Despite the prevalence of the attention sink phenomenon in Large Language Models (LLMs), where initial tokens disproportionately monopolize attention scores, its structural origins remain elusive. This work provides a \textit{mechanistic explanation} for this phenomenon. First, we trace its root to the value aggregation process inherent in self-attention, which induces a systematic variance discrepancy. We further demonstrate that this discrepancy is drastically amplified by the activation of super neurons within Feed-Forward Network (FFN) layers. Specifically, the channel-sparse down-projections trigger a dimension disparity of the first-token representation, necessitating the formation of attention sinks as a structural anchor. Then, we validate this causal chain through two controlled interventions: (i) isolating the aggregation effect via attention mask modifications and (ii) amplifying the variance of targeted token representations. Both interventions can replicate attention sinks at arbitrary positions. Our mechanistic understanding offers a foundation for the systematic control of sink formation. Finally, as a proof of concept, we propose \textit{head-wise RMSNorm}, an architectural modification that stabilizes value aggregation outputs during pre-training. Our experiments demonstrate that restoring statistical parity across positions significantly accelerates convergence.

We generalize the attention mechanism by viewing it through the lens of Entropic Optimal Transport, revealing that standard attention corresponds to a transport problem regularized by an implicit uniform prior. We introduce Generalized Optimal transport Attention with Trainable priors (GOAT), a new attention mechanism that replaces this naive assumption with a learnable, continuous prior. This prior maintains full compatibility with optimized kernels such as FlashAttention. GOAT also provides an EOT-based explanation of attention sinks and materializes a solution for them, avoiding the representational trade-offs of standard attention. Finally, by absorbing spatial information into the core attention computation, GOAT learns an extrapolatable prior that combines the flexibility of learned positional embeddings with the length generalization of fixed encodings.

Transformers and more specifically decoder-only transformers dominate modern LLM architectures. While they have shown to work exceptionally well, they are not without issues, resulting in surprising failure modes and predictably asymmetric performance degradation. This article is a study of many of these observed failure modes of transformers through the lens of graph neural network (GNN) theory. We first make the case that much of deep learning, including transformers, is about learnable information mixing and propagation. This makes the study of model failure modes a study of bottlenecks in information propagation. This naturally leads to GNN theory, where there is already a rich literature on information propagation bottlenecks and theoretical failure modes of models. We then make the case that many issues faced by GNNs are also experienced by transformers. In addition, we analyze how the causal nature of decoder-only transformers create interesting geometric properties in information propagation, resulting in predictable and potentially devastating failure modes. Finally, we observe that existing solutions in transformer research tend to be ad-hoc and driven by intuition rather than grounded theoretical motivation. As such, we unify many such solutions under a more theoretical perspective, providing insight into why they work, what problem they are actually solving, and how they can be further improved to target specific failure modes of transformers. Overall, this article is an attempt to bridge the gap between observed failure modes in transformers and a general lack of theoretical understanding of them in this space. Much of modern deep learning can be understood as the study of learnable information mixing and propagation, a perspective that unifies seemingly disparate architectures under a common lens.

Masked Diffusion Language Models (DLMs) have recently emerged as a promising alternative to traditional Autoregressive Models (ARMs). DLMs employ transformer encoders with bidirectional attention, enabling parallel token generation while maintaining competitive performance. Although their efficiency and effectiveness have been extensively studied, the internal mechanisms that govern DLMs remain largely unexplored. In this work, we conduct an empirical analysis of DLM attention patterns, focusing on the attention sinking phenomenon, an effect previously observed in various transformer-based architectures. Our findings reveal that DLMs also exhibit attention sinks, but with distinct characteristics. First, unlike in ARMs, the sink positions in DLMs tend to shift throughout the generation process, displaying a dynamic behaviour. Second, while ARMs are highly sensitive to the removal of attention sinks, DLMs remain robust: masking sinks leads to only a minor degradation in performance. These results provide new insights into the inner workings of diffusion-based language models and highlight fundamental differences in how they allocate and utilize attention compared to autoregressive models.

Current motion-conditioned video generation methods suffer from prohibitive latency (minutes per video) and non-causal processing that prevents real-time interaction. We present MotionStream, enabling sub-second latency with up to 29 FPS streaming generation on a single GPU. Our approach begins by augmenting a text-to-video model with motion control, which generates high-quality videos that adhere to the global text prompt and local motion guidance, but does not perform inference on the fly. As such, we distill this bidirectional teacher into a causal student through Self Forcing with Distribution Matching Distillation, enabling real-time streaming inference. Several key challenges arise when generating videos of long, potentially infinite time-horizons -- (1) bridging the domain gap from training on finite length and extrapolating to infinite horizons, (2) sustaining high quality by preventing error accumulation, and (3) maintaining fast inference, without incurring growth in computational cost due to increasing context windows. A key to our approach is introducing carefully designed sliding-window causal attention, combined with attention sinks. By incorporating self-rollout with attention sinks and KV cache rolling during training, we properly simulate inference-time extrapolations with a fixed context window, enabling constant-speed generation of arbitrarily long videos. Our models achieve state-of-the-art results in motion following and video quality while being two orders of magnitude faster, uniquely enabling infinite-length streaming. With MotionStream, users can paint trajectories, control cameras, or transfer motion, and see results unfold in real-time, delivering a truly interactive experience.

