-FB. Extensive simulation results demonstrate that the proposed PTURA in conjunction with the IBR-FB surpasses the existing state-of-the-art unsourced random access scheme in terms of accuracy and computational complexity.
Large language models (LLMs) demonstrate outstanding performance in various tasks in machine learning and have thus become one of the most important workloads in today's computing landscape. However, deploying LLM inference poses challenges due to the high compute and memory requirements stemming from the enormous model size and the difficulty of running it in the integer pipelines. In this paper, we present Tender, an algorithm-hardware co-design solution that enables efficient deployment of LLM inference at low precision. Based on our analysis of outlier values in LLMs, we propose a decomposed quantization technique in which the scale factors of decomposed matrices are powers of two apart. The proposed scheme allows us to avoid explicit requantization (i.e., dequantization/quantization) when accumulating the partial sums from the decomposed matrices, with a minimal extension to the commodity tensor compute hardware. Our evaluation shows that Tender achieves higher accuracy and inference performance compared to the state-of-the-art methods while also being significantly less intrusive to the existing accelerators.
Emphasis in the tensor literature on random embeddings (tools for low-distortion dimension reduction) for the canonical polyadic (CP) tensor decomposition has left analogous results for the more expressive Tucker decomposition comparatively lacking. This work establishes general Johnson-Lindenstrauss (JL) type guarantees for the estimation of Tucker decompositions when an oblivious random embedding is applied along each mode. When these embeddings are drawn from a JL-optimal family, the decomposition can be estimated within $\varepsilon$ relative error under restrictions on the embedding dimension that are in line with recent CP results. We implement a higher-order orthogonal iteration (HOOI) decomposition algorithm with random embeddings to demonstrate the practical benefits of this approach and its potential to improve the accessibility of otherwise prohibitive tensor analyses. On moderately large face image and fMRI neuroimaging datasets, empirical results show that substantial dimension reduction is possible with minimal increase in reconstruction error relative to traditional HOOI ($\leq$5% larger error, 50%-60% lower computation time for large models with 50% dimension reduction along each mode). Especially for large tensors, our method outperforms traditional higher-order singular value decomposition (HOSVD) and recently proposed TensorSketch methods.
Traditionally, the sensitivity analysis of a Bayesian network studies the impact of individually modifying the entries of its conditional probability tables in a one-at-a-time (OAT) fashion. However, this approach fails to give a comprehensive account of each inputs' relevance, since simultaneous perturbations in two or more parameters often entail higher-order effects that cannot be captured by an OAT analysis. We propose to conduct global variance-based sensitivity analysis instead, whereby $n$ parameters are viewed as uncertain at once and their importance is assessed jointly. Our method works by encoding the uncertainties as $n$ additional variables of the network. To prevent the curse of dimensionality while adding these dimensions, we use low-rank tensor decomposition to break down the new potentials into smaller factors. Last, we apply the method of Sobol to the resulting network to obtain $n$ global sensitivity indices. Using a benchmark array of both expert-elicited and learned Bayesian networks, we demonstrate that the Sobol indices can significantly differ from the OAT indices, thus revealing the true influence of uncertain parameters and their interactions.
Second-order Recurrent Neural Networks (2RNNs) extend RNNs by leveraging second-order interactions for sequence modelling. These models are provably more expressive than their first-order counterparts and have connections to well-studied models from formal language theory. However, their large parameter tensor makes computations intractable. To circumvent this issue, one approach known as MIRNN consists in limiting the type of interactions used by the model. Another is to leverage tensor decomposition to diminish the parameter count. In this work, we study the model resulting from parameterizing 2RNNs using the CP decomposition, which we call CPRNN. Intuitively, the rank of the decomposition should reduce expressivity. We analyze how rank and hidden size affect model capacity and show the relationships between RNNs, 2RNNs, MIRNNs, and CPRNNs based on these parameters. We support these results empirically with experiments on the Penn Treebank dataset which demonstrate that, with a fixed parameter budget, CPRNNs outperforms RNNs, 2RNNs, and MIRNNs with the right choice of rank and hidden size.
Deep Click-Through Rate (CTR) prediction models play an important role in modern industrial recommendation scenarios. However, high memory overhead and computational costs limit their deployment in resource-constrained environments. Low-rank approximation is an effective method for computer vision and natural language processing models, but its application in compressing CTR prediction models has been less explored. Due to the limited memory and computing resources, compression of CTR prediction models often confronts three fundamental challenges, i.e., (1). How to reduce the model sizes to adapt to edge devices? (2). How to speed up CTR prediction model inference? (3). How to retain the capabilities of original models after compression? Previous low-rank compression research mostly uses tensor decomposition, which can achieve a high parameter compression ratio, but brings in AUC degradation and additional computing overhead. To address these challenges, we propose a unified low-rank decomposition framework for compressing CTR prediction models. We find that even with the most classic matrix decomposition SVD method, our framework can achieve better performance than the original model. To further improve the effectiveness of our framework, we locally compress the output features instead of compressing the model weights. Our unified low-rank compression framework can be applied to embedding tables and MLP layers in various CTR prediction models. Extensive experiments on two academic datasets and one real industrial benchmark demonstrate that, with 3-5x model size reduction, our compressed models can achieve both faster inference and higher AUC than the uncompressed original models. Our code is at https://github.com/yuhao318/Atomic_Feature_Mimicking.
