Siyuan He, Bokai Yang, Jie Hu +2stat.ML cs.LG math.ST
Mixture-of-experts (MoE) architectures increase model capacity by combining a collection of expert predictors through input-dependent routing, while often activating only a small subset of experts for each input. Despite their growing importance in modern large-scale models, the statistical roles of their design choices, especially routing, sparse activation, and shared experts, remain only partially understood, as existing theory has largely focused on parametric or correctly specified MoE models. In this paper, we view MoE as a form of localized aggregation and show how this localization reshapes the approximation-estimation-computation tradeoff. We derive oracle risk bounds for learning dense and sparse routing with evolving experts, separating approximation, expert-learning, and router-estimation errors, and characterize how sparse Top-K routing can retain the benefits of localized aggregation while controlling per-input computation. We also interpret gating through the geometry of input space, relating routing performance to regions of local expert advantage, and show how shared experts, as adopted in architectures such as DeepSeekMoE, can extract common predictive structure so that routed experts focus on residual local variation. Together, these results provide a unified statistical framework for understanding MoE through input-dependent expert aggregation, in which expert specialization and computational tradeoffs are governed by local predictive structure.
Modularity in deep neural networks has been proposed as a means of improving both interpretability and training by promoting disentangled representations and reducing redundancy. In this work, we study the emergence of modular structure through competition dynamics between groups of neurons during training. We introduce a method that (i) maintains near-baseline accuracy, (ii) induces usage-based modularity by sparsely routing inputs to neuron groups, and (iii) encourages specialization of these modules, such that their activations are correlated with input classes. We evaluate the proposed approach on ImageNet-100 and CIFAR-100 and show that with it, specialized modules emerge without module-level supervision. These modules capture a meaningful high-level structure in the data, with individual modules responding to semantic categories (e.g., dogs or vehicles). We also study the emergence of a hierarchical partition of sub-tasks depending on the number of modules. Our results suggest that competitive dynamics can serve as a simple mechanism for inducing functional modularity in standard architectures.
Vision foundation backbones provide strong representations for dense prediction, yet a single shared feature still needs to support tasks with different, image-dependent adaptation requirements. We propose MemMTL, a multi-task dense prediction framework that estimates a compact task state from global visual context and refines it through a learnable task-state prototype memory. The refined state is converted into task-conditioned expert logits and combined with token-level logits before sparse top-$k$ selection over a local expert bank shared by all tasks. A separate task-agnostic residual bank provides a common adaptation path, and both paths are added once to the backbone feature before task-specific prediction. We specify a matched evaluation protocol on NYUD-v2 and PASCAL-Context with SAM 3 and ViT-L backbones to measure predictive quality, computational cost, and the contributions of task-state conditioning, prototype retrieval, and sparse routing. The numerical record in the present working draft predates this canonical implementation and must be regenerated before it can support empirical claims.
Deploying high-dimensional multimodal features in industrial recommender systems incurs substantial storage and latency overhead. Hard quantization is compact but introduces boundary distortion, whereas dense soft quantization couples representation quality to the limited storage budget. We propose Sparse Activation-based Residual Soft Quantization (SA-RSQ), which uses Top-K sparse routing and softmax weights to store compact (Index, Probability) tuples. The stored tuples decouple per-item storage from codebook dimensionality; for a fixed selected support, gradients propagate through the routing weights and weighted reconstruction without relying on a straight-through estimator. Experiments on a proprietary food-delivery advertising dataset show favorable reconstruction-performance and CTR trade-offs across storage budgets of 8-48 bytes per item. A preliminary Next-Distribution Prediction study and a one-week online A/B test further demonstrate the practical potential of SA-RSQ, with relative lifts of +2.51% in CTR and +3.66% in CPM.
Recent byte-level large language models (LLMs) have made tokenizer-free modeling increasingly competitive by grouping bytes into dynamically sized patches. However, existing byte-patch architectures still apply the same dense feed-forward computation to every patch. This uniform computation cannot adapt model capacity to variations in patch semantics and granularity. We address this limitation with EntropyMoE, a Mixture-of-Experts (MoE) architecture designed for dynamic byte patches. EntropyMoE replaces the dense feed-forward modules in the global patch Transformer with Top-K expert layers. Each dynamic patch serves as the basic unit of expert routing, and its byte coverage determines its contribution to workload accounting. The router selects experts directly from patch entropy, using the same granularity signal that underlies dynamic patch construction to organize sparse computation. Patch entropy and length jointly define the feature space for regulating expert specialization. Experiments show that EntropyMoE achieves the lowest held-out bits-per-byte among matched dense and sparse baselines while maintaining comparable downstream accuracy. These results establish patch entropy as an effective routing coordinate for sparse conditional computation and extend Mixture-of-Experts modeling beyond tokenizer-based representations.
