Crossbar Pruning in Neural Accelerators

Updated 11 July 2026

Crossbar pruning is a neural network compression method that removes weights and entire crossbar units based on accelerator structures and constraints.
It employs structured optimization techniques like ADMM, iterative pruning, and differentiable masking to achieve hardware-realizable sparsity.
Pruning strategies balance compression and reliability by reducing ADC cost, mitigating device non-idealities, and enhancing fault tolerance in analog in-memory systems.

Searching arXiv for recent and foundational work on crossbar pruning. Crossbar pruning denotes a class of neural-network compression methods in which pruning decisions are made with explicit reference to the structure, constraints, and non-ideal behavior of crossbar-based accelerators, including memristor, ReRAM, RRAM, and analog in-memory processing systems. In this setting, the objective is not merely to create sparse weight tensors, but to remove weights, rows, columns, blocks, kernels, channels, or entire crossbar-aligned units in ways that translate into realizable reductions in crossbar count, area, power, ADC cost, or fault sensitivity. The central distinction from conventional pruning is that sparsity is constrained by mapping granularity, conductance representation, crossbar dimensions, peripheral circuitry, and, in several works, device non-idealities such as stuck-at faults, write variations, state drift, aging, and interconnect parasitics (Liang et al., 2018, Yuan et al., 2019, Bhattacharjee et al., 2022, Huai et al., 9 Jul 2026).

1. Historical emergence and problem formulation

Early work on memristive and crossbar-based deployment identified a basic incompatibility between conventional sparse neural networks and rigid crossbar fabrics. Standard network pruning removes redundant connections, but the resulting irregular sparsity often leaves crosspoints physically allocated and peripheral circuits still active, producing low utilization and limited hardware benefit. This issue was articulated in work on Memristive Crossbar Array deployment, which argued that pruning-induced irregular connectivity is incoherent to the crossbar structure and can produce hardware inefficiency in area and energy (Ankit et al., 2017). A related formulation for CNN accelerators observed that previous pruning methods did not consider the crossbar architecture and corresponding mapping method, and therefore could not be directly utilized by crossbar-based neural network accelerators (Liang et al., 2018).

This line of work led to the idea that pruning should be co-designed with mapping. In one formulation, crossbar-aware pruning is cast as an $L_0$ -norm constrained optimization problem that selects a subset of crossbars or crossbar columns whose combined outputs best approximate the original layer output (Liang et al., 2018). In another, pruning and quantization are embedded directly into training by Alternating Direction Method of Multipliers (ADMM), with constraints $\mathbf{W}_i \in \mathbf{P}_i$ for structured pruning and $\mathbf{W}_i \in \mathbf{Q}_i$ for quantization, so that crossbar blocks, conductance range, and mismatch between weight value and real devices are handled during optimization rather than after mapping (Yuan et al., 2019). More recent work extends this principle to crossbar-aligned compression, where pruning is designed to eliminate the hardware units needed for data aligning and to avoid additional floating-point or masking hardware (Huai et al., 9 Jul 2026).

A consistent theme across the literature is that the pruning objective is hardware-realizable sparsity rather than abstract parameter reduction. This includes crossbar count reduction, compute-crossbar reduction, removal of entire rows or columns that can be powered down or repurposed, lowering ADC precision requirements, and increasing tolerance to fabrication defects or analog non-idealities (Liang et al., 2018, Joardar et al., 2021, Ibrayev et al., 2024).

2. Structural granularities and mapping-aligned sparsity

Crossbar pruning has been implemented at several structural granularities. One strand uses crossbar-grain and column-grain sparsity. In the crossbar-aware pruning framework for CNNs, crossbar-grain sparsity eliminates entire crossbars whose contributions are smallest, whereas column-grain sparsity prunes at the level of crossbar columns and then performs output recombination so that active columns from different crossbars can be recombined to form new crossbars (Liang et al., 2018). This directly connects pruning masks to physical array removal.

