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Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for achieving acceleration, based on the recently introduced notion of fixed-time stability of dynamical systems. The method presents itself as a generalization of simple gradient-based methods suitably scaled to achieve convergence to the optimizer in a fixed-time, independent of the initialization. We achieve this by first leveraging a continuous-time framework for designing fixed-time stable dynamical systems, and later providing a consistent discretization strategy, such that the equivalent discrete-time algorithm tracks the optimizer in a practically fixed number of iterations. We also provide a theoretical analysis of the convergence behavior of the proposed gradient flows, and their robustness to additive disturbances for a range of functions obeying strong convexity, strict convexity, and possibly nonconvexity but satisfying the Polyak-Åojasiewicz inequality. We also show that the regret bound on the convergence rate is constant by virtue of the fixed-time convergence. The hyperparameters have intuitive interpretations and can be tuned to fit the requirements on the desired convergence rates. We validate the accelerated convergence properties of the proposed schemes on a range of numerical examples against the state-of-the-art optimization algorithms. Our work provides insights on developing novel optimization algorithms via discretization of continuous-time flows.

AAAI 2022

Breaking the Convergence Barrier: Optimization via Fixed-Time Convergent Flows

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

This paper proposes a representational model for image pairs such as consecutive video frames that are related by local pixel displacements, in the hope that the model may shed light on motion perception in primary visual cortex (V1). The model couples the following two components: (1) the vector representations of local contents of images and (2) the matrix representations of local pixel displacements caused by the relative motions between the agent and the objects in the 3D scene. When the image frame undergoes changes due to local pixel displacements, the vectors are multiplied by the matrices that represent the local displacements. Thus the vector representation is equivariant as it varies according to the local displacements. Our experiments show that our model can learn Gabor-like filter pairs of quadrature phases. The profiles of the learned filters match those of simple cells in Macaque V1. Moreover, we demonstrate that the model can learn to infer local motions in either a supervised or unsupervised manner. With such a simple model, we achieve competitive results on optical flow estimation.

Learning V1 Simple Cells with Vector Representation of Local Content and Matrix Representation of Local Motion

We introduce NaturalInversion, a novel model inversion-based method to synthesize images that agrees well with the original data distribution without using real data. In NaturalInversion, we propose: (1) a Feature Transfer Pyramid which uses enhanced image prior of the original data by combining the multi-scale feature maps extracted from the pre-trained classifier, (2) a one-to-one approach generative model where only one batch of images are synthesized by one generator to bring the non-linearity to optimization and to ease the overall optimizing process, (3) learnable Adaptive Channel Scaling parameters which are end-to-end trained to scale the output image channel to utilize the original image prior further. With our NaturalInversion, we synthesize images from classifiers trained on CIFAR-10/100 and show that our images are more consistent with original data distribution than prior works by visualization and additional analysis. Furthermore, our synthesized images outperform prior works on various applications such as knowledge distillation and pruning, demonstrating the effectiveness of our proposed method.

NaturalInversion: Data-Free Image Synthesis Improving Real-World Consistency

Acquiring the most representative examples via active learning (AL) can benefit many data-dependent computer vision tasks by minimizing efforts of image-level or pixel-wise annotations. In this paper, we propose a novel Collaborative Panoptic-Regional Active Learning framework (CPRAL) to address the semantic segmentation task. For a small batch of images initially sampled with pixel-wise annotations, we employ panoptic information to initially select unlabeled samples. Considering the class imbalance in the segmentation dataset, we import a Regional Gaussian Attention module (RGA) to achieve semantics-biased selection. The subset is highlighted by vote entropy and then attended by Gaussian kernels to maximize the biased regions. We also propose a Contextual Labels Extension (CLE) to boost regional annotations with contextual attention guidance. With the collaboration of semantics-agnostic panoptic matching and region-biased selection and extension, our CPRAL can strike a balance between labeling efforts and performance and compromise the semantics distribution. We perform extensive experiments on Cityscapes and BDD10K datasets and show that CPRAL outperforms the cutting-edge methods with impressive results and less labeling proportion.

CPRAL: Collaborative Panoptic-Regional Active Learning for Semantic Segmentation

This paper studies defender patrol deception in general Stackelberg security games (SSGs), where a defender attempts to alter the attacker's perception of the defender's patrolling intensity so as to influence the attacker's decision making. We are interested in understanding the complexity and effectiveness of optimal defender deception under different attacker behavior models. Specifically, we consider three different attacker strategies of response (to the defender's deception) with increasing sophistication, and design efficient polynomial-time algorithms to compute the equilibrium for each. Moreover, we prove formal separation for the effectiveness of patrol deception when facing an attacker of increasing sophistication, until it becomes even harmful to the defender when facing the most intelligent attacker we consider. Our results shed light on when and how deception should be used in SSGs. We conduct extensive experiments to illustrate our theoretical results in various game settings.

When Can the Defender Effectively Deceive Attackers in Security Games?

When designing algorithms for finite-time-horizon episodic reinforcement learning problems, a common approach is to introduce a fictitious discount factor and use stationary policies for approximations. Empirically, it has been shown that the fictitious discount factor helps reduce variance, and stationary policies serve to save the per-iteration computational cost. Theoretically, however, there is no existing work on convergence analysis for algorithms with this fictitious discount recipe. This paper takes the first step towards analyzing these algorithms. It focuses on two vanilla policy gradient (VPG) variants: the first being a widely used variant with discounted advantage estimations (DAE), the second with an additional fictitious discount factor in the score functions of the policy gradient estimators. Non-asymptotic convergence guarantees are established for both algorithms, and the additional discount factor is shown to reduce the bias introduced in DAE and thus improve the algorithm convergence asymptotically. A key ingredient of our analysis is to connect three settings of Markov decision processes (MDPs): the finite-time-horizon, the average reward and the discounted settings. To our best knowledge, this is the first theoretical guarantee on fictitious discount algorithms for the episodic reinforcement learning of finite-time-horizon MDPs, which also leads to the (first) global convergence of policy gradient methods for finite-time-horizon episodic reinforcement learning.

