Tommaso Mencattini

Giorgio Strano, Luca Cerovaz, Michele Mancusi et al.

Modern VAEs are rarely trained with the pointwise likelihood implied by the standard $β$-VAE objective. In practice, pointwise reconstruction is often combined with perceptual and adversarial losses, despite a lack of understanding of how this changes the latent dynamics of the model. We show that the choice of reconstruction loss reshapes the rate-distortion problem itself, altering both the information content and the geometry of the learned latent space in ways that may be invisible from reconstructions alone. First, we prove and verify empirically that augmenting pointwise reconstruction with neural terms, such as perceptual and adversarial objectives, reduces the amount of information stored in the latent representations. Second, we show that neural reconstruction losses systematically change the geometry of the latent space: they make representations more isotropic and distribute uncertainty more evenly across latent dimensions, producing different posterior variance profiles. These findings highlight how the rate-distortion tradeoff is not a comprehensive lens to understand the behavior of VAEs, and we propose a more mechanistic approach to investigate how the choice of a distortion metric reshapes the optimization problem.

Tommaso Mencattini, Adrian Robert Minut, Donato Crisostomi et al.

Evolutionary model merging enables the creation of high-performing multi-task models but remains computationally prohibitive for consumer hardware. We introduce MERGE$^3$, an efficient framework that makes evolutionary merging feasible on a single GPU by reducing fitness computation costs 50$\times$ while preserving performance. MERGE$^3$ achieves this by Extracting a reduced dataset for evaluation, Estimating model abilities using Item Response Theory (IRT), and Evolving optimal merges via IRT-based performance estimators. Our method enables state-of-the-art multilingual and cross-lingual merging, transferring knowledge across languages with significantly lower computational overhead. We provide theoretical guarantees and an open-source library, democratizing high-quality model merging.

Tommaso Mencattini, Francesco Montagna, Francesco Locatello

Sparse Autoencoders (SAEs) that can accurately reconstruct their input (minimizing distortion) by making efficient use of few features (minimizing the rate) often fail to learn monosemantic representations (highly interpretable), limiting their usefulness for mechanistic interpretability. In this paper, we characterise this tension in learning faithful, efficient, and interpretable explanations, introducing the Rate-Distortion-Polysemanticity tradeoff in SAEs. Under toy-modeling assumptions, we theoretically and empirically show that restricting the SAE to be monosemantic necessarily comes with an increase in rate and distortion. Assuming a generative model behind the input observations, we further demonstrate that the degree of polysemanticity of optimal SAEs is determined by the training data distribution, especially by the probability of features to co-occur. Finally, we extend the analysis to real-world settings by deriving necessary conditions that a polysemanticity measure should satisfy when the data-generating process is unknown, and we benchmark existing proxy metrics on SAEs trained on Large Language Models. Taken together, our findings show that polysemanticity is a data problem that should be accounted for when addressing it at the architectural and optimization level.

Mario Iacobelli, Adrian Robert Minut, Tommaso Mencattini et al.

Reasoning models have demonstrated remarkable capabilities in solving complex problems by leveraging long chains of thought. However, this more deliberate reasoning comes with substantial computational overhead at inference time. The Long-to-Short (L2S) reasoning problem seeks to maintain high accuracy using fewer tokens, but current training-free model merging approaches rely on scalarized, fixed-hyperparameter arithmetic methods that are highly brittle and force suboptimal compromises. To address this gap, we introduce Evo-L2S, a novel framework that formulates L2S reasoning as a multi-objective optimization challenge. By leveraging evolutionary model merging, Evo-L2S explicitly optimizes the trade-off between accuracy and output length to produce a robust Pareto front of merged models. To make this search computationally tractable for large language models, we propose an entropy-based subset sampling technique that drastically reduces the overhead of fitness estimation. Comprehensive experiments across 1.5B, 7B, and 14B parameter scales on six mathematical reasoning benchmarks demonstrate that Evo-L2S can reduce the length of generated reasoning traces by over 50% while preserving, or even improving, the problem-solving accuracy of the original reasoning models.

Giorgos Nikolaou, Tommaso Mencattini, Donato Crisostomi et al.

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.

Tommaso Mencattini, Riccardo Cadei, Francesco Locatello

Randomized Controlled Trials are one of the pillars of science; nevertheless, they rely on hand-crafted hypotheses and expensive analysis. Such constraints prevent causal effect estimation at scale, potentially anchoring on popular yet incomplete hypotheses. We propose to discover the unknown effects of a treatment directly from data. For this, we turn unstructured data from a trial into meaningful representations via pretrained foundation models and interpret them via a sparse autoencoder. However, discovering significant causal effects at the neural level is not trivial due to multiple-testing issues and effects entanglement. To address these challenges, we introduce Neural Effect Search, a novel recursive procedure solving both issues by progressive stratification. After assessing the robustness of our algorithm on semi-synthetic experiments, we showcase, in the context of experimental ecology, the first successful unsupervised causal effect identification on a real-world scientific trial.