Memristor-based ADMM frameworks instead emphasize structured weight pruning with filter-wise, channel-wise, and shape-wise sparsity after reshaping tensors into GEMM format to align with crossbar mapping. In this setting, crossbar block pruning reduces entire rows, columns, or blocks of the weight matrix, so that structural sparsity in weights becomes hardware-level savings in complete crossbar subarrays or blocks (Yuan et al., 2019). A related memristor framework likewise adopts filter-wise, channel-wise, and shape-wise pruning because the resulting regular matrices can be seamlessly partitioned onto fixed-size memristor crossbars such as $128 \times 64$ , avoiding the irregularity, index storage, and unbalanced hardware utilization associated with unstructured pruning (Ma et al., 2019).

A different axis of granularity appears in ReaLPrune, which integrates lottery ticket pruning with crossbar-aware structured sparsity. It prunes filters to remove entire output channels, prunes channels to remove specific input channels across filters and thus zero full crossbar columns, and prunes indices at the same position across multiple filters, which zeros crossbar rows. The procedure proceeds in a coarse-to-fine iteration, beginning with filter-wise pruning and shifting to channel-wise and then index-wise pruning as accuracy constraints tighten (Joardar et al., 2021). This suggests that pruning granularity can be treated as an adaptive control variable rather than a fixed design choice.

Other formulations are shaped by the target hardware bottleneck. For analog in-memory accelerators dominated by ADC cost, pruning is organized around tile-level columns rather than conventional layer structures. The D.U.B. framework requires sparsity within crossbar tiles to be Discrete, Unstructured, and Balanced: the least sparse column within a crossbar must have a sparsity level that is a discrete power of two, sparsity within each column remains unstructured, and sparsity is balanced across columns in a crossbar so that the least sparse column dictates useful ADC precision reduction (Ibrayev et al., 2024).

The following table organizes the principal pruning granularities reported in the literature.

Granularity	Representative formulation	Intended hardware effect
Crossbar-grain / column-grain	Crossbar-aware neural network pruning (Liang et al., 2018)	Remove whole crossbars or columns; enable recombination
Filter-wise / channel-wise / shape-wise / crossbar block	Memristor ADMM frameworks (Yuan et al., 2019, Ma et al., 2019)	Save complete crossbar subarrays or blocks
Filter-wise / channel-wise / index-wise	ReaLPrune (Joardar et al., 2021)	Zero full rows or columns and reduce required ReRAM crossbars
Kernel-group / crossbar pruning	CRIMP (Huai et al., 9 Jul 2026)	Remove hardware units needed for data aligning
Column-wise D.U.B. sparsity	ADC-oriented pruning (Ibrayev et al., 2024)	Reduce ADC precision and ADC energy

These granularities are not interchangeable. Crossbar-aware work repeatedly distinguishes structured pruning, which is directly exploitable by crossbar mapping, from unstructured pruning, which can maximize sparsity with minimal software accuracy loss but often does not directly yield hardware savings or acceleration unless paired with a special mapping or fault-tolerance objective (Yuan et al., 2021, Joardar et al., 2021).

3. Optimization methods and training pipelines

A major family of methods solves crossbar pruning as a constrained optimization problem. In the ADMM-based memristor framework, the training objective is

$\begin{aligned} & \min_{ \{ \mathbf{W}_i, \mathbf{b}_i \} } f\left( \{ \mathbf{W}_i \}_{i=1}^N, \{ \mathbf{b}_i \}_{i=1}^N \right) \ & \text{subject to} \qquad \mathbf{W}_i \in \mathbf{P}_i, \; \mathbf{W}_i \in \mathbf{Q}_i \quad \forall i=1,\dots,N, \end{aligned}$

with $\mathbf{P}_i$ denoting structured pruning constraints and $\mathbf{Q}_i$ denoting quantization constraints. Indicator functions convert these constraints into an ADMM objective, auxiliary and dual variables are introduced, and each ADMM iteration solves three subproblems: minimization of DNN loss plus quadratic penalties, Euclidean projection onto the structured pruning set, and Euclidean projection onto the quantization set (Yuan et al., 2019). The framework is organized into three steps: memristor-based ADMM regularized optimization, masked mapping, and retraining (Yuan et al., 2019). A closely related framework uses the same ADMM structure but adds post-processing through Network Purification and Unused Path Removal after discovering non-optimality of the ADMM solution in weight pruning and the unused data path in a structured pruned model (Ma et al., 2019).

