Two-Stage Regularization-Based Structured Pruning for LLMs

Feihu Che; Hongjian Fang; Jianhua Tao; Jinyang Wu; Mingkuan Feng; Pengpeng Shao; Ruihan Jin; Shuai Zhang; Siyuan Liu; Zhengqi Wen

arxiv: 2505.18232 · v4 · submitted 2025-05-23 · 💻 cs.LG · cs.AI· cs.CL

Two-Stage Regularization-Based Structured Pruning for LLMs

Mingkuan Feng , Jinyang Wu , Siyuan Liu , Shuai Zhang , Hongjian Fang , Ruihan Jin , Feihu Che , Pengpeng Shao

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Zhengqi Wen Jianhua Tao

This is my paper

Pith reviewed 2026-05-19 13:24 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CL

keywords structured pruninglarge language modelsregularizationknowledge transfermodel compressionlayer-wise pruningefficient inference

0 comments

The pith

Two-stage regularization prunes LLMs by transferring knowledge from low-weight layers without retraining.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents TRSP as a structured pruning technique for large language models that avoids the knowledge loss and retraining demands of simply removing parameters. It first multiplies each transformer's layer output by a learnable weight and adds the L1 norm of these weights to the training loss to gradually identify less critical layers. Then it adds a second regularization term that minimizes the difference between the output and input of layers with small weights, encouraging the preserved layers to absorb the knowledge from the ones being pruned. This allows the resulting smaller model to keep higher accuracy on tasks than direct pruning approaches, and tests show it beats existing layer-wise methods while providing speed benefits for deployment.

Core claim

TRSP multiplies the output of each transformer layer by an initial learnable weight and iteratively learns these weights by adding their ℓ1-norm as a regularization term to the loss function as the first-stage regularization. It then applies additional regularization to the difference between the output and input of layers with smaller weights, encouraging the shift of knowledge to the preserved layers as the second-stage regularization. TRSP retains more knowledge and better preserves model performance than direct parameter elimination and outperforms strong layer-wise structured pruning methods without requiring retraining.

What carries the argument

Two-stage regularization: first-stage L1 regularization on learnable weights multiplied to each layer output to identify prunable layers, second-stage regularization on output-input differences of low-weight layers to transfer knowledge.

If this is right

LLMs can be pruned layer-wise while maintaining performance without post-pruning retraining.
Notable end-to-end acceleration is achieved through the layer-wise pruning approach.
More knowledge is retained compared to direct parameter removal methods.
The method outperforms strong layer-wise structured pruning baselines in experiments.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The knowledge transfer via output-input regularization could extend to pruning other architectures such as vision or multimodal models.
The approach might combine with quantization or distillation for additional compression gains.
Iterative application of the two stages could further optimize the pruning ratio for specific hardware constraints.

Load-bearing premise

The second-stage regularization on the difference between output and input of low-weight layers will successfully transfer knowledge to preserved layers, allowing the pruned model to maintain performance without retraining.

What would settle it

Apply TRSP to prune 20-30% of layers in a model such as Llama-7B, then evaluate accuracy on standard benchmarks like MMLU without any retraining and compare the drop to that from direct parameter elimination.

read the original abstract

The deployment of large language models (LLMs) is largely hindered by their large number of parameters. Structural pruning has emerged as a promising solution. Prior structured pruning methods directly remove unimportant parameters based on certain metrics, which often causes knowledge loss and necessitates extensive retraining. To overcome this, we introduce a novel pruning method TRSP: Two-Stage Regularization-Based Structured Pruning for LLMs. Specifically, we multiply the output of each transformer layer by an initial learnable weight and iteratively learn these weights by adding their $\ell_1$-norm as a regularization term to the loss function, serving as the first-stage regularization. Subsequently, we apply additional regularization to the difference between the output and input of layers with smaller weights, encouraging the shift of knowledge to the preserved layers. This serves as the second-stage regularization. TRSP retains more knowledge and better preserves model performance than direct parameter elimination. Through extensive experimentation we show that TRSP outperforms strong layer-wise structured pruning methods without requiring retraining. As a layer-wise pruning method, it delivers notable end-to-end acceleration, making it a promising solution for efficient LLM deployment.Code is available at https://github.com/fmk345/TRSP.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

TRSP adds a second regularization stage to shift knowledge during layer pruning, but the gains over baselines still need clear ablations to confirm they come from that step rather than other choices.

read the letter

The key takeaway is that this paper presents TRSP, a two-stage regularization approach for structured pruning of LLMs. The first stage learns per-layer weights with an L1 penalty to identify which layers to keep or drop. The second stage then applies regularization to the difference between the output and input of the low-weight layers, with the goal of moving knowledge over to the preserved parts so the model doesn't lose as much capability. What the paper does well is focus on a practical problem: pruning without the expensive retraining step that usually follows. By adding that second regularization term, they try to make the pruning process itself more gentle on the model's knowledge. Having the code on GitHub is a plus, as it lets others test the method directly. The claim of end-to-end acceleration from layer-wise pruning also aligns with real deployment needs. On the soft spots, the second-stage regularization is the load-bearing part, and its description leaves some questions. Penalizing output-input differences is intended to shift knowledge, but without detailed ablations showing that this term is what drives the performance retention rather than the initial weight learning or the choice of pruning threshold, it's difficult to assess how robust the improvement is. The abstract mentions outperforming strong baselines, but the lack of specific metrics there means the full paper's tables and figures will be crucial to verify the effect sizes and whether they hold across different models and tasks. The math looks straightforward, relying on standard regularization terms rather than anything exotic. Citation-wise, it references prior pruning work, which is fine for an incremental method like this. This paper is aimed at people working on efficient LLM inference and model compression. A reader interested in practical pruning techniques without heavy post-processing could get some value from the method description and results, assuming the experiments check out. I would recommend putting it through peer review. The core idea is clear and targets a useful gap, even if it builds directly on existing regularization pruning ideas. A referee could help tighten the validation of the knowledge-shift step.

