PATCH: Learnable Tile-level Hybrid Sparsity for LLMs

Younes Hourri; Mohammad Mozaffari; Maryam Mehri Dehnavi

cs.LGSep 27, 2025

PATCH: Learnable Tile-level Hybrid Sparsity for LLMs

Authors: Younes Hourri, Mohammad Mozaffari, Maryam Mehri Dehnavi

Organizations: Department of Computer Science University of Toronto

Abstract

Large language models (LLMs) deliver impressive performance but incur prohibitive memory and compute costs at deployment. Model pruning is an effective way to reduce these overheads, yet existing approaches face challenges: unstructured sparsity, where nonzeros can appear anywhere, preserves accuracy but yields irregular access patterns that prevent GPU acceleration, while semi-structured 2:4 sparsity is hardware-friendly but enforces a rigid 50% pattern that degrades model quality. To bridge this gap, we introduce PATCH, a hybrid sparsity framework that enables a continuous sparsity ratio between 0% and 50%. PATCH partitions weight matrices into tiles, assigning each tile to be either dense or 2:4 sparse via a learnable mask selection mechanism. This design provides fine-grained control over accuracy-acceleration tradeoffs and supports non-uniform sparsity across layers, leading to superior overall quality. Across models from 0.5B to 13B parameters, PATCH consistently narrows the gap to dense accuracy while delivering practical speedups. For instance, on LLaMA-2 7B with an A6000 GPU, PATCH achieves 1.18x-1.38x end-to-end speedup over dense baselines while improving accuracy by 0.37%-2.96% compared to the state-of-the-art 2:4 pruning method, MaskLLM.

Figures & tables

Figure 1 : Illustration of the PATCH learning process for generating tile-level hybrid masks. Each tile is parameterized by a learnable distribution and sampled with Gumbel Softmax to produce

\tilde{{\bm{M}}}_{\text{tile}}

. The dense probability is expanded and merged with a 2:4 mask

\tilde{{\bm{M}}}_{2:4}

, which can be fixed or jointly learned during training, yielding

\tilde{{\bm{M}}}

. The final mask assigns each tile to remain dense or follow the 2:4 pattern, enabling flexible sparsity across the weight matrix.

Sparsity	Method	Pattern	Qwen-2.5 0.5B		LLaMA-3.2 1B		Gemma-3 1B
			Acc (% $\uparrow$ )	PPL ( $\downarrow$ )	Acc (% $\uparrow$ )	PPL ( $\downarrow$ )	Acc (% $\uparrow$ )	PPL ( $\downarrow$ )
0%	Dense	-	46.00	12.08	47.70	9.06	47.01	11.67
50%	Magnitude	2:4	30.16	6734.97	29.66	563.44	31.66	5005.56
	Wanda	2:4	32.97	72.48	31.61	78.18	34.16	69.41
	SparseGPT	2:4	34.81	36.59	35.55	32.73	35.58	44.59
	Thanos	2:4	31.31	37.32	35.71	33.03	35.09	62.63

Table 1: Model quality (average accuracy across eight zero-shot tasks and perplexity on WikiText2 dataset) for different pruning methods. By jointly optimizing the location of dense tiles and the sparsity pattern within the sparse tiles, PATCH Joint allows for a continuous sparsity ratio for the models, providing a flexible tradeoff between sparsity and model quality.

Sparsity	Method	Pattern	LLaMA-2 7B		LLaMA-2 13B		LLaMA-3.1 8B
			Acc (% $\uparrow$ )	PPL ( $\downarrow$ )	Acc (% $\uparrow$ )	PPL ( $\downarrow$ )	Acc (% $\uparrow$ )	PPL ( $\downarrow$ )
0%	Dense	-	54.61	5.12	58.38	4.89	60.31	5.84
50%	Magnitude	2:4	43.44	54.39	45.94	8.89	35.93	765.92
	Wanda	2:4	44.30	11.15	47.95	8.91	41.77	21.29
	SparseGPT	2:4	45.09	10.12	49.67	8.86	45.53	15.11
	Thanos	2:4	44.80	11.19	49.33	8.80	45.72	16.09

Table 2: Model quality (average accuracy across eight zero-shot tasks and perplexity on WikiText2 dataset) for different pruning methods. By only optimizing the location of dense tiles while keeping sparsity pattern within the sparse tiles frozen, PATCH Tile provides a memory efficient variant for PATCH Joint , allowing for a continuous sparsity ratio for the models and providing a flexible tradeoff between sparsity and model quality.

