Inductive biases for efficient information transfer in artificial networks

Malgré des progrès remarquables dans une grande variété de sujets, les réseaux de neurones éprouvent toujours des difficultés à exécuter certaines tâches simples pour lesquelles les humains excellent. Comme indiqué dans des travaux récents, nous émettons l'hypothèse que l'écart qualitatif entre l'apprentissage en profondeur actuel et l'intelligence humaine est le résultat de biais inductifs essentiels manquants. En d'autres termes, en identifiant certains de ces biais inductifs essentiels, nous améliorerons le transfert d'informations dans les réseaux artificiels, ainsi que certaines de leurs limitations actuelles les plus importantes sur un grand ensemble de tâches. Les limites sur lesquelles nous nous concentrerons dans cette thèse sont la généralisation systématique hors distribution et la capacité d'apprendre sur des échelles de temps extrêmement longues. Dans le premier article, nous nous concentrerons sur l'extension des réseaux de neurones récurrents (RNN) à contraintes spectrales et proposerons une nouvelle structure de connectivité basée sur la décomposition de Schur, en conservant les avantages de stabilité et la vitesse d'entraînement des RNN orthogonaux tout en améliorant l'expressivité pour les calculs complexes à court terme par des dynamiques transientes. Cela sert de première étape pour atténuer le problème du "exploding vanishing gradient" (EVGP). Dans le deuxième article, nous nous concentrerons sur les RNN avec une mémoire externe et un mécanisme d'auto-attention comme un moyen alternatif de résoudre le problème du EVGP. Ici, la contribution principale sera une analyse formelle sur la stabilité asymptotique du gradient, et nous identifierons la pertinence d'événements comme un ingrédient clé pour mettre à l'échelle les systèmes d'attention. Nous exploitons ensuite ces résultats théoriques pour fournir un nouveau mécanisme de dépistage de la pertinence, qui permet de concentrer l'auto-attention ainsi que de la mettre à l'échelle, tout en maintenant une bonne propagation du gradient sur de longues séquences. Enfin, dans le troisième article, nous distillons un ensemble minimal de biais inductifs pour les tâches cognitives purement relationnelles et identifions que la séparation des informations relationnelles des entrées sensorielles est un ingrédient inductif clé pour la généralisation OoD sur des entrées invisibles. Nous discutons en outre des extensions aux relations non-vues ainsi que des entrées avec des signaux parasites.Despite remarkable advances in a wide variety of subjects, neural networks are still struggling on simple tasks humans excel at. As outlined in recent work, we hypothesize that the qualitative gap between current deep learning and human-level artificial intelligence is the result of missing essential inductive biases. In other words, by identifying some of these key inductive biases, we will improve information transfer in artificial networks, as well as improve on some of their current most important limitations on a wide range of tasks. The limitations we will focus on in this thesis are out-of-distribution systematic generalization and the ability to learn over extremely long-time scales. In the First Article, we will focus on extending spectrally constrained Recurrent Neural Networks (RNNs), and propose a novel connectivity structure based on the Schur decomposition, retaining the stability advantages and training speed of orthogonal RNNs while enhancing expressivity for short-term complex computations via transient dynamics. This serves as a first step in mitigating the Exploding Vanishing Gradient Problem (EVGP). In the Second Article, we will focus on memory augmented self-attention RNNs as an alternative way to tackling the Exploding Vanishing Gradient Problem (EVGP). Here the main contribution will be a formal analysis on asymptotic gradient stability, and we will identify event relevancy as a key ingredient to scale attention systems. We then leverage these theoretical results to provide a novel relevancy screening mechanism, which makes self-attention sparse and scalable, while maintaining good gradient propagation over long sequences. Finally, in the Third Article, we distill a minimal set of inductive biases for purely relational cognitive tasks, and identify that separating relational information from sensory input is a key inductive ingredient for OoD generalization on unseen inputs. We further discuss extensions to unseen relations as well as settings with spurious features

Non-normal Recurrent Neural Network (nnRNN): learning long time dependencies while improving expressivity with transient dynamics

A recent strategy to circumvent the exploding and vanishing gradient problem in RNNs, and to allow the stable propagation of signals over long time scales, is to constrain recurrent connectivity matrices to be orthogonal or unitary. This ensures eigenvalues with unit norm and thus stable dynamics and training. However this comes at the cost of reduced expressivity due to the limited variety of orthogonal transformations. We propose a novel connectivity structure based on the Schur decomposition and a splitting of the Schur form into normal and non-normal parts. This allows to parametrize matrices with unit-norm eigenspectra without orthogonality constraints on eigenbases. The resulting architecture ensures access to a larger space of spectrally constrained matrices, of which orthogonal matrices are a subset. This crucial difference retains the stability advantages and training speed of orthogonal RNNs while enhancing expressivity, especially on tasks that require computations over ongoing input sequences

On Neural Architecture Inductive Biases for Relational Tasks

Current deep learning approaches have shown good in-distribution generalization performance, but struggle with out-of-distribution generalization. This is especially true in the case of tasks involving abstract relations like recognizing rules in sequences, as we find in many intelligence tests. Recent work has explored how forcing relational representations to remain distinct from sensory representations, as it seems to be the case in the brain, can help artificial systems. Building on this work, we further explore and formalize the advantages afforded by 'partitioned' representations of relations and sensory details, and how this inductive bias can help recompose learned relational structure in newly encountered settings. We introduce a simple architecture based on similarity scores which we name Compositional Relational Network (CoRelNet). Using this model, we investigate a series of inductive biases that ensure abstract relations are learned and represented distinctly from sensory data, and explore their effects on out-of-distribution generalization for a series of relational psychophysics tasks. We find that simple architectural choices can outperform existing models in out-of-distribution generalization. Together, these results show that partitioning relational representations from other information streams may be a simple way to augment existing network architectures' robustness when performing out-of-distribution relational computations