Reweighting MLP Blocks

• Reweighting MLP blocks are strategies that adapt the influence and structure of MLP modules using dynamic weighting, pruning, and parameter fine-tuning based on meta-learning.
• They enhance robust learning by automatically tuning sample importance and inducing structured sparsity to address class imbalance and noisy data.
• These methods facilitate efficient deployment in vision and transformer models through architectural shifts, gradient sparsification, and entropy-guided block adjustments.

Reweighting MLP blocks refers to the class of strategies that dynamically or structurally adapt the functional influence, sparsity, and/or training signals within multi-layer perceptron (MLP) modules or blocks. This encompasses learned sample weighting (for robust learning), structured or dynamic pruning, architectural modulation to favor certain information pathways, data-dependent dynamic weighting at the block or sample level, and PEFT (parameter-efficient fine-tuning) strategies that adapt the effective influence of subsets of MLP parameters. Methods in this area are grounded in meta-learning, adaptive regularization, structured parameterization, and sparse and block-wise gradient methodologies.

1. Adaptive Sample Reweighting via Meta-Learned MLPs

A foundational approach to reweighting in MLP-based networks is provided by Meta-Weight-Net (MW-Net), which employs a MLP block as an explicit, adaptable weighting function to assign importance to each sample based on its training loss. The MW-Net strategy bypasses the need to predefine weighting heuristics by parameterizing the sample weighting function as a single-hidden-layer MLP (input: scalar loss; 100 hidden units, ReLU; output: sigmoid activation for weights). This MLP serves as a universal approximator for continuous weighting functions, allowing it to match or exceed the adaptivity of conventional weighting schemes.

The MW-Net optimizes two objectives in tandem:

• The main DNN parameters are updated with losses weighted by MLP output:

$$\mathbf{w}^*(\Theta) = \arg\min_{\mathbf{w}} \frac{1}{N} \sum_{i=1}^N \mathcal{V}(L^{\text{train}}_i(\mathbf{w});\,\Theta)\,L^{\text{train}}_i(\mathbf{w})$$

• The MLP’s parameters $\Theta$ are meta-learned to minimize validation loss on an unbiased small meta-set:

$$\Theta^* = \arg\min_{\Theta} \frac{1}{M} \sum_{i=1}^M L^{\text{meta}}_i(\mathbf{w}^*(\Theta))$$

The learned weighting function adapts automatically to data regimes:

• For class imbalance, it generally yields an increasing weighting function, prioritizing hard, minority-class instances.
• For label noise, it learns a decreasing function, thus discounting probable outliers.
• For complex real-world biases, it can synthesize non-monotonic weighting shapes.

Unlike traditional methods, this approach obviates manual tuning and is validated by empirical superiority on class-imbalanced and noisy-label real and synthetic datasets.

2. Structured and Dynamic Reweighting for Efficient Inference

Block-based structured reweighting and pruning are critical for large-scale DNNs where resource constraints matter. BLK-REW exemplifies this by partitioning MLP (and other DNN) weight matrices into multiple blocks (e.g., $m\times n$) and then applying iterative, data-adaptive (reweighted) group lasso penalties. The regularization penalty for each block row or column is scaled as the inverse squared L2-norm, thus adapting the force of regularization away from significant (large-magnitude) blocks and towards unimportant (small-magnitude) ones: $$(\mathcal{P}_i^{(t+1)})_p = \frac{1}{\|[\mathbf{W}_{ij}]_{p,:}^{(t)}\|_2^2 + \epsilon}$$ This induces sparsity in less informative structures while guarding critical computation. The dynamic update, combined with block-level manipulation, improves training speed, accuracy retention at high compression ratios (e.g., $50\times$ on VGG-16, no accuracy drop), and enables the use of compiler-level acceleration for real-time inference on mobile and edge hardware.

Compared to L1/group lasso (which lack adaptivity and can indiscriminately eliminate important weights), or ADMM (which is slower and requires manual per-layer constraint tuning), BLK-REW’s block-adaptive approach leads to both universality (CNNs, RNNs, MLPs) and improved hardware utilization.

3. Reweighting in Vision-Focused MLP Block Design

Several architectural innovations introduce blockwise reweighting operations in vision-oriented MLPs, emphasizing spatial context and selectivity:

• AS-MLP axially shifts channel groups spatially before the point-wise MLP. This selective, shift-then-reweight pattern controls the receptive field granularity— unlike fully-global “patch-mixing” MLPs—allowing explicit parameterization of locality and dilation. The learnable MLP after shift acts to reweight local spatial feature neighborhoods in a data-adaptive, low-overhead manner.
• Hire-MLP employs hierarchical rearrangement: local feature rearrangement within spatial regions via channel concat–MLP–restore, followed by cross-region circular shifting to periodically mix features globally. This stepping workflow dynamically reweights which spatial tokens co-interact per MLP block, facilitating local-global exchange without attention.
• Round-Roll MLP (R$^2$-MLP) generalizes to multi-view tasks by rolling channel groups along the view axis. Purely via channel and spatial shifting, it enables information propagation across spatial and view dimensions (parameter-free), thus implicitly reweighting both local and inter-view representations.

