Catastrophic forgetting, the phenomenon of forgetting previously learned tasks when learning a new one, is a major hurdle in developing continual learning algorithms. A popular method to alleviate forgetting is to use a memory buffer, which stores a subset of previously learned task examples for use during training on new tasks. The de facto method of filling memory is by randomly selecting previous examples. However, this process could introduce outliers or noisy samples that could hurt the generalization of the model. This paper introduces Memory Outlier Elimination (MOE), a method for identifying and eliminating outliers in the memory buffer by choosing samples from label-homogeneous subpopulations. We show that a space with a high homogeneity is related to a feature space that is more representative of the class distribution. In practice, MOE removes a sample if it is surrounded by samples from different labels. We demonstrate the effectiveness of MOE on CIFAR-10, CIFAR-100, and CORe50, outperforming previous well-known memory population methods.

The structure learning problem consists of fitting data generated by a Directed Acyclic Graph (DAG) to correctly reconstruct its arcs. In this context, differentiable approaches constrain or regularize the optimization problem using a continuous relaxation of the acyclicity property. The computational cost of evaluating graph acyclicity is cubic on the number of nodes and significantly affects scalability. In this paper we introduce COSMO, a constraint-free continuous optimization scheme for acyclic structure learning. At the core of our method, we define a differentiable approximation of an orientation matrix parameterized by a single priority vector. Differently from previous work, our parameterization fits a smooth orientation matrix and the resulting acyclic adjacency matrix without evaluating acyclicity at any step. Despite the absence of explicit constraints, we prove that COSMO always converges to an acyclic solution. In addition to being asymptotically faster, our empirical analysis highlights how COSMO performance on graph reconstruction compares favorably with competing structure learning methods.

We propose an extension of the Contextual Graph Markov Model, a deep and probabilistic machine learning model for graphs, to model the distribution of edge features. Our approach is architectural, as we introduce an additional Bayesian network mapping edge features into discrete states to be used by the original model. In doing so, we are also able to build richer graph representations even in the absence of edge features, which is confirmed by the performance improvements on standard graph classification benchmarks. Moreover, we successfully test our proposal in a graph regression scenario where edge features are of fundamental importance, and we show that the learned edge representation provides substantial performance improvements against the original model on three link prediction tasks. By keeping the computational complexity linear in the number of edges, the proposed model is amenable to large-scale graph processing.

Graphs can be leveraged to model polyphonic multitrack symbolic music, where notes, chords and entire sections may be linked at different levels of the musical hierarchy by tonal and rhythmic relationships. Nonetheless, there is a lack of works that consider graph representations in the context of deep learning systems for music generation. This paper bridges this gap by introducing a novel graph representation for music and a deep Variational Autoencoder that generates the structure and the content of musical graphs separately, one after the other, with a hierarchical architecture that matches the structural priors of music. By separating the structure and content of musical graphs, it is possible to condition generation by specifying which instruments are played at certain times. This opens the door to a new form of human-computer interaction in the context of music co-creation. After training the model on existing MIDI datasets, the experiments show that the model is able to generate appealing short and long musical sequences and to realistically interpolate between them, producing music that is tonally and rhythmically consistent. Finally, the visualization of the embeddings shows that the model is able to organize its latent space in accordance with known musical concepts.

Continual Learning trains models on a stream of data, with the aim of learning new information without forgetting previous knowledge. Given the dynamic nature of such environments, explaining the predictions of these models can be challenging. We study the behavior of SHAP values explanations in Continual Learning and propose an evaluation protocol to robustly assess the change of explanations in Class-Incremental scenarios. We observed that, while Replay strategies enforce the stability of SHAP values in feedforward/convolutional models, they are not able to do the same with fully-trained recurrent models. We show that alternative recurrent approaches, like randomized recurrent models, are more effective in keeping the explanations stable over time.

