Despite being only an example scheme, one advantage of Naive AutoML over black-box optimization that already becomes clear here is that it directly generates important insights that can signiﬁcantly support the data scientist working with it. For example, even such a simple question as “what is the potential of feature selection on the given data?” cannot be directly answered by the existing black-box approaches. In our scheme, the ﬁltering stage (cf. Sec. A.3) is a very good basis to give an initial answer to this question. More complex stage schemes, e.g. including wrapping , can answer such questions even in much more detail. In this sense, Naive AutoML presents itself as more amenable to the growing demand for meaningful interaction between the tool and the human Wang et al. Crisan and Fiore-Gartland (2021); Drozdal et al. ; Wang et al. compared to the currently adopted black-box approaches.

Despite being only an example scheme, one advantage of Naive AutoML that already becomes clear here is that it directly generates important insights that can signiﬁcantly support the data scientist working with it. For example, a question like “what is the potential of feature selection on the given data?” can be answered by black-box approaches only after some post-processing, if at all. In our scheme, the ﬁltering stage (cf. Sec. A.3) is a very good basis to give an initial answer to this question. In this sense, Naive AutoML presents itself as more amenable to the growing demand for meaningful interaction between the tool and the human (Wang et al., 2019; Crisan and Fiore-Gartland, 2021; Drozdal et al., 2020; Wang et al., 2021) compared to the currently adopted black-box approaches.

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We evaluate Pareto HyperNetworks (PHNs) on a set of diverse multi-objective problems. The experiments show the superiority of PHN over other MOO methods. Wewill make our  code publicly available in order to facilitate further research.

We evaluate Pareto HyperNetworks (PHNs) on a set of diverse multi-objective problems. The experiments show the superiority of PHN over previous MOO methods. We make our source code publicly available at: https://github.com/AvivNavon/pareto-hypernetworks .


Our proposed method in this paper belongs to the category of construction heuristics leaners in the sense of producing a one-shot solution per problem instance. But unlike previous methods which generate the solutions via a constructive Markov decision process (MDP) with rather costly decoding steps (adding one un-visited node per step to a partial solution), we introduce a compact continuesspace to parameterize the underlying distribution of discrete candidate solutions, and to allow efficient sampling from such distribution without costly neural network-involved decoding.

Our proposed method in this paper belongs to the category of construction heuristics learners in the sense of producing a one-shot solution per problem instance. However, there are major distinctions between previous methods and ours. One distinction is how to construct solutions. Unlike previous methods which generate the solutions via a constructive Markov decision process (MDP) with rather costly decoding steps (adding one un-visited node per step to a partial solution), we introduce a compact continuous space to parameterize the underlying distribution of discrete candidate solutions, and to allow efficient sampling from that distribution without costly neural network-involved decoding. Another distinction is about the training framework.


Hopper-v2 ) from the OpenAI Gym MuJoCo locomotion tasks. For each environment, we use the medium-v2 , medium-replay-v2 and medium-expert-v2 datasets to construct the expert demonstrations and the unlabeled dataset. For the expert demonstrations, we choose the best episodes from the D4RL dataset based on the episodic return. In practice, the expert demonstrations can be provided separately and we are only selecting the expert demonstration in this way for ease of evaluation. To obtain the unlabeled dataset, we discard the original reward information in the dataset. We then run OTR to label the dataset based on the optimal coupling between the unlabeled episodes and the chosen expert demonstrations. Afterward, we proceed with running the offline RL algorithm.

Hopper-v2 ) from the OpenAI Gym MuJoCo locomotion tasks. For each environment, we use the medium-v2 , medium-replay-v2 and medium-expert-v2 datasets to construct the expert demonstrations and the unlabeled dataset. For the expert demonstrations, we choose the best episodes from the D4RL dataset based on the episodic return. 2 To obtain the unlabeled dataset, we discard the original reward information in the dataset. We then run OTR to label the dataset based on the optimal coupling between the unlabeled episodes and the chosen expert demonstrations. Afterward, we proceed with running the offline RL algorithm.

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Much (though not all) work on program synthesis is focused on domain speciﬁc languages that are less than maximally expressive (Gulwani, 2011; Balog et al., 2016; Wang et al., 2017; Alur et al., 2015). We would like to focus on the synthesis of programs in a Turing complete language, but this presents technical challenges: First, general purpose languages such as C++ or Python are typically quite complicated and sometimes not fully speciﬁed; this makes it a challenge to search over partial programs in those languages. Second, sandboxing and executing code written in these languages is nontrivial. Finally, searching over and executing many programs in these languages can be quite slow, since this is not what they were designed for.

Much (though not all) work on program synthesis is focused on domain speciﬁc languages that are less than maximally expressive (Gulwani, 2011; Balog et al., 2016; Wang et al., 2017; Alur et al., the search procedure used will tend to emit ‘shorter’ programs ﬁrst, and so there is an Occam’s-Razor-type argument (Spade & Panaccio, 2019) to be made that you should get this for free. We would like to focus on the synthesis of programs in a Turing complete language, but this presents technical challenges: First, general purpose languages such as C++ or Python are typically quite complicated and sometimes not fully speciﬁed; this makes it a challenge to search over partial programs in those languages. Second, sandboxing and executing code written in these languages is nontrivial. Finally, searching over and executing many programs in these languages can be quite slow, since this is not what they were designed for.


Here the higher valued θ i,j means the higher probability for the edge from node i to node j to be sampled. More importantly, notice that we use matrix θ ∈ R n × n to parameterize the probabilisticdistribution of n ! discrete feasible solutions. The compact, continuous and differentiable spaceof θ allows us to leverage gradient-based optimization without costly MDP-based construction offeasible solutions, which has been a bottleneck for scaling up in representative DRL solvers so far. Inother words, we also no longer need costly MCMC-based sampling for optimizing our model dueto the chain-rule decomposition. Instead, we use autoregressive factorization for sampling from theauxiliary distribution, which is faster than sampling with MCMC from the distribution defined by theenergy function.

Here a higher valued θ i,j corresponds to a higher probability for the edge from node i to node j to be sampled. The compact, continuous and differentiable space of θ allows us to leverage gradientbased optimization without costly MDP-based construction of feasible solutions, which has been a bottleneck for scaling up in representative DRL solvers so far. In other words, we also no longer need costly MCMC-based sampling for optimizing our model due to the chain-rule decomposition. Instead, we use autoregressive factorization for sampling from the auxiliary distribution, which is faster than sampling with MCMC from the distribution defined by the energy function.

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Our initial experiments compare our agent to baseline agents trained on a single policy. For these experiments, we use the navigation environment deﬁned previously with three objectives: stay on the road, avoid hazards, and move right. Note that the opposite of each of these objectives are also included in possible behavior speciﬁcations due to the semantics of our language that enable minimization. We deﬁne a set of 50,000 speciﬁcations to sample from during training, with which the agent learns to generalize to novel speciﬁcations. The left plot in Figure 3 shows the average episodic reward for 100 never-before-seen test speciﬁcations throughout training for our agent with and without curriculum learning. We compare the results of these two agents with 100 baseline DQN agents trained on each of these 100 behaviors. The error bars in Figure 3 show one standard deviation in average reward for multiple agent initializations.

Our initial experiments compare our agent to baseline agents trained on a single policy. For these experiments, we use the navigation environment deﬁned previously with three objectives: stay on the road, avoid hazards, and move right. Note that the opposite of each of these objectives are also included in possible behavior speciﬁcations due to the semantics of our language that enable minimization. We deﬁne a set of 50,000 speciﬁcations to sample from during training, with which the agent learns to generalize to novel speciﬁcations. These speciﬁcations are randomly generated according to number of atomic statements, logical connectives, hard vs. soft constraints, and value of constraints. We randomly sample test speciﬁcations from these generated speciﬁcations. The left plot in Figure 3 shows the average episodic reward for 100 never-before-seen test speciﬁcations throughout training for our agent with and without curriculum learning. We compare the results of these two agents with 100 baseline DQN agents trained on each of these 100 behaviors. The error bars in Figure 3 show one standard deviation in average reward for multiple agent initializations.


Mirkovic, 2009; Binder & Desai, 2011). The idea of learning from the context information  was ﬁrst successfully applied to vector representation learning for words in Mikolov et al. (2013b) and learning from the occurrence of words also succeeded in Pennington et al.

Mirkovic, 2009; Binder & Desai, 2011). The idea of learning from the context information (Turney & Pantel, 2010) was recently successfully applied to vector representation learning for words in Mikolov et al. (2013); Pennington et al. Collobert et al.


We further compare our network pruning method with representative model compression techniques for image SR. Speciﬁcally, we compare with neural architecture search based methods (Chu et al., 2019b;a) and knowledge distillation (KD) based methods (Lee et al., 2020). We provide quantitative results  in Tab. 4. Our SRPN-L obtains the best performance with the least parameter number and Mult-Adds. With our SRP pruning method, we do not have to search lots of architectures or train a teacher network, which  consumes extra computation resources. These comparisons show that our SRP method has great potential  for efﬁcient image SR.We provide more discussions and comparisons with related works (e.g., DCP (Zhuang et al., 2018), DHP (Li et al., 2020)) in the appendix.

We further compare our SRP to other representative efﬁcient image SR approaches via model compression. Concretely, neural architecture search based methods (Chu et al., 2019b;a) and knowledge distillation (KD) based methods (Lee et al., 2020) are compared to. Quantitative results at × 2 scale are presented in Tab. 4, where our SRPN-Lite delivers better PSNR results across different datasets with fewer parameters and Mult-Adds. With our SRP pruning method, there is no need to search massive network architectures or pretraining a teacher network, which usually consumes considerable computation resources. These comparisons show that our SRP, as a network pruning method, has as much potential (if not more) as other model compression techniques for efﬁcient image SR.

