Neuron-Wise Partitioning in Deep Neural Networks

• Neuron-wise partitioning is a set of techniques that decomposes neural computations at the individual neuron or group level to enable modular training and specialized processing.
• It encompasses diverse strategies such as width-wise local learning, subspace correction, functional separation, and hardware-aware placement, each balancing isolation with inter-group communication.
• Empirical results reveal trade-offs between finer partition granularity and accuracy, highlighting the critical role of coupling mechanisms like stop-gradient communication and diversity penalties.

Neuron-wise partitioning is a family of techniques that decomposes neural computation below the scale of whole layers. In the literature, the partitioned object varies: some methods split the width of a layer into non-overlapping neuron groups and attach separate local objectives; some separate individual neurons into functional sets and tune them differently; some decompose parameter space into one optimization block per neuron; and some assign neurons, or matrix rows corresponding to neurons, to processors or crossbars for scalable execution. Adjacent usages are broader and should be distinguished carefully: several papers partition input space, activation trajectories, or dynamical phase space using neuron-derived structure rather than partitioning neurons directly (Patel et al., 2023, Kim et al., 2 Apr 2026, Demirci et al., 2021, Park et al., 2022).

1. Definition, scope, and granularity

A central difficulty in discussing neuron-wise partitioning is that the phrase is used at different granularities. In its strictest sense, it denotes a decomposition over individual neurons, as in attribution-based splitting of FFN neurons into relevant-only, irrelevant-only, and shared sets in robust retrieval-augmented language modeling, or the decomposition of a shallow network’s nonlinear parameter space into one subspace per neuron for subspace correction (Kim et al., 2 Apr 2026, Park et al., 2022). In a broader but still direct sense, it includes group-wise splits of channels or features within a layer, such as width-wise modularity in local learning, and hardware placement schemes in which each neuron is assigned to a processor or crossbar and synapse locality is induced by that assignment (Patel et al., 2023, Das et al., 2019).

Other papers are only indirectly related. YASENN partitions the input space by a discretized sequence of layer-wise activation codes rather than by isolating neurons one at a time, and piecewise INR methods partition the spatial domain into sub-regions handled by separate subnetworks rather than by neuron subsets inside one shared network (Zharov et al., 2018, Liu et al., 2023). A recurrent misconception is therefore that any method mentioning neurons performs literal one-neuron-per-loss or one-neuron-per-partition decomposition. Several influential methods do not.

Partitioning mode	Partitioned object	Representative papers
Width-wise local learning	Non-overlapping channel/feature groups within layers	(Patel et al., 2023)
Functional neuron separation	FFN neurons split into relevant, irrelevant, and shared sets	(Kim et al., 2 Apr 2026)
Rank-and-prune partitioning	Retained versus pruned neurons in a target layer	(Jin et al., 13 Jun 2025)
Subspace correction	Parameter space $A \oplus \bigoplus_i W_i$	(Park et al., 2022)
Distributed ownership	Matrix rows or neurons assigned to processors/crossbars	(Demirci et al., 2021, Das et al., 2019)
Activation-sequence partitioning	Input space partitioned by discretized activation streams	(Zharov et al., 2018)

2. Width-wise modularity and local learning

A direct formulation of within-layer neuron partitioning appears in Grouped Neuron DGL (GN-DGL). Starting from decoupled greedy learning, GN-DGL splits each layer $j$ into $G$ non-overlapping groups and assigns each group its own auxiliary network and local objective $C(y,x;\gamma_j^i,\theta_j^i)$, where $x$ is the subset of the layer representation corresponding to group $i$. In convolutional layers these groups are channel groups; in fully connected layers they are feature or neuron groups. The groups are approximately equal in size. For each minibatch, each group computes $x_j^i \leftarrow f_{\theta_j^i}(x_{j-1})$, updates $(\theta_j^i,\gamma_j^i)$ from $$\nabla_{(\gamma_j^i,\theta_j^i)} C(y,x_j^i;\gamma_j^i,\theta_j^i)$$, and receives no backward signal from later layers or neighboring groups. The forward coupling remains full across adjacent layers: each neuron group $i$ at layer $j$0 receives as input the output representations from all groups of the previous layer $j$1. A stop-gradient variant augments each group’s auxiliary network with detached same-layer outputs $j$2, and a diversity penalty uses cosine similarity between non-target-masked softmax distributions $j$3 and $j$4 to discourage correlated non-target errors. This makes the method explicitly group-wise rather than fully per-neuron in the experimental sense, but it is a clear form of neuron/group-level partitioning within layers (Patel et al., 2023).

