Multi-scale Feature Learning Dynamics: Insights for Double Descent
Mohammad Pezeshki
Amartya Mitra
Yoshua Bengio
Guillaume Lajoie
A key challenge in building theoretical foundations for deep learning is the complex optimization dynamics of neural networks, resulting fro… (voir plus)m the high-dimensional interactions between the large number of network parameters. Such non-trivial interactions lead to intriguing model behaviors such as the phenomenon of "double descent" of the generalization error. The more commonly studied aspect of this phenomenon corresponds to model-wise double descent where the test error exhibits a second descent with increasing model complexity, beyond the classical U-shaped error curve. In this work, we investigate the origins of the less studied epoch-wise double descent in which the test error undergoes two non-monotonous transitions, or descents as the training time increases. We study a linear teacher-student setup exhibiting epoch-wise double descent similar to that in deep neural networks. In this setting, we derive closed-form analytical expressions for the evolution of generalization error over training. We find that double descent can be attributed to distinct features being learned at different scales: as fast-learning features overfit, slower-learning features start to fit, resulting in a second descent in test error. We validate our findings through numerical experiments where our theory accurately predicts empirical findings and remains consistent with observations in deep neural networks.
2022-06-28
Proceedings of the 39th International Conference on Machine Learning (publié)
proceedings.mlr.press
openreview.net
Only tails matter: Average-Case Universality and Robustness in the Convex Regime
Leonardo Cunha
Gauthier Gidel
Fabian Pedregosa
Damien Scieur
Courtney Paquette
2022-06-28
Proceedings of the 39th International Conference on Machine Learning (publié)
doi.org
openreview.net
Proving theorems using Incremental Learning and Hindsight Experience Replay
Maxwell Crouse
Eser Aygün
Laurent Orseau
Bassem Makni
Vernon Ralph Austel
Ankit Anand
Xavier Glorot
Cristina Cornelio
Shajith Ikbal
Stephen M Mcaleer
Vlad Firoiu
Pavan Kapanipathi
Lei M Zhang
Ndivhuwo Makondo
Doina Precup
Shibl Mourad
The highest performing ATP systems (e.g., [7, 18]) in first order logic have been evolving for decades and have grown to use an increasing n… (voir plus)umber of manually designed heuristics mixed with some machine learning, to obtain a large number of search strategies that are tried sequentially or in parallel. Some recent works [5, 13, 19] build on top of these provers, using modern machine learning techniques to augment, select or prioritize their already existing heuristics, with some success. Other recent works do not build on top of other provers, but still require existing proof examples as input (e.g., [9, 23]). Such machine-learning-based ATP systems can struggle to solve difficult problems when the training dataset does not provide problems of sufficiently diverse difficulties. In this paper, we propose an approach which can build a strong theorem prover without relying on existing domain-specific heuristics or on prior input data (in the form of proofs) to prime the learning. We strive to design a learning methodology for ATP that allows a system to improve even when there are large gaps in the difficulty of given set of theorems. In particular, given a set of conjectures without proofs, our system trains itself, based on its own attempts and (dis)proves an increasing number of conjectures, an approach which can be viewed as a form of incremental learning. Additionally, all the previous approaches [19, 1, 13] learn exclusively on successful proof attempts. When no new theorem can be proven, the learner may not be able to improve anymore and thus the system may not be able to obtain more training data. This could in principle happen even at the very start of training, if all the theorems available are too hard. To tackle this challenge, we adapt the idea of hindsight experience replay (HER) [3] to ATP: Clauses reached during proof attempts (whether successful or not) are turned into goals in hindsight, producing a large amount of ‘auxiliary’ theorems with proofs of varied difficulties for the learner, even in principle when no theorem from the original set can be proven initially. This leads to a smoother learning regime and a constantly improving learner. We evaluate our approach on two popular benchmarks: MPTP2078 [2] and M2k [17] and compare it both with TRAIL [1], a recent machine learning prover as well as with E prover [24, 7], one of the leading heuristic provers. Our proposed approach substantially outperforms TRAIL [1] on both datasets, surpasses E in the auto configuration with a 100s time limit, and is competitive with E in the autoschedule configuration with a 7 days time limit. In addition, our approach almost always (99.5% of cases) finds shorter proofs than E.
