N-slim: N-balanced structured channel pruning for onboard solar flare forecasting

1 Introduction

The deployment of machine learning models directly onboard satellites has become a growing research area in recent years. Low-power edge hardware accelerators and neural network compression techniques have made in-orbit inference technically feasible for several Earth-observation tasks, including onboard hyperspectral cloud detection (Giuffrida et al., 2021) and real-time scene classification on radiation-tolerant edge processors (Furano et al., 2020). These efforts are part of a transition from store-and-forward systems, where raw sensor data are transmitted to the ground for analysis, to systems that perform inference locally and downlink only results or alerts. This transition reduces bandwidth demand and also eliminates the round-trip latency between observation and actionable response.

Autonomous solar flare prediction is a particularly compelling use case for onboard inference. Solar flares release intense bursts of electromagnetic radiation and energetic particles. These emissions can disrupt satellite communications, degrade photovoltaic performance, and increase the radiation dose received by onboard electronics (Schrijver et al., 2015). Ground-based forecasting centres issue predictions with useful skill, but the time required to acquire observations, relay data to the ground, obtain forecasts, and uplink protective commands can exceed the available warning window for many autonomy scenarios. A classifier deployed directly on the satellite could detect precursory magnetic-field configurations in solar active-region magnetograms and trigger protective measures autonomously, closing this latency gap. Motivated by this, deep learning methods based on convolutional neural networks (CNNs) have been applied to magnetogram data, achieving encouraging results (Huang et al., 2018; Park et al., 2018). However, three challenges impede their direct deployment on satellites.

First, satellite onboard computers, particularly those on small-satellite platforms, operate under strict constraints on computational throughput, memory capacity, and power consumption. State-of-the-art CNN-based solar flare classifiers contain millions of parameters and require floating-point operation counts that far exceed the capacity of representative onboard processors. Therefore, model compression is a prerequisite for practical deployment.

Second, the weight values stored in satellite onboard SRAM are susceptible to radiation-induced bit upsets from cosmic rays and solar energetic particles (Baumann, 2005; Furano et al., 2020). As SRAM scales to smaller feature sizes, a single particle strike increasingly causes multiple-bit upsets (MBUs), i.e., upsets involving several physically neighbouring memory cells. Published SRAM and SRAM-based FPGA studies report multi-cell upset multiplicities that can extend to approximately 2 − 8 cells under device- and irradiation-dependent conditions (Ibe et al., 2010; Radaelli et al., 2005; Tarrillo et al., 2015). Depending on the memory layout, an MBU may corrupt several bits within one floating-point value, distorting its magnitude by orders of magnitude, or it may span multiple distinct weight parameters. In either case, the corrupted feature maps propagate through all downstream layers without structural containment, and no retraining is feasible between orbital passes. The model should therefore tolerate such multi-bit faults by design.

Third, a satellite in low Earth orbit (LEO) alternates between sunlit and eclipse phases at approximately 90-min intervals. This alternation produces systematic variation in the power available for inference (Furano et al., 2020). Additional transient power reductions arise from competing high-power operations such as downlink transmission, attitude-control manoeuvres, and thermal regulation. A single fixed model cannot meet accuracy requirements when power is abundant, and also meet latency requirements when power is scarce. A portfolio of models at different channel pruning rates is therefore preferable to a single static deployment.

We propose N-Slim, a network slimming framework that tackles compression, MBU tolerance, and power adaptivity together. The framework uses focal-loss training, knowledge distillation, and stochastic channel rejuvenation to maintain recall under the severe class imbalance typical of solar flare datasets (∼ 4 % positive rate). Without these measures, standard BN-magnitude pruning tends to remove channels that are selective for the minority class. The central algorithmic idea is N-balanced structured channel pruning. Each layer’s channels are partitioned into groups of width N, and pruning distributes the retained channels roughly evenly across groups instead of allowing them to cluster. Under a sparse storage layout, this spacing ensures that a single MBU can corrupt at most one retained channel per layer. Running the pruning procedure at a geometric sequence of group sizes yields subnets at different compression levels, from which an onboard scheduler can select at runtime.

The main contributions of this work are as follows.

• We propose N-Slim, a unified network slimming framework that compresses CNN-based solar flare classifiers for satellite-onboard deployment while maintaining high-accuracy solar flare forecasting under severe class imbalance via focal-loss training, knowledge distillation fine-tuning, and stochastic channel rejuvenation.
• We introduce N-balanced structured channel pruning, which partitions each layer’s output channels into non-overlapping groups of width N and distributes retained channels approximately uniformly across groups. It increases the minimum inter-channel spacing in weight memory and limiting the number of retained channels that a single MBU event can simultaneously corrupt.
• We apply N-balanced pruning across a geometric sequence of group sizes, generating a portfolio of subnets at different channel pruning rates and inference costs from a single training pipeline.

This work represents an initial exploration of radiation-aware structured pruning for onboard solar flare forecasting. The MBU robustness evaluation is conducted under a simplified software-level fault model, and the observed advantage of N-balanced pruning is architecture-dependent. Substantial gains are demonstrated on ResNet and DenseNet, whose skip and dense connections serve as error-containment pathways that amplify the benefit of balanced channel spacing, whereas on VGG, which lacks such bypass structures, N-balanced pruning yields robustness comparable to standard pruning. The multi-rate subnet portfolio generated by the framework provides a structural prerequisite that could facilitate power-adaptive deployment. The design and validation of a runtime scheduling policy, including power-to-subnet mapping and multi-model memory management, are beyond the scope of this study and are left for future work.

2 Related work

2.1 Deep learning for solar flare forecasting

Deep learning methods for solar flare prediction have advanced rapidly over the past decade. Huang et al. (2018) applied CNN-based models to SDO/HMI magnetograms for binary-flare classification, achieving competitive performance compared with handcrafted-feature approaches. Nishizuka et al. (2018) applied deep neural networks to multivariate solar observation features for flare forecasting. Zheng et al. (2019) explored full-disk magnetograms with deep architectures. Guesmi et al. (2024) recently proposed EoFNets, which use a Temporal Convolutional Networks (TCNs) (Lea et al., 2016) for solar flare prediction. More recent efforts have adopted LSTM (Sun et al., 2022) and Transformer-based architectures (Abduallah et al., 2023). However, none of the methods mentioned above has considered onboard computational constraints or radiation-induced weight faults.

2.2 Structured channel pruning

Network pruning reduces model complexity by removing redundant parameters or structures. Unstructured pruning (Han et al., 2016) zeros individual weights but requires sparse-matrix hardware for acceleration. Structured pruning (Li H. et al., 2017; He et al., 2017; Liu et al., 2017) removes entire channels or filters, yielding models executable on standard hardware. Liu et al. (2017) introduced network slimming by imposing ℓ 1 regularisation on BN scaling factors, which serves as the foundation of our sparsity learning phase. Recent works have explored automated pruning ratio search (He et al., 2018) and lottery ticket hypothesis (Frankle and Carbin, 2019). In the solar physics domain, Feng et al. (2023) applied pruning and knowledge distillation to compress solar flare forecasting models while preserving prediction skill, demonstrating the feasibility of lightweight deployment for space-weather applications. N-Slim differs from prior structured pruning methods in that its group-balanced channel selection constraint is motivated by radiation fault tolerance, not by compression efficiency alone.

2.3 Radiation tolerance for neural networks

The vulnerability of neural network weights to radiation-induced bit upsets has been studied in the context of safety-critical deployment (Reagen et al., 2018; Mittal, 2020). Reagen et al. (2018) proposed Ares, a framework for evaluating the resilience of DNNs to soft errors through fault injection. Algorithm-based fault tolerance (ABFT) methods insert redundant computations to detect and correct errors at runtime (Zhao et al., 2020). Selective hardening protects only the most critical parameters (Santos et al., 2019). N-Slim takes a different approach and addresses fault tolerance at the model architecture level through the spatial distribution of retained channels. It requires neither runtime detection nor redundant computation.

2.4 Onboard AI for satellite applications

The deployment of machine learning on satellite platforms has been demonstrated for cloud detection (Giuffrida et al., 2021), ship detection, and land-use classification. Furano et al. (2020) provided a comprehensive survey of AI processors for space applications, highlighting the constraints of power, radiation, and computational throughput. We are not aware of previous work that jointly optimises model compression, MBU robustness, and power-adaptive inference for onboard solar flare forecasting.

3 Data

3.1 Data source

The input to the forecasting model is the line-of-sight photospheric magnetogram of a solar active region (AR). The model output provides a binary prediction indicating the occurrence of at least one GOES M-class or larger flare within a 48-h forecast window after the observation time. Magnetograms are obtained from the Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) (Pesnell et al., 2012; Scherrer et al., 2012). Routine AR coverage began on 2010 April 30 and is publicly accessible through the Joint Science Operations Center (JSOC) database (Joint Science Operations Center, 2026) at a native pixel scale of 0.5 per pixel and in this study we sample the AR sequences every 96 min. Flare event records are drawn from the National Oceanic and Atmospheric Administration (NOAA) National Centers for Environmental Information (NCEI) GOES X-ray flare lists (NOAA National Centers for Environmental Information, 2026). A magnetogram is assigned a positive (flaring) label if at least one GOES M-class or stronger flare is recorded within the 48-h window following the observation timestamp. Otherwise, it receives a negative (non-flaring) label. The full dataset spans 2010 May 4 to 2019 January 26 and contains 2,988 positive samples and 70,822 negative samples, for a total of 73,810 observations.