The mathematical structure of the post-processing is also explicit. Network Purification and Unused Path Removal define an emptiness ratio

$\eta_{i, j} = \frac{\sum_{k=1}^{\delta} (column_k \neq 0)}{\delta}$

and an importance score

$\sigma_{i, j} = \frac{\sum_{k=1}^{\delta} \|column_k\|_F^2}{\delta},$

then remove channels or filters when threshold conditions indicate that paths left after ADMM are effectively redundant (Ma et al., 2019). This suggests that structured pruning alone may not remove all hardware-irrelevant connectivity unless downstream and upstream dependencies are explicitly analyzed.

A second family uses direct sparse optimization over crossbar masks. Crossbar-aware neural network pruning formulates pruning as

$\underset{\pmb{\beta}_{L_0}^j}{\text{minimize}\quad \|\pmb{Y} - \pmb{X}\pmb{\beta}_{L_0}^j\|_2^2$

subject to

$\mathbf{W}_i \in \mathbf{P}_i$ 0

where $\mathbf{W}_i \in \mathbf{P}_i$ 1 is a binary pruning mask selecting crossbars or crossbar columns to keep (Liang et al., 2018). Because the problem is NP-hard, the paper proposes $\mathbf{W}_i \in \mathbf{P}_i$ 2-norm constrained gradient descent with Relaxant Probabilistic Projection. The gradient step is

$\mathbf{W}_i \in \mathbf{P}_i$ 3

and RPP samples $\mathbf{W}_i \in \mathbf{P}_i$ 4 elements from the top $\mathbf{W}_i \in \mathbf{P}_i$ 5 candidates rather than deterministically selecting the largest- $\mathbf{W}_i \in \mathbf{P}_i$ 6 entries (Liang et al., 2018).

A third family uses iterative pruning and reset procedures inspired by the Lottery Ticket Hypothesis. ReaLPrune initializes weights, trains for $\mathbf{W}_i \in \mathbf{P}_i$ 7 epochs, prunes the lowest $\mathbf{W}_i \in \mathbf{P}_i$ 8-percentile by average magnitude at the current structural granularity, reverts the last pruning step and switches to a finer granularity if accuracy falls below the unpruned baseline, and resets the remaining weights to the initial weights as in Lottery Ticket Pruning (Joardar et al., 2021). This framework is explicitly one-time and offline for pruning, after which edge devices train from scratch directly on the pruned, crossbar-aware model (Joardar et al., 2021).

Recent work also introduces differentiable mask-layer training for crossbar blocks. In CRIMP, crossbar pruning is implemented by mask layers added after each trainable layer; each mask entry corresponds to one crossbar, and setting a mask to zero removes its associated crossbar from computation. Kernel-group pruning is performed first to keep remaining kernels as multiples of the crossbar width, then crossbar pruning refines the model by zeroing out less important crossbar-blocks. Zero-recovery epochs with momentum allow temporarily zeroed masks and kernels to recover (Huai et al., 9 Jul 2026).

4. Hardware constraints, non-idealities, and reliability objectives

Crossbar pruning is unusually sensitive to hardware constraints because the representation and execution substrate is analog or mixed-signal rather than an abstract sparse tensor format. Several frameworks therefore embed physical constraints into pruning itself. In the ADMM-based memristor framework, these include conductance range constraints, discrete device-supported quantization levels, device mismatch, positive-only weights implemented through separate positive and negative branches, and crossbar size limitations to minimize read/write variability (Yuan et al., 2019). The mapping stage explicitly avoids assigning zero weights to the crossbar through masked mapping, and only non-zero structured blocks are mapped to hardware (Yuan et al., 2019).