2022-06-28
Proceedings of the 39th International Conference on Machine Learning (publié)
proceedings.mlr.press
openreview.net
The Primacy Bias in Deep Reinforcement Learning
Evgenii Nikishin
Max Schwarzer
Pierluca D'Oro
Pierre-Luc Bacon
Aaron Courville
2022-06-28
Proceedings of the 39th International Conference on Machine Learning (publié)
doi.org
arxiv.org
Towards efficient representation identification in supervised learning
Kartik Ahuja
Divyat Mahajan
Vasilis Syrgkanis
Ioannis Mitliagkas
Humans have a remarkable ability to disentangle complex sensory inputs (e.g., image, text) into simple factors of variation (e.g., shape, co… (voir plus)lor) without much supervision. This ability has inspired many works that attempt to solve the following question: how do we invert the data generation process to extract those factors with minimal or no supervision? Several works in the literature on non-linear independent component analysis have established this negative result; without some knowledge of the data generation process or appropriate inductive biases, it is impossible to perform this inversion. In recent years, a lot of progress has been made on disentanglement under structural assumptions, e.g., when we have access to auxiliary information that makes the factors of variation conditionally independent. However, existing work requires a lot of auxiliary information, e.g., in supervised classification, it prescribes that the number of label classes should be at least equal to the total dimension of all factors of variation. In this work, we depart from these assumptions and ask: a) How can we get disentanglement when the auxiliary information does not provide conditional independence over the factors of variation? b) Can we reduce the amount of auxiliary information required for disentanglement? For a class of models where auxiliary information does not ensure conditional independence, we show theoretically and experimentally that disentanglement (to a large extent) is possible even when the auxiliary information dimension is much less than the dimension of the true latent representation.
2022-06-28
Proceedings of the First Conference on Causal Learning and Reasoning (publié)
doi.org
openreview.net
Towards Scaling Difference Target Propagation by Learning Backprop Targets
Maxence Ernoult
Fabrice Normandin
Abhinav Moudgil
Sean Spinney
Eugene Belilovsky
Irina Rish
Blake Richards
Yoshua Bengio
The development of biologically-plausible learning algorithms is important for understanding learning in the brain, but most of them fail to… (voir plus) scale-up to real-world tasks, limiting their potential as explanations for learning by real brains. As such, it is important to explore learning algorithms that come with strong theoretical guarantees and can match the performance of backpropagation (BP) on complex tasks. One such algorithm is Difference Target Propagation (DTP), a biologically-plausible learning algorithm whose close relation with Gauss-Newton (GN) optimization has been recently established. However, the conditions under which this connection rigorously holds preclude layer-wise training of the feedback pathway synaptic weights (which is more biologically plausible). Moreover, good alignment between DTP weight updates and loss gradients is only loosely guaranteed and under very specific conditions for the architecture being trained. In this paper, we propose a novel feedback weight training scheme that ensures both that DTP approximates BP and that layer-wise feedback weight training can be restored without sacrificing any theoretical guarantees. Our theory is corroborated by experimental results and we report the best performance ever achieved by DTP on CIFAR-10 and ImageNet 32
2022-06-28
Proceedings of the 39th International Conference on Machine Learning (publié)
proceedings.mlr.press
arxiv.org
VIM: Variational Independent Modules for Video Prediction
Rim Assouel
Lluis Castrejon
Aaron Courville
Nicolas Ballas
Yoshua Bengio
We introduce a variational inference model called VIM, for Variational Independent Modules, for sequential data that learns and infers laten… (voir plus)t representations as a set of objects and discovers modular causal mechanisms over these objects. These mechanisms - which we call modules - are independently parametrized, define the stochastic transitions of entities and are shared across entities. At each time step, our model infers from a low-level input sequence a high-level sequence of categorical latent variables to select which transition modules to apply to which high-level object. We evaluate this model in video prediction tasks where the goal is to predict multi-modal future events given previous observations. We demonstrate empirically that VIM can model 2D visual sequences in an interpretable way and is able to identify the underlying dynamically instantiated mechanisms of the generation process. We additionally show that the learnt modules can be composed at test time to generalize to out-of-distribution observations.
2022-06-28
Proceedings of the First Conference on Causal Learning and Reasoning (publié)
proceedings.mlr.press
openreview.net
Why Should I Trust You, Bellman? The Bellman Error is a Poor Replacement for Value Error
Scott Fujimoto
David Meger
Doina Precup
Ofir Nachum
Shixiang Shane Gu
In this work, we study the use of the Bellman equation as a surrogate objective for value prediction accuracy. While the Bellman equation is… (voir plus) uniquely solved by the true value function over all state-action pairs, we find that the Bellman error (the difference between both sides of the equation) is a poor proxy for the accuracy of the value function. In particular, we show that (1) due to cancellations from both sides of the Bellman equation, the magnitude of the Bellman error is only weakly related to the distance to the true value function, even when considering all state-action pairs, and (2) in the finite data regime, the Bellman equation can be satisfied exactly by infinitely many suboptimal solutions. This means that the Bellman error can be minimized without improving the accuracy of the value function. We demonstrate these phenomena through a series of propositions, illustrative toy examples, and empirical analysis in standard benchmark domains.
