United States

Hamiltonian systems represent an important class of dynamical systems such as pendulums, molecular dynamics, and cosmic systems. The choice of solvers is significant to the accuracy when simulating Hamiltonian systems, where symplectic solvers show great significance. Recent advances in neural network-based hypersolvers, though achieve competitive results, still lack the symplecity necessary for reliable simulations, especially over long time horizons. To alleviate this, we introduce Hyperverlet, a new hypersolver composing the traditional, symplectic velocity Verlet and symplectic neural network-based solvers. More specifically, we propose a parameterization of symplectic neural networks and prove that hyperbolic tangent is r-finite expanding the set of allowable activation functions for symplectic neural networks, improving the accuracy. Extensive experiments on a spring-mass and a pendulum system justify the design choices and suggest that Hyperverlet outperforms both traditional solvers and hypersolvers.

AAAI 2022

Hyperverlet: A Symplectic Hypersolver for Hamiltonian Systems

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

technical paper

We study the additive distortion of social choice functions in the implicit utilitarian model, and argue that it is a more appropriate metric than multiplicative distortion when an alternative that confers significant social welfare may exist (i.e., when the stakes are high). We define a randomized analog of positional scoring rules, and present a rule which is asymptotically optimal within this class as the number of alternatives increases. We then show that the instance-optimal social choice function can be efficiently computed. Next, we take a beyond-worst-case view, bounding the additive distortion of prominent voting rules as a function of the best welfare attainable in an instance. Lastly, we evaluate the additive distortion of a range of rules on real-world election data.

Worst-Case Voting When the Stakes are High

Recent advances in large-scale pre-training such as GPT-3 allow seemingly high quality text to be generated from a given prompt. However, such generation systems often suffer from problems of hallucinated facts, and are not inherently designed to incorporate useful external information. Grounded generation models appear to offer remedies, but their training typically relies on rarely-available parallel data where information-relevant documents are provided for context. We propose a framework that alleviates this data constraint by jointly training a grounded generator and document retriever on the language model signal. The model learns to reward retrieval of the documents with the highest utility in generation, and attentively combines them using a Mixture-of-Experts (MoE) ensemble to generate follow-on text.  We demonstrate that both generator and retriever can take advantage of this joint training and work synergistically to produce more informative and relevant text in both prose and dialogue generation.

RetGen: A Joint Framework for Retrieval and Grounded Text Generation Modeling

The problem of knowledge-based visual question answering involves answering questions that require external knowledge in addition to the content of the image. Such knowledge typically comes in various forms, including visual, textual, and commonsense knowledge. Using more knowledge sources increases the chance of retrieving more irrelevant or noisy facts, making it challenging to comprehend the facts and find the answer. To address this challenge, we propose Multi-modal Answer Validation using External knowledge (MAVEx), where the idea is to validate a set of promising answer candidates based on answer-specific knowledge retrieval. Instead of searching for the answer in a vast collection of often irrelevant facts as most existing approaches do, MAVEx aims to learn how to extract relevant knowledge from noisy sources, which knowledge source to trust for each answer candidate, and how to validate the candidate using that source.
Our multi-modal setting is the first to leverage external visual knowledge (images searched using Google), in addition to textual knowledge in the form of Wikipedia sentences and ConceptNet concepts. Our experiments with OK-VQA, a challenging knowledge-based VQA dataset, demonstrate that MAVEx achieves new state-of-the-art results. Our code is available at https://github.com/jialinwu17/MAVEX

Multi-Modal Answer Validation for Knowledge-Based VQA

We study the performance of voting mechanisms from a utilitarian standpoint, under the recently introduced framework of metric-distortion, offering new insights along two main lines. First, if d represents the doubling dimension of the metric space, we show that the distortion of STV is O(d log log m), where m represents the number of candidates. For doubling metrics this implies an exponential improvement over the lower bound for general metrics, and as a special case it effectively answers a question left open by Skowron and Elkind (AAAI '17) regarding the distortion of STV under low-dimensional Euclidean spaces. More broadly, this constitutes the first nexus between the performance of any voting rule and the ``intrinsic dimensionality'' of the underlying metric space. We also establish a nearly-matching lower bound, refining the construction of Skowron and Elkind. Moreover, motivated by the efficiency of STV, we investigate whether natural learning rules can lead to low-distortion outcomes. Specifically, we introduce simple, deterministic and decentralized exploration/exploitation dynamics, and we show that they converge to a candidate with O(1) distortion.