Knowledge-intensive multimodal question answering (KI-MMQA) sits at the intersection of three expensive primitives: long visual token sequences, dense retrieval over large external corpora, and full cross-modal fusion. Existing systems pay all three costs uniformly per query, even though only a small fraction of visual content and retrieved knowledge is actually relevant to any given question. We introduce SKIP (Salient Knowledge-Injected Pathways), a unified inference architecture that routes computation along sparse pathways jointly conditioned on the question, the image, and a difficulty estimate. SKIP combines question-guided visual token pruning, region-conditional sparse retrieval, bipartite sparse cross-attention, and speculative knowledge verification with an adaptive budget controller that allocates compute proportional to predicted question difficulty. We derive an information-bottleneck bound showing that the optimal visual sparsity rate scales as $O(1/\sqrt{N})$ under realistic question-image mutual-information assumptions, with retained accuracy guarantees. Across five KI-MMQA benchmarks (OK-VQA, A-OKVQA, InfoSeek, Encyclopedic-VQA, and ViQuAE), SKIP matches or exceeds the accuracy of strong dense baselines while using $3.4$--$6.8\times$ fewer FLOPs and $2.7\times$ less end-to-end latency. Code available at: https://pmlrbd.github.io/skip/
Existing ViT-based weather forecasting models apply uniform computation across all spatial tokens, even though nearby atmospheric grid points often contain similar values and large regions evolve smoothly over time. This makes much of the intermediate per-token computation redundant. Standard token-efficiency methods, such as pruning or merging, reduce cost by removing or fusing tokens. However, weather forecasting is a spatiotemporal dense prediction problem in which a history of atmospheric states must be mapped to future values on the original latitude-longitude grid. Thus, every grid cell must retain a physically meaningful representation, especially under autoregressive rollout. We introduce Sparse-Reslim, a parameter-free plug-in routing module that makes sparse token processing compatible with this fixed-grid requirement. Sparse-Reslim routes only 25% of spatial tokens through the expensive middle transformer blocks and treats those blocks as residual updates: it computes the change produced for the routed tokens and scatters only this delta back to the full sequence. Unselected tokens keep their pre-routing representations exactly, so no grid cell is dropped or replaced by a mask token, and no fusion layer or additional parameters are introduced. Across ERA5 resolutions up to the operational 0.25\textdegree{} standard and two model families, a deterministic Transformer and a diffusion model, Sparse-Reslim improves forecast accuracy on every evaluated variable while substantially reducing cost: training is about 2.5x faster in the main settings and reaches 3.18x speedup at 0.25\textdegree{}, with over 2.2x lower peak memory. A controlled decomposition shows that the accuracy gain comes primarily from sparse routing itself, while random token selection provides an additional regularization benefit without selector overhead.
Implicit sentiment analysis is challenging because sentiment toward an aspect is often inferred from events rather than expressed through explicit opinion words. Existing models typically learn from the final polarity label, which provides limited guidance for reasoning about sentiment from the context. Motivated by cognitive appraisal theory, we propose an appraisal-aware multi-task learning (MTL) framework for implicit sentiment analysis that provides polarity prediction with two complementary auxiliary tasks: implicit sentiment detection and cognitive rationale generation. However, training several objectives with different targets and sharing a single backbone across tasks in MTL limits flexibility and can lead to task interference. To reduce interference among these related but distinct objectives, we adopt task-level mixture-of-experts models in which all tasks share a common set of experts, and task identity controls the sparse combination of these experts. Our method builds on an encoder-decoder architecture and replaces a subset of encoder and decoder blocks with these sparse mixtures. We use a task-conditioned router to select sparse expert mixtures for each task, and a task-separated routing objective to encourage different tasks to learn distinct expert-selection patterns. Experimental results show that our model outperforms recently proposed approaches, with strong gains on the implicit sentiment subset. Our code is available at https://github.com/yaping166/TRMoE-ISA.