LinDeps: CNN Post-Pruning via Layer Dependency Analysis

• LinDeps is a post-pruning method for CNNs that identifies and removes redundant feature maps via pivoted QR decomposition, effectively reducing model complexity.
• It employs a recovery step that adjusts subsequent layer kernels to reconstruct pruned signals, preserving performance without additional fine-tuning.
• Empirical results show that when combined with techniques like APIB or NORTON, LinDeps can achieve significant extra pruning and speedup, with up to 30% additional compression and minimal accuracy loss.

LinDeps is a post-pruning method for convolutional neural networks (CNNs) that identifies and removes layer-wise linear dependencies between feature maps or filters. It is designed as a pruning method that can be applied on top of an existing structured-pruning pipeline, with the explicit aim of removing residual redundancy without fine-tuning. Its central mechanism is a layer-wise linear dependency analysis based on pivoted QR decomposition, followed by a signal recovery step that adjusts the next layer’s kernels so that compatibility and performance are preserved as much as possible (Henry et al., 29 Jul 2025).

1. Problem setting and conceptual role

LinDeps addresses a limitation of many pruning methods: they remove filters by an importance heuristic, but often overlook the possibility that some output channels in a layer are linearly dependent on others. In that setting, a feature map that lies in the span of other feature maps is redundant. LinDeps is therefore designed to detect such dependencies, prune the corresponding filters, and recover the signal so that the next layer remains compatible, all without fine-tuning. The method is especially positioned as a post-pruning step after an existing pruning technique such as APIB or NORTON (Henry et al., 29 Jul 2025).

The method is explicitly not presented as a replacement for a main pruning strategy. Its intended role is additive: a base pruning method may remove many low-importance channels while still leaving behind channels that are linearly dependent or otherwise duplicative. LinDeps performs a second-stage cleanup by targeting those leftovers. This suggests a division of labor between a first-stage pruning criterion and a second-stage redundancy elimination mechanism.

2. Layer-wise procedure

For a layer $i$, LinDeps forwards a batch of $B$ images through the network and obtains feature maps of shape $C \times H \times W$. Each channel is flattened and concatenated over all spatial locations and batch examples, producing a matrix

$A \in \mathbb{R}^{C \times (B \cdot H \cdot W)}.$

Each row of $A$ is one feature map or channel viewed as a long vector. LinDeps then applies pivoted QR decomposition to the transpose $A^\top$:

$$A^{\top} P = Q R = Q \begin{bmatrix} R_{11} & R_{12} \ \mathbf{0} & \mathbf{0} \end{bmatrix}.$$

Here, $Q$ is orthonormal, $R$ is upper triangular in block form, $P$ is a permutation matrix, $B$0 is the leading triangular block, and the effective rank $B$1 is the number of independent rows or channels retained. The pivoting reorders channels so that the most “independent” or informative ones appear first. The diagonal entries of $B$2 are used to reveal rank and dependency structure (Henry et al., 29 Jul 2025).

The pruning rule uses a threshold parameter $B$3:

$B$4

If $B$5, only exactly linearly dependent channels are removed. If $B$6, channels that are nearly dependent can also be removed. Compared with pairwise similarity checks, the use of pivoted QR is intended to capture dependence among multiple channels rather than only pairs.

After pruning channels in layer $B$7, the next convolution layer $B$8 no longer matches the input dimensionality. LinDeps therefore computes a recovery matrix $B$9 such that

$C \times H \times W$0

The paper states that $C \times H \times W$1 is obtained via least squares. Each row of $C \times H \times W$2 describes how an original channel can be approximated from the retained channels. A convolution kernel in layer $C \times H \times W$3 originally has shape

$C \times H \times W$4

where $C \times H \times W$5 is the spatial kernel size, typically $C \times H \times W$6. LinDeps flattens the kernel weights to a matrix, multiplies by $C \times H \times W$7, and reshapes the result into a new kernel of size

$C \times H \times W$8

This is the method’s fine-tuning-free compensation step: it adjusts the next layer so that the pruned representation remains usable.

3. Guaranteed performance preservation

The phrase “guaranteed performance preservation” is used in a restricted sense. The guarantee is tied to the case of strictly linearly dependent channels. If the pruned channels are strictly linearly dependent on the retained ones and $C \times H \times W$9, then the recovery matrix can reconstruct the removed signal exactly in theory, so the network output can be preserved exactly, modulo numerical precision (Henry et al., 29 Jul 2025).

In practice, the implementation notes that finite precision matters and that very small diagonal values in QR can be numerically unstable. For that reason, the paper uses a practical “lossless pruning” threshold of $A \in \mathbb{R}^{C \times (B \cdot H \cdot W)}.$0 rather than exactly zero. The strongest reading of the guarantee is therefore limited to the strict dependence case; once $A \in \mathbb{R}^{C \times (B \cdot H \cdot W)}.$1 is used, the preservation claim becomes approximate rather than exact.

This distinction is important because it separates two regimes. One regime removes only exact dependencies and supports a theoretical exactness claim. The other removes near-dependencies and aims at empirical preservation of performance while achieving more aggressive compression. A plausible implication is that the method’s practical utility depends on balancing redundancy removal against the numerical stability of the recovered representation.