3.2 Data partitioning

Observations from 2011 to 2015 are held out for testing, while observations from all other years are used for training. The test set contains 20,829 samples, including 905 positive samples and 19,924 negative samples. The training set contains 52,981 samples, including 2,083 positive samples and 50,898 negative samples. These two test years were selected because 2011 falls in the ascending phase of Solar Cycle 24, when flare activity was increasing rapidly, whereas 2015 falls in the declining phase after the cycle maximum and represents a different activity regime. Evaluation across these two test years tests the model under varying solar conditions. Separating the training set and the test set by year reduces data leakage due to the strong temporal autocorrelation of AR magnetogram sequences, since the same active region can appear in hundreds of consecutive observations with a 96-min cadence. Under this splitting strategy, an active region can appear in both the training and test sets only if its disk passage spans a year boundary between a test year and a training year. We checked all four such year boundaries using HARP identifiers. Only nine HARP identifiers appear in both the training set and the test set, and all samples associated with these identifiers are labeled as negative. No HARP identifier associated with any positive sample crosses any of these year boundaries. Therefore, none of the active regions that produce flares in the test set appears in the training set.

The positive class constitutes approximately 4.0% of the full dataset, and this severe imbalance is present in both partitions. For structured channel pruning (He et al., 2017; Li H. et al., 2017; Liu et al., 2017), class imbalance introduces an additional challenge. Pruning decisions based on batch normalisation (BN) (Ioffe and Szegedy, 2015) scaling magnitudes are driven primarily by the majority class, and channels selective for rare positive patterns may be disproportionately removed even though they are critical for recall. Therefore, the N-Slim training objective incorporates explicit measures to handle this imbalance.

3.3 Data preprocessing

Each raw AR magnetogram is resized to 128 × 128 pixels using bilinear interpolation (Li et al., 2020). This resolution retains the large-scale magnetic morphology relevant to flare forecasting while substantially reducing the computational and memory costs of both training and inference. After resizing, pixel-level normalisation is applied:where x is the raw pixel intensity, and μ train and σ train are the channel mean and standard deviation computed from the training setand kept fixed during inference to prevent information leakage. Because magnetogram pixels encode signed line-of-sight magnetic flux density and can span a wide dynamic range, normalisation is important for stabilising gradient flow across layers (LeCun et al., 2012). During training, random horizontal and vertical flips are applied independently. These augmentations are standard regularisation techniques for training convolutional networks on limited-size datasets (Shorten and Khoshgoftaar, 2019; Li et al., 2020). They increase effective sample diversity without requiring additional observations and help reduce overfitting to the specific orientation of the training samples. No augmentation is applied during evaluation.

x ̂ = x − μ train σ train ,

4 Methods

4.1 Framework overview

N-Slim proceeds in three phases, each initialized from the weights of the previous one. The overall training process is illustrated in Figure 1. Baseline pretraining (Section 4.2) trains the CNN from scratch with focal loss. Sparsity learning (Section 4.3) adds ℓ 1 regularisation on BN scaling factors to separate informative channels from dispensable ones (Liu et al., 2017). Iterative slimming (Section 4.4) then prunes channels in repeated cycles, each followed by knowledge-distillation fine-tuning, to produce a portfolio of compressed subnets.

4.2 Baseline pretraining

Baseline pretraining trains each target CNN from scratch using focal loss (Lin et al., 2017) to produce a well-converged full-precision model. Focal loss down-weights easy, correctly classified examples by a modulating factor ( 1 − p t ) ζ, directing gradient updates toward hard and minority-class samples:where p t is the predicted probability for the ground-truth class y and ζ ≥ 0 is the focusing exponent. The optional class-balancing weight α t from the original formulation (Lin et al., 2017) is set to 1.0 for both classes (i.e., not used), as preliminary experiments indicated that the modulating factor ( 1 − p t ) ζ alone was sufficient to address the class imbalance at the observed 4% positive rate.

L FL z , y = − 1 − p t ζ ⁡ log p t ,

Three CNN families with distinct structural characteristics are evaluated. VGG (Simonyan and Zisserman, 2015) stacks nineteen weight layers of Conv-BN-ReLU blocks with max-pooling after selected groups and a single linear output layer. Its uniform structure provides a straightforward baseline for channel pruning without residual connections. ResNet (He et al., 2016) employs residual connections, directly adding the input of each module to its output, thus pruning should respect the channel-dimension consistency imposed by shortcut projections. DenseNet (Huang et al., 2017) connects each layer to all preceding layers within the same dense block by concatenating feature maps, with transition layers reducing channel counts between dense stages.

In these three architectures, each BN layer is followed by a lightweight channel-selection gate. A BN layer normalises its input to zero mean and unit variance and then applies a learned affine transformation parameterised by a scaling factor γ i and a shift β i for each channel i. The magnitude | γ i | is used throughout N-Slim as the channel importance score. During baseline pretraining and sparsity learning, the gate behaves as an identity mapping. During iterative slimming, it is configured to pass only the retained channels to the downstream convolution, enabling physically compact weight reconstruction.

4.3 Sparsity learning

Before pruning, the BN scaling magnitudes | γ i | must separate informative channels from expendable ones clearly enough for score-based selection to be reliable. Sparsity learning achieves this by adding an ℓ 1 penalty on the BN scaling factors to the focal losswhere λ s is the regularisation coefficient. The subgradient of | γ i | with respect to γ i is sgn ( γ i ) and is applied as an additive correction to the gradient at each parameter update. This regularisation continuously drives small-magnitude scaling factors toward zero, while the task-loss gradients offset this shrinkage for discriminative channels, preserving or increasing their BN-scale magnitudes. The result is a polarised | γ i | distribution that makes importance-score-based channel selection in the iterative slimming phase reliable. Sparsity learning is initialised from the baseline pretraining weights and uses the same optimiser and learning rate schedule.

L sparse = L FL + λ s ∑ i | γ i | , (1)

4.4 Iterative slimming

The iterative slimming phase applies progressive structured channel pruning to the sparse model trained in the previous phase. Starting from the sparse model, the target cumulative channel pruning rate is increased by a fixed increment at each iteration until the per-N maximum is reached. After each pruning step, the resulting subnet is fine-tuned using focal loss, knowledge distillation, and stochastic channel rejuvenation. When N-balanced pruning is enabled, the channel selection step is modified to distribute retained channels approximately uniformly across groups of N consecutive channels, reducing the sensitivity of predictions to MBU-induced parameter perturbations. It is worth noting that every pruning operation is applied independently to each convolutional layer. No selection, grouping, or swap step mixes channels across layers, and each quantity defined below, including M, K, N, and S, are defined separately for each layer. Subnets at different channel pruning rates are recorded for each group size in the geometric sequence, forming the power-adaptive subnet portfolio.

4.4.1 Standard structured channel pruning

Pruning is performed progressively rather than by removing a fixed fraction of channels in a single step (Han et al., 2016; Zhu and Gupta, 2017). Starting from an initial pruning rate P 0, the target cumulative channel pruning rate is increased by a fixed increment Δ P at each iteration until the per-N maximum rate P max is reached. Specifically, iteration k targets a cumulative pruning rate P k = P 0 + k Δ P. At each iteration, pruning is applied independently to each convolutional layer. For a layer with C output channels, the per-layer retention budget M is the number of channels kept after pruning. It is computed aswhere P k is the cumulative pruning rate at iteration k, K = ⌈ C / N ⌉ is the number of groups of N consecutive channels, and C min is the minimum number of channels retained per layer. The floor K ensures that the retention budget is sufficient to allow at least one channel per group. This coverage is enforced only by the N-balanced rebalancing step. Standard pruning uses the same budget but does not impose group coverage. The M channels with the highest BN scaling magnitudes | γ i | within that layer are selected into the retained set S. All remaining channels are marked for removal. Because the pruning threshold is determined separately for each layer, layers whose BN scaling distributions are concentrated at higher magnitudes naturally retain more channels than layers with lower-magnitude distributions, avoiding the risk that a single global threshold over-prunes some layers while leaving others nearly untouched. This progressive schedule reduces the capacity gap between consecutive subnets, making post-pruning fine-tuning more stable and preserving the effectiveness of knowledge distillation.

M = max r o u n d C ⋅ 1 − P k , K , C min , (2)

After channel selection, the compact network is explicitly reconstructed. For a convolutional layer, a new tensor is formed by selecting the retained indices along the output- and input-channel dimensions. The associated BN parameters are indexed by the retained output channels, and the affected linear-layer weights are adjusted to match the retained feature dimensions. The reconstructed network contains only the retained weight values and executes every forward pass with the reduced channel counts, reducing both parameter count and arithmetic operations during fine-tuning and inference.