2022-06-28
Proceedings of the 39th International Conference on Machine Learning (publié)
proceedings.mlr.press
arxiv.org
PhyloPGM: boosting regulatory function prediction accuracy using evolutionary information
Faizy Ahsan
Zichao Yan
Doina Precup
Mathieu Blanchette
Abstract Motivation The computational prediction of regulatory function associated with a genomic sequence is of utter importance in -omics … (voir plus)study, which facilitates our understanding of the underlying mechanisms underpinning the vast gene regulatory network. Prominent examples in this area include the binding prediction of transcription factors in DNA regulatory regions, and predicting RNA–protein interaction in the context of post-transcriptional gene expression. However, existing computational methods have suffered from high false-positive rates and have seldom used any evolutionary information, despite the vast amount of available orthologous data across multitudes of extant and ancestral genomes, which readily present an opportunity to improve the accuracy of existing computational methods. Results In this study, we present a novel probabilistic approach called PhyloPGM that leverages previously trained TFBS or RNA–RBP binding predictors by aggregating their predictions from various orthologous regions, in order to boost the overall prediction accuracy on human sequences. Throughout our experiments, PhyloPGM has shown significant improvement over baselines such as the sequence-based RNA–RBP binding predictor RNATracker and the sequence-based TFBS predictor that is known as FactorNet. PhyloPGM is simple in principle, easy to implement and yet, yields impressive results. Availability and implementation The PhyloPGM package is available at https://github.com/BlanchetteLab/PhyloPGM Supplementary information Supplementary data are available at Bioinformatics online.
2022-06-27
Bioinformatics (publié)
doi.org
YOUR AUTOREGRESSIVE GENERATIVE MODEL CAN BE BETTER IF YOU TREAT IT AS AN ENERGY-BASED ONE
Yezhen Wang
Tong Che
Bo Li
Kaitao Song
Hengzhi Pei
Yoshua Bengio
Dongsheng Li
2022-06-26
ArXiv (prépublication)
doi.org
openreview.net
GP.2 Deep learning prediction of response to disease modifying therapy in primary progressive multiple sclerosis
JR Falet
Joshua D. Durso-Finley
Brennan Nichyporuk
Julien Schroeter
Francesca Bovis
M Sormani
D Precup
Tal Arbel
DL Arnold
Background: Only one disease modifying therapy (DMT), ocrelizumab, was found to slow disability progression in primary progressive multiple … (voir plus)sclerosis (PPMS). Modeling the conditional average treatment effect (CATE) using deep learning could identify individuals more responsive to DMTs, allowing for predictive enrichment to increase the power of future clinical trials. Methods: Baseline clinical and MRI data were acquired as part of three placebo-controlled randomized clinical trials: ORATORIO (ocrelizumab), OLYMPUS (rituximab) and ARPEGGIO (laquinimod). Data from ORATORIO and OLYMPUS was separated into a training (70%) and testing (30%) set, while ARPEGGIO served as additional validation. An ensemble of multitask multilayer perceptrons was trained to predict the rate of disability progression on both treatment and placebo to estimate CATE. Results: The model could separate individuals based on their predicted treatment effect. The top 25% of individuals predicted to respond most have a larger effect size (HR 0.442, p=0.0497) than the entire group (HR 0.787, p=0.292). The model could also identify responders to laquinimod. A simulated study where the 50% most responsive individuals are randomized would require 6-times less participants to detect a significant effect. Conclusions: Individuals with PPMS who respond favourably to DMTs can be identified using deep learning based on their baseline clinical and imaging characteristics.
2022-06-24
Canadian Journal of Neurological Sciences / Journal Canadien des Sciences Neurologiques (publié)
doi.org
Augmenting Human Selves Through Artificial Agents – Lessons From the Brain
Georg Northoff
Maia Fraser
John Griffiths
Dimitris A. Pinotsis
Prakash Panangaden
Rosalyn Moran
Karl Friston
Much of current artificial intelligence (AI) and the drive toward artificial general intelligence (AGI) focuses on developing machines for f… (voir plus)unctional tasks that humans accomplish. These may be narrowly specified tasks as in AI, or more general tasks as in AGI – but typically these tasks do not target higher-level human cognitive abilities, such as consciousness or morality; these are left to the realm of so-called “strong AI” or “artificial consciousness.” In this paper, we focus on how a machine can augment humans rather than do what they do, and we extend this beyond AGI-style tasks to augmenting peculiarly personal human capacities, such as wellbeing and morality. We base this proposal on associating such capacities with the “self,” which we define as the “environment-agent nexus”; namely, a fine-tuned interaction of brain with environment in all its relevant variables. We consider richly adaptive architectures that have the potential to implement this interaction by taking lessons from the brain. In particular, we suggest conjoining the free energy principle (FEP) with the dynamic temporo-spatial (TSD) view of neuro-mental processes. Our proposed integration of FEP and TSD – in the implementation of artificial agents – offers a novel, expressive, and explainable way for artificial agents to adapt to different environmental contexts. The targeted applications are broad: from adaptive intelligence augmenting agents (IA’s) that assist psychiatric self-regulation to environmental disaster prediction and personal assistants. This reflects the central role of the mind and moral decision-making in most of what we do as humans.
2022-06-23
Frontiers in Computational Neuroscience (publié)
doi.org