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We collect  interaction data for one month for a listwise online campaign recommender system. Users are represented by attributes such as age, occupation, and localities. Items attributes are also given such as text features, image features, and reward points of campaigns. We simulate a representative RL environment by training a reward model on a set of 68,775 users and 57 items to estimate the click likelihood of the users(Appendix A.4). Weaugment the user reward model with the CPR reward to incentivize the agent to recommend high-CPR user-relevant items. We train a VAE (Kingma & Welling, 2013) to learn action representations, which are given to the RL agent as input. The test data consists of 82,445 users and 58 items, about 30 of which are shared with the training items. We  report the test reward for models trained with CDQN algorithm.

We collect four-week interaction data in a listwise online campaign recommender system. Users are represented by attributes such as age, occupation, and localities. Item attributes include text features, image features, and reward points of campaigns. We train a VAE (Kingma & Welling, 2013) to learn item representations. We create a representative RL environment by training two click-estimation models using data from the ﬁrst two weeks for training and the last two weeks for evaluation. The training environment consists of 68,775 users and 57 items, while testing has 82,445 users anditems, with an overlap of 30 items. The reward function combines the user-click and CPR value of the list. The explicit CPR reward is a representative scenario for when the designer has listwise objectives in addition to user satisfaction. We train with CDQN and report the test reward.

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The shot-number k only appears in ﬁrst two terms of the denominator. It does not contribute to the last term of the denominator. This implies diminishing returns in expected accuracy  when more support data is added without altering φ . 2. By observing the degree of terms in equation 7 (and treating the last term of the denominator as a constant), it is clear that increasing k will decrease the sensitivity (magnitude of partial derivative) of this lower bound to Σ c , and increase its sensitivity to Σ . 3. If one postulates that meta-learning updates on φ is similar to gradient ascent on this accuracy lower bound, then learning with smaller k emphasizes minimizing noise, while learning with higher k emphasizes maximizing signal.

The shot-number k only appears in ﬁrst two terms of the denominator, implying that the bound saturates quickly with increasing k . This is also in agreement with the empirical observation that meta-testing accuracy has diminishing improvements when more support data is added. By observing the degree of terms in equation 7 (and treating the last term of the denominator as a constant), it is clear that increasing k will decrease the sensitivity (magnitude of partial derivative) of this lower bound to Σ c , and increase its sensitivity to Σ . 3. If one postulates that meta-learning updates on φ is similar to gradient ascent on this accuracy lower bound, then learning with smaller k emphasizes minimizing noise, while learning with higher k emphasizes maximizing signal.


A gap in the literature seems to be a practical completeness threshold for cost optimal planning problems that have actions with 0-cost. This is one hurdle to the application of SAT-based planning to such problems since, without a reasonable completeness threshold, optimality can only be proved after solving the compilation for a horizon that is the number of states in the state space. This is impractical for most problems since it can be exponentially bigger than the size of the given problem. It should be noted that some approaches try to circumvent the need for a tight completeness threshold, such the ones by Robinson et al. and Leofante et al., which add an over-approximation of the transition relation underlying the planning problem to the encoding. Optimality of a given solution is then proved when this over-approximation is unsatisﬁable. Nonetheless, these approaches still need to compute compilations for multiple horizons and they are susceptible to having to solve compilations for an exponential horizon, unless a tighter completeness threshold is available, since the over-approximation is a relaxation of the given problem, i.e. it could be solvable even if the concrete problem is not solvable.

A gap in the literature seems to be a practical completeness threshold for cost optimal planning problems that have actions with 0-cost. This is one hurdle to the application of SAT-based planning to such problems, since without a reasonable completeness threshold, optimality can only be proved after solving the compilation for a horizon that is the number of states in the state space. This is impractical for most problems since it can be exponentially bigger than the size of the given problem. It should be noted that some approaches try to circumvent the need for a tight completeness threshold, such the ones by Robinson et al. and Leofante et al., which add an over-approximation of the transition relation underlying the planning problem to the encoding. Optimality of a given solution is then proved when this over-approximation is unsatisﬁable. Nonetheless, these approaches still need to compute compilations for multiple horizons and they are suscepteble to having to solve compilations for the same exponential horizon, since the overapproximation is generally incomplete, i.e. it could be solvable even if the concrete system is not solvable.

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Evaluation We compute the accuracy at the sample-level, meaning a predicted set is considered correct if and only if every element is correct. The baselines are very volatile during training, further resulting in very large variances at the end of training. To reduce this variance, we pick the best model according to the validation accuracy which we evaluate every 500 training steps. We report the accuracy on the test set for the best model. Each run samples new datasets based on the random seed, so we evaluate all models using the same set of random seeds.

Evaluation. We compute the accuracy at the sample-level, meaning a predicted set is considered correct only if every element is correct. The predicted ID for each predicted element is obtained by taking the argmax over the elements’ dimensions in the output. The baselines are very volatile during training, which results in very large variances at the end of training. To reduce this variance, we pick the best model according to the validation accuracy, evaluated every 500 training steps. We report the accuracy on the test set for the best model. Each run samples new datasets based on the random seed, so we evaluate all models using the same set of random seeds.


Implicit DSPN. Motivated by our analysis on exclusive multiset-equivariance, we seek tofurther improve  DSPN. We propose implicit DSPN (iDSPN) in Section 3: a version of DSPN that uses  implicit differentiation, which enables  better optimizers and more iterations to be used at a constant memory cost and less computation time. We then simplify this approach to avoid computing a Hessianentirely while still keeping the same beneﬁts.

Implicit DSPN. Despite this beneﬁcial property, DSPN is outperformed by the set-equivariant Slot Attention (Locatello et al., 2020), which motivates us to improve other aspects of DSPN. We propose implicit DSPN (iDSPN) in Section 3: a version of DSPN that uses approximate implicit differentiation. Implicit differentiation enables us to use better optimizers and more iterations at a constant memory cost and less computation time. The approximation makes this faster to run and easier to implement by avoiding the computation of a Hessian while still having the same beneﬁts.


FetchPush . As shown in Figure 5(c), in the fetch environment, the agent is trained to fetch an object from the initial position (rectangle  in green) to a distant position (rectangle  in red). Although the fetch tasks are more complicated than they reach ones in the maze, GSRL also yields large performance gain, as shown in Figure 6(c).

FetchPush . As shown in Figure 11(c), in the fetch environment, the agent is trained to fetch an object from the initial position (rectangle depicted in green) to a distant position (rectangle depicted in red). Let the origin (0 , 0 , 0) denote the projection of the gripper’s initial coordinate on the table. The object is uniformly generated on the segment from ( − 0 . 0 , − 0 . 0 , 0) to (8 , 8 , 0) , and the goal is uniformly generated on the segment from ( − 0 . 0 , − 0 . 0 , 0) to (8 , 8 , 0) .


Traditional computational approaches are mainly based on biophysics and statistics (Schymkowitz et al., 2005; Park et al., 2016; Alford et al., 2017). Though having dominated the area for years, their limitations are non-negligible. In general, biophysics-based methods face the trade-off between efficiency and accuracy as they rely on sampling from energy functions. Statistical methods are efficient but their capacity is limited by the descriptors considered in the model. Both biophysics and statistics-based methodsrely heavily  on human knowledge. Thus, they can hardly benefit from the fast-growing ofavailable protein structures. These limitations mark that predicting the effect of mutation on protein binding remains an open problem.

Traditional computational approaches are mainly based on biophysics and statistics (Schymkowitz et al., 2005; Park et al., 2016; Alford et al., 2017). Although these methods have dominated the field for years, they have several limitations. Biophysics-based methods face a trade-off between efficiency and accuracy since they rely on sampling from energy functions. Statistical methods are more efficient, but their capacity is limited by the descriptors considered in the model. Furthermore, both biophysics and statistics-based methods heavily rely on human knowledge, preventing it to ∗ Equal contribution. benefit from the growing availability of protein structures. As a result, predicting the effects of mutations on protein-protein binding remains an open problem.


In addition, both DeiT and ViT utilize an extra learnable class token to perform classiﬁcation ( i.e ., cls token shown in Figure 1 (a) and (b)). By design, the class token is not translation-invariant although it can learn to be so. A simple alternative is to directly replace it with a global average pooling (GAP), which is inherently translation-invariant, resulting in our CVPT-GAP. Together with the translation-equivariant positional encodings, CVPT-GAP is uttermost translation-invariant and thus can achieve much better image classiﬁcation performance.

In addition, both DeiT and ViT utilize an extra learnable class token to perform classiﬁcation ( i.e ., cls token shown in Figure 1 (a) and (b)). By design, the class token is not translation-invariant although it can learn to be so. A simple alternative is to directly replace it with a global average pooling (GAP), which is inherently translation-invariant, resulting in our CVPT-GAP. Together with the conditional positional encodings, CVPT-GAP can achieve much better image classiﬁcation performance.

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When compared with all previous methods, our SRPN-L performs the best on all the datasets with all scaling factors. Different from careful network designs as most compared methods have done, we start with the existing EDSR baseline (Lim et al., 2017) and prune it to a much smaller network, showing the effectiveness of our proposed SRP.

