Zehao Dong, Muhan Zhang, Fuhai Li, Yixin Chen

Optimization of directed acyclic graph (DAG) structures has many applications, such as neural architecture search (NAS) and probabilistic graphical model learning. Encoding DAGs into real vectors is a dominant component in most neural-network-based DAG optimization frameworks.Currently, most popular DAG encoders use an asynchronous message passing scheme which sequentially processes nodes according to the dependency between nodes in a DAG. That is, a node must not be processed until all its predecessors are processed. As a result, they are inherently not parallelizable. In this work, we propose a Parallelizable Attention-based Computation structure Encoder (PACE) that processes nodes simultaneously and encodes DAGs in parallel. We demonstrate the superiority of PACE through encoder-dependent optimization subroutines that search the optimal DAG structure based on the learned DAG embeddings. Experiments show that PACE not only improves the effectiveness over previous sequential DAG encoders with a significantly boosted training and inference speed, but also generates smooth latent (DAG encoding) spaces that are beneficial to downstream optimization subroutines.

Munteanu, Alexander, Schwiegelshohn, Chris, Sohler, Christian, Woodruff, David

Coresets are one of the central methods to facilitate the analysis of large data. We continue a recent line of research applying the theory of coresets to logistic regression. First, we show the negative result that no strongly sublinear sized coresets exist for logistic regression. To deal with intractable worst-case instances we introduce a complexity measure $\mu (X)$, which quantifies the hardness of compressing a data set for logistic regression. $\mu (X)$ has an intuitive statistical interpretation that may be of independent interest. For data sets with bounded $\mu (X)$-complexity, we show that a novel sensitivity sampling scheme produces the first provably sublinear $(1\pm \text{eps})$-coreset. We illustrate the performance of our method by comparing to uniform sampling as well as to state of the art methods in the area. The experiments are conducted on real world benchmark data for logistic regression.

Zahavy, Tom, Haroush, Matan, Merlis, Nadav, Mankowitz, Daniel J., Mannor, Shie

Learning how to act when there are many available actions in each state is a challenging task for Reinforcement Learning (RL) agents, especially when many of the actions are redundant or irrelevant. In such cases, it is easier to learn which actions not to take. In this work, we propose the Action-Elimination Deep Q-Network (AE-DQN) architecture that combines a Deep RL algorithm with an Action Elimination Network (AEN) that eliminates sub-optimal actions. The AEN is trained to predict invalid actions, supervised by an external elimination signal provided by the environment. Simulations demonstrate a considerable speedup and added robustness over vanilla DQN in text-based games with over a thousand discrete actions.

Zhenqiao Song, Yunlong Zhao, Wenxian Shi, Wengong Jin, Yang Yang, Lei Li

Enzymes are genetically encoded biocatalysts capable of accelerating chemical reactions. How can we automatically design functional enzymes? In this paper, we propose EnzyGen, an approach to learn a unified model to design enzymes across all functional families. Our key idea is to generate an enzyme's amino acid sequence and their three-dimensional (3D) coordinates based on functionally important sites and substrates corresponding to a desired catalytic function. These sites are automatically mined from enzyme databases. EnzyGen consists of a novel interleaving network of attention and neighborhood equivariant layers, which captures both long-range correlation in an entire protein sequence and local influence from nearest amino acids in 3D space. To learn the generative model, we devise a joint training objective, including a sequence generation loss, a position prediction loss and an enzyme-substrate interaction loss. We further construct EnzyBench, a dataset with 3157 enzyme families, covering all available enzymes within the protein data bank (PDB). Experimental results show that our EnzyGen consistently achieves the best performance across all 323 testing families, surpassing the best baseline by 10.79% in terms of substrate binding affinity. These findings demonstrate EnzyGen's superior capability in designing well-folded and effective enzymes binding to specific substrates with high affinities. Our code, model and dataset are provided at https://github.com/LeiLiLab/EnzyGen.

Ilias Diakonikolas, Daniel Kane, Ankit Pensia, Thanasis Pittas

We study high-dimensional robust statistics tasks in the streaming model. A recent line of work obtained computationally efficient algorithms for a range of high-dimensional robust statistics tasks. Unfortunately, all previous algorithms require storing the entire dataset, incurring memory at least quadratic in the dimension. In this work, we develop the first efficient streaming algorithms for high-dimensional robust statistics with near-optimal memory requirements (up to logarithmic factors). Our main result is for the task of high-dimensional robust mean estimation in (a strengthening of) Huber's contamination model. We give an efficient single-pass streaming algorithm for this task with near-optimal error guarantees and space complexity nearly-linear in the dimension. As a corollary, we obtain streaming algorithms with near-optimal space complexity for several more complex tasks, including robust covariance estimation, robust regression, and more generally robust stochastic optimization.

Jihun Hamm, Yung-Kyun Noh

Minimax optimization plays a key role in adversarial training of machine learning algorithms, such as learning generative models, domain adaptation, privacy preservation, and robust learning. In this paper, we demonstrate the failure of alternating gradient descent in minimax optimization problems due to the discontinuity of solutions of the inner maximization. To address this, we propose a new $ϵ$-subgradient descent algorithm that addresses this problem by simultaneously tracking $K$ candidate solutions. Practically, the algorithm can find solutions that previous saddle-point algorithms cannot find, with only a sublinear increase of complexity in $K$. We analyze the conditions under which the algorithm converges to the true solution in detail. A significant improvement in stability and convergence speed of the algorithm is observed in simple representative problems, GAN training, and domain-adaptation problems.

Suggala, Arun, Prasad, Adarsh, Ravikumar, Pradeep K.

