Multiplicative gating is widely used in neural architectures and has recently been applied to attention layers to improve performance and training stability in large language models. Despite the success of gated attention, the mathematical implications of gated attention mechanisms remain poorly understood. We study attention through the geometry of its representations by modeling outputs as mean parameters of Gaussian distributions and analyzing the induced Fisher--Rao geometry. We show that ungated attention operator is restricted to intrinsically flat statistical manifolds due to its affine structure, while multiplicative gating enables non-flat geometries, including positively curved manifolds that are unattainable in the ungated setting. These results establish a geometric expressivity gap between ungated and gated attention. Empirically, we show that gated models exhibit higher representation curvature and improved performance on tasks requiring nonlinear decision boundaries whereas they provide no consistent advantage on tasks with linear decision boundaries. Furthermore, we identify a structured regime in which curvature accumulates under composition, yielding a systematic depth amplification effect.

Diffusion Transformers (DiT) excel at image and video generation but face computational challenges due to the quadratic complexity of self-attention operators. We propose DiTFastAttn, a post-training compression method to alleviate the computational bottleneck of DiT.

We develop a unified mathematical framework for certified Top-$k$ attention truncation that quantifies approximation error at both the distribution and output levels. For a single attention distribution $P$ and its Top-$k$ truncation $\hat P$, we show that the total-variation distance coincides with the discarded softmax tail mass and satisfies $\mathrm{TV}(P,\hat P)=1-e^{-\mathrm{KL}(\hat P\Vert P)}$, yielding sharp Top-$k$-specific bounds in place of generic inequalities. From this we derive non-asymptotic deterministic bounds -- from a single boundary gap through multi-gap and blockwise variants -- that control $\mathrm{TV}(P,\hat P)$ using only the ordered logits. Using an exact head-tail decomposition, we prove that the output error factorizes as $\|\mathrm{Attn}(q,K,V)-\mathrm{Attn}_k(q,K,V)\|_2=τ\|μ_{\mathrm{tail}}-μ_{\mathrm{head}}\|_2$ with $τ=\mathrm{TV}(P,\hat P)$, yielding a new head-tail diameter bound $\|\mathrm{Attn}(q,K,V)-\mathrm{Attn}_k(q,K,V)\|_2\leτ\,\mathrm{diam}_{H,T}$ and refinements linking the error to $\mathrm{Var}_P(V)$. Under an i.i.d. Gaussian score model $s_i\sim\mathcal N(μ,σ^2)$ we derive closed-form tail masses and an asymptotic rule for the minimal $k_\varepsilon$ ensuring $\mathrm{TV}(P,\hat P)\le\varepsilon$, namely $k_\varepsilon/n\approxΦ_c(σ+Φ^{-1}(\varepsilon))$. Experiments on bert-base-uncased and synthetic logits confirm the predicted scaling of $k_\varepsilon/n$ and show that certified Top-$k$ can reduce scored keys by 2-4$\times$ on average while meeting the prescribed total-variation budget.

As training billion-scale transformers becomes increasingly common, employing multiple distributed GPUs along with parallel training methods has become a standard practice. However, existing transformer designs suffer from significant communication overhead, especially in Tensor Parallelism (TP), where each block's MHA-MLP connection requires an all-reduce communication. Through our investigation, we show that the MHA-MLP connections can be bypassed for efficiency, while the attention output of the first layer can serve as an alternative signal for the bypassed connection. Motivated by the observations, we propose FAL (First Attentions Last), an efficient transformer architecture that redirects the first MHA output to the MLP inputs of the following layers, eliminating the per-block MHA-MLP connections. This removes the all-reduce communication and enables parallel execution of MHA and MLP on a single GPU. We also introduce FAL+, which adds the normalized first attention output to the MHA outputs of the following layers to augment the MLP input for the model quality. Our evaluation shows that FAL reduces multi-GPU training time by up to 44%, improves single-GPU throughput by up to 1.18x, and achieves better perplexity compared to the baseline GPT. FAL+ achieves even lower perplexity without increasing the training time than the baseline. Codes are available at: https://github.com/CASL-KU/FAL