The empirical pattern is a trade-off between finer partition granularity and accuracy. On VGG6a for CIFAR-10, standard depth-wise DGL gives $j$5, while 2-group, 4-group, 6-group, 8-group, and 10-group GN-DGL give $j$6, $j$7, $j$8, $j$9, and $G$0, respectively. For 6-group GN-DGL, plain GN-DGL gives $G$1, adding diversity gives $G$2, and adding both stop-gradient communication and diversity gives $G$3, nearly recovering DGL’s $G$4. With wider models, 6-group GN-DGL improves from $G$5 on VGG6a to $G$6 on $G$7VGG6a and $G$8 on $G$9VGG6a, while corresponding DGL scores are $C(y,x;\gamma_j^i,\theta_j^i)$0, $C(y,x;\gamma_j^i,\theta_j^i)$1, and $C(y,x;\gamma_j^i,\theta_j^i)$2. The same work generalizes the decomposition to $C(y,x;\gamma_j^i,\theta_j^i)$3 local modules over depth and width, studies maximum per-node training time measured in MACs, and reports that $C(y,x;\gamma_j^i,\theta_j^i)$4 configurations trend substantially better than DGL or InfoPro on harder datasets such as CIFAR-100 and ImageNet32. This suggests that width-wise modularity primarily expands model-parallel units beyond the number of layers, while stop-gradient communication, diversity regularization, widening, and layerwise ensembling compensate for the representational redundancy induced by isolated local supervision (Patel et al., 2023).

3. Functional neuron sets for robustness and unlearning

A stricter neuron-level partition appears in Neuro-RIT for robust retrieval-augmented language modeling. The method mines individual FFN neurons using Integrated Gradients over the activation difference between a query-only input and a query-plus-document input, using controlled relevant and irrelevant contexts. For each query and each context type, it filters for the top $C(y,x;\gamma_j^i,\theta_j^i)$5 and selects the top 20 highest-scoring neurons, aggregates these selections across queries, and obtains initial candidate sets $C(y,x;\gamma_j^i,\theta_j^i)$6 and $C(y,x;\gamma_j^i,\theta_j^i)$7. The paper reports 7,380 relevant and 7,036 irrelevant candidate neurons with an overlap of 6,240 neurons. It then defines $C(y,x;\gamma_j^i,\theta_j^i)$8, removes the overlap, and yields final sets of 100 neurons for $C(y,x;\gamma_j^i,\theta_j^i)$9, 100 neurons for $x$0, and 30 neurons for $x$1 using about 400 HotpotQA subsamples and a frequency occurrence threshold $x$2. The partition is static rather than dynamic at inference. Stage one instruction-tunes the irrelevant-context-aware neurons to emit an End-of-Text token on queries paired with five irrelevant retrieved documents; stage two targets layers 29, 30, and 31 of LLaMA-3-8B-Instruct for full fine-tuning while applying group-specific gradient masking to $x$3, $x$4, and $x$5. Full fine-tuning would update about 8B parameters, whereas this method updates about 0.529B, approximately $x$6 of the model, i.e. a $x$7 reduction in trainable parameters. Neuro-RIT + Reranker achieves the best average accuracy $x$8, and ablations reduce average accuracy from $x$9 to $i$0 without denoising, to $i$1 without stage-two noise filtering enhancement, to $i$2 without the selected layers, and to $i$3 without the selected neurons (Kim et al., 2 Apr 2026).

