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.

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.

We visualize the attention map of ViT(Dic-Attn).