We study the implicit regularization properties of optimization techniques by explicitly connecting their optimization paths to the regularization paths of ``corresponding'' regularized problems. This surprising connection shows that iterates of optimization techniques such as gradient descent and mirror descent are \emph{pointwise} close to solutions of appropriately regularized objectives. While such a tight connection between optimization and regularization is of independent intellectual interest, it also has important implications for machine learning: we can port results from regularized estimators to optimization, and vice versa. We investigate one key consequence, that borrows from the well-studied analysis of regularized estimators, to then obtain tight excess risk bounds of the iterates generated by optimization techniques.

Claudio Gentile, Zhilei Wang, Tong Zhang

We consider a batch active learning scenario where the learner adaptively issues batches of points to a labeling oracle. Sampling labels in batches is highly desirable in practice due to the smaller number of interactive rounds with the labeling oracle (often human beings). However, batch active learning typically pays the price of a reduced adaptivity, leading to suboptimal results. In this paper we propose a solution which requires a careful trade off between the informativeness of the queried points and their diversity. We theoretically investigate batch active learning in the practically relevant scenario where the unlabeled pool of data is available beforehand ({\em pool-based} active learning). We analyze a novel stage-wise greedy algorithm and show that, as a function of the label complexity, the excess risk of this algorithm%operating in the realizable setting for which we prove matches the known minimax rates in standard statistical learning settings. Our results also exhibit a mild dependence on the batch size. These are the first theoretical results that employ careful trade offs between informativeness and diversity to rigorously quantify the statistical performance of batch active learning in the pool-based scenario.

Balaji, Yogesh, Sankaranarayanan, Swami, Chellappa, Rama

Training models that generalize to new domains at test time is a problem of fundamental importance in machine learning. In this work, we encode this notion of domain generalization using a novel regularization function. We pose the problem of finding such a regularization function in a Learning to Learn (or) meta-learning framework. The objective of domain generalization is explicitly modeled by learning a regularizer that makes the model trained on one domain to perform well on another domain. Experimental validations on computer vision and natural language datasets indicate that our method can learn regularizers that achieve good cross-domain generalization.

Santhosh Kumar Ramakrishnan, Ziad Al-Halah, Kristen Grauman

The goal in episodic memory (EM) is to search a long egocentric video to answer a natural language query (e.g., “where did I leave my purse?”). Existing EM methods exhaustively extract expensive fixed-length clip features to look everywhere in the video for the answer, which is infeasible for long wearable-camera videos that span hours or even days. We propose SpotEM, an approach to achieve efficiency for a given EM method while maintaining good accuracy. SpotEM consists of three key ideas: 1) a novel clip selector that learns to identify promising video regions to search conditioned on the language query; 2) a set of low-cost semantic indexing features that capture the context of rooms, objects, and interactions that suggest where to look; and 3) distillation losses that address the optimization issues arising from end-to-end joint training of the clip selector and EM model. Our experiments on 200+ hours of video from the Ego4D EM Natural Language Queries benchmark and three different EM models demonstrate the effectiveness of our approach: computing only 10% – 25% of the clip features, we preserve 84% – 97% of the original EM model’s accuracy. Project page: https://vision.cs.utexas.edu/projects/spotem

Michael Tschannen, Aran Khanna, Animashree Anandkumar

A large fraction of the arithmetic operations required to evaluate deep neural networks (DNNs) consists of matrix multiplications, in both convolution and fully connected layers. We perform end-to-end learning of low-cost approximations of matrix multiplications in DNN layers by casting matrix multiplications as 2-layer sum-product networks (SPNs) (arithmetic circuits) and learning their (ternary) edge weights from data. The SPNs disentangle multiplication and addition operations and enable us to impose a budget on the number of multiplication operations. Combining our method with knowledge distillation and applying it to image classification DNNs (trained on ImageNet) and language modeling DNNs (using LSTMs), we obtain a first-of-a-kind reduction in number of multiplications (over 99.5%) while maintaining the predictive performance of the full-precision models. Finally, we demonstrate that the proposed framework is able to rediscover Strassen’s matrix multiplication algorithm, learning to multiply $2\times 2$ matrices using only 7 multiplications instead of 8.

Liam Collins, Aryan Mokhtari, Sewoong Oh, Sanjay Shakkottai

Recent empirical evidence has driven conventional wisdom to believe that gradient-based meta-learning (GBML) methods perform well at few-shot learning because they learn an expressive data representation that is shared across tasks. However, the mechanics of GBML have remained largely mysterious from a theoretical perspective. In this paper, we prove that two well-known GBML methods, MAML and ANIL, as well as their first-order approximations, are capable of learning common representation among a set of given tasks. Specifically, in the well-known multi-task linear representation learning setting, they are able to recover the ground-truth representation at an exponentially fast rate. Moreover, our analysis illuminates that the driving force causing MAML and ANIL to recover the underlying representation is that they adapt the final layer of their model, which harnesses the underlying task diversity to improve the representation in all directions of interest. To the best of our knowledge, these are the first results to show that MAML and/or ANIL learn expressive representations and to rigorously explain why they do so.

Hsieh, Ya-Ping, Kavis, Ali, Rolland, Paul, Cevher, Volkan

We consider the problem of sampling from constrained distributions, which has posed significant challenges to both non-asymptotic analysis and algorithmic design. We propose a unified framework, which is inspired by the classical mirror descent, to derive novel first-order sampling schemes. We prove that, for a general target distribution with strongly convex potential, our framework implies the existence of a first-order algorithm achieving O~(\epsilon^{-2}d) convergence, suggesting that the state-of-the-art O~(\epsilon^{-6}d^5) can be vastly improved. With the important Latent Dirichlet Allocation (LDA) application in mind, we specialize our algorithm to sample from Dirichlet posteriors, and derive the first non-asymptotic O~(\epsilon^{-2}d^2) rate for first-order sampling. We further extend our framework to the mini-batch setting and prove convergence rates when only stochastic gradients are available. Finally, we report promising experimental results for LDA on real datasets.