A different neuron partition is used in RLAP, which first partitions data and then partitions neurons into retained and pruned subsets. Sample-wise attribution vectors $i$4 are obtained from $i$5 and clustered with a Gaussian Mixture Model with $i$6 components into $i$7 and $i$8, interpreted as high-quality and noise-corrupted subsets. A least-squares regression then predicts the binary quality label $i$9 from layer-$x_j^i \leftarrow f_{\theta_j^i}(x_{j-1})$0 activations $x_j^i \leftarrow f_{\theta_j^i}(x_{j-1})$1, producing coefficients $x_j^i \leftarrow f_{\theta_j^i}(x_{j-1})$2; neurons are ranked by the sensitivity score $x_j^i \leftarrow f_{\theta_j^i}(x_{j-1})$3, the top-$x_j^i \leftarrow f_{\theta_j^i}(x_{j-1})$4 fraction is selected, and pruning sets $x_j^i \leftarrow f_{\theta_j^i}(x_{j-1})$5 and $x_j^i \leftarrow f_{\theta_j^i}(x_{j-1})$6 for $x_j^i \leftarrow f_{\theta_j^i}(x_{j-1})$7. The paper fixes $x_j^i \leftarrow f_{\theta_j^i}(x_{j-1})$8 and applies pruning only to the FNN layer of a hybrid CNN-FNN architecture. On CIFAR-10 with 50k training examples, the initial noisy model gives $x_j^i \leftarrow f_{\theta_j^i}(x_{j-1})$9, retraining on the refined subset gives $(\theta_j^i,\gamma_j^i)$0, L-FT gives $(\theta_j^i,\gamma_j^i)$1, and F-FT gives $(\theta_j^i,\gamma_j^i)$2. On Speech Commands, the corresponding numbers are $(\theta_j^i,\gamma_j^i)$3, $(\theta_j^i,\gamma_j^i)$4, $(\theta_j^i,\gamma_j^i)$5, and $(\theta_j^i,\gamma_j^i)$6. The paper also notes a notational inconsistency: Eq. $(\theta_j^i,\gamma_j^i)$7 uses a scalar intercept $(\theta_j^i,\gamma_j^i)$8, whereas Eq. $(\theta_j^i,\gamma_j^i)$9 uses $$\nabla_{(\gamma_j^i,\theta_j^i)} C(y,x_j^i;\gamma_j^i,\theta_j^i)$$0 as if it were neuron-specific. This indicates that the method is best understood as rank-and-prune partitioning rather than a richer functional taxonomy (Jin et al., 13 Jun 2025).

4. Regularization and optimization through neuron partitions

In deep multi-view learning, CorrReg reinterprets a hidden or fusion layer as a multi-view object by partitioning the input neurons of that layer into multiple subsets, specifically two subsets in the main development. For a layer input $$\nabla_{(\gamma_j^i,\theta_j^i)} C(y,x_j^i;\gamma_j^i,\theta_j^i)$$1, a random two-way partition yields $$\nabla_{(\gamma_j^i,\theta_j^i)} C(y,x_j^i;\gamma_j^i,\theta_j^i)$$2 and $$\nabla_{(\gamma_j^i,\theta_j^i)} C(y,x_j^i;\gamma_j^i,\theta_j^i)$$3 with corresponding weight submatrices $$\nabla_{(\gamma_j^i,\theta_j^i)} C(y,x_j^i;\gamma_j^i,\theta_j^i)$$4 and $$\nabla_{(\gamma_j^i,\theta_j^i)} C(y,x_j^i;\gamma_j^i,\theta_j^i)$$5, so that $$\nabla_{(\gamma_j^i,\theta_j^i)} C(y,x_j^i;\gamma_j^i,\theta_j^i)$$6. For one output neuron, this induces two scalar internal features $$\nabla_{(\gamma_j^i,\theta_j^i)} C(y,x_j^i;\gamma_j^i,\theta_j^i)$$7 and $$\nabla_{(\gamma_j^i,\theta_j^i)} C(y,x_j^i;\gamma_j^i,\theta_j^i)$$8; CorrReg maximizes their batchwise correlation rather than performing full CCA over the whole layer. The training objective is $$\nabla_{(\gamma_j^i,\theta_j^i)} C(y,x_j^i;\gamma_j^i,\theta_j^i)$$9. The partition is fixed by design rather than learned: it is random in generic DNNs and modality-defined in fusion layers. CorrReg is implemented as a correlation-regularized network layer that leaves the forward pass unchanged and augments the backward pass with correlation gradients. Standard layer cost remains $i$0, whereas full CCA regularization would require $i$1. On CIFAR-10, applying CorrReg consistently improves over the baseline, is generally more effective on upper FC layers, performs comparably to Dropout, and CorrReg plus Dropout performs best. On RGB-D object recognition, direct upper-level concatenation yields $i$2, L2 regularization $i$3, CorrReg $i$4, and CorrReg plus Dropout $i$5; with stronger ResNet-based streams, direct concatenation gives $i$6, CorrReg $i$7, and CorrReg plus Dropout $i$8 (Jia et al., 2019).