When compared with all previous methods, our SRPN-Lite performs the best on all the datasets under all scaling factors. Unlike most comparison methods, which achieve efﬁciency through careful network designs, our work starts with the existing EDSR baseline (Lim et al., 2017) and prunes it to a much smaller network, showing the effectiveness of our proposed SRP.

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Shan et al. (2022) identifies 5 single-point mutations on a human antibody against SARS-CoV-2 that enhance neutralization (effectiveness). There are  494 possible single-point mutations on the heavy chain CDR region of the antibody in total. We use the most competitive methods benchmarked in Section 4.1 to predict ∆∆ G s for all the  mutations and rank them in ascending order (lowest ∆∆ G in the top). A predictor is considered more effective if it ranks more favorable mutations  in the top place. Table 2 shows that RDE-Network and DDGPred successfully identify three mutations (Ranking ≤ 10%), and RDE-Network ranks them higher.

In Shan et al. , the authors report five single-point mutations on a human antibody against SARS-CoV-2 that enhance neutralization effectiveness. These mutations are among the 494 possible single-point mutations on the heavy chain CDR region of the antibody. We use the most competitive methods benchmarked in Section 4.1 to predict ∆∆ G s for all the single-point mutations and rank them in ascending order (lowest ∆∆ G in the top). The effectiveness of a predictor is determined by the number of favorable mutations ranked in the top place. As shown in Table 2, RDE-Network and DDGPred successfully identify three mutations (Ranking ≤ 10%), with RDE-Network ranking them higher.

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Given the issue above, it is necessary to prune all the Conv layers in residual blocks if we seek acceleration of practical use. Thus, we need a method to align the pruned indices in all constrained Conv layers. Regularization then arises as a natural solution given its prevailing use to impose priors on the sparsity structure in pruning (Reed, 1993; Wen et al., 2016; Wang et al., 2021).

Given this issue, it is imperative to prune all the Conv layers in residual blocks, thus calling for an approach to align the pruned indices of all constrained Conv layers. Regularization then arises as a promising solution considering it has been widely used before to impose priors on the sparsity structure in classiﬁcation (Reed, 1993; Wen et al., 2016; Wang et al., 2021).

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We have implemented Stars as part of[redacted for blind review] which is based on the Adaptive Massively Parallel Computation (AMPC) model [7]. Each logical unit of computation is automatically distributed across a number of worker machines, with the experiments in this paper scaling to thousands of individual workers.

We have implemented Stars as part of the Grale [25] graph building system using Flume - a C++ counterpart to FlumeJava [13]. which is based on the Adaptive Massively Parallel Computation (AMPC) model [7]. Each logical unit of computation is automatically distributed across a number of worker machines, with the experiments in this paper scaling to thousands of individual workers.


Note that exclusive multiset-equivariance is not always obtained in DSPN, but  depends on the choice of encoder. For instance, a DeepSets encoder (Zaheer et al., 2017) – which is based on sum pooling – has the same gradients for equal elements, which would make DSPN set-equivariant. It is speciﬁcally the use of the exclusively multiset-equivariant gradient of sorting that makes DSPN exclusively multiset-equivariant.

Note that DSPN is not always exclusively multiset-equivariant, but it depends on the choice of encoder. A DeepSets encoder (Zaheer et al., 2017) – which is based on sum pooling – has the same gradients for equal elements, which would make DSPN set-equivariant. It is speciﬁcally the use of the exclusively multiset-equivariant gradient of sorting that makes DSPN exclusively multiset-equivariant.

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• Implicit Curricula: Examples are learned in a consistent order (Section 2). We show that the order in which examples are learned is consistent across runs, similar training methods, and similar architectures. Furthermore, we show that it is possible to change this order by changing the order in which examples are presented during training. Finally, we establish that well-known notions of sample difﬁculty are highly correlated with each other. • Curricula achieve (almost) no improvement in the standard setting (Section 4). We show curriculum learning, random, and anti-curriculum learning perform almost equally well in the standard setting. Furthermore, we establish that using similar techniques to remove examples from the training set (as opposed to introducing them) also does not help. • Curriculum learning improves over standard training when training time is limited (Section 5). Imitating the large data regime, where training for multiple epochs is not feasible, we limit the number of iterations in the training algorithm and compare curriculum, random and anti-curriculum ordering against standard training. Our experiments reveal a clear advantage of curriculum learning over other methods. • Curricula improves over standard training in noisy regime (Section 5). Finally, we mimic noisy data by adding label noise. Similar to Jiang et al. ; Saxena et al. ; Guo et al. , our experiments indicate that curriculum learning has a clear advantage over other curricula and standard training.

• Implicit Curricula: Examples are learned in a consistent order (Section 2). We show that the order in which examples are learned is consistent across runs, similar training methods, and similar architectures. Furthermore, we show that it is possible to change this order by changing the order in which examples are presented during training. Finally, we establish that well-known notions of sample difﬁculty are highly correlated with each other. • Curricula achieve (almost) no improvement in the standard setting (Section 4 and 6). We show curriculum learning, random, and anti-curriculum learning perform almost equally well in the standard setting.• Curriculum learning improves over standard training when training time is limited (Section 5 and 6) . Imitating the large data regime, where training for multiple epochs is not feasible, we limit the number of iterations in the training algorithm and compare curriculum, random and anti-curriculum ordering against standard training. Our experiments reveal a clear advantage of curriculum learning over other methods. • Curricula improves over standard training in noisy regime (Section 5 and 6). Finally, we mimic noisy data by adding label noise. Similar to Jiang et al. ; Saxena et al. ; Guo et al. , our experiments indicate that curriculum learning has a clear advantage over other curricula and standard training.

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We develop our approach focusing on the shape space of discrete shells, where shapes are given by triangle meshes and the manifold is equipped with an elasticity-based metric. In principle, our approach is also applicable to other shape spaces such as manifolds of images, and we will include remarks on how we propose this could work. We evaluate our approach with experiments on data manifolds of triangle meshes, both synthetic ones and ones extracted from data via SPGA, and we demonstrate that the proposed composite network architecture outperforms a monolithic fully connected network architecture as well as an approach based on the affine combination of the factors. We see this work as a first step to use NN to accelerate the complex computations of shape manifold parameterizations.


We trained all the learning-based control policies in a mix of 60 instances of the Blank Environment containing 1 to 6 humans (uniformly sampled). Each training run has 500,000 steps of environment interactions. For fair evaluation, we report all of the mean metrics based on the data of a hundred 500-step episodes. In all experiments, the cameras and humans interact in a 10m × 10m area.

We trained all the learning-based control policies in a mix of 28 instances of the BlankEnv uniformly containing 1 to 6 humans. Each training run has 700,000 steps (1,000 training iterations). For fair evaluation, we report all of the mean metrics based on the data from the latest hundred 500-steps episodes. In all experiments, the cameras and humans interact in a 10m × 10m area.


Kullback-Leibler divergence) fails (Seguy et al., 2018). In addition, it does not require adversarial training and is, therefore, easier to optimize than adversarial-based measures (Kallus, 2020).

Kullback-Leibler divergence) fails (Seguy et al., 2018). In addition, the calculated discrepancy can be optimized with the traditional supervised learning framework instead of the adversarial learning framework, and is therefore easier to optimize than adversarial-based methods (Kallus, 2020).


Action Graph  The input to our policy framework consists of the state s and a list C = [ c a 0 , ..., c a k ] of action representations for each action a i ∈ A . We build a fully connected action graph G with vertices corresponding to each  action. If certain action relations are predeﬁned in domain knowledge, we can remove other edges to ease training (Appendix B.1). The relations that we must infer depend on the current state. For instance, a screwdriver is relevant to a screw while repairing furniture, but a drill machine is more related when the screw is for a wall. Following this insight, we join  state and action representations, c (cid:48) a k = ( s, c a k ) to form the input nodes of the graph. In Sec. 6.3.2, we validate this insight by comparing against having graph nodes as action representations only.

Action Graph : The input to our policy framework consists of the state s and a list C = [ c a 0 , ..., c a k ] of action representations for each action a i ∈ A . We build a fully connected action graph G with vertices corresponding to each available action. If certain action relations are predeﬁned via domain knowledge, we can reduce some edges to ease training (Appendix B.1). We note that the action relations can vary depending on the environment state. For instance, a screwdriver is related to a screw for furniture repair, but a drill machine is more related when the screw is for a wall. Therefore, we join the state and action representations, c (cid:48) a i = ( s, c a i ) to obtain the nodes of the graph. Sec. 6.3. validates that learning state-dependent action relations leads to more optimal solutions.

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Adult dataset. The de-biased classifier achieves higher recall while maintaining predictive ability evidenced by its precision value. We note that trade-off between precision and recall can be regulated by changing the number of epochs and not resetting the weights for each batch. Our code generates a full log of performance metrics for the biased and de-biased classifiers for every run of the algorithm.

Adult dataset. The de-biased classifier achieves higher recall while maintaining predictive ability evidenced by its precision value. Our code generates a full log of performance metrics for the biased and de-biased classifiers for every run of the algorithm.

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Recently, deep learning-based approaches to predicting mutational effects on protein binding have emerged. We group them into three categories: end-to-end models, pre-training-based models, and unsupervised models. End-to-end models take both mutant and wild-type(not mutated) protein structuresalong with other features as input and directly predict the difference in binding free energy. End-to-end models achieve satisfactory correlation between prediction and ground truth on the whole SKEMPI benchmark consisting of many different structures (Shan et al., 2022), but the perstructure correlation, which is more relevant to practical use, is still low. In attempt to settle the issue of data scarcity, another line of work proposes to pre-train a feature extraction networkand then use regression models to predict the effect of mutations based on the learned features (Liu et al., 2021; Yang et al.,  2022).