Table 4

Sparsity (0.5B)	MaskLLM	SparseGPT (no update)	Wanda	Mag.	PATCH Joint
45%	15.06	21.84	21.83	21.33	14.57
35%	14.55	17.29	17.96	19.90	13.84
25%	14.17	14.89	15.09	16.05	13.47

Table 5 : Impact of fixed 2:4 mask selection for PATCH Tile , compared with joint optimization (

\downarrow

is better). PATCH Joint achieves the lowest perplexity overall, while for PATCH Tile , MaskLLM provides the best frozen mask. Mag . refers to Magnitude pruning.

Figure 2 : Layer-wise sparsity allocation under different global sparsity budgets for various models. PATCH achieves the target global sparsity while flexibly distributing pruning across transformer layers.

Sparsity	Method	Bit	LoRA	LLaMA-2-7B		LLaMA-3.1-8B		Comp.
				Acc (% $\uparrow$ )	PPL ( $\downarrow$ )	Acc (% $\uparrow$ )	PPL ( $\downarrow$ )	Ratio
0%	Dense	-	-	54.61	5.12	60.31	5.84	1x
50%	MaskLLM	4	-	47.98	7.64	51.12	9.92	5.33x
45%	PATCH Tile	4	-	48.19	7.34	52.47	9.68	5.16x
45%	PATCH Tile	4	SLiM -LoRA	50.71	6.83	54.04	9.12	4.10x
35%	PATCH Tile	4	-	49.38	6.92	53.81	9.26	4.85x

Table 6 : Average accuracy (

\uparrow

indicates better) across eight zero-shot downstream tasks and WikiText2 perplexity (

\downarrow

indicates better) of compressed models with 4-bit weight-only quantization . Please note that using LoRA adds additional parameters to the model. Comp. Ratio refers to the theoretical weight memory compression factor relative to the dense model; LoRA adapters are quantized to 4-bit integers.

Figure 3 : Accuracy–efficiency trade-off on LLaMA-2 7B (A6000, batch size 16, prefill and generation length 128). Eight-task average accuracy versus end-to-end speedup over dense (left) and versus weight memory relative to dense (right). Dense and full 2:4 (MaskLLM, speedup measured with STOICC) are single operating points; PATCH at 25%, 35%, and 45% sparsity fills the region between them, and every PATCH point lies above the full-2:4 accuracy (dashed).

Appendix figures & tables30 assets

Supplementary material from the paper’s appendix.

Appendix

Method	Sparsity	Avg Acc (% $\uparrow$ )	Speedup ( $\uparrow$ )	Weight memory ( $\downarrow$ )
Dense	0%	54.61	1.00 $\times$	1.00 $\times$
MaskLLM (full 2:4)	50%	48.62	1.47 $\times$ / 1.40 $\times$	0.56 $\times$
PATCH	45%	48.99	1.38 $\times$	0.59 $\times$
PATCH	35%	50.08	1.27 $\times$	0.68 $\times$
PATCH	25%	51.58	1.18 $\times$	0.76 $\times$

Appendix

Table 7 : Accuracy, speedup, and weight memory of LLaMA-2 7B on an A6000 GPU (batch size 16, prefill length 128, generation length 128). Throughput of a full 2:4 model is determined by the sparsity format, so the full-2:4 throughput of Table 23 applies to MaskLLM; its speedup is given as STOICC / cuSPARSELt.

Sparsity	Prefill length	Tokens generated	Throughput (tok/s)	Speedup vs. dense
0%	128	128	1023.80	1.00 $\times$
25%	128	128	1212.79	1.18 $\times$
35%	128	128	1304.46	1.27 $\times$
45%	128	128	1410.20	1.38 $\times$
0%	128	1024	435.42	1.00 $\times$
25%	128	1024	493.33	1.13 $\times$

Appendix

Table 8 : Throughput of LLaMA-2 7B with mixed sparsity compared to the dense model. Measurements taken on an A6000 GPU with batch size 16. Throughput is reported in tokens processed/sec.

