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This paper presents a combination of the inception architecture with residual networks. This is done by adding a shortcut connection to each inception module. This can alternatively be seen as a resnet where the 2 conv layers are replaced by a (slightly modified) inception module. The paper (claims to) provide results against the hypothesis that adding residual connections improves training, rather increasing the model size is what makes the difference. |
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This paper describes how to apply the idea of batch normalization (BN) successfully to recurrent neural networks, specifically to LSTM networks. The technique involves the 3 following ideas: **1) Careful initialization of the BN scaling parameter.** While standard practice is to initialize it to 1 (to have unit variance), they show that this situation creates problems with the gradient flow through time, which vanishes quickly. A value around 0.1 (used in the experiments) preserves gradient flow much better. **2) Separate BN for the "hiddens to hiddens pre-activation and for the "inputs to hiddens" pre-activation.** In other words, 2 separate BN operators are applied on each contributions to the pre-activation, before summing and passing through the tanh and sigmoid non-linearities. **3) Use of largest time-step BN statistics for longer test-time sequences.** Indeed, one issue with applying BN to RNNs is that if the input sequences have varying length, and if one uses per-time-step mean/variance statistics in the BN transformation (which is the natural thing to do), it hasn't been clear how do deal with the last time steps of longer sequences seen at test time, for which BN has no statistics from the training set. The paper shows evidence that the pre-activation statistics tend to gradually converge to stationary values over time steps, which supports the idea of simply using the training set's last time step statistics. Among these ideas, I believe the most impactful idea is 1). The papers mentions towards the end that improper initialization of the BN scaling parameter probably explains previous failed attempts to apply BN to recurrent networks. Experiments on 4 datasets confirms the method's success. **My two cents** This is an excellent development for LSTMs. BN has had an important impact on our success in training deep neural networks, and this approach might very well have a similar impact on the success of LSTMs in practice. |
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This paper presents a feed-forward neural network architecture for processing graphs as inputs, inspired from previous work on Graph Neural Networks. In brief, the architecture of the GG-NN corresponds to $T$ steps of GRU-like (gated recurrent units) updates, where T is a hyper-parameter. At each step, a vector representation is computed for all nodes in the graph, where a node's representation at step t is computed from the representation of nodes at step $t-1$. Specifically, the representation of a node will be updated based on the representation of its neighbors in the graph. Incoming and outgoing edges in the graph are treated differently by the neural network, by using different parameter matrices for each. Moreover, if edges have labels, separate parameters can be learned for the different types of edges (meaning that edge labels determine the configuration of parameter sharing in the model). Finally, GG-NNs can incorporate node-level attributes, by using them in the initialization (time step 0) of the nodes' representations. GG-NNs can be used to perform a variety of tasks on graphs. The per-node representations can be used to make per-node predictions by feeding them to a neural network (shared across nodes). A graph-level predictor can also be obtained using a soft attention architecture, where per-node outputs are used as scores into a softmax in order to pool the representations across the graph, and feed this graph-level representation to a neural network. The attention mechanism can be conditioned on a "question" (e.g. on a task to predict the shortest path in a graph, the question would be the identity of the beginning and end nodes of the path to find), which is fed to the node scorer of the soft attention mechanism. Moreover, the authors describe how to chain GG-NNs to go beyond predicting individual labels and predict sequences. Experiments on several datasets are presented. These include tasks where a single output is required (on a few bAbI tasks) as well as tasks where a sequential output is required, such as outputting the shortest path or the Eulerian circuit of a graph. Moreover, experiments on a much more complex and interesting program verification task are presented. |