After each pruning step, the pruned subnet is fine-tuned using knowledge distillation (Hinton et al., 2015). The fine-tuned subnet from the preceding pruning iteration serving as the teacher, and the combined loss iswhere z s and z t are the pre-softmax logits of the student (current pruned subnet) and teacher (preceding pruning iteration), s o f t m a x ( ⋅ ) denotes the softmax function, D KL is the Kullback–Leibler divergence, T is the distillation temperature, and λ p balances the distillation and task-loss terms. The factor T 2 compensates for the gradient-scale reduction introduced by temperature scaling. Fine-tuning uses stochastic gradient descent (SGD) with a linear learning-rate warm-up over the first 20% of epochs and cosine annealing (Loshchilov and Hutter, 2017) over the remainder. After each iteration, the fine-tuned student becomes the teacher for the next pruning step. To mitigate the degradation in which the BN scaling factors of retained channels drift toward zero during fine-tuning, a stochastic channel rejuvenation step is applied at regular training intervals. If a retained channel’s scaling magnitude falls below a small threshold, its BN parameters are re-sampled from the empirical distribution of the retained channels that remain above the threshold. This reactivates the channel without altering the other parameters.

L KD = λ p T 2 D KL s o f t m a x z t T ∥ s o f t m a x z s T + 1 − λ p L FL ,

4.4.2 N-balanced structured channel pruning

The goal of the N-balanced method is to target a retention budget M comparable to that of Standard pruning, while distributing the retained channels among groups that each contain N consecutive channels. N-balanced pruning starts with selection based on BN scores and then moves channel parameters with high scores into groups with insufficient representation before reconstruction and fine tuning. Thus, the paired N-Slim and Standard pruning results are matched under the same N / P configuration.

This design assumes the MBU-protected sparse storage layout described in Section 4.4.1. In that layout, channels with adjacent indices are stored in adjacent memory regions. Channel-index distance is therefore used as a proxy for physical distance in SRAM. Pruned channels are stored as inactive or zeroed positions. These positions act as buffers between retained channels.

We use the following notation. Let S be the retained set and G k the k-th group. The number of retained channels in group k is n k = | S ∩ G k |. The balanced target for that group is Q k. A group with n k > Q k is a donor group. A group with n k < Q k is a receiver group.

The method operates independently per layer and consists of two stages, namely, standard top-M selection followed by swap-based rebalancing across groups. The full procedure is summarised in Algorithm 1.

Algorithm 1 N-balanced Channel Selection (applied independently per layer).

4.4.2.1 Stage 1: standard selection and target computation

For a layer with C output channels, the M channels with the highest BN scaling magnitudes | γ i | are first selected into S, exactly as in Standard pruning, where M is given by Equation 2. The channels are then partitioned into K = ⌈ C / N ⌉ consecutive non-overlapping groups of width N:A balanced per-group target is then computed. Each group retains either ⌊ M / K ⌋ or ⌈ M / K ⌉ channels, and the first ( M mod K ) groups receive the higher count. The targets sum exactly to M.

G k = k − 1 N + 1 , … , min k N , C , k = 1 , … , K . (3)

4.4.2.2 Stage 2: swap-based rebalancing

The donor groups form the set V = { k : n k > Q k }. The receiver groups form the set U = { k : n k < Q k }. The method iteratively rebalances the channel distribution through pairwise position swaps between donor and receiver groups.

For each receiver group G u, the unselected position with the highest score in that group is identified as the incoming position c in. Among all donor groups, the group with the nearest index is chosen as G v. The excess retained position with the lowest score in G v is identified as the outgoing position c out. The exchange is implemented as a consistent channel permutation. All tensors that use this channel index are exchanged together. This includes the output filter, the BN affine parameters, and the corresponding input slices along the channel dimension in downstream layers. After the exchange, the trained feature originally located at c out is relocated to c in. The retained set is updated as S ← ( S \ { c out } ) ∪ { c in }. The total retained count remains | S | = M.

Under the sparse deployment layout of Section 4.4.1, zeroed-out channels act as physical buffers in SRAM. The minimum separation between any two retained channels rises from one channel width (standard pruning) to roughly N / ⌈ M / K ⌉ channel widths. This increased spacing is the property exploited for MBU resilience (Section 4.5). If the retained count falls below C min, the highest-scoring unselected channels are appended. The output binary mask is:

m i = 1 i f i ∈ S , 0 o t h e r w i s e , i = 1 , … , C .

Physical swapping of channel parameters is essential, rather than mere mask reassignment. Simply deselecting a retained channel in a donor group and selecting an unretained channel in a receiver would place a poorly trained channel in the receiver position. By exchanging all learnable parameters between the two positions, the selected feature with a high score in the donor group is moved to the receiver group. After each exchange, the retained index set S is updated so that the final binary mask identifies the physical positions of the moved channels with high scores. This operation preserves the moved feature within the local rebalancing step. It does not imply that the final N Slim subnet is a functional copy of an independently reconstructed and fine-tuned Standard pruning subnet.

For onboard deployment, weight tensors are stored in their original (unpruned) layout with pruned channels zeroed. Only channels with m i = 1 participate in forward computation. An MBU event striking a zeroed position produces no change in inference output, and the spacing between retained channels makes it unlikely that a single event corrupts more than one. The storage cost equals that of the unpruned model, which is a trade-off justified by the MBU protection. Computational savings depend on the number of retained channels and are unaffected by the storage layout.

4.4.3 Power-adaptive subnet portfolio

Starting from a maximum group size N max, a geometric group-size sequence is generated by the recurrence N j + 1 = ⌊ ( N j + 1 ) / 2 ⌋, terminating when N j < 4:where J is the largest index for which N j ≥ 4. In the experiments reported here, N max = 16, yielding the sequence { 4 , 8 , 16 }, which corresponds to approximate minimum-budget channel pruning rates of { 75 % , 87.5 % , 93.75 % } per layer. The lower bound N j ≥ 4 is imposed so that the group-coverage floor K = ⌈ C / N j ⌉ remains sufficiently large relative to the layer widths of VGG, ResNet, and DenseNet, ensuring that the minimum retained channel count per layer is numerically stable throughout pruning. At each pruning iteration, the N-balanced structured channel pruning method is applied independently for each N j. Because the group-coverage floor K decreases as N j increases, a larger group size yields a lower per-layer retention budget and hence a higher pruning ratio. Different values of N j also produce different retained channel sets. Each N j imposes a distinct partition on the channel index space, and the group-coverage requirement determines a different S j for each j.

N j j = 0 J = N max , ⌊ N max + 1 / 2 ⌋ , … , N j ≥ 4 .

The inference cost of a convolutional network is largely determined by the number of retained channels across layers (He et al., 2017). Since N-Slim produces subnets at different channel pruning rates from a single training pipeline, each subnet corresponds to a distinct inference energy level. This property matches the power constraints of satellites in low Earth orbit (LEO) well. Available power varies throughout each orbit due to alternation between sunlit and eclipse phases, competing high-power operations, and transient load changes triggered by solar energetic particle events (Furano et al., 2020). The resulting subnet portfolio provides the model set needed for power-adaptive deployment. The onboard software could, in principle, select a higher-accuracy subnet when power is abundant and fall back to a lighter subnet when power is constrained. The design of the specific runtime selection policy, including switching latency, multi-model memory management, and the mapping from power budget to subnet, depends on the target satellite platform and is beyond the scope of this work.

4.5 Multiple-bit upset fault model

4.5.1 Physical mechanism and impact on model inference

A multiple-bit upset (MBU) occurs when a single ionising particle deposits sufficient charge in an SRAM array to flip two or more physically adjacent memory cells simultaneously (Baumann, 2005). As SRAM feature sizes shrink below 28 nm, the charge-diffusion radius of a particle strike encompasses an increasing number of bit cells (Baumann, 2005; Ibe et al., 2010), and the ratio of MBU events to classical single-bit upsets rises from a few percent at 130 nm to a substantial fraction at advanced nodes below 22 nm (Ibe et al., 2010; Radaelli et al., 2005). For CNN weights stored on satellite onboard processors, this trend means that a single particle strike can corrupt multiple bits of one or more weight values during any orbital pass through the radiation environment. MBU is therefore a qualitatively more severe threat to model integrity than classical single-bit upsets.

The specific impact of an MBU event on model inference depends on the SRAM memory layout. In a non-interleaved layout, where the 32 bits of each IEEE 754 float32 value occupy contiguous memory cells, an MBU event flips several bits within the same weight value. If the affected bits include exponent or sign fields, the stored weight can change by many orders of magnitude (Mittal, 2020), producing a corrupted output feature map at all spatial positions computed using that kernel element. In an interleaved layout, where bit j of word i is stored adjacent to bit j of word i + 1, an MBU event instead flips the same bit position across several consecutive weight values, corrupting multiple parameters with single-bit damage each. In both layouts, the corrupted feature maps propagate through BN and subsequent convolutional layers via channel mixing (Li G. et al., 2017; Reagen et al., 2018). The simulation in this work adopts the non-interleaved layout as the worst-case baseline, as detailed below.