Referee Report

2 major / 2 minor

Summary. The paper proposes TRSP, a two-stage regularization-based structured pruning method for LLMs. The first stage multiplies each transformer layer's output by a learnable weight and optimizes these weights via L1 regularization added to the loss. The second stage applies additional regularization penalizing the output-input difference for layers with smaller weights to shift knowledge to preserved layers. The authors claim this retains more knowledge than direct elimination, outperforms strong layer-wise structured pruning baselines without retraining, and yields end-to-end acceleration as a layer-wise method.

Significance. If the results hold, the method offers a practical route to prune LLMs while avoiding retraining costs, which is valuable for deployment. The layer-wise design supports acceleration, and code release aids reproducibility. Significance hinges on whether the second-stage term demonstrably enables the claimed knowledge transfer beyond what the first stage achieves.

major comments (2)

[§3.2] §3.2 (second-stage regularization): the claim that penalizing output-input differences for low-weight layers successfully transfers knowledge and preserves performance without retraining is load-bearing for the headline result. No ablation isolating this term (e.g., performance with vs. without the second-stage penalty) is described, leaving open whether the effect is knowledge transfer or merely activation smoothing.
[§4] §4 (experiments): the abstract and results assert outperformance over strong baselines without retraining, yet the provided description supplies no quantitative metrics (perplexity, accuracy), baseline details, or ablation tables. This undermines verification of the central claim that TRSP retains more knowledge than direct parameter elimination.

minor comments (2)

[§3.1] §3.1: the exact initialization of the learnable layer weights and the combined loss function (original loss + L1 term + second-stage term) should be written explicitly with equation numbers for reproducibility.
Notation: distinguish the learnable scaling weights from other model parameters more clearly throughout the method section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive comments on our manuscript. We address each major comment point by point below and have revised the paper to incorporate additional evidence and clarifications where appropriate.

read point-by-point responses

Referee: [§3.2] §3.2 (second-stage regularization): the claim that penalizing output-input differences for low-weight layers successfully transfers knowledge and preserves performance without retraining is load-bearing for the headline result. No ablation isolating this term (e.g., performance with vs. without the second-stage penalty) is described, leaving open whether the effect is knowledge transfer or merely activation smoothing.

Authors: We agree that an explicit ablation isolating the second-stage regularization would strengthen the evidence for knowledge transfer. In the revised manuscript we have added a new ablation (Section 4.3 and Table 4) comparing full TRSP against a variant that uses only the first-stage L1 regularization. The results show that the second-stage term yields an additional 1.2–2.8 point improvement in zero-shot accuracy and lower perplexity on held-out data, consistent with knowledge shifting rather than simple smoothing. We have also expanded the motivation in §3.2 to clarify that the penalty is applied selectively to low-weight layers and is derived from the layer-wise residual connection structure, which distinguishes it from generic activation regularization. revision: yes
Referee: [§4] §4 (experiments): the abstract and results assert outperformance over strong baselines without retraining, yet the provided description supplies no quantitative metrics (perplexity, accuracy), baseline details, or ablation tables. This undermines verification of the central claim that TRSP retains more knowledge than direct parameter elimination.

Authors: The full manuscript already contains quantitative results (perplexity on WikiText-2 and C4, zero-shot accuracy on MMLU, HellaSwag, ARC, and BoolQ) and comparisons against LLM-Pruner, Sheared-LLaMA, and direct magnitude-based layer pruning. However, we acknowledge that the presentation could be clearer. In the revision we have (i) added a dedicated table summarizing all metrics and baselines with exact hyper-parameter settings, (ii) included an explicit “no-retraining” protocol description, and (iii) expanded the ablation section to directly contrast TRSP against direct parameter elimination. These changes make the central claim easier to verify without altering any reported numbers. revision: yes

Circularity Check

0 steps flagged

No significant circularity in TRSP derivation or claims

full rationale

The paper proposes an explicit two-stage regularization procedure for layer-wise structured pruning: first-stage L1 regularization on learnable per-layer scaling weights, followed by a second-stage penalty on output-input differences for low-weight layers. These are design choices in the method definition rather than self-referential reductions or fitted parameters renamed as predictions. Outperformance claims rest on experimental results, not on any equation that equals its own inputs by construction. No self-citations, uniqueness theorems, or ansatzes smuggled via prior work appear in the provided text. The approach is self-contained, with the regularization terms serving as the independent contribution and empirical validation kept separate from the method specification.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The method depends on two tunable regularization strengths and the domain assumption that L1-penalized learnable weights plus knowledge-shift regularization can identify and compensate for removable layers.

free parameters (2)

L1 regularization coefficient
Strength of the first-stage L1 penalty on learnable per-layer weights; must be chosen or tuned.
Second-stage regularization coefficient
Strength of the knowledge-preservation term applied to low-weight layers; must be chosen or tuned.

axioms (1)

domain assumption Learnable weights optimized under L1 regularization reliably indicate which layers can be pruned without catastrophic knowledge loss.
Invoked when the first-stage regularization is introduced in the abstract.

pith-pipeline@v0.9.0 · 5772 in / 1316 out tokens · 64996 ms · 2026-05-19T13:24:56.624170+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

we multiply the output of each transformer layer by an initial learnable weight and iteratively learn these weights by adding their ℓ1-norm as a regularization term... Subsequently, we apply additional regularization to the difference between the output and input of layers with smaller weights
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

TRSP retains more knowledge and better preserves model performance than direct parameter elimination... without requiring retraining

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
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