Recently, deep learning-based approaches have emerged. We group them into three categories: endto-end models, pre-training-based models, and unsupervised models. End-to-end models directly predict the difference in binding free energy by taking both mutant and wild-type protein structures as input (Shan et al., 2022). Pre-training-based models attempt to address data scarcity by pre-training a feature extraction network (Liu et al., 2021; Yang et al., 2022; Zhang et al., 2022).

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Previous uses of implicit differentation in meta-learning [iMAML] and neural architecture search [iDARTS] also involve solving a linear system, but their Y corresponds to the neural network parameters and thus usually has millions of entries. In contrast, in our setting we work with a much smaller Y , which for example only contains 190 entries in sec [].

Previous uses of implicit differentiation in meta-learning (Rajeswaran et al., 2019) and neural architecture search (Zhang et al., 2021b) also involve solving a linear system, but their Y corresponds to the neural network parameters and thus usually has millions of entries. In contrast, in our setting we work with a much smaller Y , which for example only contains 190 entries in Section 4.3. Regularization. In Rajeswaran et al.


Main results Table 1 displays the accuracy of each model on the test set of each dataset, after they were training on ImageNet-only or all datasets. Trafﬁc Signs and MSCOCO are not used for training in either case, as they are reserved for evaluation. We propose to use the average (over the datasets) rank of each method as our metric for comparison, where smaller is better. A method receives rankif it has the highest accuracy, rank 2 if it has the second highest, and so on. If two models share the best accuracy, they both get rank 1.5, and so on. We ﬁnd that fo-Proto-MAML is the top-performer according to this metric,  the Finetune Baseline notably presents a worthy opponent, while fo-MAML, to our surprise, performs quite poorly on M ETA -D ATASET . We include more detailed versions of these tables displaying conﬁdence intervals and per-dataset ranks in the Appendix.

Main results Table 1 displays the accuracy of each model on the test set of each dataset, after they were trained on ImageNet-only or all datasets. Trafﬁc Signs and MSCOCO are not used for training in either case, as they are reserved for evaluation. We propose to use the average (over the datasets) rank of each method as our metric for comparison, where smaller is better. A method receives rankif it has the highest accuracy, rank 2 if it has the second highest, and so on. If two models share the best accuracy, they both get rank 1.5, and so on. We ﬁnd that fo-Proto-MAML is the top-performer according to this metric, Prototypical Networks also perform strongly, and the Finetune Baseline notably presents a worthy opponent 3 . We include more detailed versions of these tables displaying conﬁdence intervals and per-dataset ranks in the Appendix.


To encourage evasion with fewer mutation turns. We further update the reward over a mutation period using the reward function deﬁned as R t = R t − 1 − nσ where the value for R t is either given by R l or R s depending the environment used, n is the number of mutation turns within current episode, and σ is the constant step penalty, which is set to be 0.1 in our environment.

To encourage evasion with fewer mutation turns. We further update the reward over a mutation period using the reward function deﬁned as R = R t − σt where the value for R t is either given by R l or R s at step t inside one episode, and σ is the constant step penalty, which is set to be 0.1 in our environment.


We adopted the idea proposed in Chen et al. They aim to build a model for supervised SNLI task (Bowman et al., 2015), and the model concatenates the outputs from a global mean-pooling function and a global max-pooling function to serve as a sentence representation, and shows a performance boost on the SNLI dataset. Besides, Conneau et al. (2017) found that the model with global max-pooling function has stronger transferability than the model with a global mean-pooling function after supervised training on SNLI.

We followed the idea proposed in Chen et al. They built a model for supervised SNLI task (Bowman et al., 2015) that concatenates the outputs from a global mean pooling and a global max pooling to serve as a sentence representation, and showed a performance boost on the SNLI dataset. Also, Conneau et al. (2017) found that the model with global max pooling function has stronger transferability than the model with a global mean pooling function after supervised training on SNLI.

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In this work, we propose the rotamer density estimator (RDE) that estimates the distribution of rotamers. We find the entropy of the estimated distributions and the unsupervised representations produced by the RDE enable more accurate prediction of binding ∆∆ G . One  of the major limitations of this work is that it cannot directly model backbone flexibility. Neither do all the considered baselines. Therefore, an importantnon-trivial future direction is extending the proposed model to backbone-flexible cases.

In this work, we introduce the Rotamer Density Estimator (RDE) which estimates the distribution of rotamers for protein sidechains. We demonstrate that RDE leads to improved accuracy in predicting binding ∆∆ G compared to other methods. One limitation of RDE is the inability to model backbone flexibility directly which is an important future direction for extending the proposed model. Nonetheless, our work highlights the potential of using machine learning techniques to improve mutational effect prediction for protein-protein interaction.


Reminders are among the most common technological interventions to improve adherence to medication [4,27,28]. Reminders can take many forms, including interventions of caregivers through video and voice calls [29] and text messages [30], smart pill boxes [10], and computer applications [13]. Focusing on systems that visually represent reminder events to stay within the scope of this research, we identified two relevant technological interventions. The first one is a health literacy tool called Medication Calen- dar [14]. It was designed to improve antihypertensive medication adherence. The Medication Calendar provides a graphical view of medication to be taken during a given section of a day. Its layout shows Morning, Afternoon, Evening, and Bedtime as columns and the medications as rows. It displays (in text format) the medication name; the time of day that it should be consumed, the number of times daily that it should be taken; the dose of medication administered; and  clinical indication for medication. The application then triggers reminders when it is time to take a medication. The second relevant intervention is a tool for representing graph- ically enhanced interventions in coronary heart disease [31] The tool they designed also shows Morning, Afternoon, Evening, and Bedtime as columns, the These two contributions provide foundational design elements to consider for visualizing medications and their reminders in a calendar design. Specifically, the layout (columns and rows) and design concepts (graphical representation of drug entities) provide a starting point for  design.

Reminders are among the most common technological interventions to improve adherence to medication [4,26,27]. Reminders can take many forms, including interventions of caregivers through video and voice calls [28] and text messages [29], smart pill boxes [10], and computer applications [13]. Focusing on systems that visually represent reminder events to stay within the scope of this research, we identified two relevant technological interventions. The first one is a health literacy tool called Medication Calendar [14]. It was designed to improve antihypertensive medication adherence. The Medication Calendar provides a graphical view of medication to be taken during a given section of a day. Its layout shows Morning, Afternoon, Evening, and Bedtime as columns and the medications as rows. It displays (in text format) the name of the medication, the time of day that it should be administered, the number of times daily that it should be taken, dosage information, and additional clinical indications. The application then triggers reminders when it is time to administer the medication. The second relevant intervention is a tool for representing graphically enhanced interventions for coronary heart disease [30] The tool shows the time of day (Morning, Afternoon, Evening, and Bedtime) as columns and the list of medication as rows. An additional col- umn indicates the purpose of the medication. Row headers include medication name, dosage, and the time of day when it should be administered. The novelty in this work is that the table cells contain graphical images of the corresponding medication. These two contributions provide foundational design elements to consider for visualizing medications and their reminders in a calendar-style design. Specifically, the layout (columns and rows) and design concepts (graphical representation of drug entities) pro- vide a starting point for an integrated design.


Optimal Transport The Optimal Transport [30] is initially introduced to solve the problem of howto reduce the cost when moving  several items simultaneously. Recently, OT theory has drawn wideattention in the machine learning and computer vision community by comparing distributions readilyavailable to them under the form of feature sets [37]. Due to the brilliant property of distributionmatching, OT has been applied in many theoretic and application tasks including generative models [1,45, 60], structural matching [4, 57, 61, 56] (e.g. sequence matching [4] and graph matching [56]),and other distribution-based tasks (such as clustering [22], distribution estimation [2], and causaldiscovery [50]). In this paper, we use OT  to align the features of vision and language modalitieswhich represents thedata structure by learning an adaptive transport plan [44].

Optimal Transport The Optimal Transport [30] is initially introduced to solve the problem of howto reduce the cost when moving simultaneously several items. Recently, OT theory has drawn wideattention in the machine learning and computer vision community by comparing distributions readilyavailable to them under the form of feature sets [37]. Due to the brilliant property of distributionmatching, OT has been applied in many theoretic and application tasks including generative models [1,44, 59], structural matching [4, 56, 60, 55] (e.g. sequence matching [4] and graph matching [55]),and other distribution-based tasks (such as clustering [22], distribution estimation [2], and causaldiscovery [49]). In this paper, we use OT distance to align the features of vision and languagemodalities and propose a two-stage learning strategy to guide the learning of multiple prompts.

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Generalization of meta learning. The excess risk , as a metric of generalization ability of gradientbased meta learning has been analyzed recently [3,4,9,14,18,42]. The generalization of meta learninghas been studied in [27] in the context of mixed linear regression, where the focus is on investigatingwhen abundant tasks with small data can compensate for lack of tasks with big data. Generalization performance has also been studied in a relevant but different setting - representation based metalearning [13,16]. Information theoretical bounds have been proposed in [10,26], which bound thegeneralization error in terms of mutual information between the input training data and the output of the meta-learning algorithms. The PAC-Bayes framework has been extended to meta learning to provide a PAC-Bayes meta-population risk bound [1,15,19,34]. These works mostly focus on the case where the meta learning model is underparameterized; that is, the total number of meta training data from all tasks is larger than the dimension of the model parameter. Recently, overparameterized metalearning has attracted much attention. Bernacchia [6] suggests that in overparameterized MAML,negative learning rate in the inner loop is optimal during meta training for linear models with Gaussian data. Sun et al. [39] shows that the optimal representation in representation-based meta learning isoverparameterized and provides sample complexity  for the method of moment estimator.

