Donato Crisostomi

Transformer components such as non-linear activations and normalization are inherently non-injective, suggesting that different inputs could map to the same output and prevent exact recovery of the input from a model's representations. In this paper, we challenge this view. First, we prove mathematically that transformer language models mapping discrete input sequences to their corresponding sequence of continuous representations are injective and therefore lossless, a property established at initialization and preserved during training. Second, we confirm this result empirically through billions of collision tests on six state-of-the-art language models, and observe no collisions. Third, we operationalize injectivity: we introduce SipIt, the first algorithm that provably and efficiently reconstructs the exact input text from hidden activations, establishing linear-time guarantees and demonstrating exact invertibility in practice. Overall, our work establishes injectivity as a fundamental and exploitable property of language models, with direct implications for transparency, interpretability, and safe deployment.

Generative audio models, based on diffusion and autoregressive architectures, have advanced rapidly in both quality and expressiveness. This progress, however, raises pressing copyright concerns, as such models are often trained on vast corpora of artistic and commercial works. A central question is whether one can reliably verify if an artist's material was included in training, thereby providing a means for copyright holders to protect their content. In this work, we investigate the feasibility of such verification through membership inference attacks (MIA) on open-source generative audio models, which attempt to determine whether a specific audio sample was part of the training set. Our empirical results show that membership inference alone is of limited effectiveness at scale, as the per-sample membership signal is weak for models trained on large and diverse datasets. However, artists and media owners typically hold collections of works rather than isolated samples. Building on prior work in text and vision domains, in this work we focus on dataset inference (DI), which aggregates diverse membership evidence across multiple samples. We find that DI is successful in the audio domain, offering a more practical mechanism for assessing whether an artist's works contributed to model training. Our results suggest DI as a promising direction for copyright protection and dataset accountability in the era of large audio generative models.