Group-Wise Sequential Pruning Strategy

• Group-wise sequential pruning is a model compression technique that organizes parameters into meaningful groups and prunes them sequentially for improved efficiency.
• It employs regularization, differentiable block selection, and sequential inclusion methods to achieve structured sparsity that aligns with hardware architectures.
• Empirical evaluations show significant reductions in FLOPs and parameters with minimal accuracy loss, yielding interpretable and hardware-friendly models.

Group-wise sequential pruning strategy is a class of model compression techniques wherein parameters are partitioned into meaningful groups—such as spatial positions, feature maps, layers, blocks, or heads—and pruning decisions are made collectively for each group, often in a staged, sequential manner. This approach contrasts with unstructured pruning, which removes individual weights, by targeting structured sparsity that is both hardware-friendly and functionally interpretable. Group-wise sequential pruning is now established across domains such as convolutional networks (Lebedev et al., 2015), ensemble variable selection (Zhang et al., 2017), hybrid LLM architectures (Taghibakhshi et al., 15 Apr 2025), multimodal LLMs (Jiang et al., 25 Aug 2025), block-wise deep network pruning (Yasuda et al., 27 Feb 2024), and generative diffusion models (Zhu et al., 8 Oct 2025), among others.

1. Principles of Group-Wise Sequential Pruning

The central principle is to organize parameters into structurally meaningful groups (e.g., filters, channels, blocks, heads, Transformer layers, or even visual tokens) and apply sparsity-inducing regularization or explicit selection to entire groups, driving their contributions toward zero. Sequentiality may refer to temporal ordering (progressive pruning), architectural traversal (layer-by-layer or group-by-group), or iterative refinement (re-evaluating group importance as earlier pruning changes the network’s structure).

For convolutional networks, parameters $K \in \mathbb{R}^{d \times d \times S \times T}$ are grouped by spatial position and input channel, $\Gamma_{i,j,s} = K(i, j, s, :)$; a group-wisely regularized loss takes the form:

$$L_\text{total} = L_\text{original} + \Omega_{2,1}(K), \quad \Omega_{2,1}(K) = \lambda \sum_{i,j,s} \left( \sum_{t=1}^T K(i, j, s, t)^2 \right)^{1/2}$$

where the $\ell_{2,1}$-norm regularizer induces structured, spatially- and channel-organized sparsity (Lebedev et al., 2015).

2. Methodological Variants

a) Regularization-Based Pruning

Group-sparsity regularization (e.g., $\ell_{2,1}$, bounded-Lp) is applied to gates, scaling parameters, or direct parameter groups. Exponential gating functions and bounded-L1 regularizers have been introduced to interpolate between $\ell_{1}$ and $\ell_{0}$, achieving higher pruning rates with minimal accuracy loss (Mummadi et al., 2019). For transformers or multimodal models, module-wise pruning error (MoPE) metrics quantify the performance drop caused by ablating entire modules (attention heads, FFN groups, layers), forming a basis for sequential width-then-depth pruning (Lin et al., 12 Mar 2024).

b) Differentiable/Combinatorial Block Selection

SequentialAttention++ combines differentiable softmax-masking of blocks/groups with combinatorial support selection (iterative hard thresholding/local search) (Yasuda et al., 27 Feb 2024). The underlying objective connects to group LASSO and nonconvex regularization:

$$\min_{\beta \in \mathbb{R}^n} L(\beta) + \lambda \cdot q^{-1}\left( \sum_{i=1}^t q(\| \beta|_{T_i}\|_2) \right)$$

where $T_i$ denotes parameter blocks and $q$ is a strictly increasing subadditive function.

c) Sequential Inclusion/Ordering

Variable selection ensemble pruning applies greedy, sequential member inclusion based on a partial-correlation criterion, balancing diversity and strength. Candidates are added if their incremental effect on ensemble loss satisfies

$$\frac{(r_k - r_{-k})^\top(r^* - r_{-k})}{\| r_k - r_{-k} \| \| r^* - r_{-k} \|} > \frac{1}{2u} \frac{\| r_k - r_{-k} \|}{\| r^* - r_{-k} \|}$$

where $r_k$ is a candidate’s importance, $r^*$ is the true vector, and $u$ is current ensemble size (Zhang et al., 2017).

d) Training-Free Optimal Pruning

OBS-Diff adapts Optimal Brain Surgeon for large diffusion models, supporting both structured and unstructured granularities. A computationally efficient group-wise sequential pruning strategy amortizes the collection of activation statistics and Hessian construction across module "packages," enabling accurate weight and group pruning in one shot (Zhu et al., 8 Oct 2025).

3. Structural Guarantees and Hardware Alignment

Group-wise strategies typically align sparsity patterns with hardware capabilities, such as thinning matrix-multiplication rows/columns after grouped pruning in convolutional layers (Lebedev et al., 2015), enforcing group-wise per-head selection for SSM blocks in hybrid LLMs (Taghibakhshi et al., 15 Apr 2025), or block-level sparsification for accelerator compatibility (Yasuda et al., 27 Feb 2024). These approaches preserve the semantic coherence of grouped connections, minimize irregular memory access, and yield practical speedups far beyond those possible with random/entrywise sparsity.