The attention mechanism of a transformer has a quadratic complexity, leading to high inference costs and latency for long sequences. However, attention matrices are mostly sparse, which implies that many entries may be omitted from computation for efficient inference. Sparse attention inference methods aim to reduce this computational burden; however, they also come with a troublesome performance degradation. We discover that one reason for this degradation is that the sparse calculation induces a distributional shift in the attention outputs. The distributional shift causes decoding-time queries to fail to align well with the appropriate keys from the prefill stage, leading to a drop in performance. We propose a simple, novel, and effective procedure for correcting this distributional shift, bringing the distribution of sparse attention outputs closer to that of quadratic attention. Our method can be applied on top of any sparse attention method, and results in an average 36%pt performance increase, recovering 88% of quadratic attention accuracy on the 131K RULER benchmark when applied on top of sliding window attention with sink tokens while only adding a small overhead. Our method can maintain approximately 98.5% sparsity over full quadratic attention, making our model 32 times faster than Flash Attention 2 when processing 1M token prefills.

Deterministically controlling the target generation language of large multilingual language models (LLMs) remains a fundamental challenge, particularly in zero-shot settings where neither explicit language prompts nor fine-tuning are available. In this work, we investigate whether sparse autoencoder (SAE) features, previously shown to correlate with interpretable model behaviors, can be leveraged to steer the generated language of LLMs during inference. Leveraging pretrained SAEs on the residual streams of Gemma-2B and Gemma-9B, we identify features whose activations differ most significantly between English and four target languages: Chinese, Japanese, Spanish, and French. By modifying just a single SAE feature at one transformer layer, we achieve controlled language shifts with up to 90\% success, as measured by FastText language classification, while preserving semantic fidelity according to LaBSE (Language-Agnostic BERT Sentence Embedding) similarity. Our analysis reveals that language steering is most effective in mid-to-late transformer layers and is amplified by specific attention heads disproportionately associated with language-sensitive SAE features. These results demonstrate the promise of sparse feature steering as a lightweight and interpretable mechanism for controllable multilingual generation.

Transformers' quadratic computational complexity limits their scalability despite remarkable performance. While linear attention reduces this to linear complexity, pre-training such models from scratch remains, in most cases, prohibitively expensive. Recent post-training linearisation methods convert pre-trained Transformers to linear models efficiently, often using hybrid approaches that combine linear attention with sliding-window softmax. We identify a critical flaw: existing hybrid methods inadvertently bypass the linear component, relying almost entirely on SWA. Component-level diagnostics reveal this previously undetected behaviour stems from overlooked evaluation practices on common-sense benchmarks. We propose three solutions to ensure balanced component usage: (i) inference-time hybridisation of linear-only conversions with sliding-window softmax; (ii) HedgeCATs, combining attention-weight transfer with targeted LoRA fine-tuning; and (iii) Scheduled Sliding-window Dropout (SSD), which stochastically suppresses the softmax branch during training to prevent component collapse. Our methods maintain computational efficiency while recovering most base model performance and ensuring genuine linear attention adoption, restoring the validity of performance attributions in hybrid conversions.

Large language models (LLMs) with extended context windows enable powerful downstream applications but impose significant memory overhead, as caching all key-value (KV) states scales linearly with sequence length and batch size. Existing cache eviction methods address this by exploiting attention sparsity, yet they typically rank tokens heuristically using accumulated attention weights without considering their true impact on attention outputs. We propose Optimal Brain Cache (OBCache), a principled framework that formulates cache eviction as a layer-wise structured pruning problem. Building upon the Optimal Brain Damage (OBD) theory, OBCache quantifies token saliency by measuring the perturbation in attention outputs induced by pruning tokens, with closed-form scores derived for isolated keys, isolated values, and joint key-value pairs. Our scores account not only for attention weights but also for information from value states and attention outputs, thereby enhancing existing eviction strategies with output-aware signals. Experiments on LLaMA and Qwen models demonstrate that replacing the heuristic scores in existing works, which estimate token saliency across different query positions, with OBCache's output-aware scores consistently improves long-context accuracy.