Generalization of meta learning. The excess risk , as a metric of generalization ability of nestedmeta learning has been analyzed recently [3,4,9,13,17,41]. Generalization performance has also been studied in a relevant but different setting - representation based meta learning [12,15]. Informationtheoretical generalization bounds have been proposed in [10,25], which bound the generalization errorin terms of mutual information between the input training data and the output of the meta-learning algorithms. The PAC-Bayes framework has been extended to meta learning to provide a PAC-Bayes meta-population risk bound [1,14,18,32]. These works mostly focus on the case where the meta learning model is underparameterized; that is, the total number of meta training data from all tasks is larger than the dimension of the model parameter. Recently, overparameterized meta learninghas attracted much attention. Bernacchia [6] suggests that in overparameterized MAML, negativelearning rate in the inner loop is optimal during meta training for linear models with Gaussian data. Sun et al. [37] shows that the optimal representation in representation-based meta linear regression isoverparameterized and provides sample complexity bounds for the method of moment estimator.

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Consistency layers. Approaches ensuring consistency by embedding the constraints into the predictive layer as in SPLs include MultiplexNet [37] and HMCCN [31]. MultiplexNet is able to encode only constraints in disjunctive normal form, which is problematic for generality (D4) and efﬁciency (D6) as neuro-symbolic SOP tasks involve an intractably large number of clauses – e.g. our pathﬁnding experiments involves billions of clauses. HMCCN encodes label dependencies as fuzzy relaxation and is the current state-of-the-art model for HMLC [31]. Even its recent extension [32] is restricted to a certainfamily of constraints(D4) that can be represented with fuzzy logic.

Consistency layers. Approaches ensuring consistency by embedding the constraints into the predictive layer as in SPLs include MultiplexNet [38] and HMCCN [32]. MultiplexNet is able to encode only constraints in disjunctive normal form, which is problematic for generality (D4) and efﬁciency (D6) as neuro-symbolic SOP tasks involve an intractably large number of clauses – e.g. our pathﬁnding experiments involves billions of clauses. HMCCN encodes label dependencies as fuzzy relaxation and is the current state-of-the-art model for HMLC [32]. HMCCN and even its recent extension [33] are restricted to only certain constraints that can be exactly encoded with fuzzy logic easily. SPLs instead can express constraints encoded as arbitrary propositional logical formulas (D4).


Unimodal losses such as mean squared error are not very useful when predicting high dimensional data, due to the stochasticity of the output space. Researchers have tried to handle such stochasticity using latent variable models (Loehlin, 1987) or autoregressive prediction of the output pixel space, which involves sampling each pixel value from a categorical distribution conditioned on the output thus far (Van den Oord et al., 2016). Another option is to make predictions in a latent feature space. Recently, Oord et al. (2018) followed this direction and used an objective that preserves  mutual information between the future bottom-up extracted features and the predicted contextual latent features, applying it  in speech, text and image patches in single images. The view contrastive loss proposed in this work is a non-probabilistic version of their contrastive objective. However, our work focuses on the video domain as opposed to image patches, and uses drastically different architectures for both the contextual and bottom-up representations, using a 3D representation bottleneck.

Unimodal losses such as mean squared error are not very useful when predicting high dimensional data, due to the stochasticity of the output space. Researchers have tried to handle such stochasticity using latent variable models (Loehlin, 1987) or autoregressive prediction of the output pixel space, which involves sampling each pixel value from a categorical distribution conditioned on the output thus far (Van den Oord et al., 2016). Another option is to make predictions in a feature space which is less stochastic than the input. Recently, Oord et al. (2018) followed this direction and used an objective that preserves the mutual information between “top-down” contextual features predicted from input observations, and “bottom-up” features produced from future observations; it applied this objective in speech, text, and image crops. The view-contrastive loss proposed in this work is a non-probabilistic version of their contrastive objective. However, our work focuses on the video domain as opposed to image patches, and uses drastically different architectures for both the top-down and bottom-up representations, involving a 3D egomotion-stabilized bottleneck.


• The NTK is deﬁned using the gradient of the DNN output with respect to weight parameter space . In contrast, the linear approximation Lemma in this paper) is deﬁned using the gradient of the DNN output with respect to input parameter space . In other words, the variables to be differentiated are different. • Although NTK analysis is limited to gradient descent , our analysis can be applied to stochastic gradient descent . • The random walk analysis indicates that over-parameterized ReLU DNNs interpolate almost linearly between the data points. For ReLU activation, since the NTK kernel mapping is not Lipschitz but 1 / 2 -H ¨ older, it is difﬁcult to obtain such a result in the NTK analysis without a tradeoff between smoothness and approximation (Bietti & Mairal, 2019).

• The NTK is deﬁned using the gradient of the DNN output with respect to weight parameter space . In contrast, the linear approximation (Lemma 3 in this paper) is deﬁned using the gradient of the DNN output with respect to input parameter space . In other words, the variables to be differentiated are different. • The random walk analysis indicates that over-parameterized ReLU DNNs interpolate almost linearly between the data points. For ReLU activation, since the NTK kernel mapping is not Lipschitz but 1 / 2 -H ¨ older, it is difﬁcult to obtain such a result in the NTK analysis without a tradeoff between smoothness and approximation (Bietti & Mairal, 2019).

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Dataset The  input  of every example is represented by a 64 × 4 matrix, where each row is a one-hot vector that is sampled i.i.d. from the multinomial distribution over the equally weighted 4 classes. We generate the target matrix of  size  64 × 64 by counting the occurrences for each unique input class sequentially from top to bottom and represent the count as a64 dimensional one-hot vector. The setting with 1 × samples has a training dataset of size 640. We additionally use a validation set of size 6,400 and a test set of size 64,000.

MSE as pairwise loss for DSPN/iDSPN and cross-entropy as pairwise loss for the other models. The baselines perform worse with MSE as pairwise loss. For each example, the input multiset has a size of 64 with 4-dimensional elements corresponding toclasses. This is represented as a 64 × 4 matrix where each row is a one-hot vector that is sampled i.i.d. from the multinomial distribution over the equally-weighted 4 classes. We generate the target multiset of the same set size with 64-dimensional elements ( 64 × 64 matrix), each element being a one-hot vector that represents a number. For each class, we number the corresponding elements sequentially. The setting with 1 × samples has a training dataset of size 640. We additionally use a validation set of size 6,400 and a test set of size 64,000 for every run.


Our method provides a solution to  the aforementioned challenges. Training the rotamer density estimator requires only protein structures. Thus, itis an unsupervised learner of the  effectof mutations on binding and it alleviates the difficulty rising from the scarcity of annotated mutation data. In addition, our method does not require the structure of the mutated protein  as input. Rather, it treats mutated structures as latent variables and the rotamer density estimator is an approximator of the latent distribution. Our method outperforms  empirical energy functions and machine learning models for  ∆∆ G prediction . In addition, as a generative model for rotamers, the RDE  predicts sidechain conformations accurately .

Our method is an attempt to address the aforementioned challenges. The Rotamer Density Estimator is trained solely on protein structures, not requiring other labels, making it an unsupervised learner of the mutation effect on protein-protein interaction. This feature mitigates the challenge posed by the scarcity of annotated mutation data. Moreover, our method does not require the mutated protein structure as input. Instead, it treats mutated structures as latent variables, which are approximated by RDE. Our method outperforms both empirical energy functions and machine learning models for predicting ∆∆ G . Additionally, as a generative model for rotamers, the RDE accurately predicts sidechain conformations.

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In this section we describe our main contribution, Adversarial Optimism (AdOpt) in detail. At a high level, AdOpt uses two classifiers. The first one is a  classifier trained on all the accepted data thus far, without any de-biasing. We refer to this as the “biased” classifier hereafter. The second one is our adversarially de-biased classfier trained on the same data. AdOpt then proceeds as follows:

In this section we describe our main contribution, Adversarial Optimism (AdOpt) in detail. AdOpt uses two classifiers. The first one is a “biased” classifier trained on all the accepted data thus far. The second one is our adversarially de-biased classifier. AdOpt then proceeds as follows:

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Besides improving fine-tuning on low-resource data by removing irrelevant features, we expect VIB to improve on out-of-domain data because it removes redundant features. In particular, annotation artifacts in a specific dataset are known to create shortcut features, which are superficial cues correlated with a label (Gururangan et al., 2018). We hypothesize that these shortcuts are easy to learn (especially when the amount of data is not sufficient), but are actually redundant with deeper features, which capture the true generalizations in the task. By compressing the input embeddings, VIB encourages learning these desirable general features(Shamir et al., 2010; Tishby and Zaslavsky, 2015). By removing the redundant features,  the trained model generalizes better  to out-of-domain datasets that lack these shortcut features (Belinkov et al., 2019). To evaluate out-of-domain generalization, we take NLI models trained on medium-sized 6K subsampled SNLI and MNLI in Section 3.2 and test their generalization to several NLI datasets.