4. Empirical results

The evaluation uses CIFAR-10 and ImageNet, with VGG-16, ResNet-56, ResNet-110, and ResNet-50 as backbones. LinDeps is evaluated on top of APIB and NORTON, and it is also tested as a standalone pruning method on VGG-16/CIFAR-10. The reported metrics are FLOPs reduction, Parameter reduction, Top-1 accuracy, and, in low-resource experiments, pruning runtime and inference latency (Henry et al., 29 Jul 2025).

On VGG-16/CIFAR-10, LinDeps on top of APIB increases FLOPs reduction by about 0.54% to 1.26% depending on the pruning level. On top of NORTON, it also improves compression, and the combination is reported to achieve a new state of the art on VGG-16/CIFAR-10. On ResNet-56/CIFAR-10, LinDeps on top of NORTON improves FLOPs reduction by around 0.16% to 2.57% while preserving accuracy. On ResNet-110/CIFAR-10, the corresponding improvement is around 0.21% to 2.82%. On ResNet-50/ImageNet, the gains are smaller, up to about 0.17% extra compression at the same top-1 accuracy. The paper suggests that the smaller gain on ImageNet may be due to noisier feature maps and lower baseline accuracy, which make dependencies harder to exploit cleanly.

The standalone results are more limited. With $A \in \mathbb{R}^{C \times (B \cdot H \cdot W)}.$2 on VGG-16/CIFAR-10, LinDeps alone achieves a 24.9% pruning ratio with 93.68% top-1 accuracy and essentially no accuracy loss. As $A \in \mathbb{R}^{C \times (B \cdot H \cdot W)}.$3 increases, pruning becomes more aggressive but accuracy drops sharply: 34.9% pruning gives 92.65%, 40.8% gives 91.08%, 43.2% gives 78.60%, and 64.2% gives 23.2%. The paper therefore characterizes LinDeps as best used as a complement rather than as a standalone replacement for modern pruning methods.

A major practical result concerns low-resource scenarios in which no retraining can be performed. In that setting, applying LinDeps on top of an already pruned network can yield up to 30% extra pruning with less than 0.3% accuracy loss. The paper also reports significant pruning-runtime improvements and inference-latency speedups, with speedups around 23%–33% depending on device. The devices listed include an RTX 3070 laptop GPU, Intel CPU, MacBook M1, Orin AGX, and Raspberry Pi CPU.

5. Relation to prior pruning methods and main caveats

The paper positions LinDeps against several pruning families. Compared with low-importance pruning, its claim is that importance-based criteria may miss channels that are highly redundant but still appear individually important. Compared with similarity-based pruning, the stated limitation of prior work is that pairwise similarity can miss higher-order layer-wise dependencies. Compared with LDFM, the main difference is that LinDeps adds a recovery mechanism that allows pruning without fine-tuning, making it more practical as a post-pruning add-on. Compared with hybrid pruning methods, LinDeps is described as conceptually hybrid, but it does not mix low-importance and similarity criteria internally; instead, it acts as a second-stage cleanup tool after another pruning method (Henry et al., 29 Jul 2025).

The caveats are also explicit. LinDeps is not a standalone replacement for a good pruning criterion. Its gains depend on finding meaningful linear dependencies in feature maps. Those gains are larger when the feature maps are cleaner and more redundant, and smaller on noisier large-scale settings such as ImageNet. The strongest form of the preservation guarantee holds in the strict dependence case; with approximate thresholds, preservation becomes empirical rather than exact. The method is also developed for CNNs, not transformers.

6. Other uses of the name

The label “LinDeps” is not unique across the literature. In some contexts it refers to technically unrelated systems, and the surrounding field determines the meaning. In distributed dependency discovery, the cited paper does not present “LinDeps” as a separate algorithm with that exact name; the closest concept is a primitive-based framework built around logical discovery plans (LDPs) and physical discovery plans (PDPs) for discovering dependencies such as FDs, UCCs, ODs, and DCs in shared-nothing distributed environments (Saxena et al., 2019).

In quantitative dependency syntax, “LinDeps” is used for the Linear Arrangement Library (LAL), an open-source toolkit for computing metrics on syntactic dependency structures, treebanks, and collections of treebanks. Its scope includes dependency distance, crossings, random and extremal baselines, and tree generation under constraints such as planarity and projectivity (Alemany-Puig et al., 2021). In type theory and information-flow analysis, “LinDeps” may denote the Linear Dependency Calculus (LDC), a framework that unifies linearity analysis and dependency analysis by using one graded judgmental system that can be interpreted over a preordered semiring for usage or over a lattice for dependency (Choudhury, 2023). In MLOps, the name is also used for a data-source dependency analysis framework that statically extracts which upstream data sources a model depends on, directly and transitively, and exposes the resulting dependency map as a REST API (Boué et al., 2022).

Within current machine learning usage, however, LinDeps most prominently denotes the fine-tuning-free post-pruning method for CNNs that removes layer-wise linear dependencies by pivoted QR decomposition and compensates the following layer by a recovery transform.