Dupré la Tour, Tom, Moreau, Thomas, Jas, Mainak, Gramfort, Alexandre

Frequency-specific patterns of neural activity are traditionally interpreted as sustained rhythmic oscillations, and related to cognitive mechanisms such as attention, high level visual processing or motor control. While alpha waves (8--12\,Hz) are known to closely resemble short sinusoids, and thus are revealed by Fourier analysis or wavelet transforms, there is an evolving debate that electromagnetic neural signals are composed of more complex waveforms that cannot be analyzed by linear filters and traditional signal representations. In this paper, we propose to learn dedicated representations of such recordings using a multivariate convolutional sparse coding (CSC) algorithm. Applied to electroencephalography (EEG) or magnetoencephalography (MEG) data, this method is able to learn not only prototypical temporal waveforms, but also associated spatial patterns so their origin can be localized in the brain. Our algorithm is based on alternated minimization and a greedy coordinate descent solver that leads to state-of-the-art running time on long time series. To demonstrate the implications of this method, we apply it to MEG data and show that it is able to recover biological artifacts. More remarkably, our approach also reveals the presence of non-sinusoidal mu-shaped patterns, along with their topographic maps related to the somatosensory cortex.

Buddhika Nettasinghe, Samrat Chatterjee, Ramakrishna Tipireddy, Mahantesh Halappanavar

Conformal prediction is a widely used method to quantify the uncertainty of a classifier under the assumption of exchangeability (e.g., IID data). We generalize conformal prediction to the Hidden Markov Model (HMM) framework where the assumption of exchangeability is not valid. The key idea of the proposed method is to partition the non-exchangeable Markovian data from the HMM into exchangeable blocks by exploiting the de Finetti's Theorem for Markov Chains discovered by Diaconis and Freedman (1980). The permutations of the exchangeable blocks are viewed as randomizations of the observed Markovian data from the HMM. The proposed method provably retains all desirable theoretical guarantees offered by the classical conformal prediction framework in both exchangeable and Markovian settings. In particular, while the lack of exchangeability introduced by Markovian samples constitutes a violation of a crucial assumption for classical conformal prediction, the proposed method views it as an advantage that can be exploited to improve the performance further. Detailed numerical and empirical results that complement the theoretical conclusions are provided to illustrate the practical feasibility of the proposed method.

Stephen Tu, Benjamin Recht

Reinforcement learning (RL) has been successfully used to solve many continuous control tasks. Despite its impressive results however, fundamental questions regarding the sample complexity of RL on continuous problems remain open. We study the performance of RL in this setting by considering the behavior of the Least-Squares Temporal Difference (LSTD) estimator on the classic Linear Quadratic Regulator (LQR) problem from optimal control. We give the first finite-time analysis of the number of samples needed to estimate the value function for a fixed static state-feedback policy to within epsilon-relative error. In the process of deriving our result, we give a general characterization for when the minimum eigenvalue of the empirical covariance matrix formed along the sample path of a fast-mixing stochastic process concentrates above zero, extending a result by Koltchinskii and Mendelson in the independent covariates setting. Finally, we provide experimental evidence indicating that our analysis correctly captures the qualitative behavior of LSTD on several LQR instances.

Yang, Xin, Xu, Ke, Chen, Shaozhe, He, Shengfeng, Yin, Baocai Yin, Lau, Rynson

Image matting is an ill-posed problem. It requires a user input trimap or some strokes to obtain an alpha matte of the foreground object. A fine user input is essential to obtain a good result, which is either time consuming or suitable for experienced users who know where to place the strokes. In this paper, we explore the intrinsic relationship between the user input and the matting algorithm to address the problem of where and when the user should provide the input. Our aim is to discover the most informative sequence of regions for user input in order to produce a good alpha matte with minimum labeling efforts. To this end, we propose an active matting method with recurrent reinforcement learning. The proposed framework involves human in the loop by sequentially detecting informative regions for trivial human judgement. Comparing to traditional matting algorithms, the proposed framework requires much less efforts, and can produce satisfactory results with just 10 regions. Through extensive experiments, we show that the proposed model reduces user efforts significantly and achieves comparable performance to dense trimaps in a user-friendly manner. We further show that the learned informative knowledge can be generalized across different matting algorithms.

O'Kelly, Matthew, Sinha, Aman, Namkoong, Hongseok, Tedrake, Russ, Duchi, John C.

While recent developments in autonomous vehicle (AV) technology highlight substantial progress, we lack tools for rigorous and scalable testing. Real-world testing, the de facto evaluation environment, places the public in danger, and, due to the rare nature of accidents, will require billions of miles in order to statistically validate performance claims. We implement a simulation framework that can test an entire modern autonomous driving system, including, in particular, systems that employ deep-learning perception and control algorithms. Using adaptive importance-sampling methods to accelerate rare-event probability evaluation, we estimate the probability of an accident under a base distribution governing standard traffic behavior. We demonstrate our framework on a highway scenario, accelerating system evaluation by 2-20 times over naive Monte Carlo sampling methods and 10-300P times (where P is the number of processors) over real-world testing.

