Tokenization -- the process of decomposing a given text into a sequence of subwords called tokens -- is one of the key components in the development of language models. Particularly, auto-regressive language models generate texts token by token, i.e., by predicting the next-token distribution given the previous ones, and thus tokenization directly affects their efficiency in text generation. Since each language model has their own vocabulary as a set of possible tokens, they struggle to cooperate with each other at the level of next-token distributions such as model ensemble. In this paper, we establish a theoretical framework of lossless vocabulary reduction, which efficiently converts a given auto-regressive language model into the one with an arbitrarily small vocabulary without any loss in accuracy. As an application, we demonstrate that language models with different tokenization can cooperate with each other efficiently through their maximal common vocabulary.

Synthetic data can improve generalization when real data is scarce, but excessive reliance may introduce distributional mismatches that degrade performance. In this paper, we present a learning-theoretic framework to quantify the trade-off between synthetic and real data. Our approach leverages algorithmic stability to derive generalization error bounds, characterizing the optimal synthetic-to-real data ratio that minimizes expected test error as a function of the Wasserstein distance between the real and synthetic distributions. We motivate our framework in the setting of kernel ridge regression with mixed data, offering a detailed analysis that may be of independent interest. Our theory predicts the existence of an optimal ratio, leading to a U-shaped behavior of test error with respect to the proportion of synthetic data. Empirically, we validate this prediction on CIFAR-10 and a clinical brain MRI dataset. Our theory extends to the important scenario of domain adaptation, showing that carefully blending synthetic target data with limited source data can mitigate domain shift and enhance generalization. We conclude with practical guidance for applying our results to both in-domain and out-of-domain scenarios.

We propose refined GRFs (GRFs++), a new class of Graph Random Features (GRFs) for efficient and accurate computations involving kernels defined on the nodes of a graph. GRFs++ resolve some of the long-standing limitations of regular GRFs, including difficulty modeling relationships between more distant nodes. They reduce dependence on sampling long graph random walks via a novel walk-stitching technique, concatenating several shorter walks without breaking unbiasedness. By applying these techniques, GRFs++ inherit the approximation quality provided by longer walks but with greater efficiency, trading sequential, inefficient sampling of a long walk for parallel computation of short walks and matrix-matrix multiplication. Furthermore, GRFs++ extend the simplistic GRFs walk termination mechanism (Bernoulli schemes with fixed halting probabilities) to a broader class of strategies, applying general distributions on the walks' lengths. This improves the approximation accuracy of graph kernels, without incurring extra computational cost. We provide empirical evaluations to showcase all our claims and complement our results with theoretical analysis.

This dataset includes over 3.5 million documents with rich metadata, making it one of the most extensive collections of debate evidence.

Despite these advancements, QAOA's practical efficacy is challenged by the quantum coherence limits of modern quantum devices, as there is a ceiling on the allowable maximum circuit depth

We also show that MatrixNet respects group relations allowing generalization to group elements of greater word length than in the training set.

Social media platforms capture diverse attack sequence samples through both machine and manual screening processes. Investigating effective ways to leverage these adversarial samples to enhance robustness is imperative.