A more literal optimization-time neuron partition is given by the Neuron-wise Parallel Subspace Correction Method (NPSC) for the finite neuron method. A shallow ReLU network $i$9 induces a parameter decomposition $j$00, where $j$01 contains the linear coefficients $j$02 and each $j$03 contains the nonlinear parameters $j$04 of one neuron. The method alternates between solving the linear-layer problem $j$05 and solving $j$06 single-neuron problems in parallel, followed by a relaxed assembly with backtracking. The motivation is twofold: the linear layer is ill-conditioned, with $j$07 in a model $j$08 setting, while the single-neuron problem has a more favorable local landscape. In one dimension, the paper constructs a preconditioner $j$09 such that $j$10, with a constant independent of $j$11, $j$12, and $j$13; PCG uses the stopping criterion $j$14. For single-neuron optimization it uses Levenberg–Marquardt, and proves that any nontrivial critical point $j$15 of the local problem satisfies $j$16. Numerical experiments on function approximation and PDEs report better performance than GD, Adam, and LSGD. This suggests a distinct interpretation of neuron-wise partitioning: not modular execution or selective tuning, but a structured block decomposition of parameter space into one nonlinear block per neuron (Park et al., 2022).

5. Distributed execution and hardware-aware placement

In sparse deep neural networks, row-wise partitioning of weight matrices is effectively neuron-wise partitioning because each row of $j$17 corresponds to one destination neuron in layer $j$18. If processor $j$19 owns a subset of rows, it owns the corresponding destination neurons, computes their pre-activations $j$20, activations $j$21, local error entries $j$22, and local SGD updates. Feedforward performs distributed sparse matrix-vector multiplication $j$23, with communication sets $j$24 and $j$25 specifying which source activations must be exchanged; backpropagation computes $j$26 and sends partial sums back to the owners of predecessor neurons. A hypergraph $j$27 models row vertices, column nets, and fixed vertices so that minimizing the connectivity cut $j$28 with $j$29 exactly minimizes total communication volume for forward and backward passes together. Compared with random row assignment, hypergraph-based neuron assignment reduces average or total communication volume by about $j$30–$j$31 for $j$32, $j$33–$j$34 for $j$35, $j$36–$j$37 for $j$38, and $j$39–$j$40 for $j$41, while runtime improves by about $j$42–$j$43, $j$44–$j$45, $j$46–$j$47, and $j$48–$j$49, respectively (Demirci et al., 2021).

On neuromorphic hardware, the primary decision variable can also be neuron assignment. In one approach, $j$50 indicates whether neuron $j$51 is assigned to crossbar $j$52, with search-space dimension $j$53. Synapses become local when both endpoint neurons map to the same crossbar and global otherwise, so local/global synapse partitioning is induced by neuron placement. The optimization minimizes total spikes on the global synapse interconnect, effectively a weighted graph cut in which the edge weight is the number of spike events $j$54. Compared with PACMAN, this gives average global interconnect energy improvement of $j$55, and for realistic applications $j$56 on average; it also yields average $j$57 fewer ISI distortion cycles, average $j$58 lower spike disorder count, and $j$59 lower latency. A related but distinct method, eSpine, first uses Kernighan–Lin graph partitioning to produce crossbar-fit clusters of neurons and synapses and then maps clusters to tiles while maximizing the minimum effective lifetime $j$60. eSpine is therefore cluster-based rather than pure independent neuron-by-neuron partitioning, but it adds activation-ordered intra-crossbar placement so that highly active synapses are mapped to higher-endurance memristors. It reports $j$61 average effective lifetime improvement over SpiNeMap with average $j$62 higher total energy (Das et al., 2019, Titirsha et al., 2021).