David Steinmann, Wolfgang Stammer, Felix Friedrich, Kristian Kersting

While deep learning models often lack interpretability, concept bottleneck models (CBMs) provide inherent explanations via their concept representations. Moreover, they allow users to perform interventional interactions on these concepts by updating the concept values and thus correcting the predictive output of the model. Up to this point, these interventions were typically applied to the model just once and then discarded. To rectify this, we present concept bottleneck memory models (CB2Ms), which keep a memory of past interventions. Specifically, CB2Ms leverage a two-fold memory to generalize interventions to appropriate novel situations, enabling the model to identify errors and reapply previous interventions. This way, a CB2M learns to automatically improve model performance from a few initially obtained interventions. If no prior human interventions are available, a CB2M can detect potential mistakes of the CBM bottleneck and request targeted interventions. Our experimental evaluations on challenging scenarios like handling distribution shifts and confounded data demonstrate that CB2Ms are able to successfully generalize interventions to unseen data and can indeed identify wrongly inferred concepts. Hence, CB2Ms are a valuable tool for users to provide interactive feedback on CBMs, by guiding a user's interaction and requiring fewer interventions.

Zhang, Xiaoxuan, Liu, Mingrui, Zhou, Xun, Yang, Tianbao

In this paper, we consider online F-measure optimization (OFO). Unlike traditional performance metrics (e.g., classification error rate), F-measure is non-decomposable over training examples and is a non-convex function of model parameters, making it much more difficult to be optimized in an online fashion. Most existing results of OFO usually suffer from high memory/computational costs and/or lack statistical consistency guarantee for optimizing F-measure at the population level. To advance OFO, we propose an efficient online algorithm based on simultaneously learning a posterior probability of class and learning an optimal threshold by minimizing a stochastic strongly convex function with unknown strong convexity parameter. A key component of the proposed method is a novel stochastic algorithm with low memory and computational costs, which can enjoy a convergence rate of $\tilde{O}(1/\sqrt{n})$ for learning the optimal threshold under a mild condition on the convergence of the posterior probability, where $n$ is the number of processed examples. It is provably faster than its predecessor based on a heuristic for updating the threshold. The experiments verify the efficiency of the proposed algorithm in comparison with state-of-the-art OFO algorithms.

Walter, Jörg, Ritter, Helge

We propose a hierarchical scheme for rapid learning of context dependent "skills" that is based on the recently introduced "Parameterized Self(cid:173) Organizing Map" ("PSOM"). The underlying idea is to first invest some learning effort to specialize the system into a rapid learner for a more restricted range of contexts. The specialization is carried out by a prior "investment learning stage", during which the system acquires a set of basis mappings or "skills" for a set of prototypical contexts. Adaptation of a "skill" to a new context can then be achieved by interpolating in the space of the basis mappings and thus can be extremely rapid. We demonstrate the potential of this approach for the task of a 3D visuo(cid:173) motor map for a Puma robot and two cameras. This includes the for(cid:173) ward and backward robot kinematics in 3D end effector coordinates, the 2D+2D retina coordinates and also the 6D joint angles. After the invest(cid:173) ment phase the transformation can be learned for a new camera set-up with a single observation.

Saha, Avijit, Christian, Jim, Tang, Dun-Sung, Chuan-Lin, Wu

We introduce oriented non-radial basis function networks (ONRBF) as a generalization of Radial Basis Function networks (RBF)- wherein the Euclidean distance metric in the exponent of the Gaussian is re(cid:173) placed by a more general polynomial. This permits the definition of more general regions and in particular- hyper-ellipses with orienta(cid:173) tions. In the case of hyper-surface estimation this scheme requires a smaller number of hidden units and alleviates the "curse of dimen(cid:173) sionality" associated kernel type approximators.In the case of an im(cid:173) age, the hidden units correspond to features in the image and the parameters associated with each unit correspond to the rotation, scal(cid:173) ing and translation properties of that particular "feature". In the con(cid:173) text of the ONBF scheme, this means that an image can be represented by a small number of features. Since, transformation of an image by rotation, scaling and translation correspond to identical transformations of the individual features, the ONBF scheme can be used to considerable advantage for the purposes of image recognition and analysis.

Samuel Daulton, Sait Cakmak, Maximilian Balandat, Michael A Osborne, Enlu Zhou, Eytan Bakshy

Bayesian optimization (BO) is a sample-efficient approach for tuning design parameters to optimize expensive-to-evaluate, black-box performance metrics. In many manufacturing processes, the design parameters are subject to random input noise, resulting in a product that is often less performant than expected. Although BO methods have been proposed for optimizing a single objective under input noise, no existing method addresses the practical scenario where there are multiple objectives that are sensitive to input perturbations. In this work, we propose the first multi-objective BO method that is robust to input noise. We formalize our goal as optimizing the multivariate value-at-risk (MVaR), a risk measure of the uncertain objectives. Since directly optimizing MVaR is computationally infeasible in many settings, we propose a scalable, theoretically-grounded approach for optimizing MVaR using random scalarizations. Empirically, we find that our approach significantly outperforms alternative methods and efficiently identifies optimal robust designs that will satisfy specifications across multiple metrics with high probability.

Han, Yanlin, Gmytrasiewicz, Piotr

Interactive partially observable Markov decision processes (I-POMDPs) provide a principled framework for planning and acting in a partially observable, stochastic and multi-agent environment. It extends POMDPs to multi-agent settings by including models of other agents in the state space and forming a hierarchical belief structure. In order to predict other agents' actions using I-POMDPs, we propose an approach that effectively uses Bayesian inference and sequential Monte Carlo sampling to learn others' intentional models which ascribe to them beliefs, preferences and rationality in action selection. Empirical results show that our algorithm accurately learns models of the other agent and has superior performance than methods that use subintentional models. Our approach serves as a generalized Bayesian learning algorithm that learns other agents' beliefs, strategy levels, and transition, observation and reward functions. It also effectively mitigates the belief space complexity due to the nested belief hierarchy.