Dimensionality and Coordination in Voting: The Distortion of STV

As a key characteristic in audio-visual speech recognition (AVSR), relating linguistic information observed across visual and audio data has been a challenge, benefiting not only audio/visual speech recognition (ASR/VSR) but also for manipulating data within/across modalities. In this paper, we present a feature disentanglement-based framework for jointly addressing the above tasks. By advancing cross-modal mutual learning strategies, our model is able to convert visual or audio-based linguistic features into modality-agnostic representations. Such derived linguistic representations not only allow one to perform ASR, VSR, and AVSR, but also to manipulate audio and visual data output based on the desirable subject identity and linguistic content information. We perform extensive experiments on different recognition and synthesis tasks to show that our model performs favorably against state-of-the-art approaches on each individual task, while ours is a unified solution that is able to jointly tackle the aforementioned audio-visual learning tasks.

Cross-Modal Mutual Learning for Audio-Visual Speech Recognition and Manipulation

Aggregating opinions of a collection of agents is a question of interest to a broad array of researchers, ranging from ensemble-learning theorists to political scientists designing democratic institutions. This work investigates the optimal number of agents needed to decide on a binary issue under majority rule. We take an epistemic view where the issue at hand has a ground truth ``correct'' outcome and each one of n voters votes correctly with a fixed probability, known as their competence level or competence. These competencies come from a fixed distribution D. Observing the competencies, we must choose a specific group that will represent the population. Finally, voters sample a decision (either correct or not), and the group is correct as long as more than half the chosen representatives voted correctly. Assuming that we can identify the best experts, i.e., those with the highest competence, to form an epistemic congress we find that the optimal congress size should be linear in the population size. This result is striking because it holds even when allowing the top representatives to become arbitrarily accurate, choosing the correct outcome with probabilities approaching 1. We then analyze real-world data, observing that the actual sizes of representative bodies are much smaller than the optimal ones our theoretical results suggest. We conclude by examining under what conditions congresses of sub-optimal sizes would still outperform direct democracy, in which all voters vote. We find that a small congress would beat direct democracy if the rate at which the societal bias towards the ground truth decreases with the population size fast enough, and we quantify the speed needed for constant and polynomial congress sizes.

How Many Representatives Do We Need? The Optimal Size of a Congress Voting on Binary Issues

In Mixed Integer Linear Programming (MIP), a (strong) backdoor is a ``small" subset of an instance's integer variables with the following property: in a branch-and-bound procedure, the instance can be solved to global optimality by branching only on the variables in the backdoor. Constructing datasets of pre-computed backdoors for widely used MIP benchmark sets or particular problem families can enable new questions around novel structural properties of a MIP, or explain why a problem that is hard in theory can be solved efficiently in practice. Existing algorithms for finding backdoors rely on sampling candidate variable subsets in various ways, an approach which has demonstrated the existence of backdoors for some instances from MIPLIB2003 and MIPLIB2010. However, these algorithms fall short of consistently succeeding at the task due to an imbalance between exploration and exploitation. We propose BaMCTS, a Monte Carlo Tree Search framework for finding backdoors to MIPs. Extensive algorithmic engineering, hybridization with traditional MIP concepts, and close integration with the CPLEX solver have enabled our method to outperform baselines on MIPLIB2017 instances, finding backdoors more frequently and more efficiently.