Model	Sparsity	Prefill	Generated	Throughput (tok/s)	Speedup vs. dense
LLaMA-2 7B	0%	128	128	1876.24	1.00 $\times$
	25%	128	128	2002.02	1.07 $\times$
	35%	128	128	2088.98	1.11 $\times$
	45%	128	128	2180.88	1.16 $\times$
	0%	128	1024	812.55	1.00 $\times$
	25%	128	1024	864.66	1.06 $\times$

Appendix

Table 9 : Throughput of LLaMA-2 7B and LLaMA-2 13B with mixed sparsity compared to the dense model. Measurements taken on an A100 GPU with batch size 16. Throughput is reported in tokens processed/sec.

Component	Dense	PATCH 25%	PATCH 35%	PATCH 45%
Weights	13.5 GB (1.00 $\times$ )	$\approx$ 10.3 GB (0.76 $\times$ )	$\approx$ 9.2 GB (0.68 $\times$ )	$\approx$ 8.0 GB (0.59 $\times$ )
KV cache (128 generated)	$\approx$ 2 GB	$\approx$ 2 GB	$\approx$ 2 GB	$\approx$ 2 GB
KV cache (1024 generated)	$\approx$ 9 GB	$\approx$ 9 GB	$\approx$ 9 GB	$\approx$ 9 GB
Transient activations	$<$ 0.5 GB	$<$ 0.5 GB	$<$ 0.5 GB	$<$ 0.5 GB
Analytical peak (128 generated)	$\approx$ 16.0 GB	$\approx$ 12.8 GB	$\approx$ 11.7 GB	$\approx$ 10.5 GB
Empirical peak (128 generated)	16.721 GB	14.189 GB	12.530 GB	11.769 GB

Appendix

Table 10 : Peak GPU memory breakdown of LLaMA-2 7B in FP16 at inference (A6000, batch size 16, prefill length 128). PATCH reduces only the weights; the KV cache and transient activations are identical to the dense model. Analytical peaks sum the components; empirical peaks are measured.

Sparsity	Method	Pattern	MMLU	PIQA	ARC-E	ARC-C	WinoG.	OBQA	RACE	HellaS.	Avg
0%	Dense	-	47.71	70.24	64.48	29.52	56.20	24.20	35.02	40.63	46.00
50%	Magnitude	2:4	23.00	54.24	31.23	19.20	49.96	13.60	23.44	26.59	30.16
	Wanda	2:4	24.43	58.71	43.18	17.75	51.62	12.20	26.32	29.58	32.97
	SparseGPT	2:4	22.93	60.77	46.60	20.82	52.88	14.00	29.57	30.93	34.81
	Thanos	2:4	22.97	60.17	45.37	19.20	53.59	15.20	31.00	31.31	34.85
	ProxSparse	2:4	23.00	57.34	40.53	18.26	48.62	14.00	25.65	29.02	32.05

Appendix

Table 11: Model quality (task accuracy across eight zero-shot tasks, reported in %) for Qwen-2.5 0.5B with different pruning methods. PATCH Joint optimizes dense tile locations and sparsity patterns, enabling a flexible sparsity-quality tradeoff.

Sparsity	Method	Pattern	MMLU	PIQA	ARC-E	ARC-C	WinoG.	OBQA	RACE	HellaS.	Avg
0%	Dense	-	41.82	78.07	76.35	43.52	69.06	31.40	39.52	57.13	54.61
50%	Magnitude	2:4	25.82	70.02	61.78	30.12	61.01	21.80	31.48	45.45	43.44
	Wanda	2:4	25.80	71.00	63.80	30.29	61.09	25.20	35.50	41.75	44.30
	SparseGPT	2:4	26.17	70.73	63.80	30.63	65.04	24.00	37.13	43.18	45.09
	Thanos	2:4	25.27	70.78	63.43	30.97	64.56	23.80	36.46	43.11	44.80
	ProxSparse	2:4	26.77	71.60	65.70	33.02	62.90	24.20	35.31	47.84	45.92

Appendix

Table 12: Model quality (task accuracy across eight zero-shot tasks, reported in %) for LLaMA-2 7B with different pruning methods. PATCH Tile optimizes tile-based sparsity, enabling a flexible sparsity-quality tradeoff.