Harley Wiltzer, David Meger, Marc Bellemare

Continuous-time reinforcement learning offers an appealing formalism for describing control problems in which the passage of time is not naturally divided into discrete increments.Here we consider the problem of predicting the distribution of returns obtained by an agent interacting in a continuous-time, stochastic environment. Accurate return predictions have proven useful for determining optimal policies for risk-sensitive control, learning state representations, multiagent coordination, and more.We begin by establishing the distributional analogue of the Hamilton-Jacobi-Bellman (HJB) equation for Ito diffusions and the broader class of Feller-Dynkin processes.We then specialize this equation to the setting in which the return distribution is approximated by N uniformly-weighted particles, a common design choice in distributional algorithms.Our derivation highlights additional terms due to statistical diffusivity which arise from the proper handling of distributions in the continuous-time setting. Based on this, we propose a tractable algorithm for approximately solving the distributional HJB based on a JKO scheme, which can be implemented in an online, control algorithm. We demonstrate the effectiveness of such an algorithm in a synthetic control problem.

Kalra, Agastya, Rashwan, Abdullah, Hsu, Wei-Shou, Poupart, Pascal, Doshi, Prashant, Trimponias, Georgios

Sum-product networks have recently emerged as an attractive representation due to their dual view as a special type of deep neural network with clear semantics and a special type of probabilistic graphical model for which inference is always tractable. Those properties follow from some conditions (i.e., completeness and decomposability) that must be respected by the structure of the network. As a result, it is not easy to specify a valid sum-product network by hand and therefore structure learning techniques are typically used in practice. This paper describes a new online structure learning technique for feed-forward and recurrent SPNs. The algorithm is demonstrated on real-world datasets with continuous features for which it is not clear what network architecture might be best, including sequence datasets of varying length.

George Tucker, Surya Bhupatiraju, Shixiang Gu, Richard Turner, Zoubin Ghahramani, Sergey Levine

Policy gradient methods are a widely used class of model-free reinforcement learning algorithms where a state-dependent baseline is used to reduce gradient estimator variance. Several recent papers extend the baseline to depend on both the state and action and suggest that this significantly reduces variance and improves sample efficiency without introducing bias into the gradient estimates. To better understand this development, we decompose the variance of the policy gradient estimator and numerically show that learned state-action-dependent baselines do not in fact reduce variance over a state-dependent baseline in commonly tested benchmark domains. We confirm this unexpected result by reviewing the open-source code accompanying these prior papers, and show that subtle implementation decisions cause deviations from the methods presented in the papers and explain the source of the previously observed empirical gains. Furthermore, the variance decomposition highlights areas for improvement, which we demonstrate by illustrating a simple change to the typical value function parameterization that can significantly improve performance.

Ihler, Alexander, Fisher, John, Willsky, Alan

Belief propagation (BP) is an increasingly popular method of perform- ing approximate inference on arbitrary graphical models. At times, even further approximations are required, whether from quantization or other simplified message representations or from stochastic approxima- tion methods. Introducing such errors into the BP message computations has the potential to adversely affect the solution obtained. We analyze this effect with respect to a particular measure of message error, and show bounds on the accumulation of errors in the system. This leads both to convergence conditions and error bounds in traditional and approximate BP message passing.

Kallus, Nathan

We present a new approach to the problems of evaluating and learning personalized decision policies from observational data of past contexts, decisions, and outcomes. Only the outcome of the enacted decision is available and the historical policy is unknown. These problems arise in personalized medicine using electronic health records and in internet advertising. Existing approaches use inverse propensity weighting (or, doubly robust versions) to make historical outcome (or, residual) data look like it were generated by a new policy being evaluated or learned. But this relies on a plug-in approach that rejects data points with a decision that disagrees with the new policy, leading to high variance estimates and ineffective learning. We propose a new, balance-based approach that too makes the data look like the new policy but does so directly by finding weights that optimize for balance between the weighted data and the target policy in the given, finite sample, which is equivalent to minimizing worst-case or posterior conditional mean square error. Our policy learner proceeds as a two-level optimization problem over policies and weights. We demonstrate that this approach markedly outperforms existing ones both in evaluation and learning, which is unsurprising given the wider support of balance-based weights. We establish extensive theoretical consistency guarantees and regret bounds that support this empirical success.

Moritz Stephan, Alexander Khazatsky, Eric Mitchell, Annie Chen, Sheryl Hsu, Archit Sharma, Chelsea Finn

The diversity of contexts in which large language models (LLMs) are deployed requires the ability to modify or customize default model behaviors to incorporate nuanced requirements and preferences. A convenient interface to specify such model adjustments is high-level verbal feedback, such as “Don’t use emojis when drafting emails to my boss.” However, while writing high-level feedback is far simpler than collecting annotations for reinforcement learning from human feedback (RLHF), we find that simply prompting a model with such feedback leads to $\text{overgeneralization}$–applying feedback in contexts where it is not relevant. We propose a new method Contextualized Critiques with Constrained Preference Optimization (C3PO) to learn from high-level verbal feedback while reducing overgeneralization compared to current work. C3PO uses a piece of high-level feedback to generate a small synthetic preference dataset to specify when and how the feedback should (and should not) be applied. It then fine-tunes the model in accordance with the synthetic preference data while minimizing the divergence from the original model for prompts where the feedback does not apply. Our experimental results indicate that our approach effectively applies verbal feedback to relevant scenarios while preserving existing behaviors for other contexts more than current methods. For both human- and GPT-4-generated high-level feedback, C3PO effectively adheres to the given feedback comparably to in-context baselines while reducing overgeneralization by 30%.

Joseph Campbell, Heni Ben Amor

This paper introduces a fully Bayesian reformulation of Interaction Primitives for human-robot interaction and collaboration. A key insight is that a subset of human-robot interaction is conceptually related to simultaneous localization and mapping techniques. Leveraging this insight we can significantly increase the accuracy of temporal estimation and inferred trajectories while simultaneously reducing the associated computational complexity. We show that this enables more complex human-robot interaction scenarios involving more degrees of freedom.

