Router Sensitivity Under Lightweight Fine-Tuning Identifies Prunable Experts in Mixture-of-Experts Models

Mixture-of-Experts (MoE) models decouple total parameters from per-token compute, but deployment still requires storing every expert. Recent theory shows that pruning experts with the smallest router-norm changes during fine-tuning can preserve accuracy, but assumes full fine-tuning. We test whether lightweight adaptation can recover this signal. We briefly fine-tune with a parameter-efficient adapter, rank experts by the induced $\ell_2$ router change, and prune the least-changed experts in one shot. On Mixtral-8$\times$7B-Instruct (44.83% MMLU-Pro), router-only LoRA trains 0.002% of parameters and outperforms all-module LoRA at matched rank with half the experts removed (27.54% vs. 24.42%); signal quality declines as adaptation spreads to attention and expert weights. Accuracy improves monotonically with LoRA rank, reaching 28.76%. IA3, which leaves router weights frozen, matches direct router adaptation, whereas unconstrained additive adapters degrade the signal. Router-guided MMLU-Pro accuracy decays quasi-linearly rather than collapsing, remains nearly 1.8 times that of magnitude-based or random pruning at maximal compression, and reduces memory by 49% and per-token latency by 37%. At 25% compression, retention is competitive with methods using full activation statistics. The criterion also transfers to Qwen1.5-MoE fine-tuned for mathematics, retaining 49.7% mean accuracy over eleven benchmarks with half the experts removed while random pruning falls to single digits. Router sensitivity under lightweight fine-tuning therefore makes provably motivated expert pruning practical at scale.

Post-Grokking Collapse at the Representation-Readout Interface in Muon-Trained Transformers

Under the standard split, Muon gets hidden matrices and AdamW embeddings/output head. Muon groks modular addition faster, but its solutions do not hold. All nine configurations on $(a+b) \bmod 113$ grok and later lose generalization. Across five seeds the selected AdamW reference falls below threshold on four, reaching 27.59%. Instability persists across two moduli, two widths, two training fractions, subtraction, and depth. The failure arises at the representation-readout interface, identified only jointly up to an invertible map unselected by the loss. After solving the training set, the gradient falls to order $10^{-6}$ and the optimizers respond differently: step-size elasticity is -0.03 for Muon versus +1.5 for AdamW, and the Muon group moves 8.0 times faster per parameter. From bit-identical states, freezing either group prevents failure. Freezing embeddings/readout removes it in five runs over 451,400 post-grokking steps and five paired seeds: unfrozen arms record 137-321 sub-threshold evaluations, frozen arms none. Removing Muon's normalization and orthogonalization is no substitute: it collapses representation from 326 effective conjugate pairs to 4, shows no recurrent collapse, and fails terminally. Fourier filtering separates circuit failure from masking. Across 43 checkpoints over five seeds and three regimes, the task-aligned family reaches exactly 100% alone. In circuit failure it no longer solves the task; in masking it remains perfect while the full model reaches 45.85%, giving a positive margin on every example, including errors, but being outvoted by a near-equal adversarial remainder. Rescaling it restores 99.9%; grokking is the same condition resolving upward. The task selects the family, swapping $(k,k)$ for $(k,-k)$ under subtraction. Across an abrupt collapse, standard Fourier support is unchanged and the power-distribution cosine remains 0.9899.

Uncertainty-Aware Multimodal Emotion Recognition through Dirichlet Parameterization

In this work, we present a lightweight and privacy-preserving Multimodal Emotion Recognition (MER) framework designed for deployment on edge devices. To demonstrate framework's versatility, our implementation uses three modalities - speech, text and facial imagery. However, the system is fully modular, and can be extended to support other modalities or tasks. Each modality is processed through a dedicated backbone optimized for inference efficiency: Emotion2Vec for speech, a ResNet-based model for facial expressions, and DistilRoBERTa for text. To reconcile uncertainty across modalities, we introduce a model- and task-agnostic fusion mechanism grounded in Dempster-Shafer theory and Dirichlet evidence. Operating directly on model logits, this approach captures predictive uncertainty without requiring additional training or joint distribution estimation, making it broadly applicable beyond emotion recognition. Validation on five benchmark datasets (eNTERFACE05, MEAD, MELD, RAVDESS and CREMA-D) show that our method achieves competitive accuracy while remaining computationally efficient and robust to ambiguous or missing inputs. Overall, the proposed framework emphasizes modularity, scalability, and real-world feasibility, paving the way toward uncertainty-aware multimodal systems for healthcare, human-computer interaction, and other emotion-informed applications.