Sparsity	Method	Pattern	MMLU	PIQA	ARC-E	ARC-C	WinoG.	OBQA	RACE	HellaS.	Avg
0%	Dense	-	52.07	79.16	79.42	48.46	71.98	35.40	40.48	60.08	58.38
50%	Magnitude	2:4	27.53	72.03	62.46	32.17	62.35	24.20	36.65	50.10	45.94
	Wanda	2:4	29.51	73.01	68.90	35.07	66.93	24.80	38.76	46.61	47.95
	SparseGPT	2:4	33.42	73.56	68.60	36.86	69.61	28.00	39.52	47.78	49.67
	Thanos	2:4	33.51	73.50	68.90	36.92	66.90	28.00	39.03	47.86	49.33
	ProxSparse	2:4	34.86	75.68	71.46	38.31	66.85	28.60	37.51	53.09	50.80

Appendix

Table 13: Model quality (task accuracy across eight zero-shot tasks, reported in %) for LLaMA-2 13B with different pruning methods. PATCH Tile optimizes tile-based sparsity, enabling a flexible sparsity-quality tradeoff. The Avg column reports the eight-task average. MaskLLM is omitted from this table because no public LLaMA-2 13B checkpoint is available and reproducing it would require approximately 2304 A100 GPU-hours, beyond our compute budget.

Sparsity	Method	Pattern	MMLU	PIQA	ARC-E	ARC-C	WinoG.	OBQA	RACE	HellaS.	Avg
0%	Dense	-	63.57	80.09	81.44	51.37	73.48	33.40	39.14	60.02	60.31
50%	Magnitude	2:4	23.06	63.82	45.33	25.94	53.91	15.20	26.70	33.49	35.93
	Wanda	2:4	27.85	68.88	58.33	26.71	60.93	19.00	33.78	38.70	41.77
	SparseGPT	2:4	31.82	70.46	63.85	31.74	64.56	21.60	37.22	42.99	45.53
	Thanos	2:4	34.23	70.40	63.13	31.40	63.61	23.20	37.03	42.75	45.72
	ProxSparse	2:4	29.89	71.71	62.63	33.28	58.56	23.80	35.22	46.03	45.14

Appendix

Table 14: Model quality (task accuracy across eight zero-shot tasks, reported in %) for LLaMA-3.1 8B with different pruning methods. PATCH Tile optimizes tile-based sparsity, enabling a flexible sparsity-quality tradeoff.

Sparsity	Method	Pattern	MMLU	PIQA	ARC-E	ARC-C	WinoG.	OBQA	RACE	HellaS.	Avg
0%	Dense	-	37.57	74.54	65.53	31.32	60.62	26.40	37.89	47.76	47.70
50%	Magnitude	2:4	23.31	53.81	27.74	18.94	51.38	11.80	24.02	26.26	29.66
	Wanda	2:4	22.90	58.11	37.08	19.20	49.09	13.20	25.17	28.11	31.61
	SparseGPT	2:4	22.93	61.43	45.03	22.35	54.93	15.80	29.86	32.08	35.55
	Thanos	2:4	23.12	62.40	44.91	21.76	54.30	16.00	31.10	32.09	35.71
	ProxSparse	2:4	22.96	60.83	39.44	20.31	51.54	16.80	25.17	31.37	33.55

Appendix

Table 15: Model quality (task accuracy across eight zero-shot tasks, reported in %) for LLaMA-3.2 1B with different pruning methods. PATCH Joint optimizes dense tile locations and sparsity patterns, enabling a flexible sparsity-quality tradeoff.

Sparsity	Method	Pattern	MMLU	PIQA	ARC-E	ARC-C	WinoG.	OBQA	RACE	HellaS.	Avg
0%	Dense	-	24.95	75.03	71.84	34.90	58.64	28.60	34.83	47.26	47.01
50%	Magnitude	2:4	23.08	59.79	37.29	17.66	50.59	14.00	22.87	27.97	31.66
	Wanda	2:4	23.96	59.52	48.02	18.34	51.22	14.20	27.85	30.18	34.16
	SparseGPT	2:4	23.62	62.79	49.83	19.03	51.54	15.20	30.62	31.99	35.58
	Thanos	2:4	23.44	62.24	48.86	18.34	50.12	15.60	30.81	31.28	35.09
	ProxSparse	2:4	23.10	64.25	50.72	21.59	53.43	18.00	29.09	32.86	36.63

Appendix

Table 16: Model quality (accuracy across eight zero-shot tasks) for Gemma-3 1B with different pruning methods. PATCH Joint optimizes dense tile locations and sparsity patterns, enabling a flexible sparsity-quality tradeoff.

