Neural Network Compression

Scaling models has led to significant advancements in deep learning, but training these models in decentralized settings remains challenging due to communication bottlenecks. While existing compression techniques are effective in data-parallel, they do not extend to model parallelism. Unlike data-parallel training, where weight gradients are exchanged, model-parallel requires compressing activations and activation gradients as they propagate through layers, accumulating compression errors. We propose a novel compression algorithm that compresses both forward and backward passes, enabling up to 99% compression with no convergence degradation with negligible memory/compute overhead. By leveraging a recursive structure in transformer networks, we predefine a low-dimensional subspace to confine the activations and gradients, allowing full reconstruction in subsequent layers. Our method achieves up to 100x improvement in communication efficiency and enables training billion-parameter-scale models over low-end GPUs connected via consumer-grade internet speeds as low as 80Mbps, matching the convergence of centralized datacenter systems with 100Gbps connections with model parallel.

A proposition that connects randomness and compression is put forward via Gibbs entropy over set of measurement vectors associated with a compression process. In building this connection, we use a performance of a learning task as a probe of compression, over series of compression cycles within a cascade. The Gibbs entropy at each cycle measures the degree of randomness. Consequently a lossy compression process can be seen as an equivalent to {\it directed randomness} that preserves information content under certain bounds of Gibbs entropy and the performance of the learning task. The term directed means we guide the compression process with set of mathematical rules on how to reduce the model size. We formulate this connection with a theorem using a $δ$ and $ε$ bounds, and demonstrated a logical proof via comonotonic relationship within a very small decrease in compression ratio and the performance. We have showcase the validity of this proposition with a canonical vision task in deep learning with three different model compression processes as {\it a baseline model}. We use the following, simpler to more complex model compression approaches: (1) random pruning, (2) magnitude pruning, and (3) a more complex compression by using dual tomographic compression, which utilizes compressed sensing in dual fashion. We use remaining weights of deep learning network as a measurement vector where we measure the Gibbs entropy. The proposition is supported with the experimental evidence, resulting in very high correlation between learning performance and the Gibbs entropy over compression ratios for all different compression processes. We show case the idea that there is an inherent computable connection between compression probed by performance degradation and randomness from an entropy measure on the learned model.

Tensorizing a neural network involves reshaping some or all of its dense weight matrices into higher-order tensors and approximating them using low-rank tensor network decompositions. This technique has shown promise as a model compression strategy for large-scale neural networks. However, despite encouraging empirical results, tensorized neural networks (TNNs) remain underutilized in mainstream deep learning. In this position paper, we offer a perspective on both the potential and current limitations of TNNs. We argue that TNNs represent a powerful yet underexplored framework for deep learning--one that deserves greater attention from both engineering and theoretical communities. Beyond compression, we highlight the value of TNNs as a flexible class of architectures with distinctive scaling properties and increased interpretability. A central feature of TNNs is the presence of bond indices, which introduce new latent spaces not found in conventional networks. These internal representations may provide deeper insight into the evolution of features across layers, potentially advancing the goals of mechanistic interpretability. We conclude by outlining several key research directions aimed at overcoming the practical barriers to scaling and adopting TNNs in modern deep learning workflows.

Disparity compensation represents the primary strategy in stereo video compression (SVC) for exploiting cross-view redundancy. These mechanisms can be broadly categorized into two types: one that employs explicit horizontal shifting, and another that utilizes an implicit cross-attention mechanism to reduce cross-view disparity redundancy. In this work, we propose a hybrid disparity compensation (HDC) strategy that leverages explicit pixel displacement as a robust prior feature to simplify optimization and perform implicit cross-attention mechanisms for subsequent warping operations, thereby capturing a broader range of disparity information. Specifically, HDC first computes a similarity map by fusing the horizontally shifted cross-view features to capture pixel displacement information. This similarity map is then normalized into an "explicit pixel-wise attention score" to perform the cross-attention mechanism, implicitly aligning features from one view to another. Building upon HDC, we introduce a novel end-to-end optimized neural stereo video compression framework, which integrates HDC-based modules into key coding operations, including cross-view feature extraction and reconstruction (HDC-FER) and cross-view entropy modeling (HDC-EM). Extensive experiments on SVC benchmarks, including KITTI 2012, KITTI 2015, and Nagoya, which cover both autonomous driving and general scenes, demonstrate that our framework outperforms both neural and traditional SVC methodologies.

