Attention mechanisms have achieved significant empirical success in multiple fields, but their underlying optimization objectives remain unclear yet. Moreover, the quadratic complexity of self-attention has become increasingly prohibitive. Although interpretability and efficiency are two mutually reinforcing pursuits, prior work typically investigates them separately. In this paper, we propose a unified optimization objective that derives inherently interpretable and efficient attention mechanisms through algorithm unrolling. Precisely, we construct a gradient step of the proposed objective with a set of forward-pass operations of our Contractand-Broadcast Self-Attention (CBSA), which compresses input tokens towards low-dimensional structures by contracting a few representatives of them. This novel mechanism can not only scale linearly by fixing the number of representatives, but also covers the instantiations of varied attention mechanisms when using different sets of representatives. We conduct extensive experiments to demonstrate comparable performance and superior advantages over black-box attention mechanisms on visual tasks.

Prompt-based learning has emerged as a parameter-efficient finetuning (PEFT) approach to facilitate Large Language Model (LLM) adaptation to downstream tasks by conditioning generation with task-aware guidance. Despite its successes, current prompt-based learning methods heavily rely on laborious grid searching for optimal prompt length and typically require considerable number of prompts, introducing additional computational burden. Worse yet, our pioneer findings indicate that the task-aware prompt design is inherently limited by its absence of instance-aware information, leading to a subtle attention interplay with the input sequence. In contrast, simply incorporating instance-aware information as a part of the guidance can enhance the prompt-tuned model performance without additional fine-tuning. Moreover, we find an interesting phenomenon, namely "attention anchor," that incorporating instance-aware tokens at the earliest position of the sequence can successfully preserve strong attention to critical structural information and exhibit more active attention interaction with all input tokens. In light of our observation, we introduce Capsule Prompt-Tuning (CaPT), an efficient and effective solution that leverages off-the-shelf, informative instance semantics into prompt-based learning. Our approach innovatively integrates both instanceaware and task-aware information in a nearly parameter-free manner (i.e., one single capsule prompt). Empirical results demonstrate that our method can exhibit superior performance across various language tasks (e.g., 84.03% average accuracy on T5-Large), serving as an "attention anchor," while enjoying high parameter efficiency (e.g., 0.003% of model parameters on Llama3.2-1B).

Input saliency aims to quantify the influence of input tokens on the output of large language models (LLMs), which has been widely used for prompt engineering, model interpretability, and behavior attribution. Despite the proliferation of saliency techniques, the field lacks a standardized and rigorous evaluation protocol. In this work, we introduce a stress-testing framework inspired by the needle-in-a-haystack (NIAH) setting to systematically assess the reliability of seven popular input saliency methods. Our evaluation reveals a surprising and critical flaw: existing methods consistently assign non-trivial importance to irrelevant context, and this attribution error worsens as input length increases. To address this issue, we propose a novel saliency method based on Attention Bias Optimization (ours), which explicitly optimizes the attention bias associated with each input token to quantify its causal impact on target token generation. ABO robustly outperforms existing methods by 10\sim30% in saliency accuracy across diverse NIAH tasks, maintains effectiveness up to 10K-token prompts, and enables practical applications including zero-shot detoxification, sentiment steering, and reasoning-error correction. Our findings highlight the limitations of prevalent attribution methods and establish ABO as a principled alternative for accurate token attribution.

Low-rank adaptation (LoRA) is a parameter-efficient fine-tuning (PEFT) method widely used in large language models (LLMs). LoRA essentially describes the projection of an input space into a low-dimensional output space, with the dimensionality determined by the LoRA rank. In standard LoRA, all input tokens share the same weights and undergo an identical input-output projection. This limits LoRA's ability to capture token-specific information due to the inherent semantic differences among tokens. To address this limitation, we propose **Token-wise Projected Low-Rank Adaptation (TopLoRA)**, which dynamically adjusts LoRA weights according to the input token, thereby learning token-wise input-output projections in an end-to-end manner. Formally, the weights of TopLoRA can be expressed as $B\Sigma_X A$, where $A$ and $B$ are low-rank matrices (as in standard LoRA), and $\Sigma_X$ is a diagonal matrix generated from each input token $X$. Notably, TopLoRA does not increase the rank of LoRA weights but achieves more granular adaptation by learning token-wise LoRA weights (i.e., token-wise input-output projections). Extensive experiments across multiple models and datasets demonstrate that TopLoRA consistently outperforms LoRA and its variants.

Since the proposal of transformers (Vaswani et al., 2017), these models have been limited to bounded input lengths, because of their need to attend to every token in the input. In this work, we propose Unlimiformer: a general approach that wraps any existing pretrained encoder-decoder transformer, and offloads the cross-attention computation to a single k-nearest-neighbor (kNN) index, while the returned kNN distances are the attention dot-product scores. This kNN index can be kept on either the GPU or CPU memory and queried in sub-linear time; this way, we can index practically unlimited input sequences, while every attention head in every decoder layer retrieves its top-k keys, instead of attending to every key. We evaluate Unlimiformer on several long-document and book-summarization benchmarks, showing that it can process even 500k token-long inputs from the BookSum dataset, without any input truncation at test time. We demonstrate that Unlimiformer improves pretrained models such as BART (Lewis et al., 2020a) and Longformer (Beltagy et al., 2020) by extending them to unlimited inputs without additional learned weights and without modifying their code. Our code and models are publicly available, and support LLaMA-2 as well2.

RL T efficiently finds and removes'runs' of patches that are repeated over time prior to model inference, then replaces them with a single patch and a positional encoding to represent the resulting token's new length.

Vision Transformers (ViTs) have shown impressive performance and have become a unified backbone for multiple vision tasks. However, both the attention mechanism and multi-layer perceptrons (MLPs) in ViTs are not sufficiently efficient due to dense multiplications, leading to costly training and inference. To this end, we propose to reparameterize pre-trained ViTs with a mixture of multiplication primitives, e.g., bitwise shifts and additions, towards a new type of multiplication-reduced model, dubbed $\textbf{ShiftAddViT}$, which aims to achieve end-to-end inference speedups on GPUs without requiring training from scratch. Specifically, all $\texttt{MatMuls}$ among queries, keys, and values are reparameterized using additive kernels, after mapping queries and keys to binary codes in Hamming space. The remaining MLPs or linear layers are then reparameterized with shift kernels.

This paper presents a mathematical interpretation of self-attention by connecting it to distributional semantics principles. We show that self-attention emerges from projecting corpus-level co-occurrence statistics into sequence context. Starting from the co-occurrence matrix underlying GloVe embeddings, we demonstrate how the projection naturally captures contextual influence, with the query-key-value mechanism arising as the natural asymmetric extension for modeling directional relationships. Positional encodings and multi-head attention then follow as structured refinements of this same projection principle. Our analysis demonstrates that the Transformer architecture's particular algebraic form follows from these projection principles rather than being an arbitrary design choice.