Sparsity (0.5B)	Nothing	SparseGPT	Wanda	Magnitude	Random
45%	14.80	14.57	14.50	14.48	14.51
35%	13.97	13.84	13.87	13.85	13.79
25%	13.47	13.47	13.37	13.44	13.33

Appendix

Table 17: Perplexity (

\downarrow

) under different tile prior initializations. All priors yield nearly identical performance, suggesting that the global sparsity target allows dynamic reallocation of sparsity during training, overriding the influence of fixed initialization.

Sparsity	Method	Optimizer	Logits Init	Gumbel Scaling	Gumbel	Prior(Strength)	Sparse Reg.	Weight Reg.
25%	PATCH Joint	Adam(0.001)	$\mathcal{N}(0,0.014)$	$25\rightarrow 350$	$2\rightarrow 0.05$	SparseGPT( $3$ )	7	10
35%	PATCH Joint	Adam(0.001)	$\mathcal{N}(0,0.014)$	$25\rightarrow 350$	$2\rightarrow 0.05$	SparseGPT( $3$ )	7	10
45%	PATCH Joint	Adam(0.001)	$\mathcal{N}(0,0.014)$	$25\rightarrow 350$	$4\rightarrow 0.05$	SparseGPT( $3$ )	7	10
25%	PATCH Tile	Adam(0.0001)	$\mathcal{N}(0,0.014)$	$100\rightarrow 500$	$2\rightarrow 0.05$	SparseGPT( $3$ )	3	0.1
35%	PATCH Tile	Adam(0.0001)	$\mathcal{N}(0,0.014)$	$100\rightarrow 500$	$2\rightarrow 0.05$	SparseGPT( $3$ )	3	0.1
45%	PATCH Tile	Adam(0.0001)	$\mathcal{N}(0,0.014)$	$100\rightarrow 500$	$2\rightarrow 0.05$	SparseGPT( $3$ )	3	0.1

Appendix

Table 18 : Hyper-parameters used for PATCH Joint and PATCH Tile across sparsity ratios. All hyper parameters were tuned on Qwen-2.5-0.5B.

Figure 4 : Sparsity distribution across Attention and MLP layers under varying global sparsity budgets in Qwen-2.5 0.5B.

Figure 5 : Sparsity distribution across Attention and MLP layers under varying global sparsity budgets in Gemma-3 1B.

Figure 6 : Sparsity distribution across Attention and MLP layers under varying global sparsity budgets in LLaMA-3.2 1B.

Sparsity	Method	Pattern	Qwen-2.5 0.5B		LLaMA-3.2 1B		Gemma-3 1B		LLaMA-2 7B		LLaMA-3.1 8B
			Acc (% $\uparrow$ )	PPL ( $\downarrow$ )	Acc (% $\uparrow$ )	PPL ( $\downarrow$ )	Acc (% $\uparrow$ )	PPL ( $\downarrow$ )	Acc (% $\uparrow$ )	PPL ( $\downarrow$ )	Acc (% $\uparrow$ )	PPL ( $\downarrow$ )
45%	PATCH	Dense/2:4 Tiles	40.29	14.57	42.08	12.23	42.80	11.96	48.99	6.55	53.60	8.20
45%	Wanda	Unstructured	41.45	18.81	40.76	16.56	42.87	25.38	52.72	6.36	55.67	8.24
45%	SparseGPT	Unstructured	42.31	17.65	42.66	15.01	43.52	22.26	52.77	6.46	56.70	8.21
35%	PATCH	Dense/2:4 Tiles	41.15	13.84	42.72	11.67	43.30	11.48	50.08	6.18	55.28	7.89
35%	Wanda	Unstructured	43.46	15.04	44.60	11.95	45.50	16.98	54.37	5.87	58.68	7.02

Appendix

Table 19 : Model quality (average accuracy across eight zero-shot tasks and perplexity on WikiText2 dataset) for PATCH , Wanda, and SparseGPT. For models with less than or equal to 1B parameters, PATCH Joint optimizes both dense tile locations and sparsity patterns, while for larger models PATCH Tile optimizes only dense tile locations with frozen sparsity patterns, both using Dense/2:4 Tiles pattern allowing continuous sparsity ratios and flexible tradeoffs between sparsity and model quality. Wanda and SparseGPT are unstructured pruning methods.

Figure 7 : Layer-wise sparsity distribution of OWL across models and global sparsity budgets.

Figure 8 : Layer-wise sparsity distribution of AlphaPruning across models and global sparsity budgets.