We present a novel technique for interpreting the neurons in CLIP-ResNet by decomposing their contributions to the output into individual computation paths. More specifically, we analyze all pairwise combinations of neurons and the following attention heads of CLIP's attention-pooling layer. We find that these neuron-head pairs can be approximated by a single direction in CLIP-ResNet's image-text embedding space. Leveraging this insight, we interpret each neuron-head pair by associating it with text. Additionally, we find that only a sparse set of the neuron-head pairs have a significant contribution to the output value, and that some neuron-head pairs, while polysemantic, represent sub-concepts of their corresponding neurons. We use these observations for two applications. First, we employ the pairs for training-free semantic segmentation, outperforming previous methods for CLIP-ResNet. Second, we utilize the contributions of neuron-head pairs to monitor dataset distribution shifts. Our results demonstrate that examining individual computation paths in neural networks uncovers interpretable units, and that such units can be utilized for downstream tasks.

Transformer-based vision encoders -- such as CLIP -- are central to multimodal intelligence, powering applications from autonomous web agents to robotic control. Since these applications often demand real-time processing of massive visual data, reducing the inference cost of vision encoders is critical. Quantization offers a practical path, but remains challenging even at 8-bit precision due to massive-scale activations (i.e., outliers). In this work, we propose $\textit{RegCache}$, a training-free algorithm that mitigates outliers in large-scale pretrained vision encoders and serves as a plug-in module that can be applied on top of other quantization methods. The proposed RegCache introduces outlier-prone yet semantically meaningless prefix tokens to the target vision encoder, which prevents other tokens from having outliers. Notably, we observe that outliers in vision encoders behave differently from those in language models, motivating two technical innovations: middle-layer prefixing and token deletion. Experiments show that our method consistently improves the accuracy of quantized models across both text-supervised and self-supervised vision encoders.

Leveraging the intrinsic importance differences among experts, recent research has explored expert-level compression techniques to enhance the efficiency of Mixture-of-Experts (MoE) large language models (LLMs). However, existing approaches often rely on empirical heuristics to identify critical experts, while lacking a deeper understanding into the heterogeneous importance of experts and the inner workings of MoE LLMs. In this study, we report, for the first time, the discovery and systematic investigation of a distinct subset of experts that play a pivotal role in the model's forward inference. These experts are prevalent in open-source MoE LLMs, and despite their extremely limited number, pruning them results in a substantial decline in model performance (e.g., prune just three out of 6,144 causes Qwen3-30B-A3B to generate repetitive and uninformative outputs). We refer to these experts as Super Experts (SEs). Our comprehensive analysis provides progressively deeper insights into SEs: (i) SEs are characterized by rare but extreme activation outliers in the output of the down proj, which give rise to massive activations in the hidden states between decoder layers. Moreover, the distribution of SEs is model-specific, data-agnostic, and remains unaffected by post-training processes. We show that, in MoE LLMs, SEs serve as the primary source of the systematic outlier mechanism in Transformers, and that compressing them profoundly disrupts this process, ultimately causing the collapse of attention sinks. These findings advance the understanding of the internal dynamics of MoE LLMs, filling an important gap in the current knowledge. In addition, we developed an automated tool for rapid and accurate SE profiling. Sparsely activated Mixture-of-Experts (MoE) models employ dynamic routing and sparse activation, demonstrating significant potential in enhancing the learning capacity of large language models (LLMs) (Cai et al., 2024; Mu & Lin, 2025). This paradigm has led to the development of state-of-the-art MoE LLMs, including DeepSeek (Guo et al., 2025; Liu et al., 2024b), Qwen (Y ang et al., 2025a), LongCat-Flash (Team et al., 2025) and others.

We investigate the mechanism underlying a previously identified phenomenon in Vision Transformers - the emergence of high-norm tokens that lead to noisy attention maps (Darcet et al., 2024). We observe that in multiple models (e.g., CLIP, DINOv2), a sparse set of neurons is responsible for concentrating high-norm activations on outlier tokens, leading to irregular attention patterns and degrading downstream visual processing. While the existing solution for removing these outliers involves retraining models from scratch with additional learned register tokens, we use our findings to create a training-free approach to mitigate these artifacts. By shifting the high-norm activations from our discovered register neurons into an additional untrained token, we can mimic the effect of register tokens on a model already trained without registers. We demonstrate that our method produces cleaner attention and feature maps, enhances performance over base models across multiple downstream visual tasks, and achieves results comparable to models explicitly trained with register tokens. We then extend test-time registers to off-the-shelf vision-language models, yielding cleaner attention-based, text-to-image attribution. Finally, we outline a simple mathematical model that reflects the observed behavior of register neurons and high norm tokens. Our results suggest that test-time registers effectively take on the role of register tokens at test-time, offering a training-free solution for any pre-trained model released without them.

Large language model (LLM) unlearning has become a critical mechanism for removing undesired data, knowledge, or behaviors from pre-trained models while retaining their general utility. Yet, with the rise of open-weight LLMs, we ask: can the unlearning process itself be backdoored, appearing successful under normal conditions yet reverting to pre-unlearned behavior when a hidden trigger is activated? Drawing inspiration from classical backdoor attacks that embed triggers into training data to enforce specific behaviors, we investigate backdoor unlearning, where models forget as intended in the clean setting but recover forgotten knowledge when the trigger appears. We show that designing such attacks presents unique challenges, hinging on where triggers are placed and how backdoor training is reinforced. We uncover a strong link between backdoor efficacy and the attention sink phenomenon, i.e., shallow input tokens consistently attract disproportionate attention in LLMs. Our analysis reveals that these attention sinks serve as gateways for backdoor unlearning: placing triggers at sink positions and aligning their attention values markedly enhances backdoor persistence. Extensive experiments validate these findings, showing that attention-sink-guided backdoor unlearning reliably restores forgotten knowledge in the presence of backdoor triggers, while behaving indistinguishably from a normally unlearned model when triggers are absent. Code is available at https://github.com/OPTML-Group/Unlearn-Backdoor.