4.5.2 Simulation design

To evaluate model robustness under radiation-induced memory errors, we adopt a Monte Carlo fault-injection framework. For each trial, a set of MBU events is injected into a clean deep copy of the model weights, and inference is then performed over the full test set. This process is repeated across multiple independent trials to obtain statistically meaningful degradation distributions. All learnable weight tensors are identified as fault targets, including convolutional kernel weights and BN scaling ( γ ) and shift ( β ) parameters. BN running statistics and structural pruning masks are excluded because they are either non-learnable or serve as architectural indicators rather than trainable parameters.

Given a fault-event ratio r, the total number of MBU events is computed aswhere N total denotes the sum of element counts across all target tensors. These events are distributed across tensors in proportion to their respective element counts so that larger tensors receive a commensurate share of faults. All experiments adopt the non-interleaved memory layout, in which consecutive bits of the same IEEE 754 single-precision (float32) value are stored in adjacent SRAM cells. Under this assumption, an MBU event affects multiple bits within the same floating-point word.

n events = max 1 , r o u n d r ⋅ N total ,

For each event, a target weight element is selected uniformly at random within the assigned tensor. In the main experiments, we use a maximum cluster window size of b cluster = 8 and a decay parameter of p decay = 0.65. A starting bit position b 0 is drawn uniformly from { 0,1 , … , 32 − b cluster }, so that the affected window remains within the IEEE 754 word, which contains 32 bits. Starting from b 0, the first bit is always flipped, while each subsequent bit at offset k, for k = 1 , … , b cluster − 1, is flipped independently with probability p decay k. The resulting flip mask is applied via bitwise XOR to the IEEE 754 binary representation of the target element. After flipping, any resulting NaN or infinity value is replaced with zero to prevent catastrophic error propagation. The perturbed value is further clamped to ± 21 σ l, where σ l is the standard deviation of the original clean weights in tensor l.

The starting bit position b 0 is sampled uniformly from the valid starting positions because the mapping from logical bit positions to physical SRAM cells is hardware-specific and is usually not available for radiation-tolerant processors. This assumption treats all valid cluster windows equally at the sampling stage. To estimate the possible effect of a layout bias at the bit level, we count the sign bit and the eight exponent bits as positions with large numerical impact. As a simple reference, if individual bit positions were equally likely to be struck, these positions would occupy 9 / 32, or about 28%, of the float32 word. If these positions are struck at a relative rate w compared with mantissa bits, the fraction becomes 9 w / ( 9 w + 23 ). This gives about 22% at w = 0.75 and about 44% at w = 2. This estimate only bounds the possible scale of the bias. A map from logical bit positions to physical SRAM cells for a specific device is still needed for calibrated fault injection.

Several simplifications remain. The distribution over bit positions is not calibrated using proton or heavy-ion irradiation data. The clamping threshold of 21 σ l is heuristic. The event ratios r ∈ { 0.015 , 0.03 , 0.05 } are dimensionless and are not mapped to a specific orbit, shielding geometry, or SRAM technology node. Spatially and temporally correlated fault bursts, such as those during South Atlantic Anomaly transits, are also not included. The present fault model is therefore used to compare structural MBU robustness between pruning strategies, not to predict the absolute upset rate of a flight system. A sensitivity analysis over p decay ∈ { 0.5 , 0.65 , 0.8 } and b cluster ∈ { 4,8,16 } is reported in Section 5.3.

5 Experiments

5.1 Experimental setup

5.1.1 Implementation details

All experiments are implemented in PyTorch and executed on a single NVIDIA GeForce RTX 3090 GPU. The three-phase pipeline is applied to each of the three CNN families (VGG, ResNet, DenseNet) independently. During baseline pretraining and sparsity learning, both phases run for 52 epochs using SGD with momentum 0.9, weight decay 1 0 − 4, mini-batch size 512, and an initial learning rate of 0.05 decayed by a factor of 0.1 every 30 epochs. Focal loss is used throughout both phases with focusing exponent ζ = 2.0. The ℓ 1 regularisation coefficient for BN scaling factors during sparsity learning is set to λ s = 1 0 − 4.

During iterative slimming, eight fine-tuning epochs are applied per pruning iteration, with a linear learning-rate warm-up over the first 20% of epochs followed by cosine annealing (Loshchilov and Hutter, 2017). Knowledge distillation uses a temperature of T = 3.0 and a distillation weight of λ p = 0.5. The task-loss term uses focal loss with ζ = 2.0. Stochastic channel rejuvenation is applied every 200 training iterations. The target overall pruning ratio is P target = 0.95, with a per-iteration channel reduction of approximately 15% and a minimum of C min = 2 retained channels per layer. The geometric group-size sequence { 16,8,4 } generates three N-balanced/standard subnet pairs per pruning iteration. Data augmentation (random horizontal and vertical flips) is applied on-the-fly during training as described in Section 3.

For bit-flip injection experiments, the MBU event ratio r is swept over { 0.015 , 0.03 , 0.05 }, representing increasing levels of radiation-induced multi-bit corruption. For each combination of subnet and event ratio, 20 independent Monte Carlo trials are generated. In each trial, a deep copy of the subnet weights is perturbed by injecting MBU events following exactly the fault model described in Section 4.5.2.

5.1.2 Evaluation metrics

Given the severe class imbalance (≈ 4 % positive rate), accuracy alone is an inadequate discriminator. Let TP, TN, FP, and FN denote the counts of true positives, true negatives, false positives, and false negatives on the test set, respectively. From these four quantities, all primary metrics are derived. The True Positive Rate (recall) and False Positive Rate are defined as:The Area Under the Receiver Operating Characteristic curve (AUC) integrates TPR against FPR as the decision threshold is swept across its full range:and characterises the full sensitivity–specificity tradeoff independently of any fixed threshold. The Heidke Skill Score (HSS) measures the fractional improvement of the forecast over random chance:The True Skill Statistic (TSS) measures net discriminative ability relative to a climatological forecast and is the standard skill score for operational solar flare prediction evaluation (Bloomfield et al., 2012; Bobra and Couvidat, 2015):TSS equals + 1 for a perfect classifier, 0 for a climatological forecast, and − 1 for a perfectly wrong classifier. Precision and the F1 score are defined as:Hardware efficiency is characterised by four quantities. FLOPs Φ are computed for a single 128 × 128 input using thop (https://github.com/ultralytics/thop). Total parameter count | θ | is the sum of all trainable weight elements. Mean inference latency t ̄ (ms) is measured on the evaluation GPU with CUDA synchronisation over the full test set. Energy per inference is reported as a FLOPs-based compute-energy proxy, not as total device energy. Energy per inference is estimated using a conservative round number proxy, e 0 = 10 p J / F L O P, motivated by the order of magnitude of arithmetic operation energies reported for 45 nm CMOS technology by Horowitz (2014):where E is reported in micro-joules (μJ). Under this proxy, we model only the multiplication and accumulation operations. It does not include SRAM access, data movement, or control logic. These terms can dominate total inference energy on edge hardware, especially for memory-intensive architectures such as DenseNet (Sze et al., 2017). The reported E values are therefore lower bounds on total inference energy and should be used only for relative comparison of arithmetic cost. They should not be interpreted as power estimates at the mission level.

T P R ( R e c a l l ) = T P T P + F N , F P R = F P F P + T N .

A U C = ∫ 0 1 T P R F P R − 1 t d t ,

H S S = 2 T P ⋅ T N − F P ⋅ F N T P + F N F N + T N + T P + F P F P + T N .

T S S = T P R − F P R = T P T P + F N − F P F P + T N .

F 1 = 2 ⋅ P r e c i s i o n ⋅ T P R P r e c i s i o n + T P R = 2 T P 2 T P + F P + F N .

E = Φ ⋅ e 0 ,

5.2 Network slimming effectiveness

Table 1 summarises the flare forecasting metrics for the original networks, sparse networks, and N-Slim subnets across VGG, ResNet, and DenseNet. For each architecture, the original model is the baseline pretrained with focal loss, the sparse model is the result of sparsity learning with ℓ 1 regularisation on BN scaling factors, and the N-Slim subnets are produced by iterative slimming at different group sizes N and nominal channel pruning rates P.

TABLE 1. Slimming effectiveness across classification and hardware metrics for the Original, Sparse, and N-Slim subnets in all three architectures.

N denotes the group size and P the nominal per-layer channel pruning rate applied during iterative slimming. For each N, the subnets at different P values correspond to successive iterations of the iterative slimming loop. The actual per-layer pruning rate may be lower than P in layers where the safety floor C min = 2 is binding. Energy is estimated at 10 p J / F L O P (45 nm CMOS). Size is the full-precision storage footprint in megabytes, computed as the parameter count times 4 bytes. For the Original and Sparse rows, Size equals the unpruned footprint. For each N-Slim subnet, Size equals the compact reconstructed footprint after channel removal. Under the MBU-protected sparse storage layout, the resident onboard footprint of every subnet equals the unpruned value reported in the Original and Sparse rows. Bold values indicate the best-performing result for each evaluation metric among the subnets of the same network.

