In this paper, we contend that the objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a mixture of low-dimensional Gaussian distributions supported on incoherent subspaces. The quality of the final representation can be measured by a unified objective function called sparse rate reduction. From this perspective, popular deep networks such as transformers can be naturally viewed as realizing iterative schemes to optimize this objective incrementally. Particularly, we show that the standard transformer block can be derived from alternating optimization on complementary parts of this objective: the multi-head self-attention operator can be viewed as a gradient descent step to compress the token sets by minimizing their lossy coding rate, and the subsequent multi-layer perceptron can be viewed as attempting to sparsify the representation of the tokens. This leads to a family of white-box transformer-like deep network architectures which are mathematically fully interpretable. Despite their simplicity, experiments show that these networks indeed learn to optimize the designed objective: they compress and sparsify representations of large-scale real-world vision datasets such as ImageNet, and achieve performance very close to thoroughly engineered transformers such as ViT.

A.1 Dataset Details & Evaluation Metrics As stated earlier, the main application of Extreme Multi-label Text Classification is in e-commerce - product recommendation and dynamic search advertisement - and in document tagging, where the objective of an algorithm is to correctly recommend/advertise among the top-k slots. Thus, for evaluation of the methods, we use precision at k (denoted by P@k), and its propensity scored variant (denoted by PSP@k) [17]. These are standard and widely used metrics by the XMC community [4]. Since P@k treats all the labels equally, it doesn't reveal the performance of the model on tail labels. However, because of the long-tailed distribution in XMC datasets, one of the main challenges is to predict tail labels correctly, which may be more valuable and informative compared to head classes.

Yiwen Guo leads the project and serves as the corresponding author.

Convolutional neural networks (CNNs) haveso far been the de-facto model for visualdata. Recent workhasshownthat(Vision)Transformer models (ViT)can achieve comparable or even superior performance on image classification tasks.

Large Vision-Language Models (LVLMs) have advanced multimodal learning but face high computational costs due to the large number of visual tokens, motivating token pruning to improve inference efficiency. The key challenge lies in identifying which tokens are truly important. Most existing approaches rely on attention-based criteria to estimate token importance. However, they inherently suffer from certain limitations, such as positional bias. In this work, we explore a new perspective on token importance based on token transitions in LVLMs. We observe that the transition of token representations provides a meaningful signal of semantic information. Based on this insight, we propose TransPrune, a training-free and efficient token pruning method. Specifically, TransPrune progressively prunes tokens by assessing their importance through a combination of Token Transition Variation (TTV)-which measures changes in both the magnitude and direction of token representations-and Instruction-Guided Attention (IGA), which measures how strongly the instruction attends to image tokens via attention. Extensive experiments demonstrate that TransPrune achieves comparable multimodal performance to original LVLMs, such as LLaVA-v1.5 and LLaVA-Next, across eight benchmarks, while reducing inference TFLOPs by more than half. Moreover, TTV alone can serve as an effective criterion without relying on attention, achieving performance comparable to attention-based methods. The code will be made publicly available upon acceptance of the paper at https://github.com/liaolea/TransPrune.