Large language model (LLM) tokenizers act as structured compressors: by mapping text to discrete token sequences, they determine token count (and thus compute and context usage) and the statistical structure seen by downstream models. Despite their central role in LLM pipelines, the link between tokenization, compression efficiency and induced structure is not well understood. We empirically demonstrate that tokenizer training scale redistributes entropy: as training data grows, the token stream becomes more diverse in aggregate (higher unigram entropy) yet markedly more predictable in-context (lower higher-order conditional entropies), indicating that tokenization absorbs substantial short-range regularity although these gains degrade under train-test domain mismatch. To ground these observations, we first benchmark i) pretrained GPT-family tokenizers as black-box compressors across various domains, and ii) learned tokenizers across configurations spanning vocabulary size, training scale, and domain. Next, we study tokenization as a transform for universal compression and introduce a compression-aware BPE variant. Finally, we adopt a channel lens and introduce capacity-utilization metrics to analyze tokenizer behaviour and outline implications for downstream modeling. Put together, our results expose various trade-offs between compression, induced structure, and robustness under domain shift, and motivate principled, compression-aware tokenizer design.

We introduce *Error Broadcast and Decorrelation* (EBD), a novel learning framework for neural networks that addresses credit assignment by directly broadcasting output errors to individual layers, circumventing weight transport of backpropagation. EBD is rigorously grounded in the stochastic orthogonality property of Minimum Mean Square Error estimators. This fundamental principle states that the error of an optimal estimator is orthogonal to functions of the input. Guided by this insight, EBD defines layerwise loss functions that directly penalize correlations between layer activations and output errors, thereby establishing a principled foundation for error broadcasting. This theoretically sound mechanism naturally leads to the experimentally observed three-factor learning rule and integrates with biologically plausible frameworks to enhance performance and plausibility. Numerical experiments demonstrate EBD’s competitive or better performance against other error-broadcast methods on benchmark datasets. Our findings establish EBD as an efficient, biologically plausible, and principled alternative for neural network training.

The high inference demands of transformer-based Large Language Models (LLMs) pose substantial challenges in their deployment. To this end, we introduce *Neural Block Linearization* (NBL), a novel framework for accelerating transformer model inference by replacing self-attention layers with linear approximations derived from Linear Minimum Mean Squared Error estimators. NBL leverages Canonical Correlation Analysis to compute a theoretical upper bound on the approximation error. Then, we use this bound as a criterion for substitution, selecting the LLM layers with the lowest linearization error. NBL can be efficiently applied to pre-trained LLMs without the need for fine-tuning. In experiments, NBL achieves notable computational speed-ups while preserving competitive accuracy on multiple reasoning benchmarks. For instance, applying NBL to 12 self-attention layers in *DeepSeek-R1-Distill-Llama-8B* increases the inference speed by 32% with less than 1% accuracy trade-off, making it a flexible and promising solution to improve the inference efficiency of LLMs.

This work introduces a hybrid non-Euclidean optimization method which generalizes gradient norm clipping by combining steepest descent and conditional gradient approaches. The method achieves the best of both worlds by establishing a descent property under a generalized notion of ($L_0$,$L_1$)-smoothness. Weight decay is incorporated in a principled manner by identifying a connection to the Frank-Wolfe short step. In the stochastic case, we show an order optimal $O(n^{-1/4})$ convergence rate by leveraging a momentum based gradient estimator. We discuss how to instantiate the algorithms for deep learning, which we dub Clipped Scion, and demonstrate their properties on image classification and language modeling. The code is available at https://github.com/LIONS-EPFL/ClippedScion.