Across all three architectures, N-Slim subnets achieve substantially higher F1 and HSS than both the original and sparse baselines, despite operating at a fraction of the computational cost. For VGG, the original model attains an F1 of 0.353 and an HSS of 0.313. The best N-Slim subnet (N = 16, P = 80 %) reaches an F1 of 0.437 and an HSS of 0.409, representing relative improvements of 24% and 31%, respectively, while reducing computational cost from 0.399 GFLOPs to 0.016 GFLOPs. For ResNet, the original model achieves an F1 of 0.362 and an HSS of 0.345, whereas the N-Slim subnet at N = 8, P = 88 % achieves an F1 of 0.538 and an HSS of 0.516 with only 0.002 GFLOPs, a 99% reduction in FLOPs. For DenseNet, the improvement is most pronounced: the N-Slim subnet at N = 16, P = 77 % achieves an F1 of 0.598 and an HSS of 0.581, more than doubling the original model’s F1 of 0.286 and HSS of 0.269, while reducing cost from 0.198 GFLOPs to 0.019 GFLOPs.

AUC, which characterises the overall discriminative ability independently of the decision threshold, is largely preserved or improved across all N-Slim subnets. For VGG, AUC ranges from 0.891 to 0.912 across all configurations, compared to 0.896 for the original. The most aggressively pruned subnet (N = 16, P = 94 %, retaining only 0.002 GFLOPs) in fact achieves the highest AUC of 0.912 among all VGG variants. For ResNet, all eight N-Slim subnets maintain an AUC above 0.889, with the best (N = 8, P = 88 %) reaching 0.928, matching the original 0.929. For DenseNet, all eight subnets exceed the original AUC of 0.900, with N = 16, P = 77 % achieving the highest value of 0.934. TSS follows a similar pattern. The VGG N-Slim subnet at N = 16, P = 94 % achieves a TSS of 0.627, exceeding both the original (0.479) and sparse (0.615). The ResNet subnet at N = 16, P = 56 % reaches a TSS of 0.692, the highest across all ResNet variants. The DenseNet subnet at N = 4, P = 71 % attains a TSS of 0.660, well above its original (0.189) and sparse (0.636) counterparts.

5.2.1 Effect of pruning on forecasting performance

That pruned subnets outperform unpruned ones on F1 and HSS may seem surprising, but the pattern can be examined by examining how the class-imbalance structure of the data interacts with each training phase. The original models, trained to minimise overall loss on a dataset with only ≈ 4 % positive samples, tend to classify most observations as the majority (non-flaring) class, yielding high accuracy but low recall and F1. The sparse models swing to the opposite extreme. ℓ 1 regularisation drives many BN scaling factors toward zero, effectively suppressing many channels during inference and biasing the decision boundary toward higher recall. For instance, VGG-Sparse achieves a recall of 0.923 but at the cost of a massive increase in false positives, resulting in an F1 of only 0.212 and an HSS of 0.147, which are both lower than the original. N-Slim’s iterative slimming procedure recovers a balanced precision-recall operating point. Each pruning step physically removes the least important channels, and the subsequent knowledge-distillation fine-tuning reallocates the remaining model capacity toward discriminative features for both classes. As an illustration, the DenseNet N-Slim subnet at N = 16, P = 77 % achieves a recall of 0.572 and a precision of 0.626, yielding a well-balanced F1 of 0.598 that is far above both the original (0.286) and sparse (0.385) baselines.

Part of the improvement of the pruned subnets over the original networks can be interpreted as a regularizing effect rather than as a compression effect alone. The training and pruning procedure already includes several mechanisms that mitigate overfitting and stabilize the minority class operating point, including weight decay, random horizontal and vertical flips, focal loss, the ℓ 1 penalty on BN scaling factors, knowledge distillation fine-tuning after each pruning step, and stochastic channel rejuvenation. We do not use dropout in this study because the channel importance score used by both Standard pruning and N-balanced structured channel pruning is the BN scaling magnitude | γ i |. Dropout can alter the activation statistics observed by BN during training and may make | γ i | a noisier proxy for channel importance (Li et al., 2019). Channel-wise dropout would further interfere with the sparsity pattern induced by the ℓ 1 penalty on BN scaling factors. Designing a dropout variant compatible with BN-based channel selection is left for future work.

As Table 1 shows, the forecasting performance of N-Slim subnets does not decrease monotonically with the channel pruning rate. For example, the most aggressively pruned VGG subnet (N = 16, P = 94 %, 0.002 GFLOPs) attains the highest AUC (0.912) and TSS (0.627) among all VGG variants. The ResNet subnet atN = 8, P = 88 % achieves higher F1 (0.538) and HSS (0.516) than the less compressed N = 4, P = 55 % subnet (F1 = 0.521, HSS = 0.497). The DenseNet subnet at N = 16, P = 77 % yields the best F1 (0.598) across all DenseNet configurations despite retaining only 0.019 GFLOPs. This non-monotonic behaviour arises because the final prediction quality is determined not by how many channels are retained, but by which channels are retained and how effectively the subsequent fine-tuning recovers the lost capacity. Several factors contribute to this variability. Different group sizes N impose distinct channel partitions (Equation 3), and two subnets with similar total channel counts but different group constraints can end up retaining quite different feature sets. The severe class imbalance (≈ 4 % positive rate) amplifies this effect, because the decision boundary is sensitive to whether a small number of flare-precursor-selective channels happen to survive pruning. The knowledge-distillation chain adds further unpredictability. Each pruning step inherits a different teacher, and the capacity gap between teacher and student at each step influences the fine-tuning outcome. The final performance is therefore path-dependent and cannot be predicted from the overall compression ratio alone.

5.2.2 Storage footprint of the subnets

The Size column of Table 1 reports the storage footprint of each run. The compact footprint of the N-Slim subnets is much smaller than the unpruned footprint for ResNet and DenseNet. This shows that channel removal reduces parameter storage as well as arithmetic cost in a dense deployment.

This compact footprint applies to a proxyal dense deployment. In the sparse storage layout used for MBU containment, the tensors are kept in the unpruned arrangement, and the pruned channels are stored as inactive positions or positions with zero values. Therefore, the resident onboard footprint of every protected subnet equals the unpruned size listed in the Original and Sparse rows. The relevant memory budget for the portfolio used for power adaptation depends on the unpruned footprint of the chosen architecture and on the number of subnets kept resident. This layout trades storage compactness for containment of MBU effects. The compact computational graph still reduces GFLOPs and compute energy estimated from FLOPs, because inference schedules only the retained channels. Quantization provides a complementary reduction in storage cost by reducing the bit width of all stored weights, as discussed in Section 5.5.

5.2.3 Channel retention at high pruning rates

To substantiate the non-monotonic pruning behaviour, we add two visualizations of retained channels. Figure 2 shows representative DenseNet ( N = 4 , P = 71 % ) and ResNet ( N = 8 , P = 88 % ) subnets. The upper row reports the original channel count, retained channel count, and retention ratio for each layer. N-Slim and Standard pruning have nearly identical retained counts under the same nominal N / P configuration, confirming that the comparison is matched in capacity. The curves also show that no convolutional layer is entirely removed, so nonzero feature pathways are preserved across the network depth even at high pruning rates.

The lower row of Figure 2 reports the min-max range and mean of the BN scaling magnitudes | γ i | over retained channels. Since | γ i | is the channel-importance score used by N-Slim, this tests whether N-balanced rebalancing preserves important channels or fills receiver groups with low-score ones. The means over retained channels under N-Slim remain close to those of paired Standard pruning: 0.970 versus 0.989 for ResNet and 0.988 versus 0.995 for DenseNet. Thus, N-balanced rebalancing mainly redistributes channels with high importance across groups rather than replacing them with channels with low importance.

Figure 3 visualizes the distribution of retained channels within groups of N consecutive channels. Each cell denotes a layer-group pair, and red rectangles mark empty groups. The coefficient of variation (CV) measures the unevenness of retained counts across all pairs of a layer and a group. Standard pruning produces clustered survivors with empty groups, whereas N-Slim spreads retained channels more uniformly. For ResNet at N = 8 , P = 88 %, Standard pruning leaves 26.9 % empty groups with CV = 0.967, while N-Slim leaves no empty group and has CV = 0, indicating that N-Slim achieves complete and perfectly balanced group coverage in this case. For the DenseNet N = 4 snapshot, the fraction of empty groups decreases from 6.0 % to 0.0 %, and CV decreases from 0.507 to 0.291. These heatmaps directly verify the intended group-coverage effect of N-balanced pruning.

These results show that forecasting performance is not determined by the nominal pruning rate alone. A highly pruned subnet can still perform well if it preserves compact feature pathways with large | γ i | values and distributes them across layers and channel groups. Conversely, a less pruned subnet may retain more channels but less favourable channel identities or group coverage. Therefore, the final performance depends on the identity of the retained channels, the layer-wise and group-wise distributions, and the knowledge-distillation fine-tuning path, rather than on the compression ratio alone.

5.2.4 Clean-model comparison between N-Slim and Standard pruning

Before evaluating MBU robustness, we first compare the forecasting performance of N-Slim and Standard pruning before fault injection under matched nominal N / P configurations. This comparison checks whether the paired subnets have similar forecasting behaviour before faults are injected. For each metric m, we define the paired difference before fault injection aswhere k = 1 , … , K indexes the matched N / P configurations. We report the mean absolute differenceand the relative mean absolute difference

Δ k , m = x k , m N - Slim − x k , m Standard ,

r m = | Δ m | ̄ 1 K ∑ k = 1 K x k , m N - Slim + x k , m Standard / 2 × 100 % .

