Alberto Alfarano

Maissam Barkeshli, Alberto Alfarano, Andrey Gromov

Scaling laws have played a major role in the modern AI revolution, providing practitioners predictive power over how the model performance will improve with increasing data, compute, and number of model parameters. This has spurred an intense interest in the origin of neural scaling laws, with a common suggestion being that they arise from power law structure already present in the data. In this paper we study scaling laws for transformers trained to predict random walks (bigrams) on graphs with tunable complexity. We demonstrate that this simplified setting already gives rise to neural scaling laws even in the absence of power law structure in the data correlations. We further consider dialing down the complexity of natural language systematically, by training on sequences sampled from increasingly simplified generative language models, from 4,2,1-layer transformer language models down to language bigrams, revealing a monotonic evolution of the scaling exponents. Our results also include scaling laws obtained from training on random walks on random graphs drawn from Erdös-Renyi and scale-free Barabási-Albert ensembles. Finally, we revisit conventional scaling laws for language modeling, demonstrating that several essential results can be reproduced using 2 layer transformers with context length of 50, provide a critical analysis of various fits used in prior literature, demonstrate an alternative method for obtaining compute optimal curves as compared with current practice in published literature, and provide preliminary evidence that maximal update parameterization may be more parameter efficient than standard parameterization.

Alberto Alfarano, Eshika Saxena, Emily Wenger et al.

The Learning with Errors (LWE) problem is a hard math problem in lattice-based cryptography. In the simplest case of binary secrets, it is the subset sum problem, with error. Effective ML attacks on LWE were demonstrated in the case of binary, ternary, and small secrets, succeeding on fairly sparse secrets. The ML attacks recover secrets with up to 3 active bits in the "cruel region" (Nolte et al., 2024) on samples pre-processed with BKZ. We show that using larger training sets and repeated examples enables recovery of denser secrets. Empirically, we observe a power-law relationship between model-based attempts to recover the secrets, dataset size, and repeated examples. We introduce a stepwise regression technique to recover the "cool bits" of the secret.

Liam Davis, Leopold Haller, Alberto Alfarano et al.

We introduce the Lattice Deduction Transformer (LDT), a recurrent transformer that approximates logically sound deduction by projecting its latent state through a lattice between forward passes. We train on-policy in a process that mirrors deduction in a search-based constraint solver and supervise training via a domain-agnostic, abstract-interpretation-based approximation of the set of solution candidates. An $800$K-parameter LDT achieves $100\%$ accuracy on Sudoku-Extreme and Snowflake Sudoku, at a fraction of the training cost of prior small recurrent reasoners, while remaining empirically sound: the model returns a correct answer or abstains. A $1.8$M-parameter variant reaches $99.9\%$ accuracy on Maze-Hard. Frontier LLMs score $0\%$ on all three benchmarks.

Eshika Saxena, Alberto Alfarano, François Charton et al.

AI-powered attacks on Learning with Errors (LWE), an important hard math problem in post-quantum cryptography, rival or outperform "classical" attacks on LWE under certain parameter settings. Despite the promise of this approach, a dearth of accessible data limits AI practitioners' ability to study and improve these attacks. Creating LWE data for AI model training is time- and compute-intensive and requires significant domain expertise. To fill this gap and accelerate AI research on LWE attacks, we propose the TAPAS datasets, a Toolkit for Analysis of Post-quantum cryptography using AI Systems. These datasets cover several LWE settings and can be used off-the-shelf by AI practitioners to prototype new approaches to cracking LWE. This work documents TAPAS dataset creation, establishes attack performance baselines, and lays out directions for future work.

Andrea Alfarano, Alberto Alfarano, Linda Friso et al.

Spatio-Temporal predictive Learning is a self-supervised learning paradigm that enables models to identify spatial and temporal patterns by predicting future frames based on past frames. Traditional methods, which use recurrent neural networks to capture temporal patterns, have proven their effectiveness but come with high system complexity and computational demand. Convolutions could offer a more efficient alternative but are limited by their characteristic of treating all previous frames equally, resulting in poor temporal characterization, and by their local receptive field, limiting the capacity to capture distant correlations among frames. In this paper, we propose STLight, a novel method for spatio-temporal learning that relies solely on channel-wise and depth-wise convolutions as learnable layers. STLight overcomes the limitations of traditional convolutional approaches by rearranging spatial and temporal dimensions together, using a single convolution to mix both types of features into a comprehensive spatio-temporal patch representation. This representation is then processed in a purely convolutional framework, capable of focusing simultaneously on the interaction among near and distant patches, and subsequently allowing for efficient reconstruction of the predicted frames. Our architecture achieves state-of-the-art performance on STL benchmarks across different datasets and settings, while significantly improving computational efficiency in terms of parameters and computational FLOPs. The code is publicly available