Device non-idealities have also altered the goals of pruning. A systematic study of structured-pruned DNNs on non-ideal crossbars found that highly sparse DNNs can lead to severe accuracy losses compared to unpruned DNNs mapped onto non-ideal crossbars, even when software accuracy is matched pre-mapping (Bhattacharjee et al., 2022). The paper quantified crossbar error by the non-ideality factor

$\mathbf{W}_i \in \mathbf{P}_i$ 9

and proposed two mitigation methods: crossbar-column rearrangement and Weight-Constrained Training. Crossbar-column rearrangement sorts columns using $\mathbf{W}_i \in \mathbf{Q}_i$ 0, where $\mathbf{W}_i \in \mathbf{Q}_i$ 1 and $\mathbf{W}_i \in \mathbf{Q}_i$ 2 are the mean and standard deviation of absolute weights, before mapping to hardware; Weight-Constrained Training clips weights using

$\mathbf{W}_i \in \mathbf{Q}_i$ 3

and retrains for about two epochs post-pruning (Bhattacharjee et al., 2022). Both methods increase the proportion of low conductance synapses on crossbars, thereby improving computational accuracies (Bhattacharjee et al., 2022).

Fault tolerance provides another reliability-centered objective. For ReRAM-based edge AI, weight pruning was reinterpreted not primarily as compression but as a means to statistically mask defects. If a software-pruned zero overlaps with a stuck-off cell in hardware, the mapping error vanishes. Under pruning ratio $\mathbf{W}_i \in \mathbf{Q}_i$ 4, stuck-off fault rate $\mathbf{W}_i \in \mathbf{Q}_i$ 5, and stuck-on fault rate $\mathbf{W}_i \in \mathbf{Q}_i$ 6, the expected rate of mismatches becomes

$\mathbf{W}_i \in \mathbf{Q}_i$ 7

compared to $\mathbf{W}_i \in \mathbf{Q}_i$ 8 without pruning (Yuan et al., 2021). Since pruning only helps if stuck-off is the dominant defect, the paper combined pruning with a differential mapping scheme in which each weight $\mathbf{W}_i \in \mathbf{Q}_i$ 9 is represented as the difference between two always-biased cell values: if $128 \times 64$ 0, $128 \times 64$ 1 and $128 \times 64$ 2; if $128 \times 64$ 3, $128 \times 64$ 4 and $128 \times 64$ 5, so that $128 \times 64$ 6 (Yuan et al., 2021). For pruned weights, both mapped cells are set to $128 \times 64$ 7, thereby converting pruning-induced stuck-off masking into stuck-on masking (Yuan et al., 2021).

Non-ideality-aware pruning has also been integrated directly into training. PRUNIX simulates weight quantization, state-drift, aging, and stuck-at-faults, and introduces Group Sawtooth Regularization

$128 \times 64$ 8

with grouped application across filters or channels, together with an Adaptive Pruning Algorithm that mixes filter and unstructured pruning while adjusting rates according to layer sensitivity (Alshaarawy et al., 2022). A plausible implication is that crossbar pruning increasingly serves as a reliability-control mechanism in addition to a compression mechanism.

5. Architectural targets beyond crossbar count

Although many crossbar pruning papers focus on reducing the number of physical arrays, later work targets more specific architectural bottlenecks. One such bottleneck is data alignment. CRIMP argues that current IMP-aware pruning methods require data aligning across crossbars, introducing significant memory and computing overhead, and addresses this by combining kernel-group pruning and crossbar pruning to remove the hardware units needed for data aligning (Huai et al., 9 Jul 2026). Because the remaining number of kernels is forced to be a multiple of the crossbar width, outputs of one layer can become naturally aligned inputs to the next layer without Sparsity Tables or masking units (Huai et al., 9 Jul 2026).

Another bottleneck is ADC cost. In crossbar-based analog in-memory accelerators, ADCs consume a significant portion of energy and area of every crossbar processing unit. The D.U.B. pruning framework targets this directly by requiring that the least sparse column in each crossbar tile reach discrete power-of-two sparsity levels, which permits ADC bit-reduction. The target sparsity for reducing ADC precision by $128 \times 64$ 9 bits is given as

and the normalized ADC energy is expressed as

in terms of the number of tiles requiring each ADC precision (Ibrayev et al., 2024). During training, the variance of column-wise $\begin{aligned} & \min_{ \{ \mathbf{W}_i, \mathbf{b}_i \} } f\left( \{ \mathbf{W}_i \}_{i=1}^N, \{ \mathbf{b}_i \}_{i=1}^N \right) \ & \text{subject to} \qquad \mathbf{W}_i \in \mathbf{P}_i, \; \mathbf{W}_i \in \mathbf{Q}_i \quad \forall i=1,\dots,N, \end{aligned}$ 2 norms within a tile is regularized using the Hoyer-Square proxy

with gradient gating applied only to columns denser than the tile mean (Ibrayev et al., 2024). This is a distinct interpretation of crossbar pruning: the objective is not array removal, but lower ADC energy by controlling the densest column in each tile.