Figure 4 shows that the clean AUC values of the paired N-Slim and Standard subnets are close. The mean AUC values are 0.9002 and 0.9006 for VGG, 0.9165 and 0.9170 for ResNet, and 0.9223 and 0.9154 for DenseNet. The mean absolute AUC differences are 0.0068, 0.0111, and 0.0088, respectively. The corresponding relative mean absolute differences are 0.76 %, 1.22 %, and 0.96 %. The largest clean AUC difference over all matched configurations is 0.0286. These values show that the two pruning procedures have close clean ranking performance. The metrics at a fixed threshold show larger differences. For example, the mean absolute differences for Recall are 0.0311, 0.0212, and 0.0251 for VGG, ResNet, and DenseNet. For TSS, they are 0.0430, 0.0163, and 0.0188.

These results clarify the status of the paired models. In the present experiments, however, the two subnets are produced by separate pruning, reconstruction, and fine-tuning procedures under matched nominal N / P configurations. This explains why their clean AUC values are close while their metrics at a fixed threshold can differ.

5.3 MBU robustness validation

To evaluate the MBU robustness of N-Slim subnets, bit-flip injection experiments are conducted under the non-interleaved MBU fault model described in Section 4.5.2. For each architecture and pruning configuration, N-Slim is compared with Standard pruning under the same nominal N / P configuration. Standard pruning uses unconstrained BN-score ranking. N-Slim uses N-balanced structured channel pruning, reconstruction, and fine-tuning. Three MBU event ratios r ∈ { 0.015 , 0.03 , 0.05 } are applied, and each combination is evaluated over 20 independent Monte Carlo trials. Table 2 reports the mean and standard deviation of F1, TSS, and AUC across all trials. Figures 5–7 display the corresponding ROC curves for the most aggressively pruned subnet under each group size.

TABLE 2. MBU robustness comparison between N-Slim, based on N-balanced structured channel pruning, and Standard pruning under non-interleaved MBU injection at three event ratios.

Each pair uses the same architecture and nominal N / P configuration. Values are reported as mean±std over 20 Monte Carlo trials.

One aspect of Table 2 that warrants attention is the large standard deviation observed across nearly all configurations. For example, the DenseNet Standard subnet at N = 8, P = 81 % under r = 0.05 exhibits a TSS of − 0.052 ± 0.10, meaning that some trials retain marginal discriminative ability while others fall well below random. Similarly, the ResNet N-Slim subnet at N = 16, P = 93 % under r = 0.05 yields an AUC of 0.826 ± 0.16, spanning from near-functional to severely degraded across independent realisations. This high variability is intrinsic to MBU events. Each trial samples a different random subset of weight elements for corruption, and the impact depends critically on which parameters are struck. A fault hitting a high-magnitude kernel in an early layer can cascade through the entire network, whereas the same number of faults in low-sensitivity parameters may be barely perceptible. The large standard deviations underscore that MBU-induced degradation is not a gradual, predictable process but a stochastic one with heavy tails. This behaviour reinforces the operational importance of structural robustness measures for satellite-deployed models.

5.3.1 Robustness on ResNet and DenseNet

On ResNet and DenseNet, N-Slim shows a consistent robustness advantage over Standard pruning under MBU injection, and this advantage generally widens as both the pruning rate and the MBU intensity increase. Since the paired clean models are not strictly identical, the observed differences should not be attributed only to physical channel layout. They reflect N-balanced channel selection, reconstruction, fine-tuning, and the resulting channel layout. The most striking example is ResNet at N = 16, P = 93 %. Under r = 0.03, N-Slim maintains a TSS of 0.592 ± 0.10 and an AUC of 0.923 ± 0.01, whereas Standard degrades to a TSS of 0.373 ± 0.24 and an AUC of 0.823 ± 0.13. Under the harshest condition r = 0.05, N-Slim still retains a TSS of 0.401 ± 0.25, while Standard collapses to 0.085 ± 0.12, approaching the random-forecast level. A similarly clear separation is observed at N = 8, P = 88 %, where N-Slim achieves an AUC of 0.927 ± 0.00 versus 0.898 ± 0.01 at r = 0.015, and 0.881 ± 0.07 versus 0.766 ± 0.15 at r = 0.05. N-Slim’s standard deviation is also consistently smaller than Standard’s (e.g., AUC std of 0.07 vs. 0.15 in the last example), indicating both higher mean performance and more predictable behaviour under stochastic fault conditions. The ROC curves in Figure 6 confirm this pattern. As r increases from 0.015 to 0.05, the N-Slim curves remain closer to the upper-left corner than their Standard counterparts, and the separation between the two becomes increasingly visible at higher fault rates.

These trends are corroborated by the ROC curves in Figure 7, where the Standard curves collapse toward the diagonal at r = 0.05 while the N-Slim curves largely preserve their shape. These results confirm that the N-balanced channel distribution effectively limits the number of retained channels that a single MBU event can simultaneously corrupt. By increasing the physical spacing between retained channels in weight memory, the method preserves discriminative capacity even under severe fault conditions.

5.3.2 Sensitivity to the fault model parameters

The main MBU experiments fix p decay = 0.65 and b cluster = 8. To test whether the comparison depends on these two parameters, we repeat the bit-flip injection over p decay ∈ { 0.5 , 0.65 , 0.8 } and b cluster ∈ { 4,8,16 }. This gives nine fault-model settings for each subnet pair. We evaluate each ResNet and DenseNet N-Slim subnet against its Standard counterpart at the same per-layer channel count. Each setting is averaged over 10 Monte Carlo trials. Figure 8 reports the AUC gap, computed as the mean AUC of N-Slim minus the mean AUC of Standard. A positive value means that N-Slim has the higher mean AUC.

The ranking is stable over the swept range. On ResNet, N-Slim has a positive AUC gap in 42 of 45 cells. The three negative cells are below 0.001 AUC. On DenseNet, N-Slim has a positive AUC gap in 39 of 45 cells. The six negative cells are below 0.004 AUC. These negative gaps are small compared with the Monte Carlo variation reported in Table 2. The positive gaps increase at harsher settings, especially for highly pruned subnets. For example, the ResNet subnet at N = 16 and P = 93 % reaches a gap above + 0.06 AUC. This is consistent with the error-containment explanation. A larger b cluster or a larger p decay flips more bits per event, which gives the N-balanced spacing more opportunity to limit the damage to retained channels.

This sweep proves the robustness of ResNet and DenseNet. Within the tested parameter grid, the ResNet and DenseNet results are not sensitive to the particular baseline choice p decay = 0.65 and b cluster = 8. The sweep does not remove the need for hardware calibration of the bit-position distribution, the clamping threshold, or the mapping from event ratio to physical upset rate.

5.3.3 Discussion on VGG and architectural dependence

On VGG, the two pruning strategies exhibit broadly comparable MBU robustness, and in several settings Standard pruning achieves moderately higher metrics than N-Slim. At N = 8, P = 88 %, r = 0.015, for instance, Standard F1 reaches 0.431 ± 0.09 versus 0.210 ± 0.14 for N-Slim. Similarly, at N = 16, P = 94 %, r = 0.03, Standard AUC is 0.893 ± 0.02 compared with 0.805 ± 0.14 for N-Slim. In other configurations, N-Slim holds a moderate advantage, as at N = 4, P = 55 %, r = 0.015, where N-Slim TSS is 0.517 ± 0.09 versus 0.271 ± 0.21 for Standard. The ROC curves in Figure 5 corroborate this pattern, with the two strategies overlapping substantially across all three fault rates. Overall, the MBU robustness of N-Slim and Standard pruning is statistically indistinguishable on VGG, and the clear advantage observed on ResNet and DenseNet does not generalise to this purely sequential architecture. This constitutes an important limitation of the N-balanced approach that should be weighed against the gains on the other two architectures.

The architectural dependence of this robustness advantage can be understood through error-containment pathways. N-balanced pruning increases the physical spacing between retained channels in weight memory, ensuring that a single MBU event corrupts at most one retained channel per layer. The benefit of this per-layer containment, however, depends critically on what happens after the corrupted feature map exits the affected layer. In ResNet and DenseNet, skip and dense connections carry uncorrupted activations around the damaged layer, allowing downstream layers to partially reconstruct the correct representation from bypass signals. The per-layer containment provided by N-balanced spacing is therefore amplified by architectural bypass, producing the substantial robustness gains seen in Table 2. VGG lacks any such bypass path. A corrupted feature map at layer l is the sole input to layer l + 1, and the distortion accumulates through successive convolutions, batch normalisations, and nonlinearities without structural attenuation. Under this cascading error-propagation regime, the containment benefit of N-balanced spacing is overwhelmed by amplification across the full depth, and the overall MBU robustness converges to that of Standard pruning regardless of the physical channel layout. This analysis shows that the physical channel spacing provided by N-balanced pruning is necessary but not sufficient for end-to-end MBU robustness. The architecture must also supply error-containment pathways, such as residual or dense connections, to translate per-layer containment into prediction stability. On purely sequential architectures, complementary mechanisms such as selective weight hardening or algorithmic redundancy would likely be needed to achieve robustness gains beyond those provided by compression alone.

