In standard autoregressive generation, an LLM predicts the next-token distribution, samples a discrete token, and then discards the distribution, passing only the sampled token as new input. To preserve this distribution's rich information, we propose Mixture of Inputs (MoI), a training-free method for autoregressive generation. After generating a token following the standard paradigm, we construct a new input that blends the generated discrete token with the previously discarded token distribution. Specifically, we employ a Bayesian estimation method that treats the token distribution as the prior, the sampled token as the observation, and replaces the conventional one-hot vector with the continuous posterior expectation as the new model input. MoI allows the model to maintain a richer internal representation throughout the generation process, resulting in improved text quality and reasoning capabilities. On mathematical reasoning, code generation, and PhD-level QA tasks, MoI consistently improves performance across multiple models including QwQ-32B, Nemotron-Super-49B, Gemma-3-27B, and DAPO-Qwen-32B, with no additional training and negligible computational overhead.

The work was conducted during the internship of Kerong Wang and Hanye Zhao at Microsoft Research.

Infinite visual synthesis aims to generate high-resolution images, long-duration videos, and even visual generation of infinite size. Some recent work tried to solve this task by first dividing data into processable patches and then training the models on them without considering the dependencies between patches. However, since they fail to model global dependencies between patches, the quality and consistency of the generation can be limited. To address this issue, we propose NUWA-Infinity, a patch-level \emph{``render-and-optimize''} strategy for infinite visual synthesis. Given a large image or a long video, NUWA-Infinity first splits it into non-overlapping patches and uses the ordered patch chain as a complete training instance, a rendering model autoregressively predicts each patch based on its contexts. Once a patch is predicted, it is optimized immediately and its hidden states are saved as contexts for the next \emph{``render-and-optimize''} process. This brings two advantages: ($i$) The autoregressive rendering process with information transfer between contexts provides an implicit global probabilistic distribution modeling; ($ii$) The timely optimization process alleviates the optimization stress of the model and helps convergence. Based on the above designs, NUWA-Infinity shows a strong synthesis ability on high-resolution images and long-duration videos.

Cascade optimizes time allocation in drafting for improved efficiency.

Symbolic regression refers to the task of finding a closed-form mathematical expression to fit a set of data points. Genetic programming based techniques are the most common algorithms used to tackle this problem, but recently, neural-network based approaches have gained popularity. Most of the leading neural-network based models used for symbolic regression utilize transformer-based autoregressive models to generate an equation conditioned on encoded input points. However, autoregressive generation is limited to generating tokens left-to-right, and future generated tokens are conditioned only on previously generated tokens. Motivated by the desire to generate all tokens simultaneously to produce improved closed-form equations, we propose Symbolic Diffusion, a D3PM based discrete state-space diffusion model which simultaneously generates all tokens of the equation at once using discrete token diffusion. Using the bivariate dataset developed for SymbolicGPT, we compared our diffusion-based generation approach to an autoregressive model based on SymbolicGPT, using equivalent encoder and transformer architectures. We demonstrate that our novel approach of using diffusion-based generation for symbolic regression can offer comparable and, by some metrics, improved performance over autoregressive generation in models using similar underlying architectures, opening new research opportunities in neural-network based symbolic regression.

Directly learning to generate audio waveforms in an autoregressive manner is a challenging task, due to the length of the raw sequences and the existence of important structure on many different timescales. Traditional approaches based on recurrent neural networks, as well as causal convolutions and self-attention, have only had limited success on this task. However, recent work has shown that deep state space models, also referred to as linear RNNs, can be highly efficient in this context. In this work, we push the boundaries of linear RNNs applied to raw audio modeling, investigating the effects of different architectural choices and using context-parallelism to enable training on sequences up to one minute (1M tokens) in length. We present a model, HarmonicRNN, which attains state of the art log-likelihoods and perceptual metrics on small-scale datasets.

As generative models scale to larger inputs across language, vision, and video domains, the cost of token-level computation has become a key bottleneck. While prior work suggests that only a subset of tokens significantly influence downstream predictions, most token selection methods are static, modality-specific, or incompatible with autoregressive generation. In this paper, we propose QuickMerge, a lightweight token merging framework designed for efficient next-token prediction. QuickMerge dynamically selects a reduced number of tokens based on attention norm magnitude, guided by an entropy-based budget estimator. To preserve autoregressive compatibility, we introduce a lightweight transformer prior trained over the merged token sequence. By combining semantic salience estimation, flexible token budgets, and AR alignment, QuickMerge enables accurate generation with fewer tokens. We evaluate QuickMerge across multi-modality domains, demonstrating consistent improvements in compute-accuracy tradeoffs. Specifically, QuickMerge reduces token counts sustantially while matching as well as exceeding the performance of learned tokenizers and fixed-patch baselines.

A lion man is typing in the o ffi ce. A beautiful girl is hugging a husky. A lion teacher wearing a suit is in front of a blackboard. A robot is riding under the blue and cloudy sky. Several youths are talking in a bar. A young woman is taking photos.