Pattern-based mapping targets yet another form of inefficiency. In RRAM CNN accelerators based on pattern pruning and an Operation Unit mechanism, sparse kernels are projected onto a small number of predefined patterns, reordered by pattern, compressed by removing predictable zeros, and packed into crossbars as pattern blocks. Because an Operation Unit activates only a subset of a crossbar at once, these pattern blocks are aligned with OU boundaries so that only valid computations occur in parallel (Yu et al., 2020). This work is not framed as crossbar pruning in exactly the same language, but it similarly treats the mapping granularity and peripheral scheduling constraints as first-class design parameters.

A further extension appears in sparse attention acceleration. CPSAA moves the sparsity pruning phase in-situ to crossbar arrays, generating a binary mask matrix through in-memory operations,

and stores the mask in ReCAM for subsequent scheduling of sparse attention computation (Li et al., 2022). This suggests that “crossbar pruning” can extend beyond weight pruning to on-chip generation and exploitation of activation- or attention-level sparsity when the pruning phase itself is integrated into crossbar-resident dataflow.

6. Empirical outcomes, trade-offs, and recurring limitations

Empirical results consistently show that crossbar-aware pruning can produce substantial hardware savings, but the meaning of “savings” varies by target metric. In the ADMM memristor framework that jointly applies structured pruning and quantization, the reported weight compression ratio is 29.81X for VGG-16 and 20.88X for ResNet-18, with 98.38% and 96.96% power reduction and 98.29% and 97.47% area reduction, respectively, at 0.5% and 0.76% accuracy loss compared to the original DNN models (Yuan et al., 2019). A related memristor framework with Network Purification and Unused Path Removal reports, for example, 44.67X compression on CIFAR10/VGG-16 and 52.07X on CIFAR10/ResNet-18 with near-original accuracy, while 8-bit quantization incurs nearly no accuracy loss after quantizing weights to 8-bit memristor weight representation (Ma et al., 2019).

Crossbar-aware neural network pruning reported crossbar overhead reductions of 44%–72% with little accuracy degradation across VGG8, VGG16, and ResNet18. On CIFAR-10 VGG8, compute crossbars were reduced from 1954 to 546 at 90% pruning, while accuracy changed from 94.29% to 90.18%; at 50% pruning, compute crossbars fell from 1954 to 1155 with accuracy moving from 94.29% to 93.84% (Liang et al., 2018). ReaLPrune reported that it can prune more than 90% of CNN weights, reduce required ReRAM crossbars by 77.2% on average, and accelerate CNN training by approximately 19.7X relative to unpruned networks, while pruned models can be trained from scratch without accuracy loss (Joardar et al., 2021).

Reliability-oriented approaches report different outcome measures. In ReRAM-based edge AI, pruning plus differential crossbar mapping produced only 0.2% accuracy loss at failure rate 0.001 on CIFAR10 with ResNet-18, compared with 1.2% loss for the traditional two-column mapping, and the method can tolerate almost an order of magnitude higher failure rate than the traditional two-column method without extra hardware cost (Yuan et al., 2021). PRUNIX reported an improvement of 13% test accuracy over L1 or Group Lasso when quantization and other non-ideal effects are accounted for, with overall sparsity of 85%, and stated that sparsity of 80–90% is achieved with robust tolerance to drift, aging, and faults (Alshaarawy et al., 2022).