Besides improving fine-tuning on low-resource data by removing irrelevant features, we expect VIB to improve on out-of-domain data because it removes redundant features. In particular, annotation artifacts create shortcut features, which are superficial cues correlated with a label (Gururangan et al., 2018; Poliak et al., 2018) that do not generalize well to out-of-domain datasets (Belinkov et al., 2019a). Since solving the real underlying task can be done without these superficial shortcuts, they must be redundant with the deep semantic features that are truly needed. We hypothesize that many more superficial shortcut features are needed to reach the same level of performance as a few deep semantic features. If so, then VIB should prefer to keep the concise deep features and remove the abundant superficial features, thus encouraging the classifier to rely on the deep semantic features, and therefore resulting in better generalization to outof-domain data. To evaluate out-of-domain generalization, we take NLI models trained on medium-sized 6K subsampled SNLI and MNLI in Section 3.2 and evaluate their generalization on several NLI datasets.


Feature reconstruction . A linear projection is first applied to these feature tokens to reduce C org to a smaller channel, C . Then these tokens are processed by NME and LQD. The learnable position embeddings [12, 13] are added in the attention module to inform the spatial information. Afterward, another linear projection is used to recover the channel from C to C org . After reshape,the reconstructed feature map, f rec ∈ R C org × H × W , is finally obtained.

Feature reconstruction . The feature map, f org , is first tokenized to H × W feature tokens, followedby a linear projection to reduce C org to a smaller channel, C . Then these tokens are processed by NME and LQD. The learnable position embeddings [14, 15] are added in attention modules to informthe spatial information. Afterward, another linear projection is used to recover the channel from C to C org . After reshape, the reconstructed feature map, f rec ∈ R C org × H × W , is finally obtained.


Metric learning develops a feature representation based on data grouping and separation cues. Our method (Fig. 3) segments an image by learning a pixel-wise embedding with a contrastive loss between pixels and segments. We start from deﬁning two disjoint sets – positive and negative segments (exemplars) with respect to pixel i . Our goal is to group i with positive segments while separating it from negative ones. Given latent feature φ ( i ) at pixel iand a speciﬁc distance metric, the objective is  todecrease (increase) the distance between φ ( i ) and its positive (negative) segments.

Metric learning develops a feature representation based on data grouping and separation cues. Our method (Fig. 3) segments an image by learning a pixel-wise embedding with a contrastive loss between pixels and segments: For each pixel i , we learn a latent feature φ ( i ) such that i is close to its positive segments (exemplars) and far from its negative ones in that feature space.

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Statistical Significance To show that there is a statistically significant relationship between the entropy estimated by the RDE and the experimental ∆∆ G values, we conduct linear regression analysis using the RDE-Linear model defined in Eq.9. The linear model contains 7 coefficients and 1 bias: w bound W L , w bound W R , w unbnd W L , w bound M L , w bound M R , w unbnd M L ,  ( w unbnd M R − w unbnd W R ) , and b . Here, w unbnd M R and w unbnd W R are merged because the receptor is not mutated, so the entropy estimated by the model are identical. For short, we denote the merged coefficient by w unbnd R . We perform linear regression on the SKEMPI2  dataset and present the regression coefficients, bias, and P-values in Table 3.

Statistical Significance To demonstrate a statistically significant relationship between the entropy estimated by RDE and experimental ∆∆ G values, we conduct linear regression analysis using the RDE-Linear model defined in Eq. The linear model consists of seven coefficients and one bias term: w bound W L , w bound W R , w unbnd W L , w bound M L , w bound M R , w unbnd M L , w unbnd R = ( w unbnd M R − w unbnd W R ) , and b . Note that w unbnd M R and w unbnd W R are merged into w unbnd R , as the receptor is not mutated. We perform linear regression on the SKEMPI2 single-mutation dataset and present the regression coefficients, bias, and P-values in Table 3.

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For all tasks, we see that our RNS-RNN (denoted NS+S+U) attains near-optimal cross-entropy (within 0.05 nats) on the validation set. All stack models eﬀectively solve the deterministic marked reversal and Dyck tasks, although we note that on marked reversal the NS models do not generalize well on held-out lengths. Our new model excels on the three nondeterministic tasks: unmarked reversal, padded reversal, and hardest CFL. We ﬁnd that the combination of including PDA states in the reading and allowing the action weights to be unnormalized (+S+U) greatly improves performance on unmarked reversal and hardest CFL over previous work. For unmarked reversal, merely changing the task by adding EOS causes the baseline NS model to perform worse than Gref and JM; using both enhancements (+S+U) is essential to surpassing them. For padded reversal, we see that the addition of PDA states in the stack reading (+S) proves essential to improving performance.

For all tasks, we see that our RNS-RNN (denoted NS+S+U) attains near-optimal cross-entropy (within 0.05 nats) on the validation set. All stack models eﬀectively solve the deterministic marked reversal and Dyck tasks, although we note that on marked reversal the NS models do not generalize well on held-out lengths. Our new model excels on the three nondeterministic tasks: unmarked reversal, padded reversal, and hardest CFL. We ﬁnd that the combination of both enhancements (+S+U) greatly improves performance on unmarked reversal and hardest CFL over previous work. For unmarked reversal, merely changing the task by adding EOS causes the baseline NS model to perform worse than Gref and JM; this may be because it requires the NS-RNN to learn a correlation between the two most distant time steps. Both enhancements (+S+U) in the RNS-RNN are essential here; without unnormalized weights, the model does not ﬁnd a good solution during training, and without PDA states, the model does not have enough information to make optimal decisions. For padded reversal, we see that the addition of PDA states in the stack reading (+S) proves essential to improving performance.


Mathematically, any irreversible mapping y = f(args...) can be trivially transformed to its reversible form y += f(args...) or y (cid:89) = f(args...) ( (cid:89) is the bit-wise XOR ), where y is a pre-emptied variable. But in numeric computing with ﬁnite precision, this is not always true. The reversibility of arithmetic instruction is closely related to the number system. For integer and ﬁxed point number system, y += f(args...) and y -= f(args...) are rigorously reversible. For logarithmic number system and tropical number system (Speyer & Sturmfels, 2009), y *= f(args...) and y /= f(args...) as reversible (not introducing the zero element). While for ﬂoating point numbers, none of the above operations are rigorously reversible. However, for convenience, we ignore the rounding errors in ﬂoating point + and - operations and treat them on equal footing with ﬁxed point numbers in the following discussion. Other reversible operations includes SWAP , ROT , NEG et. al., and this instruction set is extensible. One can deﬁne a reversible multiplier in NiLang as in Listing. 2.

Mathematically, any irreversible mapping y = f(args...) can be trivially transformed to its reversible form y += f(args...) or y (cid:89) = f(args...) ( (cid:89) is the bit-wise XOR ), where y is a pre-emptied variable. But in numeric computing with ﬁnite precision, this is not always true. The reversibility of arithmetic instruction is closely related to the number system. For integer and ﬁxed point number system, y += f(args...) and y -= f(args...) are rigorously reversible. For logarithmic number system and tropical number system (Speyer & Sturmfels, 2009), y *= f(args...) and y /= f(args...) as reversible (not introducing the zero element). While for ﬂoating point numbers, none of the above operations are rigorously reversible. However, for convenience, we ignore the round-o ﬀ errors in ﬂoating-point + and - operations and treat them on equal footing with ﬁxed-point numbers in the following discussion. In Appendix ?? , we will show doing this is safe in most cases provided careful implementation. Other reversible operations includes SWAP , ROT , NEG et. al., and this instruction set is extensible. One can deﬁne a reversible multiplier in NiLang as in Listing. 2.


Image semantic segmentation is the task of pixel-level semantic label allocation for recognizing objects in an image. The development of Deep Neural Networks (DNNs) has promoted the rapid development of the semantic segmentation task [6, 58, 19] in recent years. However, training sucha fully-supervised semantic segmentation model requires large numbers of pixel-wise annotations.

Image Semantic Segmentation is the task of pixel-level semantic label allocation for recognizing objects in an image. The development of Deep Neural Networks (DNNs) has promoted the rapid development of the semantic segmentation task [7, 20, 63] in recent years. However, training such a Fully-Supervised Semantic Segmentation model requires large numbers of pixel-wise annotations.

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In real-world problems, the dynamics are often nearly deterministic. We leverage this assumption  and  remove the expectation over the next states in the operator, which leads to  Expectile V -Learning, where we train the value network to minimize the following loss:

In real-world problems, the dynamics are often nearly deterministic. We leverage this assumption We consider the case where the dynamics are nearly-deterministic like robotic applications, and we remove the expectation over the next states in the operator. This leads to a practical algorithm, Expectile V -Learning, where we train the value network to minimize the following loss:


Interrupted augmentation . We wonder how generalization would change after regularizationstopped. Thus, we stop the DA during training, such as (0, 5), (0, 15). When we compare the graph Figure 2(d) and Figure 2(e), the generalization performance in Figure 2(d) rapidly decreasesafter interrupted on both (0, 5) and (0, 15). In contrast, the curves (0, 5) and (0, 15) in Figure 2(e)maintain the generalization in spite of interrupting augmentation. In training performance, InDA,which uses augmentation throughout training, performs better than PPO in Figure 2(b); however,augmentation does not improve the training performance in Figure 2(a). These results mean that the random convolution alleviates the difﬁculty by various backgrounds.

Interrupted augmentation . To determine how generalization would change after regularization stopped, we stop the DA during training, such as (0, 5), (0, 15). Jumper with easybg mode rapidly lost generalization performance (after interruption at both (0, 5) and (0, 15)) (Figure 2(d)), whereas Jumper with easy mode do not (Figure 2(e)). InDA, which uses augmentation throughout training, performs better than PPO during training (Figure 2(b)), but augmentation does not improve the training performance (Figure 2(a)). These results mean that the random convolution alleviates the difficulty by various backgrounds.