6. Interpretability, dynamical state-space partitioning, and adjacent notions

Some influential uses of partitioning are neuron-derived but not literal neuron partitions. YASENN defines the stream of an input as $j$63, distills one decision tree per layer, and encodes each layer activation by a leaf index, producing the discretized stream $j$64. Because the finite number of unique codes induces a partitioning of the input space, each partition can then be described by interpretable models such as logistic regression or decision trees. The method therefore partitions inputs according to a sequence of layer-level activation states, not according to isolated neurons. The paper explicitly positions this as “somewhere between the local and the global scopes.” This clarifies an important boundary of the topic: activation-sequence-based partitioning is conceptually adjacent to neuron-wise partitioning, but the unit of partition identity is a stream code, not a single neuron (Zharov et al., 2018).

A more mechanistic but still distinct notion appears in large-scale spiking neuron circuits, where phase space is partitioned into stable flux tubes. The phase-space state is $j$65, and basin boundaries are pre-images of spike-time collision events involving connected neuron pairs. The critical perturbation strength is $j$66, and the characteristic basin diameter is $j$67. The typical basin diameter grows with inhibitory coupling strength and shrinks with the rate of spike events. This is neuron-wise partitioning only in a dynamical, event-induced sense: boundaries are attributed to spike-time collision motifs of connected neuron pairs rather than to a static modular decomposition (Touzel et al., 2017).

A further adjacent line partitions the input domain into sub-regions and assigns a separate subnetwork to each region. In piecewise INRs, an image is represented as $j$68 with hard masks $j$69 and $j$70. Partition rules include regular grids and semantic segmentation maps. The method is not neuron-wise, but it is a useful module-level analogue because it explicitly reduces the number of discontinuity boundaries each subnetwork must fit. On a $j$71 landscape image, PoS reaches a high PSNR in less than 100 steps whereas the original SIREN needs more than 500 steps to reach the same PSNR; for ReLU-MLP, the number of steps to reach PSNR 20 drops from 957 to 672 with PoG and to 445 with PoS. This suggests that some reported benefits of “partitioning” arise from subproblem simplification rather than from per-neuron decomposition per se (Liu et al., 2023).

7. Conceptual synthesis and recurring limitations

Across these literatures, neuron-wise partitioning serves at least five distinct purposes: increasing model-parallelism beyond layer count, separating functional roles of neurons under noisy or irrelevant evidence, imposing cross-subset alignment or regularization, structuring optimization into smaller subproblems, and reducing communication or endurance costs in distributed and hardware deployments. The partitioned objects are correspondingly different: channels or features inside a layer, FFN neurons, parameter subspaces, destination-neuron rows of sparse matrices, neurons assigned to crossbars, activation-sequence codes, or dynamical basins. This suggests that “neuron-wise partitioning” is best treated as a family resemblance term rather than a single canonical construction (Patel et al., 2023, Kim et al., 2 Apr 2026, Jia et al., 2019, Demirci et al., 2021).

Several limitations recur. Finer partition granularity often hurts accuracy or capacity unless additional mechanisms compensate: GN-DGL loses accuracy as group count increases; Neuro-RIT begins from heavily overlapping relevant and irrelevant neuron pools; RLAP is limited to a target FNN layer and includes a notational inconsistency in its sensitivity score; CorrReg treats only two-way partitions in the generic derivation; NPSC has its strongest theory and preconditioning result in one dimension; and hardware methods often optimize neuron placement only indirectly through communication or endurance objectives rather than through learned functional partitioning (Patel et al., 2023, Kim et al., 2 Apr 2026, Jin et al., 13 Jun 2025, Jia et al., 2019, Park et al., 2022, Titirsha et al., 2021). A plausible implication is that the practical value of neuron-wise partitioning depends less on partitioning itself than on the coupling mechanism that remains after partitioning—forward aggregation, detached communication, diversity penalties, gradient masks, regularized fine-tuning, or hardware-aware placement.

The literature therefore supports a narrow and a broad conclusion. Narrowly, strict neuron-wise partitioning is already technically instantiated in several incompatible but concrete forms: static attribution-based neuron sets, per-neuron subspace correction, retained-versus-pruned neuron splits, and neuron ownership in distributed sparse execution. Broadly, many nearby methods demonstrate that once neural computation is decomposed below the monolithic layer level, performance hinges on how isolation, communication, and specialization are balanced.