5.4 Power-adaptive inference

The per-inference energy values in Table 1 should be interpreted as FLOPs-based compute-energy proxies. As stated in Section 5.1.2, they do not include SRAM access, data movement, or control logic. The omission is important for onboard processors because memory access can dominate total inference energy. This is especially relevant for DenseNet, where dense concatenation increases activation traffic.

The most compressed subnets consume 16.1 μ J (VGG), 8.6 μ J (ResNet), and 87.5 μ J (DenseNet) per inference, down from 3,993, 1,711, and 1,982 μ J, respectively. Across the full subnet portfolio, per-inference energy spans a roughly 20 × dynamic range (e.g., 8.6 to 170.7 μ J for ResNet). This wide energy span is a necessary condition for the power-adaptive deployment concept described in Section 4.4.3, but it is not sufficient on its own. A practical power-adaptive system would additionally require a runtime scheduler that maps instantaneous power availability to subnet selection, manages multi-model memory residency, and handles switching transients. None of these components are addressed in this work. The present contribution is limited to providing the portfolio of candidate subnets. Whether the resulting energy span is adequate for a practical scheduling policy on a specific satellite platform, and whether the switching overhead is acceptable relative to the inference cadence, remain open questions for future work.

A more complete estimate would add a term for memory access to the arithmetic energy, for example, E total = Φ e 0 + ( W e + A e ) e mem, where W e and A e are the weight and activation bytes moved per inference and e mem is the access energy per byte (Sze et al., 2017). A faithful value for e mem depends on the accelerator dataflow, the buffer capacity on the chip, and the technology node. Our measurements were taken on a GPU server used for general purpose computation rather than on the target processor designed for radiation tolerance. Without a specified accelerator, memory hierarchy, and dataflow, a single e mem value would not be reproducible. We therefore retain the arithmetic proxy in the main results and leave the estimate that accounts for memory access to future work for specific platforms.

Inference latency broadly follows the FLOP reductions, with the most compressed VGG and ResNet subnets converging to a floor of 0.019–0.035 m dominated by kernel-launch and memory-transfer overhead rather than arithmetic. DenseNet subnets settle at a higher floor (≈ 0.118 ms) due to the memory-access overhead of dense concatenation. A few moderately pruned VGG subnets exhibit latencies slightly above the unpruned baseline (e.g., 0.269 m at N = 4 , P = 55 % versus 0.241 m for the original) because GPU kernels are optimised for regular channel counts and pruning to irregular widths can reduce hardware utilisation (Ma et al., 2018). This effect would diminish on dedicated edge accelerators with channel-count-aware scheduling.

Channel pruning also compresses the weight-storage footprint. For a layer with both input and output channels pruned at rate P, the stored parameter count scales approximately as ( 1 − P ) 2. At P = 94 % this yields a ∼ 250 × per-layer reduction. The most compressed subnets fit comfortably within the one–4 MB SRAM typical of radiation-tolerant satellite processors (Furano et al., 2020). Although the sparse deployment layout retains the full tensor size in SRAM, the fraction of stored weight values belonging to retained channels (and therefore sensitive to MBU corruption) is reduced to approximately ( 1 − P ) of the original. An MBU event striking a pruned (zeroed) weight position has no effect on inference, effectively reducing the model’s functional radiation cross-section despite the unchanged physical footprint. This cross-section reduction complements the N-balanced spacing to provide two layers of MBU protection.

5.5 Direct post-training quantization as a complementary baseline

The subnets reported above are stored in 32-bit floating point. To separate N-balanced structured channel pruning from numerical precision, we evaluate post-training quantization as a baseline. The quantization target is the Sparse model with full width for each architecture. This model enters the iterative slimming phase without channel pruning. We quantize it to FP16 and INT8 without fine tuning. The results are reported in Table 3. We also apply INT8 to representative N-Slim subnets. These results are reported in Table 4. We report the quantization experiment for ResNet and DenseNet, because these two architectures show MBU robustness gains from N-balanced structured channel pruning.

TABLE 3. Post-training quantization of the full-width sparse model.

FLOPs, are invariant to numerical precision, so only stored size changes. FP16 is effectively lossless, while INT8 shifts the operating point toward higher recall at the cost of precision without reducing FLOPs.

TABLE 4. N-Slim subnets combined with INT8 post-training quantization.

Each subnet is reported at FP32 and INT8. INT8 reduces stored size by roughly three to four times with negligible change in skill, and the combined models match or exceed the quantized full-width baseline in Tabl 3 at far lower storage and FLOPs.

FP16 halves the stored size and keeps the forecasting metrics nearly unchanged. INT8 reduces the storage size to about one-quarter of the FP32 model. The skill metrics remain close to the FP32 values. For the Sparse DenseNet with full width, TSS changes from 0.636 to 0.640. For the Sparse ResNet with full width, TSS changes from 0.635 to 0.647. These small changes mainly come from shifts of the fixed decision threshold.

Quantization changes the numerical format of weights but does not change the channel structure. Therefore, FP32, FP16, and INT8 have the same FLOPs in our setting. Under the energy proxy based on FLOPs used in this work, their energy on the compute side is also the same. We do not report INT8 latency or hardware energy, because these values depend strongly on the target accelerator, the INT8 kernel implementation, and memory access costs. Our measurements were taken on a GPU used for general purpose computation rather than an INT8 processor representative of flight hardware. We therefore report the forecasting metrics, FLOPs, and stored size for FP32, FP16, INT8, and N-Slim + INT8.

Quantization and N-balanced structured channel pruning are complementary. Applying INT8 to an N-Slim subnet reduces the stored size by about three to four times, with little change in skill. For example, the INT8 DenseNet subnet at N = 4 and P = 71 % occupies 42.8 KB and has a TSS of 0.648. The INT8 DenseNet with full width occupies 406.4 KB and has a TSS of 0.640. The most compressed INT8 ResNet subnet maintains a TSS of 0.618 at 3.7 KB. Thus, pruning provides compute scaling and structural MBU containment, while quantization provides additional storage reduction.

5.6 Ablation study

The iterative slimming phase of N-Slim uses two components for fine tuning, knowledge distillation and stochastic channel rejuvenation. To assess their individual contributions, we remove each component in turn from the Full pipeline. The pruning configuration is kept unchanged. The ablation uses ResNet at N = 16, P = 93 % and DenseNet at N = 16, P = 85 %. These are highly compressed subnets from the two architectures, where N-Slim shows clear MBU robustness gains. Table 5 reports the results.

TABLE 5. Ablation of knowledge distillation and stochastic channel rejuvenation.

All rows are N-Slim subnets at the same nominal pruning configuration, where N is the group size and P the nominal per-layer channel pruning rate. The full method uses both components and matches the corresponding rows of Table 1. The other two rows each remove one component. Bold values indicate the best-performing result for each evaluation metric among the different configurations of the same network.

Knowledge distillation is the main contributor to the F1 and HSS improvement over the Sparse baseline. For ResNet, the Sparse baseline has F1 = 0.345 and HSS = 0.297, while the Full pipeline reaches F1 = 0.500 and HSS = 0.472. Without knowledge distillation, F1 and HSS fall to 0.235 and 0.226. For DenseNet, the Sparse baseline has F1 = 0.385 and HSS = 0.343, while the Full pipeline reaches F1 = 0.456 and HSS = 0.423. Without knowledge distillation, F1 and HSS fall to 0.333 and 0.297. The AUC remains relatively high in the No distillation variant, but the recall drops. This indicates that the subnet still has ranking ability, while the operating point at a fixed threshold is not well preserved under class imbalance.

Stochastic channel rejuvenation provides a smaller gain on top of knowledge distillation. For ResNet, removing stochastic channel rejuvenation changes F1 from 0.500 to 0.493 and HSS from 0.472 to 0.464. For DenseNet, it changes F1 from 0.456 to 0.453 and HSS from 0.423 to 0.421. The effect is also visible in TSS and AUC. On DenseNet, TSS increases from 0.570 to 0.612 and AUC from 0.912 to 0.933, suggesting that it helps preserve active retained channels during fine tuning.

6 Discussion

This section examines the main design choices behind N-Slim in greater detail.

6.1 Interaction of sparsification and N-balanced structured channel pruning

The reliability of the N-balanced channel selection depends on whether the BN scaling magnitudes | γ i | clearly discriminate between informative and uninformative channels, so that the Stage 1 global ranking is meaningful. sparsity learning produces this discrimination through the ℓ 1 regularisation in Equation 1. Channels that carry discriminative information maintain large | γ i | because the task-loss gradient counteracts the regularisation. Channels that do not carry discriminative information have no such counteracting gradient and converge toward zero. The resulting bimodal distribution makes the global ranking in Stage 1 robust: the gap between retained and removed channels is large, so small perturbations in score, such as those arising from mini-batch gradient noise, do not change the composition of S ( 0 ). Without sparsification, BN scaling factors remain close to their initialisation values across all channels (Liu et al., 2017), and the ranking is sensitive to gradient noise, increasing the frequency and unpredictability of Stage 2 swaps.