These architectures, through their selective spatial/temporal rearrangements and channel grouping, operationalize block reweighting by structuring the functional exchange patterns prior to the MLP block, followed by learnable mixing.

4. Sparsity-Induced and Structure-Aware Reweighting

Recent research reveals that sparseness—whether explicit or implicit—serves a critical regularization and reweighting role in high-performing wide MLP architectures:

• MLP-Mixer and its subsequent analysis show that Mixer blocks effectively operate as extremely wide, highly sparse MLPs, utilizing Kronecker-product or Monarch-structured weights. This structure provides an implicit sparse regularization, which is mathematically shown (in the linear case) to induce L1-like effects, biasing solutions toward sparse connectivity without explicit penalty.
• Empirically, Mixers with structural (Kronecker/Monarch) sparsity exhibit performance and internal representation similarities nearly indistinguishable from unstructured sparse MLPs, provided width is scaled correspondingly.
• Design guidance from such findings suggests that, for a fixed number of parameter connections, maximizing width and enforcing or respecting sparsity/blockwise structure in the MLP block—thereby inducing selective reweighting by connection pattern—improves both generalization and efficiency.

5. Fine-Tuning and Gradient-Level Reweighting in Large-Scale MLPs

Reweighting is also central to PEFT (parameter-efficient fine-tuning) for transformer-scale MLPs:

• SparseGrad targets MLP blocks by transforming weight gradients into a basis (obtained via HOSVD) where only $\sim$1% of gradient elements are significant, and then updating only these parameters:

$$\widetilde{W}^T = U W^T V^T, \qquad \frac{\partial L}{\partial \widetilde{W}}_{\text{sparse}} = S \odot \frac{\partial L}{\partial \widetilde{W}}$$

where $S$ retains the top-$k$ elements. This procedure delivers maximal adaptation for MLP-heavy layers at minimal memory cost, outperforming LoRA and MeProp in GLUE (BERT, RoBERTa, LLaMa-2), with the benefit attributed to basis-induced sparsity not realized by MeProp.

• Compared to LoRA (which adds low-rank adapters, usually in attention blocks) and MeProp (which keeps top-$k$ dense gradients without basis transformation), SparseGrad’s reweighting ensures only the most impactful directions (in the discovered basis) are adapted, thus increasing both memory efficiency and adaptation quality.

6. Entropy-Guided and Data-Driven Block-Level Reweighting in Transformers

MLP block reweighting plays a unique role in transformer simplification:

• By quantifying feature entropy in each layer, it is possible to identify attention blocks whose information content is redundant with following MLPs.
• Low-entropy attention layers can be "degenerate" into identity, assigning the subsequent MLP block responsibility for absorbing their functional role. This is achieved by gradually blending out attention during training and enhancing the expressivity of the MLP:

$$f_{\text{attn}} = M \odot \text{Attn}(\boldsymbol{x}) + (2-M)\odot \boldsymbol{x}$$

As $M \rightarrow 0$, the block becomes "MLP-only."

• Across DeiT-B and similar architectures, up to 40% of attention blocks were removed without accuracy loss (ImageNet-1k), with substantial increases in throughput and memory efficiency.

Greedy search based on transfer entropy ensures only non-critical blocks are reweighted in this manner, preserving final performance and offering practical speed/memory benefits.

7. Practical Implications and Future Directions

• In robust learning and noisy or imbalanced data regimes, learned sample reweighting MLPs facilitate automatic, data-adaptive importance modeling.
• For efficient inference, block-aware reweighted pruning (BLK-REW) and sparsity-enforcing schemes offer strong accuracy/efficiency trade-offs and hardware compliance.
• Vision MLPs benefit from structured reweighting (axial shift, region-wise mixing, channel grouping, patch rotation)—balancing local and global information, and accommodating multi-view or multimodal data efficiently.
• Sparsity and width-centric design principles, with structure-aware reweighting, should guide parameter and resource allocation when scaling up MLPs.
• PEFT should incorporate MLP block reweighting—not just adapt attention—since MLPs comprise a large proportion of model parameters and can be selectively fine-tuned with considerable efficiency gains.
• Data-driven, entropy- or information-theoretic approaches to reweighting at the block level can yield simplified, faster transformer architectures without loss of accuracy.

In sum, reweighting MLP blocks encompasses a broad spectrum of methods—ranging from learned sample importance to structural pruning, architectural restructuring, dynamic adaptation, gradient sparsification, and automated network simplification—all with strong empirical and theoretical foundations in recent literature. These methods enable robust, efficient, and adaptive deep learning across supervised, transfer, and large-scale settings.