arXiv subjects

Alessandro Achille

Publications and source records attributed to Alessandro Achille.

64 records · Page 4Linked to original sources

arXiv2019

Toward Understanding Catastrophic Forgetting in Continual Learning

We study the relationship between catastrophic forgetting and properties of task sequences. In particular, given a sequence of tasks, we would like to understand which properties of this sequence influence the error rates of continual learning algorithms trained on the sequence. To this end, we propose a new procedure that makes use of recent developments in task space modeling as well as correlation analysis to specify and analyze the properties we are interested in. As an application, we apply our procedure to study two properties of a task sequence: (1) total complexity and (2) sequential heterogeneity. We show that error rates are strongly and positively correlated to a task sequence's total complexity for some state-of-the-art algorithms. We also show that, surprisingly, the error rates have no or even negative correlations in some cases to sequential heterogeneity. Our findings suggest directions for improving continual learning benchmarks and methods.

cs.LG↗

arXiv2019

Time Matters in Regularizing Deep Networks: Weight Decay and Data Augmentation Affect Early Learning Dynamics, Matter Little Near Convergence

Regularization is typically understood as improving generalization by altering the landscape of local extrema to which the model eventually converges. Deep neural networks (DNNs), however, challenge this view: We show that removing regularization after an initial transient period has little effect on generalization, even if the final loss landscape is the same as if there had been no regularization. In some cases, generalization even improves after interrupting regularization. Conversely, if regularization is applied only after the initial transient, it has no effect on the final solution, whose generalization gap is as bad as if regularization never happened. This suggests that what matters for training deep networks is not just whether or how, but when to regularize. The phenomena we observe are manifest in different datasets (CIFAR-10, CIFAR-100), different architectures (ResNet-18, All-CNN), different regularization methods (weight decay, data augmentation), different learning rate schedules (exponential, piece-wise constant). They collectively suggest that there is a ``critical period'' for regularizing deep networks that is decisive of the final performance. More analysis should, therefore, focus on the transient rather than asymptotic behavior of learning.

cs.LG↗

arXiv2019

Dynamics and Reachability of Learning Tasks

We compute the transition probability between two learning tasks, and show that it decomposes into two factors. The first depends on the geometry of the loss landscape of a model trained on each task, independent of any particular model used. This is related to an information theoretic distance function, but is insufficient to predict success in transfer learning, as nearby tasks can be unreachable via fine-tuning. The second factor depends on the ease of traversing the path between two tasks. With this dynamic component, we derive strict lower bounds on the complexity necessary to learn a task starting from the solution to another, which is one of the most common forms of transfer learning.

cs.LG↗

arXiv2019

Critical Learning Periods in Deep Neural Networks

Similar to humans and animals, deep artificial neural networks exhibit critical periods during which a temporary stimulus deficit can impair the development of a skill. The extent of the impairment depends on the onset and length of the deficit window, as in animal models, and on the size of the neural network. Deficits that do not affect low-level statistics, such as vertical flipping of the images, have no lasting effect on performance and can be overcome with further training. To better understand this phenomenon, we use the Fisher Information of the weights to measure the effective connectivity between layers of a network during training. Counterintuitively, information rises rapidly in the early phases of training, and then decreases, preventing redistribution of information resources in a phenomenon we refer to as a loss of "Information Plasticity". Our analysis suggests that the first few epochs are critical for the creation of strong connections that are optimal relative to the input data distribution. Once such strong connections are created, they do not appear to change during additional training. These findings suggest that the initial learning transient, under-scrutinized compared to asymptotic behavior, plays a key role in determining the outcome of the training process. Our findings, combined with recent theoretical results in the literature, also suggest that forgetting (decrease of information in the weights) is critical to achieving invariance and disentanglement in representation learning. Finally, critical periods are not restricted to biological systems, but can emerge naturally in learning systems, whether biological or artificial, due to fundamental constrains arising from learning dynamics and information processing.

cs.LG↗

arXiv2019

Task2Vec: Task Embedding for Meta-Learning

We introduce a method to provide vectorial representations of visual classification tasks which can be used to reason about the nature of those tasks and their relations. Given a dataset with ground-truth labels and a loss function defined over those labels, we process images through a "probe network" and compute an embedding based on estimates of the Fisher information matrix associated with the probe network parameters. This provides a fixed-dimensional embedding of the task that is independent of details such as the number of classes and does not require any understanding of the class label semantics. We demonstrate that this embedding is capable of predicting task similarities that match our intuition about semantic and taxonomic relations between different visual tasks (e.g., tasks based on classifying different types of plants are similar) We also demonstrate the practical value of this framework for the meta-task of selecting a pre-trained feature extractor for a new task. We present a simple meta-learning framework for learning a metric on embeddings that is capable of predicting which feature extractors will perform well. Selecting a feature extractor with task embedding obtains a performance close to the best available feature extractor, while costing substantially less than exhaustively training and evaluating on all available feature extractors.

cs.LG↗

arXiv2018

Life-Long Disentangled Representation Learning with Cross-Domain Latent Homologies