Figure 9 : AlphaPruning sparsity distribution across attention and MLP layers under varying global sparsity budgets in Gemma-3 1B.

Model	Sparsity (%)	Seed 0 (default)	Seed 25	Seed 26	Seed 42
Qwen-2.5 0.5B	25	13.47	13.41	13.38	13.36
	35	13.84	13.89	13.85	13.84
	45	14.57	14.59	14.61	14.49
Llama-3.2 1B	25	11.00	11.09	11.03	11.21
	35	11.67	11.72	11.56	11.86
	45	12.23	12.32	12.26	12.55

Appendix

Table 20 : Perplexity across seeds for Qwen-2.5 0.5B and Llama-3.2 1B.

Figure 10 : Layer-wise sparsity distribution of PATCH across seeds.

Figure 11 : Sparsity distribution across attention and MLP layers under varying global sparsity budgets in Llama-3.2 1B across seeds.

Figure 12 : Sparsity distribution across attention and MLP layers under varying global sparsity budgets in Qwen-2.5 0.5B across seeds.

Model	Sparsity	Method	Wiki PPL ( $\downarrow$ )	Avg Acc (% $\uparrow$ )
Qwen-2.5 0.5B	45%	PATCH Joint	14.57	40.29
		PATCH Joint + FT	14.96	40.87
	35%	PATCH Joint	13.84	41.15
		PATCH Joint + FT	14.32	41.59
	25%	PATCH Joint	13.47	42.39
		PATCH Joint + FT	13.85	42.55

Appendix

Table 21 : Model quality (average accuracy across eight zero-shot tasks and perplexity on WikiText2 dataset) for PATCH after a short fine-tuning.

Model	Method	Sparsity (%)	PPL ( $\downarrow$ )	Avg Acc (% $\uparrow$ )
Qwen-2.5 0.5B	PATCH	45	14.57	40.29
	SparseGPT (FFN only)	44	24.79	36.84
	MaskLLM (FFN only)	44	14.54	39.34
	PATCH	35	13.84	41.15
	SparseGPT (FFN except last 5)	35	20.46	38.33
	MaskLLM (FFN except last 5)	35	13.92	40.59

Appendix

Table 22 : Comparison of PATCH against an FFN-only 2:4 pruning baseline at matched global sparsity. The baseline applies SparseGPT 2:4 pruning to FFN modules only, optionally keeping the last few decoder blocks dense (denoted “except last

k

”) to reach the target global sparsity. Rows labeled MaskLLM apply MaskLLM’s learned 2:4 masks to the FFNs with the same heuristic allocation. PATCH achieves higher average accuracy than every heuristic baseline at comparable sparsity, and lower perplexity in all but three cases, where a MaskLLM-based heuristic is marginally lower. Best value per model and sparsity group in bold .

Model	Method	Sparsity (%)	Backend	Throughput (tok/s)	Speedup
LLaMA-2 7B	Dense	0	cuBLAS	1023.80	1.00 $\times$
	PATCH	25	STOICC	1212.79	1.18 $\times$
	PATCH	35	STOICC	1304.46	1.27 $\times$
	PATCH	45	STOICC	1410.20	1.38 $\times$
	SparseGPT (FFN only)	33	cuSPARSELt	1276.67	1.25 $\times$
	SparseGPT (FFN only)	33	STOICC	1302.27	1.27 $\times$

Appendix

Table 23 : Throughput comparison of PATCH against FFN-only 2:4 pruning under the same STOICC backend on an A6000 GPU (batch size 16, prefill length 128, generation length 128). At matched global sparsity, the FFN-only baseline matches PATCH ’s throughput, but PATCH achieves significantly higher accuracy (Table 22 ). For reference, we also report fully 2:4 sparse models, which represent the upper bound of attainable acceleration.

Model	Method	Sparsity (%)	PPL ( $\downarrow$ )	Avg Acc (% $\uparrow$ )
Qwen-2.5 0.5B	SparseGPT (3:4)	25	13.99	43.34
Qwen-2.5 0.5B	PATCH	25	13.47	42.39
LLaMA-3.2 1B	SparseGPT (3:4)	25	10.88	44.66
LLaMA-3.2 1B	PATCH	25	11.00	43.81
Gemma-3 1B	SparseGPT (3:4)	25	13.96	45.27
Gemma-3 1B	PATCH	25	11.17	44.07

Appendix

Table 24 : Sparsity-matched comparison between PATCH at 25% sparsity and SparseGPT pruned to a 3:4 pattern (75% density). While SparseGPT 3:4 achieves slightly lower perplexity due to its higher per-group flexibility, the 3:4 pattern is incompatible with NVIDIA Sparse Tensor Cores (which require exactly two non-zeros per group of four) and therefore cannot be accelerated, running at dense speeds. PATCH at 25% sparsity, in contrast, mixes dense and 2:4 tiles and unlocks

\sim

1.18

\times

end-to-end speedup on standard GPUs.

