Publications tagged "efficiency"

Deep neural networks have reshaped modern machine learning by learning powerful latent representations that often align with the manifold hypothesis: high-dimensional data lie on lower-dimensional manifolds. In this paper, we establish a connection between manifold learning and computational algebra by demonstrating how vanishing ideals can characterize the latent manifolds of deep networks. To that end, we propose a new neural architecture that (i) truncates a pretrained network at an intermediate layer, (ii) approximates each class manifold via polynomial generators of the vanishing ideal, and (iii) transforms the resulting latent space into linearly separable features through a single polynomial layer. The resulting models have significantly fewer layers than their pretrained baselines, while maintaining comparable accuracy, achieving higher throughput, and utilizing fewer parameters. Furthermore, drawing on spectral complexity analysis, we derive sharper theoretical guarantees for generalization, showing that our approach can in principle offer tighter bounds than standard deep networks. Numerical experiments confirm the effectiveness and efficiency of the proposed approach.

Many existing Neural Network pruning approaches either rely on retraining to compensate for pruning-caused performance degradation or they induce strong biases to converge to a specific sparse solution throughout training. A third paradigm obtains a wide range of compression ratios from a single dense training run while also avoiding retraining. Recent work of Pokutta et al. (2020) and Miao et al. (2022) suggests that the Stochastic Frank-Wolfe (SFW) algorithm is particularly suited for training state-of-the-art models that are robust to compression. We propose leveraging k-support norm ball constraints and demonstrate significant improvements over the results of Miao et al. (2022) in the case of unstructured pruning. We also extend these ideas to the structured pruning domain and propose novel approaches to both ensure robustness to the pruning of convolutional filters as well as to low-rank tensor decompositions of convolutional layers. In the latter case, our approach performs on-par with nuclear-norm regularization baselines while requiring only half of the computational resources. Our findings also indicate that the robustness of SFW-trained models largely depends on the gradient rescaling of the learning rate and we establish a theoretical foundation for that practice.

Storing the weights of large language models (LLMs) in GPU memory for local inference is challenging due to their size. While quantization has proven successful in reducing the memory footprint of LLMs, unstructured pruning introduces overhead by requiring the non-pruned weights’ location to be encoded. This overhead hinders the efficient combination of quantization and unstructured pruning, especially for smaller batch sizes common in inference scenarios. To address this, we propose the CS256 storage format, which offers a better balance between space efficiency and hardware acceleration compared to existing formats. CS256 partitions the weight matrix into tiles and uses a hierarchical indexing scheme to locate non-zero values, reducing the overhead associated with storing sparsity patterns. Our preliminary results with one-shot pruning of LLMs show that CS256 matches the performance of unstructured sparsity while being more hardware-friendly.

Neural Networks can be effectively compressed through pruning, significantly reducing storage and compute demands while maintaining predictive performance. Simple yet effective methods like magnitude pruning remove less important parameters and typically require a costly retraining procedure to restore performance. However, with the rise of LLMs, full retraining has become infeasible due to memory and compute constraints. This study challenges the practice of retraining all parameters by showing that updating a small subset of highly expressive parameters can suffice to recover or even enhance performance after pruning. Surprisingly, retraining just 0.01%-0.05% of the parameters in GPT-architectures can match the performance of full retraining across various sparsity levels, significantly reducing compute and memory requirements, and enabling retraining of models with up to 30 billion parameters on a single GPU in minutes. To bridge the gap to full retraining in the high sparsity regime, we introduce two novel LoRA variants that, unlike standard LoRA, allow merging adapters back without compromising sparsity. Going a step further, we show that these methods can be applied for memory-efficient layer-wise reconstruction, significantly enhancing state-of-the-art retraining-free methods like Wanda (Sun et al., 2023) and SparseGPT (Frantar & Alistarh, 2023). Our findings present a promising alternative to avoiding retraining.

Neural networks can be significantly compressed by pruning, leading to sparse models requiring considerably less storage and floating-point operations while maintaining predictive performance. Model soups (Wortsman et al., 2022) improve generalization and out-of-distribution performance by averaging the parameters of multiple models into a single one without increased inference time. However, identifying models in the same loss basin to leverage both sparsity and parameter averaging is challenging, as averaging arbitrary sparse models reduces the overall sparsity due to differing sparse connectivities. In this work, we address these challenges by demonstrating that exploring a single retraining phase of Iterative Magnitude Pruning (IMP) with varying hyperparameter configurations, such as batch ordering or weight decay, produces models that are suitable for averaging and share the same sparse connectivity by design. Averaging these models significantly enhances generalization performance compared to their individual components. Building on this idea, we introduce Sparse Model Soups (SMS), a novel method for merging sparse models by initiating each prune-retrain cycle with the averaged model of the previous phase. SMS maintains sparsity, exploits sparse network benefits being modular and fully parallelizable, and substantially improves IMP’s performance. Additionally, we demonstrate that SMS can be adapted to enhance the performance of state-of-the-art pruning during training approaches.

Many Neural Network Pruning approaches consist of several iterative training and pruning steps, seemingly losing a significant amount of their performance after pruning and then recovering it in the subsequent retraining phase. Recent works of Renda et al. (2020) and Le & Hua (2021) demonstrate the significance of the learning rate schedule during the retraining phase and propose specific heuristics for choosing such a schedule for IMP (Han et al., 2015). We place these findings in the context of the results of Li et al. (2020) regarding the training of models within a fixed training budget and demonstrate that, consequently, the retraining phase can be massively shortened using a simple linear learning rate schedule. Improving on existing retraining approaches, we additionally propose a method to adaptively select the initial value of the linear schedule. Going a step further, we propose similarly imposing a budget on the initial dense training phase and show that the resulting simple and efficient method is capable of outperforming significantly more complex or heavily parameterized state-of-the-art approaches that attempt to sparsify the network during training. These findings not only advance our understanding of the retraining phase, but more broadly question the belief that one should aim to avoid the need for retraining and reduce the negative effects of ‘hard’ pruning by incorporating the sparsification process into the standard training.