Author name cluster

Jared Tanner

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5 papers

1 author row

ICML Conference 2025 Conference Paper

Mind the Gap: a Spectral Analysis of Rank Collapse and Signal Propagation in Attention Layers

Thiziri Nait Saada
Alireza Naderi
Jared Tanner

Attention layers are the core component of transformers, the current state-of-the-art neural network architecture. Alternatives to softmax-based attention are being explored due to its tendency to hinder effective information flow. Even at initialisation, it remains poorly understood why the propagation of signals and gradients through these random networks can be pathological, resulting in issues known as (i) vanishing/exploding gradients and (ii) rank collapse in depth, i. e. when all tokens converge to a single representation along layers. While rank collapse in depth naturally arises from repeated matrix multiplications—a common pattern across various architectures—we identify an additional and previously unknown challenge unique to softmax attention layers: (iii) rank collapse in width, which occurs as the context length increases. Using Random Matrix Theory, we conduct a rigorous analysis that uncovers a spectral gap between the two largest singular values of the attention matrix as the cause of (iii), which in turn exacerbates (i) and (ii). Building on this insight, we propose a novel yet simple practical solution to mitigate rank collapse in width by removing the outlier eigenvalue(s). Our theoretical framework offers a fresh perspective on recent practical studies, such as (Ye et al. , 2024; Ali et al. , 2023), whose ad hoc solutions can now be interpreted as implicit efforts to address the spectral gap issue. This work provides valuable theoretical support for ongoing large-scale empirical research, bringing theory and practice one step closer in the understanding of transformers.

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ICLR Conference 2024 Conference Paper

Beyond IID weights: sparse and low-rank deep Neural Networks are also Gaussian Processes

Thiziri Nait Saada
Alireza Naderi
Jared Tanner

The infinitely wide neural network has been proven a useful and manageable mathematical model that enables the understanding of many phenomena appearing in deep learning. One example is the convergence of random deep networks to Gaussian processes that enables a rigorous analysis of the way the choice of activation function and network weights impacts the training dynamics. In this paper, we extend the seminal proof of Matthews et al., 2018 to a larger class of initial weight distributions (which we call pseudo-iid), including the established cases of iid and orthogonal weights, as well as the emerging low-rank and structured sparse settings celebrated for their computational speed-up benefits. We show that fully-connected and convolutional networks initialised with pseudo-iid distributions are all effectively equivalent up to their variance. Using our results, one can identify the Edge of Chaos for a broader class of neural networks and tune them at criticality in order to enhance their training. Moreover, they enable the posterior distribution of Bayesian Neural Networks to be tractable across these various initialization schemes.

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ICLR Conference 2024 Conference Paper

Deep Neural Network Initialization with Sparsity Inducing activations

Ilan Price
Nicholas Daultry Ball
Adam C. Jones
Samuel C. H. Lam
Jared Tanner

Inducing and leveraging sparse activations during training and inference is a promising avenue for improving the computational efficiency of deep networks, which is increasingly important as network sizes continue to grow and their application becomes more widespread. Here we use the large width Gaussian process limit to analyze the behaviour, at random initialization, of nonlinear activations that induce sparsity in the hidden outputs. A previously unreported form of training instability is proven for arguably two of the most natural candidates for hidden layer sparsification; those being a shifted ReLU ($\phi(x)=\max(0, x-\tau)$ for $\tau\ge 0$) and soft thresholding ($\phi(x)=0$ for $|x|\le\tau$ and $x-\text{sign}(x)\tau$ for $|x|>\tau$). We show that this instability is overcome by clipping the nonlinear activation magnitude, at a level prescribed by the shape of the associated Gaussian process variance map. Numerical experiments verify the theory and show that the proposed magnitude clipped sparsifying activations can be trained with training and test fractional sparsity as high as 85\% while retaining close to full accuracy.

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ICLR Conference 2024 Conference Paper

Dynamic Sparse No Training: Training-Free Fine-tuning for Sparse LLMs

Yuxin Zhang 0002
Lirui Zhao
Mingbao Lin
Yunyun Sun
Yiwu Yao
Xingjia Han
Jared Tanner
Shiwei Liu 0003

The ever-increasing large language models (LLMs), though opening a potential path for the upcoming artificial general intelligence, sadly drops a daunting obstacle on the way towards their on-device deployment. As one of the most well-established pre-LLMs approaches in reducing model complexity, network pruning appears to lag behind in the era of LLMs, due mostly to its costly fine-tuning (or re-training) necessity under the massive volumes of model parameter and training data. To close this industry-academia gap, we introduce Dynamic Sparse No Training ($\texttt{DSNT}$), a training-free fine-tuning approach that slightly updates sparse LLMs without the expensive backpropagation and any weight updates. Inspired by the Dynamic Sparse Training, $\texttt{DSNT}$ minimizes the reconstruction error between the dense and sparse LLMs, in the fashion of performing iterative weight pruning-and-growing on top of sparse LLMs. To accomplish this purpose, $\texttt{DSNT}$ particularly takes into account the anticipated reduction in reconstruction error for pruning and growing, as well as the variance w.r.t. different input data for growing each weight. This practice can be executed efficiently in linear time since its obviates the need of backpropagation for fine-tuning LLMs. Extensive experiments on LLaMA-V1/V2, Vicuna, and OPT across various benchmarks demonstrate the effectiveness of $\texttt{DSNT}$ in enhancing the performance of sparse LLMs, especially at high sparsity levels. For instance, $\texttt{DSNT}$ is able to outperform the state-of-the-art Wanda by 26.79 perplexity at 70% sparsity with LLaMA-7B. Our paper offers fresh insights into how to fine-tune sparse LLMs in an efficient training-free manner and open new venues to scale the great potential of sparsity to LLMs. Codes are available at https://github.com/zyxxmu/DSnoT.

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ICML Conference 2021 Conference Paper

Dense for the Price of Sparse: Improved Performance of Sparsely Initialized Networks via a Subspace Offset

Ilan Price
Jared Tanner

That neural networks may be pruned to high sparsities and retain high accuracy is well established. Recent research efforts focus on pruning immediately after initialization so as to allow the computational savings afforded by sparsity to extend to the training process. In this work, we introduce a new ‘DCT plus Sparse’ layer architecture, which maintains information propagation and trainability even with as little as 0. 01% trainable parameters remaining. We show that standard training of networks built with these layers, and pruned at initialization, achieves state-of-the-art accuracy for extreme sparsities on a variety of benchmark network architectures and datasets. Moreover, these results are achieved using only simple heuristics to determine the locations of the trainable parameters in the network, and thus without having to initially store or compute with the full, unpruned network, as is required by competing prune-at-initialization algorithms. Switching from standard sparse layers to DCT plus Sparse layers does not increase the storage footprint of a network and incurs only a small additional computational overhead.

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