Risi Kondor, Shubhendu Trivedi

Convolutional neural networks have been extremely successful in the image recognition domain because they ensure equivariance with respect to translations. There have been many recent attempts to generalize this framework to other domains, including graphs and data lying on manifolds. In this paper we give a rigorous, theoretical treatment of convolution and equivariance in neural networks with respect to not just translations, but the action of any compact group. Our main result is to prove that (given some natural constraints) convolutional structure is not just a sufficient, but also a necessary condition for equivariance to the action of a compact group. Our exposition makes use of concepts from representation theory and noncommutative harmonic analysis and derives new generalized convolution formulae.

Avalos, Marta, Nock, Richard, Ong, Cheng Soon, Rouar, Julien, Sun, Ke

We consider the problem of learning a low dimensional representation for compositional data. Compositional data consists of a collection of nonnegative data that sum to a constant value. Since the parts of the collection are statistically dependent, many standard tools cannot be directly applied. Instead, compositional data must be first transformed before analysis. Focusing on principal component analysis (PCA), we propose an approach that allows low dimensional representation learning directly from the original data. Our approach combines the benefits of the log-ratio transformation from compositional data analysis and exponential family PCA. A key tool in its derivation is a generalization of the scaled Bregman theorem, that relates the perspective transform of a Bregman divergence to the Bregman divergence of a perspective transform and a remainder conformal divergence. Our proposed approach includes a convenient surrogate (upper bound) loss of the exponential family PCA which has an easy to optimize form. We also derive the corresponding form for nonlinear autoencoders. Experiments on simulated data and microbiome data show the promise of our method.

Eleni Straitouri, Manuel Gomez-Rodriguez

Decision support systems for classification tasks are predominantly designed to predict the value of the ground truth labels. However, since their predictions are not perfect, these systems also need to make human experts understand when and how to use these predictions to update their own predictions. Unfortunately, this has been proven challenging. In this context, it has been recently argued that an alternative type of decision support systems may circumvent this challenge. Rather than providing a single label prediction, these systems provide a set of label prediction values constructed using a conformal predictor, namely a prediction set, and forcefully ask experts to predict a label value from the prediction set. However, the design and evaluation of these systems have so far relied on stylized expert models, questioning their promise. In this paper, we revisit the design of this type of systems from the perspective of online learning and develop a methodology that does not require, nor assumes, an expert model. Our methodology leverages the nested structure of the prediction sets provided by any conformal predictor and a natural counterfactual monotonicity assumption to achieve an exponential improvement in regret in comparison to vanilla bandit algorithms. We conduct a large-scale human subject study ($n=2,751$) to compare our methodology to several competitive baselines. The results show that, for decision support systems based on prediction sets, limiting experts’ level of agency leads to greater performance than allowing experts to always exercise their own agency.

Bös, Siegfried

In this paper we examine a perceptron learning task. The task is realizable since it is provided by another perceptron with identi(cid:173) cal architecture. Both perceptrons have nonlinear sigmoid output functions. The gain of the output function determines the level of nonlinearity of the learning task. It is observed that a high level of nonlinearity leads to overfitting. We give an explanation for this rather surprising observation and develop a method to avoid the overfitting. This method has two possible interpretations, one is learning with noise, the other cross-validated early stopping. 1 Learning Rules from Examples The property which makes feedforward neural nets interesting for many practical applications is their ability to approximate functions, which are given only by ex(cid:173) amples. Feed-forward networks with at least one hidden layer of nonlinear units are able to approximate each continuous function on a N-dimensional hypercube arbitrarily well. While the existence of neural function approximators is already established, there is still a lack of knowledge about their practical realizations. Also major problems, which complicate a good realization, like overfitting, need a better understanding. In this work we study overfitting in a one-layer percept ron model. The model allows a good theoretical description while it exhibits already a qualitatively similar behavior as the multilayer perceptron. A one-layer perceptron has N input units and one output unit. Between input and output it has one layer of adjustable weights Wi, (i = 1, ... ,N). The output z is a possibly nonlinear function of the weighted sum of inputs Xi, i.e. z = g(h) , with

Wu, Lei, Ma, Chao, E, Weinan

The question of which global minima are accessible by a stochastic gradient decent (SGD) algorithm with specific learning rate and batch size is studied from the perspective of dynamical stability. The concept of non-uniformity is introduced, which, together with sharpness, characterizes the stability property of a global minimum and hence the accessibility of a particular SGD algorithm to that global minimum. In particular, this analysis shows that learning rate and batch size play different roles in minima selection. Extensive empirical results seem to correlate well with the theoretical findings and provide further support to these claims.

Oreshkin, Boris, Rodríguez López, Pau, Lacoste, Alexandre

Few-shot learning has become essential for producing models that generalize from few examples. In this work, we identify that metric scaling and metric task conditioning are important to improve the performance of few-shot algorithms. Our analysis reveals that simple metric scaling completely changes the nature of few-shot algorithm parameter updates. Metric scaling provides improvements up to 14% in accuracy for certain metrics on the mini-Imagenet 5-way 5-shot classification task. We further propose a simple and effective way of conditioning a learner on the task sample set, resulting in learning a task-dependent metric space. Moreover, we propose and empirically test a practical end-to-end optimization procedure based on auxiliary task co-training to learn a task-dependent metric space. The resulting few-shot learning model based on the task-dependent scaled metric achieves state of the art on mini-Imagenet. We confirm these results on another few-shot dataset that we introduce in this paper based on CIFAR100.