6.2 Swap-based rebalancing: swap cost and MBU risk

Standard structured channel pruning and N-balanced structured channel pruning target the same nominal retention budget M for each layer, where M is determined by Equation 2. The distinction is that Standard pruning follows unconstrained ranking based on BN scores, whereas N-balanced structured channel pruning adds a constraint on group coverage before reconstruction and fine tuning. Stage 1 selects an initial set of channels with high scores. The rebalancing step based on swaps then checks whether consecutive groups of N channels have insufficient representation. When a receiver group lacks enough retained channels, a feature with a high score from a donor group is moved into that group by swapping the corresponding channel parameters. The nominal retention budget remains fixed, but the final compact subnet after reconstruction and fine tuning should be viewed as the output of a different pruning procedure, not merely as a copy with reassigned indices of Standard pruning.

N-Slim reduces MBU-induced inference errors by combining two complementary mechanisms. The first is compression itself. By removing a large fraction of channels, the total memory footprint shrinks, reducing the cross-section for any incoming particle strike. The second is the group-aligned retention pattern. Even among the channels that remain after compression, the N-balanced constraint prevents the formation of dense clusters of retained-channel parameters in weight memory. Because each retained channel is separated from its nearest retained neighbour by at least N channel positions, the physical gap between retained weight regions in memory far exceeds the charge-diffusion radius of a typical MBU event. Compression reduces the probability that an MBU lands on a retained weight, while group alignment ensures that, if it does, the damage is confined to a single retained channel rather than corrupting multiple adjacent retained channels simultaneously.

The number of swaps performed by swap-based rebalancing reflects the uneven distribution of top-ranked channels across groups, and two factors amplify this unevenness. First, a higher pruning ratio leaves fewer channels in the retained set S, increasing the chance that some groups are left entirely unrepresented after global ranking and therefore requiring more corrective swaps. Second, a larger group width N means each group spans more channels, making it more likely that high-scoring channels concentrate within a subset of groups. However, the relationship between N and fault tolerance is not monotone. Larger N reduces the number of groups K, allowing higher compression at the minimum retention budget, but increases the fraction of the feature space encompassed by any single uncovered group. Smaller N increases K, providing finer-grained coverage at lower compression. The geometric sequence of N values used in the subnet portfolio (Section 4.4.3) systematically traverses this trade-off, offering a predictable range of operating points between fine-grained coverage and high compression.

A high swap count indicates that standard pruning would have concentrated the retained channels within a small, contiguous region of the weight memory, constituting a pre-existing structural vulnerability to multi-bit faults. After weight reconstruction, the weight tensor of each retained channel is physically independent of every other retained channel’s tensor, so a bit corruption in channel j affects only channel j’s output feature map and does not directly alter any other retained channel’s output. The group-coverage guarantee determines the pre-fault state from which fault propagation begins. Under standard pruning, retained channels may cluster within a narrow index range, and a single MBU event whose charge-diffusion footprint overlaps this cluster can corrupt multiple retained channels simultaneously, causing a disproportionate loss of the model’s retained representational capacity and a sharp drop in prediction accuracy. N-balanced structured channel pruning eliminates this clustering vulnerability by construction. Under the sparse deployment layout (Section 4.4.1), the zeroed inactive channels act as physical buffers between retained channels in SRAM. The minimum physical separation between any two retained channels is at least N times the per-channel kernel size in bytes, far exceeding the charge-diffusion radius of typical MBU events. An MBU event striking an inactive (zeroed) channel position produces no change in inference output, while the spacing between retained channels ensures that a single MBU event can corrupt at most one retained channel. Under the assumed sparse storage layout, N-balanced pruning reduces the clustering of retained channel regions and is intended to reduce the probability that a localized MBU overlaps multiple retained channels. The retention pattern aligned with groups, therefore, places a structural upper bound on the accuracy degradation that any single MBU event can cause.

6.3 Limitations

Although the experiments demonstrate that N-Slim works well across three CNN families, the current study has several limitations that should be noted.

First, N-Slim is evaluated exclusively on classical CNN architectures (VGG, ResNet, DenseNet). Whether the method extends to Transformer-based models remains untested. The size of the MBU robustness advantage from N-balanced pruning depends on the network architecture. On ResNet and DenseNet, which contain skip or dense connections that serve as error-containment pathways, the advantage is consistent and substantial. On VGG, which lacks such bypass paths, N-balanced pruning achieves MBU robustness comparable to standard pruning rather than a clear improvement. This result suggests that the practical benefit of the balanced channel distribution is most pronounced when the architecture itself can attenuate corrupted activations. Future work should investigate whether lightweight architectural modifications, such as adding residual connections to sequential pipelines, can extend the MBU robustness advantage to a broader class of network topologies. One concrete option is to insert minimal residual connections into the VGG pipeline, for example, an identity or 1 × 1 projection shortcut spanning every two or three Conv-BN-ReLU blocks. Such a shortcut bypasses the affected block, allowing downstream layers to combine the block’s output with an activation stream that is not directly modified by the faulty block. If a 1 × 1 projection is used, its additional weights would also need to be considered in the fault model. Forecasting performance varies non-monotonically across pruning configurations (Table 1), and the current pruning criterion does not guarantee a predictable decrease in accuracy as the pruning rate increases.

Second, the MBU evaluation is based on fault injection at the software level rather than physical radiation testing. The sensitivity analysis in Section 5.3.2 now sweeps p decay ∈ { 0.5 , 0.65 , 0.8 } and b cluster ∈ { 4,8,16 }. It shows that the relative robustness conclusion for ResNet and DenseNet is stable over this range. However, the fault model is still not calibrated to a specific SRAM device. The starting bit position is sampled uniformly across all 32 IEEE 754 bit positions because the physical mapping from bit positions to memory cells is unavailable. We added a simple estimate for possible sign and exponent bit biases, but a distribution specific to the hardware would require device-level information or data from beam tests. The clamping threshold of 21 σ l also remains heuristic. The event ratios r ∈ { 0.015 , 0.03 , 0.05 } are dimensionless and are not mapped to a particular orbit, shielding configuration, or technology node. Such a mapping would require radiation transport modelling for a concrete mission. The current simulation also does not include spatially or temporally correlated fault bursts. These limitations mean that the absolute degradation values should not be read as operational predictions. Hardware-level validation with proton or heavy-ion irradiation remains necessary before deployment claims can be made.

Third, the evaluation uses two test years, 2011 and 2015, chosen to span the ascending and the declining phases of Solar Cycle 24. The full 9-year dataset covers a single solar cycle, so the generalisation of the reported skill to other cycles, in particular cycles with markedly different activity levels, is not established here. Evaluation across additional held-out years and across multiple solar cycles is left for future work.

Overall, this work is an exploratory study of structured channel pruning, treating radiation tolerance as a primary design constraint. Addressing these limitations and validating the approach on flight-representative hardware and modern architectures will be necessary before operational deployment.

7 Conclusion

Deploying deep learning models onboard satellites for real-time solar flare forecasting requires simultaneous attention to model compression, resilience to radiation-induced weight corruption, and adaptation to time-varying power budgets. This paper presents N-Slim, a three-phase network slimming framework whose core contribution is the N-balanced structured channel pruning method that partitions each layer’s output channels into fixed-width groups and distributes retained channels approximately uniformly across groups via swap-based rebalancing. The group-aligned retention pattern ensures that the physical separation between retained channels in weight memory exceeds the charge-diffusion radius of multiple-bit upset events, structurally confining any single MBU to at most one retained channel. Experiments on VGG, ResNet, and DenseNet using SDO/HMI magnetograms demonstrated that N-Slim achieves competitive solar flare forecasting accuracy at high compression rates. On ResNet and DenseNet, the group-aligned retention pattern substantially reduces accuracy degradation under simulated MBU events compared with standard structured channel pruning at identical pruning ratios. On VGG, the two pruning strategies yield comparable MBU robustness, suggesting that the magnitude of structural protection is amplified by skip or dense connections that serve as error-containment pathways within the network.

Taken together, these results suggest that structured pruning methods designed with radiation tolerance as a primary constraint offer a promising direction for autonomous space-weather forecasting. However, the MBU robustness advantage is architecture-dependent, pronounced on ResNet and DenseNet but absent on VGG. The simplified software-level fault model requires physical calibration before the robustness claims can be considered validated. A separate deployment limitation concerns the input pipeline. This study uses line-of-sight magnetograms as the model input. SDO/HMI records polarized filtergrams at several wavelength positions, and magnetogram products are derived by the ground processing pipeline. Direct onboard use would therefore require either a compact onboard preprocessing step that estimates the line-of-sight magnetic field, or a classifier trained directly on Stokes observables or polarized filtergrams. Both options change the input pipeline and the onboard compute budget. They are left for future work.

The power-adaptive capability enabled by the multi-rate subnet portfolio is a structural byproduct of the pruning framework, whose practical utility has not been demonstrated through runtime scheduling experiments. Further work should focus on fault injection calibrated to hardware, validation with beam tests, and runtime scheduling on a processor representative of flight hardware.

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Footnotes

Edited by: Nandita Srivastava, Physical Research Laboratory, India

Reviewed by: Vishal Upendran, SETI Institute, United States

Besma Guesmi, Delft University of Technology, Netherlands