Modeling natural phenomena with artificial neural networks (ANNs) often provides highly accurate predictions. However, ANNs often suffer from over-parameterization, complicating interpretation and raising uncertainty issues. Bayesian neural networks (BNNs) address the latter by representing weights as probability distributions, allowing for predictive uncertainty evaluation. Latent binary Bayesian neural networks (LBBNNs) further handle structural uncertainty and sparsify models by removing redundant weights. This article advances LBBNNs by enabling covariates to skip to any succeeding layer or be excluded, simplifying networks and clarifying input impacts on predictions. This further allows us to learn simpler structures (e.g., linear or even constant intercept only models) when appropriate. Furthermore, the input-skip LBBNN (ISLaB) approach reduces network density significantly compared to standard LBBNNs, achieving over 99% reduction for small networks and over 99.9% for larger ones, while still maintaining high predictive accuracy and uncertainty quantification. For example, on MNIST, we reached 97% accuracy and great calibration with just 935 weights, reaching state-of-the-art for compression of neural networks. Furthermore, the proposed method accurately identifies the true covariates and adjusts for system non-linearity. The main contribution is the introduction of active paths, enhancing directly designed global and local explanations within the LBBNN framework. The latter are exact with theoretical guarantees and do not require post hoc external tools.

In recent years, vision transformers (ViTs) have emerged as powerful and promising techniques for computer vision tasks such as image classification, object detection, and segmentation. Unlike convolutional neural networks (CNNs), which rely on hierarchical feature extraction, ViTs treat images as sequences of patches and leverage self-attention mechanisms. However, their high computational complexity and memory demands pose significant challenges for deployment on resource-constrained edge devices. To address these limitations, extensive research has focused on model compression techniques and hardware-aware acceleration strategies. Nonetheless, a comprehensive review that systematically categorizes these techniques and their trade-offs in accuracy, efficiency, and hardware adaptability for edge deployment remains lacking. This survey bridges this gap by providing a structured analysis of model compression techniques, software tools for inference on edge, and hardware acceleration strategies for ViTs. We discuss their impact on accuracy, efficiency, and hardware adaptability, highlighting key challenges and emerging research directions to advance ViT deployment on edge platforms, including graphics processing units (GPUs), application-specific integrated circuit (ASICs), and field-programmable gate arrays (FPGAs). The goal is to inspire further research with a contemporary guide on optimizing ViTs for efficient deployment on edge devices.

We present TropNNC, a framework for compressing neural networks with linear and convolutional layers and ReLU-type activations using tropical geometry. By representing a network's output as a tropical rational function, TropNNC enables structured compression via reduction of the corresponding tropical polynomials. Our method identifies redundancy via similarity and improves upon the geometric approximation of previous work by adaptively selecting the weights of retained neurons. We relate it to SVD and spectral clustering, and provide insights into network compression beyond the specific setting considered. We provide the tightest known theoretical compression bound, and the first successful application of tropical geometry to convolutional layers. TropNNC requires access only to network weights - no training data - and achieves competitive performance on MNIST, CIFAR, and ImageNet, matching strong baselines such as ThiNet and CUP.

Compact appliance classifiers can support local electricity-load monitoring where memory and computation are constrained. We evaluate adaptive sparse evolutionary training and warm-start compression using synthetic aggregate windows derived from household appliance recordings. A completed convolutional network study trains 120 models over four targets and three seeds with validation-only model selection. Two analyses examine compression with approximately preserved binary accuracy and joint improvement in positive-class F1 and sparsity. Relative to a newly trained fixed sparse evolutionary baseline, the selected compressed policy changes accuracy from 91.53%, while increasing macro F1 to 92.40%. Stored weights decrease by 17.36% and active first-layer connections by 23.93%. Refinement requires additional training. Three seeds and unverified source-window independence prevent claims of statistical equivalence or unseen-house performance.