Jacob Devlin, Jonathan Uesato, Surya Bhupatiraju, Rishabh Singh, Abdel-rahman Mohamed, Pushmeet Kohli

The problem of automatically generating a computer program from some specification has been studied since the early days of AI. Recently, two competing approaches for `automatic program learning’ have received significant attention: (1) `neural program synthesis’, where a neural network is conditioned on input/output (I/O) examples and learns to generate a program, and (2) `neural program induction’, where a neural network generates new outputs directly using a latent program representation. Here, for the first time, we directly compare both approaches on a large-scale, real-world learning task and we additionally contrast to rule-based program synthesis, which uses hand-crafted semantics to guide the program generation. Our neural models use a modified attention RNN to allow encoding of variable-sized sets of I/O pairs, which achieve 92\% accuracy on a real-world test set, compared to the 34\% accuracy of the previous best neural synthesis approach. The synthesis model also outperforms a comparable induction model on this task, but we more importantly demonstrate that the strength of each approach is highly dependent on the evaluation metric and end-user application. Finally, we show that we can train our neural models to remain very robust to the type of noise expected in real-world data (e.g., typos), while a highly-engineered rule-based system fails entirely.

Karvonen, Toni, Oates, Chris J., Sarkka, Simo

This paper focusses on the formulation of numerical integration as an inferential task. To date, research effort has largely focussed on the development of Bayesian cubature, whose distributional output provides uncertainty quantification for the integral. However, the point estimators associated to Bayesian cubature can be inaccurate and acutely sensitive to the prior when the domain is high-dimensional. To address these drawbacks we introduce Bayes-Sard cubature, a probabilistic framework that combines the flexibility of Bayesian cubature with the robustness of classical cubatures which are well-established. This is achieved by considering a Gaussian process model for the integrand whose mean is a parametric regression model, with an improper prior on each regression coefficient. The features in the regression model consist of test functions which are guaranteed to be exactly integrated, with remaining degrees of freedom afforded to the non-parametric part. The asymptotic convergence of the Bayes-Sard cubature method is established and the theoretical results are numerically verified. In particular, we report two orders of magnitude reduction in error compared to Bayesian cubature in the context of a high-dimensional financial integral.

Ellis, Kevin, Ritchie, Daniel, Solar-Lezama, Armando, Tenenbaum, Josh

We introduce a model that learns to convert simple hand drawings into graphics programs written in a subset of \LaTeX.~The model combines techniques from deep learning and program synthesis. We learn a convolutional neural network that proposes plausible drawing primitives that explain an image. These drawing primitives are a specification (spec) of what the graphics program needs to draw. We learn a model that uses program synthesis techniques to recover a graphics program from that spec. These programs have constructs like variable bindings, iterative loops, or simple kinds of conditionals. With a graphics program in hand, we can correct errors made by the deep network and extrapolate drawings.

Weiyang Liu, Bo Dai, Xingguo Li, Zhen Liu, James Rehg, Le Song

In this paper, we make an important step towards the black-box machine teaching by considering the cross-space machine teaching, where the teacher and the learner use different feature representations and the teacher can not fully observe the learner’s model. In such scenario, we study how the teacher is still able to teach the learner to achieve faster convergence rate than the traditional passive learning. We propose an active teacher model that can actively query the learner (i.e., make the learner take exams) for estimating the learner’s status and provably guide the learner to achieve faster convergence. The sample complexities for both teaching and query are provided. In the experiments, we compare the proposed active teacher with the omniscient teacher and verify the effectiveness of the active teacher model.

Zhang, Lisa, Rosenblatt, Gregory, Fetaya, Ethan, Liao, Renjie, Byrd, William, Might, Matthew, Urtasun, Raquel, Zemel, Richard

Synthesizing programs using example input/outputs is a classic problem in artificial intelligence. We present a method for solving Programming By Example (PBE) problems by using a neural model to guide the search of a constraint logic programming system called miniKanren. Crucially, the neural model uses miniKanren's internal representation as input; miniKanren represents a PBE problem as recursive constraints imposed by the provided examples. We explore Recurrent Neural Network and Graph Neural Network models. We contribute a modified miniKanren, drivable by an external agent, available at https://github.com/xuexue/neuralkanren. We show that our neural-guided approach using constraints can synthesize programs faster in many cases, and importantly, can generalize to larger problems.

Ramakrishnan, Sainandan, Agrawal, Aishwarya, Lee, Stefan

Modern Visual Question Answering (VQA) models have been shown to rely heavily on superficial correlations between question and answer words learned during training -- \eg overwhelmingly reporting the type of room as kitchen or the sport being played as tennis, irrespective of the image. Most alarmingly, this shortcoming is often not well reflected during evaluation because the same strong priors exist in test distributions; however, a VQA system that fails to ground questions in image content would likely perform poorly in real-world settings. In this work, we present a novel regularization scheme for VQA that reduces this effect. We introduce a question-only model that takes as input the question encoding from the VQA model and must leverage language biases in order to succeed. We then pose training as an adversarial game between the VQA model and this question-only adversary -- discouraging the VQA model from capturing language biases in its question encoding.Further, we leverage this question-only model to estimate the mutual information between the image and answer given the question, which we maximize explicitly to encourage visual grounding. Our approach is a model agnostic training procedure and simple to implement. We show empirically that it can improve performance significantly on a bias-sensitive split of the VQA dataset for multiple base models -- achieving state-of-the-art on this task. Further, on standard VQA tasks, our approach shows significantly less drop in accuracy compared to existing bias-reducing VQA models.

