Prune-then-Quantize or Quantize-then-Prune? Understanding the Impact of Compression Order in Joint Model Compression

Modern deployment often requires trading accuracy for efficiency under tight CPU and memory constraints, yet common compression proxies such as parameter count or FLOPs do not reliably predict wall-clock inference time. In particular, unstructured sparsity can reduce model storage while failing to accelerate (and sometimes slightly slowing down) standard CPU execution due to irregular memory access and sparse kernel overhead. Motivated by this gap between compression and acceleration, we study a practical, ordered pipeline that targets measured latency by combining three widely used techniques: unstructured pruning, INT8 quantization-aware training (QAT), and knowledge distillation (KD). Empirically, INT8 QAT provides the dominant runtime benefit, while pruning mainly acts as a capacity-reduction pre-conditioner that improves the robustness of subsequent low-precision optimization; KD, applied last, recovers accuracy within the already constrained sparse INT8 regime without changing the deployment form. We evaluate on CIFAR-10/100 using three backbones (ResNet-18, WRN-28-10, and VGG-16-BN). Across all settings, the ordered pipeline achieves a stronger accuracy-size-latency frontier than any single technique alone, reaching 0.99-1.42 ms CPU latency with competitive accuracy and compact checkpoints. Controlled ordering ablations with a fixed 20/40/40 epoch allocation further confirm that stage order is consequential, with the proposed ordering generally performing best among the tested permutations. Overall, our results provide a simple guideline for edge deployment: evaluate compression choices in the joint accuracy-size-latency space using measured runtime, rather than proxy metrics alone.

Recently, the efficiency of Large Language Models (LLMs) deployment has become a critical concern in practical applications. While post-training quantization (PTQ) and structural pruning are established techniques for reducing memory footprint and inference latency, most existing PTQ approaches optimize quantization errors on a per-layer basis, overlooking how errors accumulate and propagate through the network, often resulting in suboptimal solutions. Traditional pipelines also tend to apply pruning and quantization in isolation or sequentially, further compounding sub-optimality. We introduce a novel end-to-end framework that addresses these limitations in two key ways. First, we propose a novel mixed-precision PTQ strategy that directly minimizes global error propagation across the entire model, rather than isolating layer-wise errors. Building on this, we develop a novel joint optimization approach that simultaneously learns structural pruning decisions and mixed-precision quantization policies within a unified search space. Extensive experiments show that, at ultra-low precisions (1-3 bits), our quantization method reduces WikiText perplexity by up to 21% compared to state-of-the-art (SoTA) weight-activation quantization baselines. Against leading weight-only quantization methods, it achieves up to 59% and 85% lower perplexity on WikiText and C4, respectively. Compared to the SoTA joint pruning-and-quantization techniques, our proposed method delivers superior perplexity and reasoning performance at ultra-low bits.

Prohibitive computational and environmental costs impede the scalable deployment of Large Language Models (LLMs). Traditional compression techniques (sparsity, quantization, low-rank approximations) are typically applied in isolation, and each hits an accuracy-efficiency wall. This thesis proposes the "Compression Trinity," a unified framework that applies the three pillars jointly: sparsity to reduce computation, quantization to minimize memory bandwidth, and low-rank approximations to recover accuracy. To accelerate pretraining, we apply the Trinity to the optimizer and model architecture. MKOR approximates curvature via block-diagonal sparsity and low-rank inversion, maintaining numerical stability for quantized states; it reduces curvature update complexity from $O(d^3)$ to $O(d^2)$ and accelerates convergence by up to 1.85x over KFAC. SLoPe accelerates training by up to 1.25x via a double-pruned backward pass for N:M sparsity, using low-rank "lazy" adapters in the final 1% of training to recover accuracy. For post-training compression, OPTIMA stabilizes static masks in a zero-training regime by formulating weight reconstruction as globally optimal column-wise quadratic programs, improving zero-shot accuracy by up to 3.97%. Given a fine-tuning budget, PATCH breaks the ceiling of static masks by learning a dynamic hybrid sparsity ratio between 0% and 50%, yielding up to 1.38x speedups. Finally, SLiM realizes the full Compression Trinity in one shot, using mathematically derived low-rank adapters to recover information lost to quantization and sparsity, improving accuracy by up to 5.66% over state-of-the-art methods and outperforming uncompressed dense models at equal parameter budgets by 0.6%. Together, these results show that jointly applying the Compression Trinity is essential for efficient, scalable, high-performance LLMs.