Real-world data streams naturally include the repetition of previous concepts. From a Continual Learning (CL) perspective, repetition is a property of the environment and, unlike replay, cannot be controlled by the agent. Nowadays, the Class-Incremental (CI) scenario represents the leading test-bed for assessing and comparing CL strategies. This scenario type is very easy to use, but it never allows revisiting previously seen classes, thus completely neglecting the role of repetition. We focus on the family of Class-Incremental with Repetition (CIR) scenario, where repetition is embedded in the definition of the stream. We propose two stochastic stream generators that produce a wide range of CIR streams starting from a single dataset and a few interpretable control parameters. We conduct the first comprehensive evaluation of repetition in CL by studying the behavior of existing CL strategies under different CIR streams. We then present a novel replay strategy that exploits repetition and counteracts the natural imbalance present in the stream. On both CIFAR100 and TinyImageNet, our strategy outperforms other replay approaches, which are not designed for environments with repetition. Continual Learning (CL) requires a model to learn new information from a stream of experiences presented over time, without forgetting previous knowledge (Parisi et al., 2019; Lesort et al., 2020). The nature and characteristics of the data stream can vary a lot depending on the real-world environment and target application.

Hypernetworks mitigate forgetting in continual learning (CL) by generating task-dependent weights and penalizing weight changes at a meta-model level. Unfortunately, generating all weights is not only computationally expensive for larger architectures, but also, it is not well understood whether generating all model weights is necessary. Inspired by latent replay methods in CL, we propose partial weight generation for the final layers of a model using hypernetworks while freezing the initial layers. With this objective, we first answer the question of how many layers can be frozen without compromising the final performance. Through several experiments, we empirically show that the number of layers that can be frozen is proportional to the distributional similarity in the CL stream. Then, to demonstrate the effectiveness of hypernetworks, we show that noisy streams can significantly impact the performance of latent replay methods, leading to increased forgetting when features from noisy experiences are replayed with old samples. In contrast, partial hypernetworks are more robust to noise by maintaining accuracy on previous experiences. Finally, we conduct experiments on the split CIFAR-100 and TinyImagenet benchmarks and compare different versions of partial hypernetworks to latent replay methods. We conclude that partial weight generation using hypernetworks is a promising solution to the problem of forgetting in neural networks. It can provide an effective balance between computation and final test accuracy in CL streams.

We derive a sound positive semi-definite approximation of the Hessian of deep models for which Hessian-vector products are easily computable. This enables us to provide an adaptive SGD learning rate strategy based on the minimization of the local quadratic approximation, which requires just twice the computation of a single SGD run, but performs comparably with grid search on SGD learning rates on different model architectures (CNN with and without residual connections) on classification tasks. We also compare the novel approximation with the Gauss-Newton approximation.

Distributed learning on the edge often comprises self-centered devices (SCD) which learn local tasks independently and are unwilling to contribute to the performance of other SDCs. How do we achieve forward transfer at zero cost for the single SCDs? We formalize this problem as a Distributed Continual Learning scenario, where SCD adapt to local tasks and a CL model consolidates the knowledge from the resulting stream of models without looking at the SCD's private data. Unfortunately, current CL methods are not directly applicable to this scenario. We propose Data-Agnostic Consolidation (DAC), a novel double knowledge distillation method that consolidates the stream of SC models without using the original data. DAC performs distillation in the latent space via a novel Projected Latent Distillation loss. Experimental results show that DAC enables forward transfer between SCDs and reaches state-of-the-art accuracy on Split CIFAR100, CORe50 and Split TinyImageNet, both in reharsal-free and distributed CL scenarios. Somewhat surprisingly, even a single out-of-distribution image is sufficient as the only source of data during consolidation.

Neural Algorithmic Reasoning is an emerging area of machine learning which seeks to infuse algorithmic computation in neural networks, typically by training neural models to approximate steps of classical algorithms. In this context, much of the current work has focused on learning reachability and shortest path graph algorithms, showing that joint learning on similar algorithms is beneficial for generalisation. However, when targeting more complex problems, such similar algorithms become more difficult to find. Here, we propose to learn algorithms by exploiting duality of the underlying algorithmic problem. Many algorithms solve optimisation problems. We demonstrate that simultaneously learning the dual definition of these optimisation problems in algorithmic learning allows for better learning and qualitatively better solutions. Specifically, we exploit the max-flow min-cut theorem to simultaneously learn these two algorithms over synthetically generated graphs, demonstrating the effectiveness of the proposed approach. We then validate the real-world utility of our dual algorithmic reasoner by deploying it on a challenging brain vessel classification task, which likely depends on the vessels' flow properties. We demonstrate a clear performance gain when using our model within such a context, and empirically show that learning the max-flow and min-cut algorithms together is critical for achieving such a result.