Finding Backdoors to Integer Programs: A Monte Carlo Tree Search Framework

Deep vision models have provided new capability across a spectrum of applications in transportation, manufacturing, agriculture, commerce, and security. However, recent studies have demonstrated that these models are vulnerable to adversarial attack, exposing a risk-of-use in critical applications where untrusted parties have access to the data environment or even directly to the sensor inputs. Existing adversarial defense methods are either limited to specific types of attacks or are too complex to be applied to practical vision models. More importantly, these methods rely on techniques that are not interpretable to humans. In this work, we argue that an effective defense should produce an explanation as to why the system is attacked, and by using a representation that is easily readable by a human user, e.g. a logic formalism. To this end, we propose logic adversarial defense (LogicDef), a defense framework that utilizes the scene graph of the image to provide a contextual structure for detecting and explaining object classification. Our framework first mines inductive logic rules from the extracted scene graph, and then uses these rules to construct a defense model that alerts the user when the vision model violates the consistency rules. The defense model is interpretable and its robustness is further enhanced by incorporating existing relational commonsense knowledge from projects such as ConceptNet. In order to handle the hierarchical nature of such relational reasoning, we use a curriculum learning approach based on object taxonomy, yielding additional improvements to training and performance.

LogicDef: An Interpretable Defense Framework Against Adversarial Examples via Inductive Scene Graph Reasoning

We introduce the task of open-vocabulary visual instance search (OVIS). Given an arbitrary textual search query, Open-vocabulary Visual Instance Search (OVIS) aims to return a ranked list of visual instances, i.e., image patches, that satisfies the search intent from an image database. The term ``open vocabulary'' means that there are neither restrictions to the visual instance to be searched nor restrictions to the word that can be used to compose the textual search query. We propose to address such a search challenge via visual-semantic aligned representation learning (ViSA). ViSA leverages massive image-caption pairs as weak image-level (not instance-level) supervision to learn a rich cross-modal semantic space where the representations of visual instances (not images) and those of textual queries are aligned, thus allowing us to measure the similarities between any visual instance and an arbitrary textual query. To evaluate the performance of ViSA, we build two datasets named OVIS40 and OVIS1600 and also introduce a pipeline for error analysis. Through extensive experiments on the two datasets, we demonstrate ViSA's ability to search for visual instances in images not available during training given a wide range of textual queries including those composed of uncommon words. Experimental results show that ViSA achieves an mAP@50 of 27.8% on OVIS40 and achieves a recall@30 of 21.3% on OVIS1400 dataset under the most challenging settings.

OVIS: Open-Vocabulary Visual Instance Search via Visual-Semantic Aligned Representation Learning

We consider the problem of learning action models for planning in unknown stochastic environments that can be defined using the Probabilistic Planning Domain Description Language (PPDDL). As input, we are given a set of previously executed trajectories, and the main challenge is to learn an action model that has a similar goal achievement probability to the policies used to create these trajectories. To this end, we introduce a variant of PPDDL in which there is uncertainty about the transition probabilities, specified by an interval for each factor that contains the respective true transition probabilities. Then, we present SAM+, an algorithm that learns such an imprecise-PPDDL environment model. SAM+ has a polynomial time and sample complexity, and guarantees that with high probability, the true environment is indeed captured by the defined intervals. We prove that the action model SAM+ outputs has a goal achievement probability that is almost as good or better than that of the policies used to produced the training trajectories. Then, we show how to produce a PPDDL model based on this imprecise-PPDDL model that has similar properties.

Downloads

Next from AAAI 2022

Worst-Case Voting When the Stakes are High

Similar lecture

KAM Theory Meets Statistical Learning Theory: Hamiltonian Neural Networks with Non-Zero Training Loss

.css-70qvj9{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}Downloads

Next from AAAI 2022

Worst-Case Voting When the Stakes are High

Similar lecture

KAM Theory Meets Statistical Learning Theory: Hamiltonian Neural Networks with Non-Zero Training Loss

Downloads