Theoretical Guarantees of Fictitious Discount Algorithms for Episodic Reinforcement Learning and Global Convergence of Policy Gradient Methods

We revisit the planning problem in the blocks world, and we implement a known heuristic for this task. Importantly, our implementation is biologically plausible, in the sense that it is carried out exclusively through the spiking of neurons. Even though much has been accomplished in the blocks world over the past five decades, we believe that this is the first algorithm of its kind. The input is a sequence of symbols encoding an initial set of block stacks as well as a target set, and the output is a sequence of motion commands such as "put the top block in stack 1 on the table". The program is written in the Assembly Calculus, a recently proposed computational framework meant to model computation in the brain by bridging the gap between neural activity and cognitive function. Its elementary objects are assemblies of neurons (stable sets of neurons whose simultaneous firing signifies that the subject is thinking of an object, concept, word, etc.), its commands include project and merge, and its execution model is based on widely accepted tenets of neuroscience. A program in this framework essentially sets up a dynamical system of neurons and synapses that eventually, with high probability, accomplishes the task. The purpose of this work is to establish empirically that reasonably large programs in the Assembly Calculus can execute correctly and reliably; and that rather realistic --- if idealized --- higher cognitive functions, such as planning in the blocks world, can be implemented successfully by such programs.

 Planning with Biological Neurons and Synapses

We introduce the formula-synthesis problem for Propositional Dynamic Logic with Shuffle (PDL || ). This problem, which generalises the model-checking problem againsts PDL || is the following: given a finite transition system  and a regular term-grammar that generates (possibly infinitely many) PDL || formulas, find a formula generated by the grammar that is true in the structure (or return that there is none). We prove that the problem is undecidable in general, but add certain restrictions on the input structure or on the input grammar to yield decidability. In particular, we prove that (1) if the grammar only generates formulas in PDL (without shuffle), then the problem is EXPTIME-complete, and a further restriction to linear grammars is PSPACE-complete, and a further restriction to non-recursive grammars is NP-complete,  and (2) if one restricts the input structure to have only simple paths then the problem is in 2-EXPTIME. This work is motivated by and opens up connections to other forms of synthesis from hierarchical descriptions, including HTN problems in Planning and Attack-tree Synthesis problems in Security.

Formula Synthesis in Propositional Dynamic Logic with Shuffle

Representation learners that disentangle factors of variation have already proven to be important in addressing various real world concerns such as fairness and interpretability. Initially consisting of unsupervised models with independence assumptions, more recently, weak supervision and correlated features have been explored, but without a causal view of the generative process. In contrast, we work under the regime of a causal generative process where generative factors are either independent or can be potentially confounded by a set of observed or unobserved confounders. We present an analysis of disentangled representations through the notion of disentangled causal process. We motivate the need for new metrics and datasets to study causal disentanglement and propose two evaluation metrics and a dataset. We show that our metrics capture the desiderata of disentangled causal process. Finally we perform an empirical study on state of the art disentangled representation learners using our metrics and dataset to evaluate them from causal perspective.

On Causally Disentangled Representations

Pursuing accurate and robust recognizers has been a long-lasting goal for scene text recognition (STR) researchers. Recently, attention-based methods have demonstrated their effectiveness and achieved impressive results on public benchmarks. The attention mechanism enables models to recognize scene text with severe visual distortions by leveraging contextual information. However, recent studies revealed that the implicit over-reliance of context leads to catastrophic out-of-vocabulary performance. On the contrary to the superior accuracy of the seen text, models are prone to misrecognize unseen text even with good image quality. We propose a novel framework, Context-based contrastive learning (ConCLR), to alleviate this issue. Our proposed method first generates characters with different contexts via simple image concatenation operations and then optimizes contrastive loss on their embeddings. By pulling together clusters of identical characters within various contexts and pushing apart clusters of different characters in embedding space, ConCLR suppresses the side-effect of overfitting to specific contexts and learns a more robust representation. Experiments show that ConCLR significantly improves out-of-vocabulary generalization and achieves state-of-the-art performance on public benchmarks together with attention-based recognizers.

Context-Based Contrastive Learning for Scene Text Recognition

Astronomical interferometry enables a collection of telescopes to achieve angular resolutions comparable to that of a single, much larger telescope. This is achieved by combining simultaneous observations from pairs of telescopes such that the signal is mathematically equivalent to sampling the Fourier domain of the object. However, reconstructing images from such sparse sampling is a challenging and ill-posed problem, with current methods requiring precise tuning of parameters and manual, iterative cleaning by experts. We present a novel deep learning approach in which the representation in the Fourier domain of an astronomical source is learned implicitly using a neural field representation. Data-driven priors can be added through a transformer encoder. Results on synthetically observed galaxies show that transformer-conditioned neural fields can successfully reconstruct astronomical observations even when the number of visibilities is very sparse.

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Next from AAAI 2022

Learning V1 Simple Cells with Vector Representation of Local Content and Matrix Representation of Local Motion

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Local and Global Linear Convergence of General Low-Rank Matrix Recovery Problems

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