12 papers
Across the Loss Landscape with Progressive Growth
Paul Caillon, Christophe Cerisara, Alexandre Allauzen
Deep neural networks generalize well despite their highly nonconvex, overparameterized loss landscapes, a phenomenon often associated with the geometry of the minima found by stoch…
Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs
Alex Colagrande, Paul Caillon, Eva Feillet +1
Neural operators provide deep neural networks for learning mappings between function spaces. Among them, the Fourier Neural Operator (FNO) is particularly effective: its spectral c…
Limits of Resolution Equivariance in Fourier Neural Operators
Alex Colagrande, Paul Caillon, Eva Feillet +1
Fourier Neural Operators are often assumed to generalize across spatial resolutions, enabling training on a coarse grid and deployment on a finer grid. We test this assumption by c…
Trading Complexity for Expressivity Through Structured Generalized Linear Token Mixing
Erwan Fagnou, Paul Caillon, Blaise Delattre +1
Token mixing layers play a key role in how language models can learn and generate long-range dependencies. Their efficiency relies on the necessary trade-off between decoding speed…
Structured-Sparse Attention for Entity Tracking with Subquadratic Sequence Complexity
Hangyue Zhao, Paul Caillon, Erwan Fagnou +1
Entity tracking requires maintaining and updating latent states for entities and attributes over long sequences. Recent task-specific attention operators can compress deep Transfor…
Certified Robustness under Heterogeneous Perturbations via Hybrid Randomized Smoothing
Blaise Delattre, Hengyu Wu, Paul Caillon +2
Randomized smoothing provides strong, model-agnostic robustness certificates, but existing guarantees are limited to single modalities, treating continuous and discrete inputs in i…
Forward Only Learning for Orthogonal Neural Networks of any Depth
Paul Caillon, Alex Colagrande, Erwan Fagnou +2
Backpropagation is still the de facto algorithm used today to train neural networks. With the exponential growth of recent architectures, the computational cost of this algorithm a…
Linear Attention with Global Context: A Multipole Attention Mechanism for Vision and Physics
Alex Colagrande, Paul Caillon, Eva Feillet +1
Transformers have become the de facto standard for a wide range of tasks, from image classification to physics simulations. Despite their impressive performance, the quadratic comp…
Bridging the Theoretical Gap in Randomized Smoothing
Blaise Delattre, Paul Caillon, Quentin Barthélemy +2
Randomized smoothing has become a leading approach for certifying adversarial robustness in machine learning models. However, a persistent gap remains between theoretical certified…
Fast Training of Recurrent Neural Networks with Stationary State Feedbacks
Paul Caillon, Erwan Fagnou, Alexandre Allauzen
Recurrent neural networks (RNNs) have recently demonstrated strong performance and faster inference than Transformers at comparable parameter budgets. However, the recursive gradie…
Accelerated Training through Iterative Gradient Propagation Along the Residual Path
Erwan Fagnou, Paul Caillon, Blaise Delattre +1
Despite being the cornerstone of deep learning, backpropagation is criticized for its inherent sequentiality, which can limit the scalability of very deep models. Such models faced…
Chain and Causal Attention for Efficient Entity Tracking
Erwan Fagnou, Paul Caillon, Blaise Delattre +1
This paper investigates the limitations of transformers for entity-tracking tasks in large language models. We identify a theoretical constraint, showing that transformers require…