We present an expectation-maximization (EM) based unified framework for non-negative tensor decomposition that optimizes the Kullback-Leibler divergence. To avoid iterations in each M-step and learning rate tuning, we establish a general relationship between low-rank decompositions and many-body approximations. Using this connection, we exploit that the closed-form solution of the many-body approximation updates all parameters simultaneously in the M-step. Our framework offers not only a unified methodology for a variety of low-rank structures, including CP, Tucker, and Tensor Train decompositions, but also their mixtures. Notably, the weights of each low-rank tensor in the mixture can be learned from the data, which enables us to leverage the advantage of different low-rank structures without careful selection of the structure in advance. We empirically demonstrate that our framework overall provides superior generalization in terms of discrete density estimation and classification when compared to conventional tensor-based approaches.
Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several fine-tuning techniques have been developed to update the pre-trained model weights in a more resource-efficient manner, such as through low-rank adjustments. Yet, almost all of these methods focus on linear weights, neglecting the intricacies of parameter spaces in higher dimensions like 4D. Alternatively, some methods can be adapted for high-dimensional parameter space by compressing changes in the original space into two dimensions and then employing low-rank matrix decomposition. However, these approaches destructs the structural integrity of the involved high-dimensional spaces. To tackle the diversity of dimensional spaces across different foundation models and provide a more precise representation of the changes within these spaces, this paper introduces a generalized parameter-efficient fine-tuning framework, FLoRA, designed for various dimensional parameter space. Specifically, utilizing Tucker decomposition, FLoRA asserts that changes in each dimensional parameter space are based on a low-rank core space which maintains the consistent topological structure with the original space. It then models the changes through this core space alongside corresponding weights to reconstruct alterations in the original space. FLoRA effectively preserves the structural integrity of the change of original N-dimensional parameter space, meanwhile decomposes it via low-rank tensor decomposition. Extensive experiments on computer vision, natural language processing and multi-modal tasks validate FLoRA's effectiveness. Codes are available at https://github.com/SJTU-DeepVisionLab/FLoRA.
Key-value~(KV) caching is an important technique to accelerate the inference of large language models~(LLMs), but incurs significant memory overhead. To compress the size of KV cache, existing methods often compromise precision or require extra data for calibration, limiting their practicality in LLM deployment. In this paper, we introduce \textbf{DecoQuant}, a novel data-free low-bit quantization technique based on tensor decomposition methods, to effectively compress KV cache. Our core idea is to adjust the outlier distribution of the original matrix by performing tensor decomposition, so that the quantization difficulties are migrated from the matrix to decomposed local tensors. Specially, we find that outliers mainly concentrate on small local tensors, while large tensors tend to have a narrower value range. Based on this finding, we propose to apply low-bit quantization to the large tensor, while maintaining high-precision representation for the small tensor. Furthermore, we utilize the proposed quantization method to compress the KV cache of LLMs to accelerate the inference and develop an efficient dequantization kernel tailored specifically for DecoQuant. Through extensive experiments, DecoQuant demonstrates remarkable efficiency gains, showcasing up to a $\sim$75\% reduction in memory footprint while maintaining comparable generation quality.
The $L^2$ gradient flow of the Ginzburg-Landau free energy functional leads to the Allen Cahn equation that is widely used for modeling phase separation. Machine learning methods for solving the Allen-Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives through automatic differentiation, and the large system size required by the space-time approach. To overcome these limitations, we propose a separable neural network-based approximation of the phase field in a minimizing movement scheme to solve the aforementioned gradient flow problem. At each time step, the separable neural network is used to approximate the phase field in space through a low-rank tensor decomposition thereby accelerating the derivative calculations. The minimizing movement scheme naturally allows for the use of Gauss quadrature technique to compute the functional. A `$tanh$' transformation is applied on the neural network-predicted phase field to strictly bounds the solutions within the values of the two phases. For this transformation, a theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that bounding the solution through this transformation is the key to effectively model sharp interfaces through separable neural network. The proposed method outperforms the state-of-the-art machine learning methods for phase separation problems and is an order of magnitude faster than the finite element method.