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While an RNN decoder, is designed to produce thenext word, a CNN decoder  is free to ﬁnd any relevant local patterns within the target sequences. The generation process is only conditioned on the sentence representation. Although the word order information is implicitly encoded in the CNN decoder, it is not emphasized as it is explicitly in the  RNN decoder. The  CNN decoder cares about the quality of generated sequences globally instead of  the quality of the next generated word. Relaxing the emphasis on the next word, may help the CNN decoder model to explore the contribution of context in a larger space.

In our model, the CNN decoder predicts all words at once during training, which is different from autoregressive decoders, and we call it a predict-all-words CNN decoder. We want to compare the performance of the predict-all-words decoders and that of the autoregressive decoders separate from the RNN/CNN distinction, thus we designed a predict-all-words CNN decoder and RNN decoder. The predict-all-words CNN decoder is described in Section 2, which is a stack of 3 convolutional layers, and all words are predicted once at the output of the decoder.

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As a quick example of selection collider bias, if we were to ask you the gender of some random person born in 1801,and one in 1999, you may toss a coin to determine your answer, asbirth date and gender are unconditionally independent in the real world. However, if instead we where to ask about the gender of a person born in 1801, and one in 1999, that we saw on two random Wikipedia articles today, then you may condition your guess on some combination of birth date, gender, and importantly, what gets recorded in Wikipedia.

If someone was to ask you the gender of a random person born in 1801, you may toss a coin to determine your answer, as gender at birth is invariant to time. However, if instead someone was to ask about the gender of a person born in 1801 on a random Wikipedia page, you may then inform your guess with the knowledge that the level of recognition required to be recorded in Wikipedia is not invariant to time. Thus in your answer, you would have induced a conditional dependency between date and gender, that you may reapply when asked to guess gender of a person born in 2001 on a random Wikipedia page.

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We validate the choice of using graph attention network as the relational architecture. In Figure 7, we compare GAT against a graph convolutional network (GCN) (Kipf & Welling, 2016) in the action graph of AGILE. We observe that  for thesimple grid world and RecSim tasks, GCN achieves optimal performance. This is because GCN can still act like a summarizer, despite the edge weights  notbeing learned. However, it suffers in CREATE and RecSim-pairing (Figure 16) where the action space is large and requires diverse action relations. Moreover, we believe that the attention in GAT makes the graph sparse to ease RL training, which in contrast, is difﬁcult in a fully-connected GCN.

We validate the choice of using graph attention network as the relational architecture. In Figure 7, we compare GAT against a graph convolutional network (GCN) (Kipf & Welling, 2016) to act over AGILE’s action graph. We observe that GCN achieves optimal performance for the grid world and RecSys tasks. GCN can learn simple action relations even though the edge weights are not learned. However, it suffers in CREATE and RecSim-pairing (Figure 16), where the action relations are diverse and plenty. Moreover, we believe that the attention in GAT makes the graph sparse to ease RL training, which in contrast, is difﬁcult in a fully-connected GCN.

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CNNs to tag images of road scenes from 52 possible labels. In the medical domain, (Wang et al., 2017) present a chest X-ray dataset in which one image may contain multiple abnormalities. Multilabel classiﬁcation is also prominent in natural language processing (Nam et al., 2014). Our proposed method is therefore relevant to a wide range of applications in the real world.

CNNs to tag images of road scenes from 52 possible labels. In the medical domain, (Wang et al., 2017) present a chest X-ray dataset in which one image may contain multiple abnormalities. Multilabel classiﬁcation is also prominent in natural language processing (Nam et al., 2014). Recent work also provides a theoretical analysis of multi-label classiﬁcation under various measures (Wu & Zhu, 2020). Our proposed method is therefore relevant to a wide range of applications in the real world.


Predictive coding theories suggest that the brain learns by predicting observations at various levels of abstraction. One of the most basic prediction tasks is view prediction: how would a given scene look from an alternative viewpoint? Humans excel at this task. Our ability to imagine and ﬁll in missing visual information is tightly coupled with perception: we feel as if we see the world in 3 dimensions, while in fact, information from only the front surface of the world hits our (2D) retinas. This paper explores the connection between view-predictive representation learning and its role  in the development of 3D visual recognition. We propose inverse graphics networks, which take as input 2.5D  video streams captured by a moving camera, and map to stable 3D feature maps of the scene, by disentangling the scene content from the motion of the camera. The model can also project its 3D feature maps to novel viewpoints, to predict and match against target views. We propose contrastive prediction losses that can handle stochasticity of the visual input and can scale view-predictive learning to more photorealistic scenes than those considered in previous works. We show that the proposed model learns 3D visual representations useful for (1) semi-supervised learning of 3D object detectors, and (2) unsupervised learning of 3D moving object detectors, by estimating  motion of the inferred 3D feature maps in videos of dynamic scenes. To the best of our knowledge, this is the ﬁrst work that empirically shows view prediction to be a useful and scalable self-supervised task beneﬁcial to 3D object detection.

Predictive coding theories suggest that the brain learns by predicting observations at various levels of abstraction. One of the most basic prediction tasks is view prediction: how would a given scene look from an alternative viewpoint? Humans excel at this task. Our ability to imagine and ﬁll in missing information is tightly coupled with perception: we feel as if we see the world in 3 dimensions, while in fact, information from only the front surface of the world hits our retinas. This paper explores the role of view prediction in the development of 3D visual recognition. We propose neural 3D mapping networks, which take as input 2.5D (color and depth) video streams captured by a moving camera, and lift them to stable 3D feature maps of the scene, by disentangling the scene content from the motion of the camera. The model also projects its 3D feature maps to novel viewpoints, to predict and match against target views. We propose contrastive prediction losses to replace the standard color regression loss, and show that this leads to better performance on complex photorealistic data. We show that the proposed model learns visual representations useful for (1) semi-supervised learning of 3D object detectors, and (2) unsupervised learning of 3D moving object detectors, by estimating the motion of the inferred 3D feature maps in videos of dynamic scenes. To the best of our knowledge, this is the ﬁrst work that empirically shows view prediction to be a scalable self-supervised task beneﬁcial to 3D object detection.

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Summary. This paper introduced a novel neural network architecture, speciﬁcally suitable for modeling image generators (decoders) in the context of deep generative modeling. The proposed SDN layer was analyzed in the context of: (a) a complex hierarchical VAE model, where we obtained state-of-the-art performance  in non-autoregressive density modeling; (b) a vanilla VAE, resulting in improvements in both density modeling and  representation learning.

Summary. This paper introduced a novel neural layer suitable for deep neural networks that produce images – image generators (decoders). Proposed SDN improves upon convolutional networks in terms of incorporating the prior on spatial coherence and modeling of long-range spatial dependencies. SDN was analyzed in the context of: (a) a complex hierarchical VAE model, where the state-of-the-art performance was obtained in non-autoregressive density modeling; (b) a vanilla VAE, resulting in improvements in both density modeling and disentangled representation learning.


Gansbeke et al., 2021; Yang et al., 2020). However, existing analysis typically assumes that the pre-training data distribution is the same as the target distribution, while the difference between the two is the critical reason for the trade-off focused in this work. Thus, our work needs to propose new analysis approaches. Recently, Cole et al. try to identify conditions where self-supervised contrastive representation learning methods can produce “good” visual representations and point out the “diversity-difficulty trade-off” phenomenon, which is most relevant to our work. However, they only empirically show the trade-off. They do not have a systematic study and do not give any analysis to explain why it happens. Bommasani et al. ask for further research on the issue of specialization vs. diversity in foundation model training data but do not give any thorough study as well. At the same time, our work provides a better understanding of the trade-off.

Gansbeke et al., 2021; Yang et al., 2020). However, existing analysis typically assumes that the pre-training data distribution is the same as the target distribution, while the difference between the two is the critical reason for the trade-off focused in this work. Thus, our work proposes new analysis approaches. Recently, Cole et al. have tried to identify conditions where self-supervised contrastive representation learning methods can produce “good” visual representations and point out the “diversity-difficulty trade-off” phenomenon, which is most relevant to our work. However, they only empirically show the trade-off, but do not provide a systematic study and analysis to explain why it happens. Bommasani et al. call for further research on the issue of specialization vs. diversity in foundation model training data, but do not provide a thorough study as well. Our work attempts to provide a better understanding of the trade-off between universality and label-efficiency.

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In this section, we further strengthour algorithm with SPIDER variance reduction technique [11], a variantof SARAH [31, 32], as stated in algorithm 3. Indeed, we use a large batchsize of b in every q iterations and use small batchsizes of b x and b y for the rest. We prove that SAPD+ using variance reduction, i.e., with VR-flag = true , achieves an oracle complexity of O

In this section, we equip SAPD+ with SPIDER variance reduction technique [12], a variant of SARAH [32, 33]. More precisely, for inexactly solving SCSC subproblems given in (4), we propose using VR-SAPD as stated in algorithm 3. Note VR-SAPD employs a large batchsize of b in every q iterations and use small batchsizes of b x and b y for the rest. We prove that SAPD+ using variance reduction, i.e., with VR-flag = true , achieves an oracle complexity of O


In general, the model parameter is fixed and the attacker can only provide crafted examples to foolthe model. Based on the amount of information the attacker can access, the adversarial attack canbe categorized into three classes. (1) White-box attack . The attacker has full accessto the system,including parameters and gradients of the target model, the input data, and the label. (2) Grey-boxattack . The attacker can partially access the system, including the target model and training inputdata, except the labels. (3) Black-box attack . The attacker can only access training input data butcannot access the target model and labels.

