Visual Auto-Regressive modeling (VAR) has shown promise in bridging the speed and quality gap between autoregressive image models and diffusion models. VAR reformulates autoregressive modeling by decomposing an image into successive resolution scales. During inference, an image is generated by predicting all the tokens in the next (higher-resolution) scale, conditioned on all tokens in all previous (lower-resolution) scales. However, this formulation suffers from reduced image quality due to the parallel generation of all tokens in a resolution scale; has sequence lengths scaling superlinearly in image resolution; and requires retraining to change the sampling schedule.We introduce Hierarchical Masked AutoRegressive modeling (HMAR), a new image generation algorithm that alleviates these issues using next-scale prediction and masked prediction to generate high-quality images with fast sampling. HMAR reformulates next-scale prediction as a Markovian process, wherein the prediction of each resolution scale is conditioned only on tokens in its immediate predecessor instead of the tokens in all predecessor resolutions. When predicting a resolution scale, HMAR uses a controllable multi-step masked generation procedure to generate a subset of the tokens in each step. On ImageNet 256 × 256 and 512 × 512 benchmarks, HMAR models match or outperform parameter-matched VAR, diffusion, and autoregressive baselines. We develop efficient IO-aware block-sparse attention kernels that allow HMAR to achieve faster training and inference times over VAR by over 2.5× and 1.75× respectively, as well as over 3× lower inference memory foot-print. Finally, HMAR yields additional flexibility over VAR; its sampling schedule can be changed without further training, and it can be applied to image editing tasks in a zero-shot manner.

Fine-tuning large language models (LLMs) is increasingly costly as models scale to hundreds of billions of parameters, and even parameter-efficient fine-tuning (PEFT) methods like LoRA remain resource-intensive. We introduce LowRA, the first framework to enable LoRA fine-tuning below 2 bits per parameter with minimal performance loss. LowRA optimizes fine-grained quantization—mapping, threshold selection, and precision assignment—while leveraging efficient CUDA kernels for scalable deployment. Extensive evaluations across 4 LLMs and 4 datasets show that LowRA achieves a superior performance–precision trade-off above 2 bits and remains accurate down to 1.15 bits, reducing memory usage by up to 50%. Our results highlight the potential of ultra-low-bit LoRA fine-tuning for resource-constrained environments.

Convolution models with long filters have demonstrated state-of-the-art reasoning abilities in many long-sequence tasks but lag behind the most optimized Transformers in wall-clock time. A major bottleneck is the Fast Fourier Transform (FFT)---which allows long convolutions to run in $O(N\log N)$ time in sequence length $N$ but has poor hardware utilization. In this paper, we study how to optimize the FFT convolution. We find two key bottlenecks: the FFT does not effectively use specialized matrix multiply units, and it incurs expensive I/O between layers of the memory hierarchy. In response, we propose FlashFFTConv. FlashFFTConv uses a matrix decomposition that computes the FFT using matrix multiply units and enables kernel fusion for long sequences, reducing I/O. We also present two sparse convolution algorithms---1) partial convolutions and 2) frequency-sparse convolutions---which can be implemented simply by skipping blocks in the matrix decomposition, enabling further opportunities for memory and compute savings. FlashFFTConv speeds up exact FFT convolutions by up to 8.7$\times$ over PyTorch and achieves up to 4.4$\times$ speedup end-to-end. Given the same compute budget, FlashFFTConv allows Hyena-GPT-s to achieve 2.3 points better perplexity and M2-BERT-base to achieve 3.3 points higher GLUE score---matching models with twice the parameter count. FlashFFTConv also achieves 96.1% accuracy on Path-512, a high-resolution vision task where no model had previously achieved better than 50%. Furthermore, partial convolutions enable longer-sequence models---yielding the first DNA model that can process the longest human genes (2.3M base pairs)---and frequency-sparse convolutions speed up pretrained models while maintaining or improving model quality.

Linear attentions have shown promise for improving Transformer efficiency, reducing attention's quadratic complexity to linear in sequence length. This holds exciting promise for (1) training linear Transformers from scratch, (2) `inetuned-conversion of task-specific Transformers into linear versions that recover task performance, and (3) pretrained-conversion of Transformers, such as language models, into linear versions readily finetunable on downstream tasks. However, linear attentions often underperform compared to standard softmax attention. To close this performance gap, we study the behaviors of softmax and linear attentions in various train-from-scratch and finetuned-conversion settings. We find prior linear attentions lack key properties of softmax attention tied to good performance: low-entropy (or spiky) weights and dot-product monotonicity. We further observe surprisingly simple feature maps that retain these properties match softmax performance, but are inefficient to compute in linear attention. We thus propose Hedgehog, a learnable linear attention that retains the spiky and monotonic properties of softmax attention while maintaining linear complexity. Hedgehog uses simple, trainable MLPs to produce attention weights mimicking softmax attention. Experiments show Hedgehog recovers over 99\% of standard Transformer performance in train-from-scratch and finetuned-conversion settings, outperforming prior linear attentions by up to 6 perplexity points on WikiText-103 when training causal GPT models from scratch, and up to 8.7 GLUE score points when converting finetuned bidirectional BERT models. Hedgehog also enables pretrained-conversion. Converting a pretrained GPT-2 into a linear attention variant achieves state-of-the-art 16.7 perplexity on WikiText-103 for 125M subquadratic decoder models. We finally turn a pretrained Llama-2 7B into a viable linear attention Llama. With low-rank adaptation, Hedgehog-Llama-2 7B achieves 28.1 higher ROUGE-1 points over the base standard attention model, where prior linear attentions lead to 16.5 point drops.

Recent advances in attention-free sequence models rely on convolutions as alternatives to the attention operator at the core of Transformers. In particular, long convolution sequence models have achieved state-of-the-art performance in many domains, but incur a significant cost during auto-regressive inference workloads -- naively requiring a full pass (or caching of activations) over the input sequence for each generated token -- similarly to attention-based models. In this paper, we seek to enable $\mathcal O(1)$ compute and memory cost per token in any pre-trained long convolution architecture to reduce memory footprint and increase throughput during generation. Concretely, our methods consist in extracting low-dimensional linear state-space models from each convolution layer, building upon rational interpolation and model-order reduction techniques. We further introduce architectural improvements to convolution-based layers such as Hyena: by weight-tying the filters across channels into heads, we achieve higher pre-training quality and reduce the number of filters to be distilled. The resulting model achieves 10x higher throughput than Transformers and 1.5x higher than Hyena at 1.3B parameters, without any loss in quality after distillation.