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Disclaimer: I am an author # Intro Experience replay (ER) and generative replay (GEN) are two effective continual learning strategies. In the former, samples from a stored memory are replayed to the continual learner to reduce forgetting. In the latter, old data is compressed with a generative model and generated data is replayed to the continual learner. Both of these strategies assume a random sampling of the memories. But learning a new task doesn't cause **equal** interference (forgetting) on the previous tasks! In this work, we propose a controlled sampling of the replays. Specifically, we retrieve the samples which are most interfered, i.e. whose prediction will be most negatively impacted by the foreseen parameters update. The method is called Maximally Interfered Retrieval (MIR). ## Cartoon for explanation https://i.imgur.com/5F3jT36.png Learning about dogs and horses might cause more interference on lions and zebras than on cars and oranges. Thus, replaying lions and zebras would be a more efficient strategy. # Method 1) incoming data: $(X_t,Y_t)$ 2) foreseen parameter update: $\theta^v= \theta-\alpha\nabla\mathcal{L}(f_\theta(X_t),Y_t)$ ### applied to ER (ER-MIR) 3) Search for the top-$k$ values $x$ in the stored memories using the criterion $$s_{MI}(x) = \mathcal{L}(f_{\theta^v}(x),y) -\mathcal{L}(f_{\theta}(x),y)$$ ### or applied to GEN (GEN-MIR) 3) $$ \underset{Z}{\max} \, \mathcal{L}\big(f_{\theta^v}(g_\gamma(Z)),Y^*\big) -\mathcal{L}\big(f_{\theta}(g_\gamma(Z)),Y^*\big) $$ $$ \text{s.t.} \quad ||z_i-z_j||_2^2 > \epsilon \forall z_i,z_j \in Z \,\text{with} \, z_i\neq z_j $$ i.e. search in the latent space of a generative model $g_\gamma$ for samples that are the most forgotten given the foreseen update. 4) Then add theses memories to incoming data $X_t$ and train $f_\theta$ # Results ### qualitative https://i.imgur.com/ZRNTWXe.png Whilst learning 8s and 9s (first row), GEN-MIR mainly retrieves 3s and 4s (bottom two rows) which are similar to 8s and 9s respectively. ### quantitative GEN-MIR was tested on MNIST SPLIT and Permuted MNIST, outperforming the baselines in both cases. ER-MIR was tested on MNIST SPLIT, Permuted MNIST and Split CIFAR-10, outperforming the baselines in all cases. # Other stuff ### (for avid readers) We propose a hybrid method (AE-MIR) in which the generative model is replaced with an autoencoder to facilitate the compression of harder dataset like e.g. CIFAR-10. |
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Reinforcement Learning is often broadly separated into two categories of approaches: model-free and model-based. In the former category, networks simply take observations and input and produce predicted best-actions (or predicted values of available actions) as output. In order to perform well, the model obviously needs to gain an understanding of how its actions influence the world, but it doesn't explicitly make predictions about what the state of the world will be after an action is taken. In model-based approaches, the agent explicitly builds a dynamics model, or a model in which it takes in (past state, action) and predicts next state. In theory, learning such a model can lead to both interpretability (because you can "see" what the model thinks the world is like) and robustness to different reward functions (because you're learning about the world in a way not explicitly tied up with the reward). This paper proposes an interesting melding of these two paradigms, where an agent learns a model of the world as part of an end-to-end policy learning. This works through something the authors call "observational dropout": the internal model predicts the next state of the world given the prior one and the action, and then with some probability, the state of the world that both the policy and the next iteration of the dynamics model sees is replaced with the model's prediction. This incentivizes the network to learn an effective dynamics model, because the farther the predictions of the model are from the true state of the world, the worse the performance of the learned policy will be on the iterations where the only observation it can see is the predicted one. So, this architecture is model-free in the sense that the gradient used to train the system is based on applying policy gradients to the reward, but model-based in the sense that it does have an internal world representation. https://i.imgur.com/H0TNfTh.png The authors find that, at a simple task, Swing Up Cartpole, very low probabilities of seeing the true world (and thus very high probabilities of the policy only seeing the dynamics model output) lead to world models good enough that a policy trained only on trajectories sampled from that model can perform relatively well. This suggests that at higher probabilities of the true world, there was less value in the dynamics model being accurate, and consequently less training signal for it. (Of course, policies that often could only see the predicted world performed worse during their original training iteration compared to policies that could see the real world more frequently). On a more complex task of CarRacing, the authors looked at how well a policy trained using the representations of the world model as input could perform, to examine whether it was learning useful things about the world. https://i.imgur.com/v9etll0.png They found an interesting trade-off, where at high probabilities (like before) the dynamics model had little incentive to be good, but at low probabilities it didn't have enough contact with the real dynamics of the world to learn a sensible policy. |