ADC-focused pruning shows more modest but highly specific gains: on VGG11 with CIFAR-10 and tile size $\begin{aligned} & \min_{ \{ \mathbf{W}_i, \mathbf{b}_i \} } f\left( \{ \mathbf{W}_i \}_{i=1}^N, \{ \mathbf{b}_i \}_{i=1}^N \right) \ & \text{subject to} \qquad \mathbf{W}_i \in \mathbf{P}_i, \; \mathbf{W}_i \in \mathbf{Q}_i \quad \forall i=1,\dots,N, \end{aligned}$ 5, the D.U.B. method achieved 4.0X ADC energy savings with only 0.57% accuracy drop; with tile size $\begin{aligned} & \min_{ \{ \mathbf{W}_i, \mathbf{b}_i \} } f\left( \{ \mathbf{W}_i \}_{i=1}^N, \{ \mathbf{b}_i \}_{i=1}^N \right) \ & \text{subject to} \qquad \mathbf{W}_i \in \mathbf{P}_i, \; \mathbf{W}_i \in \mathbf{Q}_i \quad \forall i=1,\dots,N, \end{aligned}$ 6, it achieved up to 7.13X ADC energy reduction; on ResNet18 with ImageNet, it achieved 1.27X savings with 0.86% accuracy drop (Ibrayev et al., 2024). CRIMP, which targets crossbar-aligned compression, reported computing power reduction of $\begin{aligned} & \min_{ \{ \mathbf{W}_i, \mathbf{b}_i \} } f\left( \{ \mathbf{W}_i \}_{i=1}^N, \{ \mathbf{b}_i \}_{i=1}^N \right) \ & \text{subject to} \qquad \mathbf{W}_i \in \mathbf{P}_i, \; \mathbf{W}_i \in \mathbf{Q}_i \quad \forall i=1,\dots,N, \end{aligned}$ 7, computing area reduction of $\begin{aligned} & \min_{ \{ \mathbf{W}_i, \mathbf{b}_i \} } f\left( \{ \mathbf{W}_i \}_{i=1}^N, \{ \mathbf{b}_i \}_{i=1}^N \right) \ & \text{subject to} \qquad \mathbf{W}_i \in \mathbf{P}_i, \; \mathbf{W}_i \in \mathbf{Q}_i \quad \forall i=1,\dots,N, \end{aligned}$ 8, total power reduction of $\begin{aligned} & \min_{ \{ \mathbf{W}_i, \mathbf{b}_i \} } f\left( \{ \mathbf{W}_i \}_{i=1}^N, \{ \mathbf{b}_i \}_{i=1}^N \right) \ & \text{subject to} \qquad \mathbf{W}_i \in \mathbf{P}_i, \; \mathbf{W}_i \in \mathbf{Q}_i \quad \forall i=1,\dots,N, \end{aligned}$ 9, and total area reduction of $\mathbf{P}_i$ 0, while producing integer-only, pruned, and reliable VGG-16 and ResNet-56 models for CIFAR-10 with accuracy drops of only 2.19% and 1.26%, respectively, without hardware overhead (Huai et al., 9 Jul 2026).

A recurrent limitation is that software-level iso-accuracy does not guarantee hardware-level iso-accuracy. Structured pruning techniques that yield significant crossbar-compression-rate can undergo substantially greater degradation on non-ideal crossbars than unpruned models. On $\mathbf{P}_i$ 1 crossbars for CIFAR10/VGG11, the unpruned model dropped by approximately 21% from the software baseline, whereas C/F pruned, XCS-pruned, and XRS-pruned versions dropped by approximately 39%, 24%, and 30%, respectively (Bhattacharjee et al., 2022). This directly counters the misconception that crossbar-aware structured sparsity automatically preserves deployment accuracy once software fine-tuning is complete.

Another recurring limitation is that maximal sparsity is not always the best objective. In fault-tolerance studies, increasing pruning initially improves robustness to stuck-off defects and then degrades it when pruning becomes too aggressive; each DNN has an optimal pruning ratio, reported as 60% for ResNet-18 on CIFAR-10 in one example (Yuan et al., 2021). In ADC-oriented pruning, over-pruning columns beyond the least sparse column produces no additional ADC benefit but does remove useful parameters (Ibrayev et al., 2024). In non-ideality-aware studies, reducing sparsity from $\mathbf{P}_i$ 2 to $\mathbf{P}_i$ 3 can recover some lost accuracy at the expense of reduced compression (Bhattacharjee et al., 2022). These findings indicate that crossbar pruning is governed by hardware-specific optima rather than by monotonic compression goals.