Transformers with linear attention (i.e., linear transfor mers) and state-space models have recently been suggested as a viable linear-time alt ernative to transformers with softmax attention. However, these models still underp erform transformers especially on tasks that require in-context retrieval. Whil e more expressive variants of linear transformers which replace the additive upda te in linear transformers with the delta rule [DeltaNet; 101 ] have been found to be more effective at associative recall, existing algorithms for training such mode ls do not parallelize over sequence length and are thus inefficient to train on modern ha rdware. This work describes a hardware-efficient algorithm for training line ar transformers with the delta rule, which exploits a memory-efficient representati on for computing products of Householder matrices [ 11 ]. This algorithm allows us to scale up DeltaNet to standard language modeling settings. We train a 1.3B mode l for 100B tokens and find that it outperforms recent linear-time baselines su ch as Mamba [ 31 ] and GLA [ 124 ] in terms of perplexity and zero-shot performance on downst ream tasks. We also experiment with two hybrid models which combine Delt aNet layers with (1) sliding-window attention layers every other layer or (2) two global attention layers, and find that these hybrids outperform strong transf ormer baselines.

We introduce Image2Struct, a benchmark to evaluate vision-language models (VLMs) on extracting structure from images.

Current approaches to mitigate these representational harms balance the number of retrieved items across population groups defined by a small number of (often binary) attributes. However, most existing methods overlook intersectional groups determined by combinations of group attributes, such as gender, race, and ethnicity.

It also extends the traditional diffusion-based model, enabling the generation of samples conditioned on the block maxima, thereby enhancing the model's

To ensure quality, all charts and questions are handpicked, curated, and verified by human experts.

Work partially completed while at Microsoft Research.

Additionally, we introduce a Bézier-boundary gradient approximation strategy within our framework to keep the "differentiability"

Coded computing has emerged as a promising framework for tackling significant challenges in large-scale distributed computing, including the presence of slow, faulty, or compromised servers. In this approach, each worker node processes a combination of the data, rather than the raw data itself. The final result then is decoded from the collective outputs of the worker nodes. However, there is a significant gap between current coded computing approaches and the broader landscape of general distributed computing, particularly when it comes to machine learning workloads. To bridge this gap, we propose a novel foundation for coded computing, integrating the principles of learning theory, and developing a framework that seamlessly adapts with machine learning applications. In this framework, the objective is to find the encoder and decoder functions that minimize the loss function, defined as the mean squared error between the estimated and true values. Facilitating the search for the optimum decoding and functions, we show that the loss function can be upper-bounded by the summation of two terms: the generalization error of the decoding function and the training error of the encoding function. Focusing on the second-order Sobolev space, we then derive the optimal encoder and decoder.

Evaluating machine learning models requires evaluation data.