A consequence is the need for structural constraints during pruning. For Mamba/SSM blocks, head permutations must adhere to original group partitions:

$$\wp(h) \in \mathcal{G}_g \quad \forall h \in \mathcal{G}_g$$

where $\wp(h)$ is a permutation of head $h$, and $\mathcal{G}_g$ is the set of heads in group $g$ (Taghibakhshi et al., 15 Apr 2025).

4. Sequential Decision Mechanisms

Group-wise sequential pruning algorithms often progress using staged importance evaluation, pruning, and possible retraining/fine-tuning. VISA (Jiang et al., 25 Aug 2025) implements sequential group-wise selection by partitioning transformer layers into groups, selecting visual tokens to keep/remove at each group boundary based on text-to-visual attention averaging, and aggregating removed token information into kept tokens via graph summarization. This progressive aggregation maintains visual signal integrity throughout deep multimodal architectures.

Pruning in a one-cycle framework integrates pre-training, pruning, and fine-tuning into a single cycle. Pruning decisions are staged according to stability of group selections as tracked by layer-wise Jaccard similarity metrics:

$$J(M_{t-i}, M_t) = \frac{1}{L} \sum_l \frac{ |F_{t-i}^l \cap F_t^l| }{ |F_{t-i}^l \cup F_t^l| }$$

with stability thresholds used to determine the optimal pruning epoch (Ghimire et al., 23 Jan 2025).

5. Performance and Empirical Outcomes

Speedup and Accuracy Retention

Empirical results consistently demonstrate that group-wise sequential pruning can yield substantial reductions in FLOPs and parameter counts (70–90% is typical), with minimal accuracy degradation (often under 1–2%). For example, group-wise pruning in AlexNet achieves 8.33× speedup with only ~0.8% drop in top-1 accuracy (Lebedev et al., 2015), while hybrid LLM pruning improves inference speed by 2× at half the parameter count, and multimodal token selection maintains >90% full-model VQA performance at high rates of token reduction (Jiang et al., 25 Aug 2025).

Robustness and Ensemble Parsimony

Iterative sensitivity-based group pruning improves robustness by preventing layer disconnection and overfitting importance signals (Verdenius et al., 2020). Ordered ensemble pruning yields more accurate, parsimonious models with lower false discovery rates, further favoring reliable model selection in high-dimensional problems (Zhang et al., 2017).

Hardware and Latency Implications

Regular structural alignment via block or group pruning allows direct mapping onto accelerator architectures, notably enabling practical hardware speedups and lower memory consumption. For diffusion models, group-wise sequential module package pruning leads to a 1.23–1.31× improvement in block throughput with preserved generation quality (Zhu et al., 8 Oct 2025).

6. Mathematical Formulations

A concise table of key formulations follows:

Strategy	Regularizer or Metric	Selection Criterion
ConvNet Group-Sparse (Lebedev et al., 2015)	$\Omega_{2,1}(K) = \lambda\sum ||\Gamma_{i,j,s}||_2$	Group norm thresholding
Ensemble Pruning (Zhang et al., 2017)	Squared Euclidean loss, partial correlation	Sequential inclusion via inequality
Block Attn+Combinatorial (Yasuda et al., 27 Feb 2024)	$L(\beta) + \lambda q^{-1}( \sum q(\|\cdot\|_2) )$	Softmax-masked scoring + iterative hard threshold
SSM Group-Aware (Taghibakhshi et al., 15 Apr 2025)	Activation-based nested scores, group constraint	Intra-group permutation, per-channel L2 scoring
MoPE-CLIP (Lin et al., 12 Mar 2024)	Pruning error: $$\mathrm{MoPE}_\theta = \mathcal{Z}[f_\varphi] - \mathcal{Z}[f_{\varphi-\theta}]$$	Width-first-then-depth sequential pruning
OBS-Diff (Zhu et al., 8 Oct 2025)	Hessian-weighted OBS score, timestep-weighted	Module package/Basic Unit segmentation

7. Implications and Future Directions

Group-wise sequential pruning strategies now span vision, language, and generative domains. They provide efficient, interpretable, and hardware-aligned model compression for resource-constrained or latency-critical deployment. Future research is likely to focus on adaptive group structures, enhanced dynamic scoring, joint multi-component pruning, and further integration with distillation, as well as context-adaptive strategies for evolving architectures (Taghibakhshi et al., 15 Apr 2025, Zhu et al., 8 Oct 2025). Extensions to video, long-context, and hybrid architectures present rich ground for investigation.

A plausible implication is that as architectures become increasingly heterogeneous and multi-modal, optimized group-wise sequential pruning will be foundational for scalable, accurate, and efficient model deployment across diverse computational platforms.