Intelligent behaviour in the real-world requires the ability to acquire new knowledge from an ongoing sequence of experiences while preserving and reusing past knowledge. We propose a novel algorithm for unsupervised representation learning from piece-wise stationary visual data: Variational Autoencoder with Shared Embeddings (VASE). Based on the Minimum Description Length principle, VASE automatically detects shifts in the data distribution and allocates spare representational capacity to new knowledge, while simultaneously protecting previously learnt representations from catastrophic forgetting. Our approach encourages the learnt representations to be disentangled, which imparts a number of desirable properties: VASE can deal sensibly with ambiguous inputs, it can enhance its own representations through imagination-based exploration, and most importantly, it exhibits semantically meaningful sharing of latents between different datasets. Compared to baselines with entangled representations, our approach is able to reason beyond surface-level statistics and perform semantically meaningful cross-domain inference.

cs.LG↗

arXiv2018

Emergence of Invariance and Disentanglement in Deep Representations

Using established principles from Statistics and Information Theory, we show that invariance to nuisance factors in a deep neural network is equivalent to information minimality of the learned representation, and that stacking layers and injecting noise during training naturally bias the network towards learning invariant representations. We then decompose the cross-entropy loss used during training and highlight the presence of an inherent overfitting term. We propose regularizing the loss by bounding such a term in two equivalent ways: One with a Kullbach-Leibler term, which relates to a PAC-Bayes perspective; the other using the information in the weights as a measure of complexity of a learned model, yielding a novel Information Bottleneck for the weights. Finally, we show that invariance and independence of the components of the representation learned by the network are bounded above and below by the information in the weights, and therefore are implicitly optimized during training. The theory enables us to quantify and predict sharp phase transitions between underfitting and overfitting of random labels when using our regularized loss, which we verify in experiments, and sheds light on the relation between the geometry of the loss function, invariance properties of the learned representation, and generalization error.

cs.LG↗

arXiv2017

A Separation Principle for Control in the Age of Deep Learning

We review the problem of defining and inferring a "state" for a control system based on complex, high-dimensional, highly uncertain measurement streams such as videos. Such a state, or representation, should contain all and only the information needed for control, and discount nuisance variability in the data. It should also have finite complexity, ideally modulated depending on available resources. This representation is what we want to store in memory in lieu of the data, as it "separates" the control task from the measurement process. For the trivial case with no dynamics, a representation can be inferred by minimizing the Information Bottleneck Lagrangian in a function class realized by deep neural networks. The resulting representation has much higher dimension than the data, already in the millions, but it is smaller in the sense of information content, retaining only what is needed for the task. This process also yields representations that are invariant to nuisance factors and having maximally independent components. We extend these ideas to the dynamic case, where the representation is the posterior density of the task variable given the measurements up to the current time, which is in general much simpler than the prediction density maintained by the classical Bayesian filter. Again this can be finitely-parametrized using a deep neural network, and already some applications are beginning to emerge. No explicit assumption of Markovianity is needed; instead, complexity trades off approximation of an optimal representation, including the degree of Markovianity.

stat.ML↗

arXiv2017

A Vietoris-Smale mapping theorem for the homotopy of hyperdefinable sets

Results of Smale (1957) and Dugundji (1969) allow to compare the homotopy groups of two topological spaces $X$ and $Y$ whenever a map $f:X\to Y$ with strong connectivity conditions on the fibers is given. We apply similar techniques in o-minimal expansions of fields to compare the o-minimal homotopy of a definable set $X$ with the homotopy of some of its bounded hyperdefinable quotients $X/E$. Under suitable assumption, we show that $π_{n}(X)^{\rm def}\congπ_{n}(X/E)$ and $\dim(X)=\dim_{\mathbb R}(X/E)$. As a special case, given a definably compact group, we obtain a new proof of Pillay's group conjecture "$\dim(G)=\dim_{\mathbb R}(G/G^{00}$)" largely independent of the group structure of $G$. We also obtain different proofs of various comparison results between classical and o-minimal homotopy.

math.LO↗

arXiv2017

Information Dropout: Learning Optimal Representations Through Noisy Computation

The cross-entropy loss commonly used in deep learning is closely related to the defining properties of optimal representations, but does not enforce some of the key properties. We show that this can be solved by adding a regularization term, which is in turn related to injecting multiplicative noise in the activations of a Deep Neural Network, a special case of which is the common practice of dropout. We show that our regularized loss function can be efficiently minimized using Information Dropout, a generalization of dropout rooted in information theoretic principles that automatically adapts to the data and can better exploit architectures of limited capacity. When the task is the reconstruction of the input, we show that our loss function yields a Variational Autoencoder as a special case, thus providing a link between representation learning, information theory and variational inference. Finally, we prove that we can promote the creation of disentangled representations simply by enforcing a factorized prior, a fact that has been observed empirically in recent work. Our experiments validate the theoretical intuitions behind our method, and we find that information dropout achieves a comparable or better generalization performance than binary dropout, especially on smaller models, since it can automatically adapt the noise to the structure of the network, as well as to the test sample.

stat.ML↗