Luigi Gresele, Julius von Kügelgen, Jonas Kübler, Elke Kirschbaum, Bernhard Schölkopf, Dominik Janzing

We introduce an approach to counterfactual inference based on merging information from multiple datasets. We consider a causal reformulation of the statistical marginal problem: given a collection of marginal structural causal models (SCMs) over distinct but overlapping sets of variables, determine the set of joint SCMs that are counterfactually consistent with the marginal ones. We formalise this approach for categorical SCMs using the response function formulation and show that it reduces the space of allowed marginal and joint SCMs. Our work thus highlights a new mode of falsifiability through additional variables, in contrast to the statistical one via additional data.

Zhou, Pan, Yuan, Xiaotong, Feng, Jiashi

As an incremental-gradient algorithm, the hybrid stochastic gradient descent (HSGD) enjoys merits of both stochastic and full gradient methods for finite-sum minimization problem. However, the existing rate-of-convergence analysis for HSGD is made under with-replacement sampling (WRS) and is restricted to convex problems. It is not clear whether HSGD still carries these advantages under the common practice of without-replacement sampling (WoRS) for non-convex problems. In this paper, we affirmatively answer this open question by showing that under WoRS and for both convex and non-convex problems, it is still possible for HSGD (with constant step-size) to match full gradient descent in rate of convergence, while maintaining comparable sample-size-independent incremental first-order oracle complexity to stochastic gradient descent. For a special class of finite-sum problems with linear prediction models, our convergence results can be further improved in some cases. Extensive numerical results confirm our theoretical affirmation and demonstrate the favorable efficiency of WoRS-based HSGD.

Balunovic, Mislav, Bielik, Pavol, Vechev, Martin

We present a new approach for learning to solve SMT formulas. We phrase the challenge of solving SMT formulas as a tree search problem where at each step a transformation is applied to the input formula until the formula is solved. Our approach works in two phases: first, given a dataset of unsolved formulas we learn a policy that for each formula selects a suitable transformation to apply at each step in order to solve the formula, and second, we synthesize a strategy in the form of a loop-free program with branches. This strategy is an interpretable representation of the policy decisions and is used to guide the SMT solver to decide formulas more efficiently, without requiring any modification to the solver itself and without needing to evaluate the learned policy at inference time. We show that our approach is effective in practice - it solves 17% more formulas over a range of benchmarks and achieves up to 100x runtime improvement over a state-of-the-art SMT solver.

Biwei Huang, Chaochao Lu, Liu Leqi, Jose Miguel Hernandez-Lobato, Clark Glymour, Bernhard Schölkopf, Kun Zhang

Perceived signals in real-world scenarios are usually high-dimensional and noisy, and finding and using their representation that contains essential and sufficient information required by downstream decision-making tasks will help improve computational efficiency and generalization ability in the tasks. In this paper, we focus on partially observable environments and propose to learn a minimal set of state representations that capture sufficient information for decision-making, termed Action-Sufficient state Representations (ASRs). We build a generative environment model for the structural relationships among variables in the system and present a principled way to characterize ASRs based on structural constraints and the goal of maximizing cumulative reward in policy learning. We then develop a structured sequential Variational Auto-Encoder to estimate the environment model and extract ASRs. Our empirical results on CarRacing and VizDoom demonstrate a clear advantage of learning and using ASRs for policy learning. Moreover, the estimated environment model and ASRs allow learning behaviors from imagined outcomes in the compact latent space to improve sample efficiency.

Harer, Jacob, Ozdemir, Onur, Lazovich, Tomo, Reale, Christopher, Russell, Rebecca, Kim, Louis, chin, peter

Motivated by the problem of automated repair of software vulnerabilities, we propose an adversarial learning approach that maps from one discrete source domain to another target domain without requiring paired labeled examples or source and target domains to be bijections. We demonstrate that the proposed adversarial learning approach is an effective technique for repairing software vulnerabilities, performing close to seq2seq approaches that require labeled pairs. The proposed Generative Adversarial Network approach is application-agnostic in that it can be applied to other problems similar to code repair, such as grammar correction or sentiment translation.

Dinglan Peng, Shuxin Zheng, Yatao Li, Guolin Ke, Di He, Tie-Yan Liu

Semantic understanding of programs is a fundamental problem for programming language processing (PLP). Recent works that learn representations of code based on pre-training techniques in NLP have pushed the frontiers in this direction. However, the semantics of PL and NL have essential differences. These being ignored, we believe it is difficult to build a model to better understand programs, by either directly applying off-the-shelf NLP pre-training techniques to the source code, or adding features to the model by the heuristic. In fact, the semantics of a program can be rigorously defined by formal semantics in PL theory. For example, the operational semantics, describes the meaning of a valid program as updating the environment (i.e., the memory address-value function) through fundamental operations, such as memory I/O and conditional branching. Inspired by this, we propose a novel program semantics learning paradigm, that the model should learn from information composed of (1) the representations which align well with the fundamental operations in operational semantics, and (2) the information of environment transition, which is indispensable for program understanding. To validate our proposal, we present a hierarchical Transformer-based pre-training model called OSCAR to better facilitate the understanding of programs. OSCAR learns from intermediate representation (IR) and an encoded representation derived from static analysis, which are used for representing the fundamental operations and approximating the environment transitions respectively. OSCAR empirically shows the outstanding capability of program semantics understanding on many practical software engineering tasks. Code and models are released at: \url{https://github.com/pdlan/OSCAR}.

Cross, Andrew, Hancock, Edwin

This paper describes a new approach to extracting 3D perspective structure from 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying point(cid:173) correspondence matches. Unification is realised by constructing a mixture model over the bi-partite graph representing the correspon(cid:173) dence match and by effecting optimisation using the EM algorithm. According to our EM framework the probabilities of structural cor(cid:173) respondence gate contributions to the expected likelihood function used to estimate maximum likelihood perspective pose parameters. This provides a means of rejecting structural outliers.