Model	Method	C4 PPL ( $\downarrow$ )	C4 Avg Acc (% $\uparrow$ )	SlimPajama PPL ( $\downarrow$ )	SlimPajama Avg Acc (% $\uparrow$ )
Qwen-2.5 0.5B	MaskLLM (50%)	16.27	38.78	15.22	39.33
	PATCH (45%)	15.30	40.02	14.57	40.29
	PATCH (35%)	14.34	40.94	13.84	41.15
	PATCH (25%)	13.81	41.91	13.47	42.39
LLaMA-3.2 1B	MaskLLM (50%)	14.23	40.97	12.93	41.04
	PATCH (45%)	13.10	41.73	12.23	42.08

Appendix

Table 25 : Robustness of PATCH mask training to the choice of calibration corpus. We train identical PATCH configurations on the C4 dataset and on SlimPajama and report WikiText2 perplexity and average zero-shot accuracy. Despite the domain shift, downstream accuracy remains within

\sim

0.6% across datasets, and PATCH outperforms MaskLLM under both calibration corpora.

Sparsity (%)	Max. Execution Tile Size	Throughput (tok/s)	Speedup vs. Dense
0	—	1023.80	1.00 $\times$
25	64 $\times$ 64	1207.08	1.18 $\times$
25	32 $\times$ 64	1075.98	1.05 $\times$
35	64 $\times$ 64	1288.54	1.26 $\times$
35	32 $\times$ 64	1142.65	1.12 $\times$
45	64 $\times$ 64	1382.13	1.35 $\times$

Appendix

Table 26 : Effect of restricting STOICC’s autotuner to specific maximum execution tile sizes on PATCH ’s end-to-end throughput, measured on LLaMA-2 7B with an A6000 GPU (batch size 16, prefill length 128, generation length 128). Limiting the autotuner to 64

\times

64 has a small effect on throughput (the unrestricted autotuner already prefers this size in most layers), while restricting it to 32

\times

64 underutilizes Tensor Cores and yields slower kernels. Tiles smaller than 32

\times

64 are not supported by STOICC’s metadata layout and compression constraints. As reported in Table 4 , model accuracy is largely insensitive to tile size, so the chosen 128

\times

128 mask-tile granularity (which the compiler subdivides at execution) provides the best balance between accuracy and hardware efficiency.

Tokens generated	Sparsity (%)	2K	2K (FA2)	8K	8K (FA2)	16K	16K (FA2)
128	25	1.18 $\times$	1.24 $\times$	1.09 $\times$	1.11 $\times$	1.02 $\times$	1.03 $\times$
	35	1.27 $\times$	1.33 $\times$	1.14 $\times$	1.17 $\times$	1.07 $\times$	1.08 $\times$
	45	1.38 $\times$	1.45 $\times$	1.22 $\times$	1.26 $\times$	1.14 $\times$	1.17 $\times$
1024	25	1.13 $\times$	1.21 $\times$	1.13 $\times$	1.16 $\times$	1.12 $\times$	1.14 $\times$
	35	1.18 $\times$	1.26 $\times$	1.16 $\times$	1.22 $\times$	1.15 $\times$	1.18 $\times$
	45	1.25 $\times$	1.38 $\times$	1.19 $\times$	1.29 $\times$	1.19 $\times$	1.23 $\times$

Appendix

Table 27 : End-to-end throughput speedup of PATCH over a dense PyTorch baseline for LLaMA-2 7B on an A6000 GPU (batch size 16) at prefill lengths of 2K, 8K, and 16K tokens, with and without the FlashAttention-2 (FA2) attention backend; FA2 speedups are relative to the dense model using the same backend. Speedups decrease as the prefill grows, since attention computation begins to dominate runtime and reduces the relative contribution of accelerating the FFN GEMMs. FA2 reduces the attention overhead and increases the speedup in every setting.

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