Biological neural networks seem qualitatively superior (e.g. in learning, flexibility, robustness) to current artificial like Multi-Layer Perceptron (MLP) or Kolmogorov-Arnold Network (KAN). Simultaneously, in contrast to them: biological have fundamentally multidirectional signal propagation \cite{axon}, also of probability distributions e.g. for uncertainty estimation, and are believed not being able to use standard backpropagation training \cite{backprop}. There are proposed novel artificial neurons based on HCR (Hierarchical Correlation Reconstruction) allowing to remove the above low level differences: with neurons containing local joint distribution model (of its connections), representing joint density on normalized variables as just linear combination of $(f_\mathbf{j})$ orthonormal polynomials: $\rho(\mathbf{x})=\sum_{\mathbf{j}\in B} a_\mathbf{j} f_\mathbf{j}(\mathbf{x})$ for $\mathbf{x} \in [0,1]^d$ and $B\subset \mathbb{N}^d$ some chosen basis. By various index summations of such $(a_\mathbf{j})_{\mathbf{j}\in B}$ tensor as neuron parameters, we get simple formulas for e.g. conditional expected values for propagation in any direction, like $E[x|y,z]$, $E[y|x]$, which degenerate to KAN-like parametrization if restricting to pairwise dependencies. Such HCR network can also propagate probability distributions (also joint) like $\rho(y,z|x)$. It also allows for additional training approaches, like direct $(a_\mathbf{j})$ estimation, through tensor decomposition, or more biologically plausible information bottleneck training: layers directly influencing only neighbors, optimizing content to maximize information about the next layer, and minimizing about the previous to remove noise, extract crucial information.
Continual learning (CL) has spurred the development of several methods aimed at consolidating previous knowledge across sequential learning. Yet, the evaluations of these methods have primarily focused on the final output, such as changes in the accuracy of predicted classes, overlooking the issue of representational forgetting within the model. In this paper, we propose a novel representation-based evaluation framework for CL models. This approach involves gathering internal representations from throughout the continual learning process and formulating three-dimensional tensors. The tensors are formed by stacking representations, such as layer activations, generated from several inputs and model `snapshots', throughout the learning process. By conducting tensor component analysis (TCA), we aim to uncover meaningful patterns about how the internal representations evolve, expecting to highlight the merits or shortcomings of examined CL strategies. We conduct our analyses across different model architectures and importance-based continual learning strategies, with a curated task selection. While the results of our approach mirror the difference in performance of various CL strategies, we found that our methodology did not directly highlight specialized clusters of neurons, nor provide an immediate understanding the evolution of filters. We believe a scaled down version of our approach will provide insight into the benefits and pitfalls of using TCA to study continual learning dynamics.
We analyze inexact Riemannian gradient descent (RGD) where Riemannian gradients and retractions are inexactly (and cheaply) computed. Our focus is on understanding when inexact RGD converges and what is the complexity in the general nonconvex and constrained setting. We answer these questions in a general framework of tangential Block Majorization-Minimization (tBMM). We establish that tBMM converges to an $\epsilon$-stationary point within $O(\epsilon^{-2})$ iterations. Under a mild assumption, the results still hold when the subproblem is solved inexactly in each iteration provided the total optimality gap is bounded. Our general analysis applies to a wide range of classical algorithms with Riemannian constraints including inexact RGD and proximal gradient method on Stiefel manifolds. We numerically validate that tBMM shows improved performance over existing methods when applied to various problems, including nonnegative tensor decomposition with Riemannian constraints, regularized nonnegative matrix factorization, and low-rank matrix recovery problems.
Deep learning has emerged as a promising approach for learning the nonlinear mapping between diffusion-weighted MR images and tissue parameters, which enables automatic and deep understanding of the brain microstructures. However, the efficiency and accuracy in estimating multiple microstructural parameters derived from multiple diffusion models are still limited since previous studies tend to estimate parameter maps from distinct models with isolated signal modeling and dense sampling. This paper proposes DeepMpMRI, an efficient framework for fast and high-fidelity multiple microstructural parameter estimation from multiple models using highly sparse sampled q-space data. DeepMpMRI is equipped with a newly designed tensor-decomposition-based regularizer to effectively capture fine details by exploiting the high-dimensional correlation across microstructural parameters. In addition, we introduce a Nesterov-based adaptive learning algorithm that optimizes the regularization parameter dynamically to enhance the performance. DeepMpMRI is an extendable framework capable of incorporating flexible network architecture. Experimental results on the HCP dataset and the Alzheimer's disease dataset both demonstrate the superiority of our approach over 5 state-of-the-art methods in simultaneously estimating multi-model microstructural parameter maps for DKI and NODDI model with fine-grained details both quantitatively and qualitatively, achieving 4.5 - 15 $\times$ acceleration compared to the dense sampling of a total of 270 diffusion gradients.