The generalization bound is a crucial theoretical tool for assessing the generalizability of learning methods and there exist vast literatures on generalizability of normal learning, adversarial learning, and data poisoning. Unlike other data poison attacks, the backdoor attack has the special property that the poisoned triggers are contained in both the training set and the test set and the purpose of the attack is two-fold. To our knowledge, the generalization bound for the backdoor attack has not been established. In this paper, we fill this gap by deriving algorithm-independent generalization bounds in the clean-label backdoor attack scenario. Precisely, based on the goals of backdoor attack, we give upper bounds for the clean sample population errors and the poison population errors in terms of the empirical error on the poisoned training dataset. Furthermore, based on the theoretical result, a new clean-label backdoor attack is proposed that computes the poisoning trigger by combining adversarial noise and indiscriminate poison. We show its effectiveness in a variety of settings.
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Artificial intelligence and machine learning frameworks have served as computationally efficient mapping between inputs and outputs for engineering problems. These mappings have enabled optimization and analysis routines that have warranted superior designs, ingenious material systems and optimized manufacturing processes. A common occurrence in such modeling endeavors is the existence of multiple source of data, each differentiated by fidelity, operating conditions, experimental conditions, and more. Data fusion frameworks have opened the possibility of combining such differentiated sources into single unified models, enabling improved accuracy and knowledge transfer. However, these frameworks encounter limitations when the different sources are heterogeneous in nature, i.e., not sharing the same input parameter space. These heterogeneous input scenarios can occur when the domains differentiated by complexity, scale, and fidelity require different parametrizations. Towards addressing this void, a heterogeneous multi-source data fusion framework is proposed based on input mapping calibration (IMC) and latent variable Gaussian process (LVGP). In the first stage, the IMC algorithm is utilized to transform the heterogeneous input parameter spaces into a unified reference parameter space. In the second stage, a multi-source data fusion model enabled by LVGP is leveraged to build a single source-aware surrogate model on the transformed reference space. The proposed framework is demonstrated and analyzed on three engineering case studies (design of cantilever beam, design of ellipsoidal void and modeling properties of Ti6Al4V alloy). The results indicate that the proposed framework provides improved predictive accuracy over a single source model and transformed but source unaware model.
We advance a recently flourishing line of work at the intersection of learning theory and computational economics by studying the learnability of two classes of mechanisms prominent in economics, namely menus of lotteries and two-part tariffs. The former is a family of randomized mechanisms designed for selling multiple items, known to achieve revenue beyond deterministic mechanisms, while the latter is designed for selling multiple units (copies) of a single item with applications in real-world scenarios such as car or bike-sharing services. We focus on learning high-revenue mechanisms of this form from buyer valuation data in both distributional settings, where we have access to buyers' valuation samples up-front, and the more challenging and less-studied online settings, where buyers arrive one-at-a-time and no distributional assumption is made about their values. We provide a suite of results with regard to these two families of mechanisms. We provide the first online learning algorithms for menus of lotteries and two-part tariffs with strong regret-bound guarantees. Since the space of parameters is infinite and the revenue functions have discontinuities, the known techniques do not readily apply. However, we are able to provide a reduction to online learning over a finite number of experts, in our case, a finite number of parameters. Furthermore, in the limited buyers type case, we show a reduction to online linear optimization, which allows us to obtain no-regret guarantees by presenting buyers with menus that correspond to a barycentric spanner. In addition, we provide algorithms with improved running times over prior work for the distributional settings. Finally, we demonstrate how techniques from the recent literature in data-driven algorithm design are insufficient for our studied problems.
Compared to physics-based computational manufacturing, data-driven models such as machine learning (ML) are alternative approaches to achieve smart manufacturing. However, the data-driven ML's "black box" nature has presented a challenge to interpreting its outcomes. On the other hand, governing physical laws are not effectively utilized to develop data-efficient ML algorithms. To leverage the advantages of ML and physical laws of advanced manufacturing, this paper focuses on the development of a physics-informed machine learning (PIML) model by integrating neural networks and physical laws to improve model accuracy, transparency, and generalization with case studies in laser metal deposition (LMD).
Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would allow for gradient-based parameter optimization, the nonlinear dynamics of ODEs often lead to many local minima and extreme sensitivity to initial conditions. We therefore propose diffusion tempering, a novel regularization technique for probabilistic numerical methods which improves convergence of gradient-based parameter optimization in ODEs. By iteratively reducing a noise parameter of the probabilistic integrator, the proposed method converges more reliably to the true parameters. We demonstrate that our method is effective for dynamical systems of different complexity and show that it obtains reliable parameter estimates for a Hodgkin-Huxley model with a practically relevant number of parameters.
Game semantics is a denotational semantics presenting compositionally the computational behaviour of various kinds of effectful programs. One of its celebrated achievement is to have obtained full abstraction results for programming languages with a variety of computational effects, in a single framework. This is known as the semantic cube or Abramsky's cube, which for sequential deterministic programs establishes a correspondence between certain conditions on strategies (''innocence'', ''well-bracketing'', ''visibility'') and the absence of matching computational effects. Outside of the sequential deterministic realm, there are still a wealth of game semantics-based full abstraction results; but they no longer fit in a unified canvas. In particular, Ghica and Murawski's fully abstract model for shared state concurrency (IA) does not have a matching notion of pure parallel program-we say that parallelism and interference (i.e. state plus semaphores) are entangled. In this paper we construct a causal version of Ghica and Murawski's model, also fully abstract for IA. We provide compositional conditions parallel innocence and sequentiality, respectively banning interference and parallelism, and leading to four full abstraction results. To our knowledge, this is the first extension of Abramsky's semantic cube programme beyond the sequential deterministic world.
Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and convergence. Multigrid is an approach with excellent applicability to elliptic problems such as the Stokes equations, and can be a solution to such challenges of scalability and efficiency. The degree of success of such methods, however, is highly contingent on the design of key components of a multigrid scheme, including the hierarchy of discretizations, and the relaxation scheme used. Additionally, in many practical cases, it may be more effective to use a multigrid scheme as a preconditioner to an iterative Krylov subspace solver, as opposed to striving for maximum efficacy of the relaxation scheme in all foreseeable settings. In this paper, we propose an efficient symmetric multigrid preconditioner for the Stokes Equations on a staggered finite-difference discretization. Our contribution is focused on crafting a preconditioner that (a) is symmetric indefinite, matching the property of the Stokes system itself, (b) is appropriate for preconditioning the SQMR iterative scheme, and (c) has the requisite symmetry properties to be used in this context. In addition, our design is efficient in terms of computational cost and facilitates scaling to large domains.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
While existing machine learning models have achieved great success for sentiment classification, they typically do not explicitly capture sentiment-oriented word interaction, which can lead to poor results for fine-grained analysis at the snippet level (a phrase or sentence). Factorization Machine provides a possible approach to learning element-wise interaction for recommender systems, but they are not directly applicable to our task due to the inability to model contexts and word sequences. In this work, we develop two Position-aware Factorization Machines which consider word interaction, context and position information. Such information is jointly encoded in a set of sentiment-oriented word interaction vectors. Compared to traditional word embeddings, SWI vectors explicitly capture sentiment-oriented word interaction and simplify the parameter learning. Experimental results show that while they have comparable performance with state-of-the-art methods for document-level classification, they benefit the snippet/sentence-level sentiment analysis.
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