Vision Transformers rely on fixed patch tokens that ignore the spatial and semantic structure of images. In this work, we introduce an end-to-end differentiable tokenizer that adapts to image content with pixel-level granularity while remaining backward-compatible with existing architectures for retrofitting pretrained models. Our method uses hierarchical model selection with information criteria to provide competitive performance in both image-level classification and dense-prediction tasks, and even supports out-of-the-box raster-to-vector conversion.

Modern tokenizers employ deterministic algorithms to map text into a single "canonical" token sequence, yet the same string can be encoded as many noncanonical tokenizations using the tokenizer vocabulary. In this work, we investigate the robustness of LMs to text encoded with non-canonical tokenizations entirely unseen during training. Surprisingly, when evaluated across 20 benchmarks, we find that instruction-tuned models retain up to 93.4% of their original performance when given a randomly sampled tokenization, and 90.8% with character-level tokenization. We see that overall stronger models tend to be more robust, and robustness diminishes as the tokenization departs farther from the canonical form. Motivated by these results, we then identify settings where non-canonical tokenization schemes can improve performance, finding that character-level segmentation improves string manipulation and code understanding tasks by up to +14%, and right-aligned digit grouping enhances large-number arithmetic by +33%. Finally, we investigate the source of this robustness, finding that it arises in the instructiontuning phase. We show that while both base and post-trained models grasp the semantics of non-canonical tokenizations (perceiving them as containing misspellings), base models try to mimic the imagined mistakes and degenerate into nonsensical output, while post-trained models are committed to fluent responses. Overall, our findings suggest that models are less tied to their tokenizer than previously believed, and demonstrate the promise of intervening on tokenization at inference time to boost performance.1

Modern tokenizers employ deterministic algorithms to map text into a single ``canonical token sequence, yet the same string can be encoded as many non-canonical tokenizations using the language model vocabulary, including tokenizing by character. In this paper, we investigate the robustness of LMs to input encoded with non-canonical tokenizations entirely unseen during training. Surprisingly, when evaluated across 20 benchmarks, we find that instruction-tuned models retain up to 93.4\% of their original performance when given a randomly sampled tokenization, and 90.8\% with character-level tokenization. We find that overall stronger models tend to be more robust, and that robustness diminishes as the tokenization departs farther from the canonical form. Motivated by these results, we identify settings where non-canonical tokenization schemes can \textit{improve} performance, finding that character level segmentation improves string manipulation and code understanding tasks by up to 15\%, and right aligned digit grouping enhances large number arithmetic by over 33\%. Finally, we investigate the source of this robustness, finding that it arises in the instruction-tuning phase. We provide evidence that both base and post-trained models grasp the semantics of non-canonical tokenizations (perceiving them as containing misspellings). However, base models try to mimic the imagined mistakes and degenerate into nonsensical output, while post-trained models are committed to fluent responses. Overall, our findings suggest that models are less committed to their tokenizer than previously believed, and highlight the promise of intervening on tokenization at inference time to boost language model performance.

Effective and efficient tokenization plays an important role in image representation and generation. Conventional methods, constrained by uniform 2D/1D grid tokenization, are inflexible to represent regions with varying shapes and textures and at different locations, limiting their efficacy of feature representation.

Foundation models for biology and physics optimize predictive accuracy, but their internal representations systematically fail to preserve the continuous geometry of the systems they model. We identify the root cause: the Geometric Alignment Tax, an intrinsic cost of forcing continuous manifolds through discrete categorical bottlenecks. Controlled ablations on synthetic dynamical systems demonstrate that replacing cross-entropy with a continuous head on an identical encoder reduces geometric distortion by up to 8.5x, while learned codebooks exhibit a non-monotonic double bind where finer quantization worsens geometry despite improving reconstruction. Under continuous objectives, three architectures differ by 1.3x; under discrete tokenization, they diverge by 3,000x. Evaluating 14 biological foundation models with rate-distortion theory and MINE, we identify three failure regimes: Local-Global Decoupling, Representational Compression, and Geometric Vacuity. A controlled experiment confirms that Evo 2's reverse-complement robustness on real DNA reflects conserved sequence composition, not learned symmetry. No model achieves simultaneously low distortion, high mutual information, and global coherence.

Tokenization is widely used in large language models because it significantly improves performance. However, tokenization imposes several disadvantages, such as performance biases, increased adversarial vulnerability, decreased character-level modeling performance, and increased modeling complexity. To address these disadvantages without sacrificing performance, we propose SpaceByte, a novel byte-level decoder architecture that closes the performance gap between byte-level and subword autoregressive language modeling. SpaceByte consists of a byte-level Transformer model, but with extra larger transformer blocks inserted in the middle of the layers. We find that performance is significantly improved by applying these larger blocks only after certain bytes, such as space characters, which typically denote word boundaries. Our experiments show that for a fixed training and inference compute budget, SpaceByte outperforms other byte-level architectures and roughly matches the performance of tokenized Transformer architectures.

While there has been a large body of research attempting to circumvent tokenization for language modeling (Clark et al. 2022, Xue et al. 2022), the current consensus is that it is a necessary initial step for designing state-of-the-art performant language models. In this paper, we investigate tokenization from a theoretical point of view by studying the behavior of transformers on simple data generating processes. When trained on data drawn from certain simple $k^{\text{th}}$-order Markov processes for $k > 1$, transformers exhibit a surprising phenomenon - in the absence of tokenization, they empirically are incredibly slow or fail to learn the right distribution and predict characters according to a unigram model (Makkuva et al. 2024). With the addition of tokenization, however, we empirically observe that transformers break through this barrier and are able to model the probabilities of sequences drawn from the source near-optimally, achieving small cross-entropy loss. With this observation as starting point, we study the end-to-end cross-entropy loss achieved by transformers with and without tokenization. With the appropriate tokenization, we show that even the simplest unigram models (over tokens) learnt by transformers are able to model the probability of sequences drawn from $k^{\text{th}}$-order Markov sources near optimally. Our analysis provides a justification for the use of tokenization in practice through studying the behavior of transformers on Markovian data.

In multilingual settings, non-Latin scripts and low-resource languages are usually disadvantaged in terms of language models' utility, efficiency, and cost. Specifically, previous studies have reported multiple modeling biases that the current tokenization algorithms introduce to non-Latin script languages, the main one being over-segmentation. In this work, we propose MAGNET-- multilingual adaptive gradient-based tokenization--to reduce over-segmentation via adaptive gradient-based subword tokenization. MAGNET learns to predict segment boundaries between byte tokens in a sequence via sub-modules within the model, which act as internal boundary predictors (tokenizers). Previous gradient-based tokenization methods aimed for uniform compression across sequences by integrating a single boundary predictor during training and optimizing it end-to-end through stochastic reparameterization alongside the next token prediction objective. However, this approach still results in over-segmentation for non-Latin script languages in multilingual settings. In contrast, MAGNET offers a customizable architecture where byte-level sequences are routed through language-script-specific predictors, each optimized for its respective language script. This modularity enforces equitable segmentation granularity across different language scripts compared to previous methods. Through extensive experiments, we demonstrate that in addition to reducing segmentation disparities, MAGNET also enables faster language modeling and improves downstream utility.

This restricts the tokenizer's ability to effectively leverage the redundancy

Consequently, it is uncertain whether the generated modalities sufficiently represent the diversity of future behaviors.