Note the adversarial attack happened in the testing stage, and the attackers cannot manipulate theforecasting model or its output. On the benign testing set, the forecasting model can perform well. Based on the amount of information the attacker can access in the testing stage, the adversarial attackcan be categorized into three classes. White-box attack . The attacker can fully access the target model,including the model architecture, the model parameters, gradients, model outputs, the input trafficstates, and the corresponding labels. Grey-box attack . The attacker can partially access the system,including the target model and the input traffic states, but without the labels. Black-box attack . Theattacker can only access the input traffic states, query the outputs of the target model or leverage asurrogate model to craft the adversarial examples.


We propose a new pruning approach to obtain sparse neural networks with state-of-the-art test accuracy. Our compression scheme uses a new saliency criterion that identiﬁes important weights in the network throughout training to propose candidate masks. As a key feature, our algorithm not only evolves the pruned sparse model alone, but jointly also a (closely related) dense model that is used in a natural way to correct for pruning errors during training. This results in better generalization properties on a wide variety of tasks, since the simplicity of the scheme allows us further to study it time sparsity low med high t

We propose a new pruning approach to obtain sparse neural networks with state-of-the-art test accuracy. Our compression scheme uses a new saliency criterion that identiﬁes important weights in the network throughout training to propose candidate masks. As a key feature, our algorithm not only evolves the pruned sparse model alone, but jointly also a (closely related) dense model that is used in a natural way to correct for pruning errors during training. This results in better generalization properties on a wide variety of tasks, since the simplicity of the scheme allows us further to study it from a theoretical point of view, and to provide further insights and interpretation. We do not require time sparsity low med high t


Listwise RL (CDQN) : To solve the combinatorial action space problem of listwise actions, we follow the Cascaded DQN (CDQN) framework of Chen et al. (2019a). The main challenge is that building the  list all at once is not feasible due to the intractably large number of possible lists. Therefore, the key is to build the list incrementally, one action at a time. Thus, each list index can be treated as an individual non-combinatorial action which can be trained with RL. We replace the Q-network of CDQN with AGILE in order to accommodate a varying action space. We share the weights of the cascaded Q-networks. Algorithm 1 provides complete details on  listwise AGILE.

Listwise RL (CDQN) : For tasks with listwise actions, we follow the Cascaded DQN (CDQN) framework of Chen et al. (2019a). The main challenge is that building the action list all at once is not feasible due to a combinatorial number of possible list-actions. Therefore, the key is to build the list incrementally, one action at a time. Thus, each list index can be treated as an individual action decision trained with independent Q-networks. We replace the Q-network of CDQN with AGILE to support a varying action space. Sharing the weights of the cascaded Q-networks led to better performance. Algorithm 1 provides complete details on CDQN for listwise AGILE.

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We conduct this study with ModelNet40, using the front and rear views. We choose ten values from an interval [10 − 9 , 10 − 3 ] as λ . We use SGD without momentum, set the learning rate to 0.1 and batch size to eight. For each combination of hyperparameters, we train three model repetitions.

We conduct this study with ModelNet40, using the front and rear views. We choose ten values from an interval [10 − 9 , 10 − 3 ] as λ . We use SGD without momentum, set the learning rate to 0.1 and batch size to eight. Using each combination of hyperparameters, we repeat training for three times with random initialization and get three models.


Datasets: We consider 12 public datasets (3 public tabular datasets, 7 public image datasets, and 2 public language datasets) to evaluate DVRL in comparison to multiple benchmark methods.public tabular datasets are (1) Blog, ( 2) Adult, (3) Rossmann; 7 public image datasets are (4) HAM 10000, (5) MNIST, (6) USPS, (7) Flower, (8) Fashion-MNIST, (9) CIFAR-10, (10) CIFAR-100;public language datasets are (11) Email Spam, (12) SMS Spam. Detailsof the datasets can be found in the provided hyper-links (in blue).

Datasets: We consider 12 public datasets (3 public tabular datasets, 7 public image datasets, andpublic language datasets) to evaluate DVRL in comparison to multiple benchmark methods. 3 public tabular datasets are (1) Blog, ( 2) Adult, (3) Rossmann; 7 public image datasets are (4) HAM 10000, (5) MNIST, (6) USPS, (7) Flower, (8) Fashion-MNIST, (9) CIFAR-10, (10) CIFAR-100; 2 public language datasets are (11) Email Spam, (12) SMS Spam. Details can be found in the hyper-links.

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A prescription is a common and important form of medical interven- tion that is used in modern clinical settings. It comes as a recommendation from an healthcare provider to a patient [1]. It indicates actions such as taking medications, following a diet, or executing physical exercises [2]. When agreed upon between the patient and the healthcare provider, the patient is expected to follow a prescription [3]. The extent to which this implementation corresponds to the agreed upon recommendation is known as adherence [2]. Non-adherence to prescriptions is a significant problem in healthcare [2,4]. Adherence rates average 50% and account for 33-69% of hospital re-admissions, resulting into billions of dollars per year [5,6].

A prescription is a common and important form of medical inter- vention provided a clinician to a patient [1]. It indicates actions such as taking medications, following a diet, or executing physical exercises [2]. When agreed upon between a patient and their healthcare provider, the patient is expected to follow their prescription [3]. The extent to which a patient follows an agreed-upon prescription is referred to as adherence [2]. Non-adherence to prescriptions is a significant problem in healthcare [2,4]. Adherence rates average 50% and account for 33-69% of hospital re-admissions, resulting into billions of dollars per year [5,6].

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• If a data point is accepted by the biased classifier,  it is accepted and added to the dataset with the true label. • If a data point is instead rejected by the biased classifier we use our de-biased classifier to decide whether to add it to the Pseudo-label dataset from PLOT. • We then apply the Pseudo-label mechanism from PLOT, i.e. retraining on optimistic lables , on these candidates  to decide final acceptance.

• If a data point is accepted by the biased classifier, we accept it and add it to the dataset with the true label. • If a data point is instead rejected by the biased classifier, we use de-biased classifier to decide whether to add it to the pseudo-label dataset. • As in PLOT, retrain on the pseudo-label candidates with optimistic labels to decide final acceptance.

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Wang et al., 2020; Fan et al., 2020; Sun et al., 2020). Xu et al. (2015) formulates all types of weak supervision as linear constraints on a SVM. Recent works (Lin et al., 2016; Kolesnikov & Lampert, 2016;Pathak et al., 2015) typically use Class Activation Map (CAM) (Zhou et al., 2016) to obtain an initial dense mask and then train a model iteratively. GAIN (Li et al., 2018) utilizes image tag or bounding box annotations to reﬁne these class-speciﬁc activation maps. Sun et al. (2020) considers within-image relationships and explores the idea of co-segmentation. Fan et al. (2020) estimates the foreground and background for each category, with which the network learns to generate more precise CAMs. Regularization is enforced at either the image level (Lin et al., 2016; Kolesnikov & Lampert, 2016; Pathak et al., 2015) or the feature level (Tang et al., 2018a;b) to produce better dense masks. We incorporate this concept into adaptive feature learning and train the model only once. It is worth noting that each of the annotations carries different assumptions, we propose to unify all these types of weak annotations  in a single contrastive learning framework.

Wang et al., 2020; Fan et al., 2020; Sun et al., 2020). Xu et al. (2015) formulates all types of weak supervision as linear constraints on a SVM. Papandreou et al. bootstraps segmentation predictions via EM-optimization. Recent works (Lin et al., 2016; Kolesnikov & Lampert, 2016; Pathak et al., 2015) typically use CAM (Zhou et al., 2016) to obtain an initial dense mask and then train a model iteratively. GAIN (Li et al., 2018) utilizes image tags or bounding boxes to reﬁne these class-speciﬁc activation maps. Sun et al. (2020) considers within-image relationships and explores the idea of co-segmentation. Fan et al. (2020) estimates the foreground and background for each category, with which the network learns to generate more precise CAMs. Regularization is enforced at either the image level (Lin et al., 2016; Kolesnikov & Lampert, 2016; Pathak et al., 2015) or the feature level (Tang et al., 2018a;b) to produce better dense masks. We incorporate this concept into adaptive feature learning and train the model only once. All types of weak annotations are dealt with in a single contrastive learning framework.


Bi-LSTM : The raw action representations of candidate actions are passed on to the 2-layer MLP followed by ReLU. Then the output of the MLP is processed by a 2-layer bidirectional LSTM (Huang et al., 2015) followed by another 2-layer MLP  to create the action-summary to be used in the subsequent utility network.

Bi-LSTM : The raw action representations of candidate actions are passed on to the 2-layer MLP followed by ReLU. Then, the output of the MLP is processed by a 2-layer bidirectional LSTM (Huang et al., 2015). Another 2-layer MLP follows this to create the action set summary to be used in the following utility network.

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We thank Yasaman Bahri for signiﬁcant code contributions, frequent discussion and useful feedback on the manuscript, Sergey Ioffe for feedback on the text, as well as Greg Yang, Ravid Ziv, and Jeffrey

We thank Yasaman Bahri for frequent discussion and useful feedback on the manuscript. We additionally appreciate both Yasaman Bahri and Greg Yang for the ongoing contributions to improve the library. We thank Sergey Ioffe for feedback on the text, as well as Ravid Ziv, and Jeffrey