Stability Analysis of Various Symbolic Rule Extraction Methods from Recurrent Neural Network

This paper analyzes two competing rule extraction methodologies: quantization and equivalence query. We trained $3600$ RNN models, extracting $18000$ DFA with a quantization approach (k-means and SOM) and $3600$ DFA by equivalence query($L^{*}$) methods across $10$ initialization seeds. We sampled the datasets from $7$ Tomita and $4$ Dyck grammars and trained them on $4$ RNN cells: LSTM, GRU, O2RNN, and MIRNN. The observations from our experiments establish the superior performance of O2RNN and quantization-based rule extraction over others. $L^{*}$, primarily proposed for regular grammars, performs similarly to quantization methods for Tomita languages when neural networks are perfectly trained. However, for partially trained RNNs, $L^{*}$ shows instability in the number of states in DFA, e.g., for Tomita 5 and Tomita 6 languages, $L^{*}$ produced more than $100$ states. In contrast, quantization methods result in rules with number of states very close to ground truth DFA. Among RNN cells, O2RNN produces stable DFA consistently compared to other cells. For Dyck Languages, we observe that although GRU outperforms other RNNs in network performance, the DFA extracted by O2RNN has higher performance and better stability. The stability is computed as the standard deviation of accuracy on test sets on networks trained across $10$ seeds. On Dyck Languages, quantization methods outperformed $L^{*}$ with better stability in accuracy and the number of states. $L^{*}$ often showed instability in accuracy in the order of $16\% - 22\%$ for GRU and MIRNN while deviation for quantization methods varied in $5\% - 15\%$. In many instances with LSTM and GRU, DFA's extracted by $L^{*}$ even failed to beat chance accuracy ($50\%$), while those extracted by quantization method had standard deviation in the $7\%-17\%$ range. For O2RNN, both rule extraction methods had deviation in the $0.5\% - 3\%$ range.

Estimating Uncertainty in Landslide Segmentation Models

Landslides are a recurring, widespread hazard. Preparation and mitigation efforts can be aided by a high-quality, large-scale dataset that covers global at-risk areas. Such a dataset currently does not exist and is impossible to construct manually. Recent automated efforts focus on deep learning models for landslide segmentation (pixel labeling) from satellite imagery. However, it is also important to characterize the uncertainty or confidence levels of such segmentations. Accurate and robust uncertainty estimates can enable low-cost (in terms of manual labor) oversight of auto-generated landslide databases to resolve errors, identify hard negative examples, and increase the size of labeled training data. In this paper, we evaluate several methods for assessing pixel-level uncertainty of the segmentation. Three methods that do not require architectural changes were compared, including Pre-Threshold activations, Monte-Carlo Dropout and Test-Time Augmentation -- a method that measures the robustness of predictions in the face of data augmentation. Experimentally, the quality of the latter method was consistently higher than the others across a variety of models and metrics in our dataset.

On the Computational Complexity and Formal Hierarchy of Second Order Recurrent Neural Networks

Artificial neural networks (ANNs) with recurrence and self-attention have been shown to be Turing-complete (TC). However, existing work has shown that these ANNs require multiple turns or unbounded computation time, even with unbounded precision in weights, in order to recognize TC grammars. However, under constraints such as fixed or bounded precision neurons and time, ANNs without memory are shown to struggle to recognize even context-free languages. In this work, we extend the theoretical foundation for the $2^{nd}$-order recurrent network ($2^{nd}$ RNN) and prove there exists a class of a $2^{nd}$ RNN that is Turing-complete with bounded time. This model is capable of directly encoding a transition table into its recurrent weights, enabling bounded time computation and is interpretable by design. We also demonstrate that $2$nd order RNNs, without memory, under bounded weights and time constraints, outperform modern-day models such as vanilla RNNs and gated recurrent units in recognizing regular grammars. We provide an upper bound and a stability analysis on the maximum number of neurons required by $2$nd order RNNs to recognize any class of regular grammar. Extensive experiments on the Tomita grammars support our findings, demonstrating the importance of tensor connections in crafting computationally efficient RNNs. Finally, we show $2^{nd}$ order RNNs are also interpretable by extraction and can extract state machines with higher success rates as compared to first-order RNNs. Our results extend the theoretical foundations of RNNs and offer promising avenues for future explainable AI research.

An Optimal and Scalable Matrix Mechanism for Noisy Marginals under Convex Loss Functions

Noisy marginals are a common form of confidentiality-protecting data release and are useful for many downstream tasks such as contingency table analysis, construction of Bayesian networks, and even synthetic data generation. Privacy mechanisms that provide unbiased noisy answers to linear queries (such as marginals) are known as matrix mechanisms. We propose ResidualPlanner, a matrix mechanism for marginals with Gaussian noise that is both optimal and scalable. ResidualPlanner can optimize for many loss functions that can be written as a convex function of marginal variances (prior work was restricted to just one predefined objective function). ResidualPlanner can optimize the accuracy of marginals in large scale settings in seconds, even when the previous state of the art (HDMM) runs out of memory. It even runs on datasets with 100 attributes in a couple of minutes. Furthermore ResidualPlanner can efficiently compute variance/covariance values for each marginal (prior methods quickly run out of memory, even for relatively small datasets).

Differentiable modeling to unify machine learning and physical models and advance Geosciences

Process-Based Modeling (PBM) and Machine Learning (ML) are often perceived as distinct paradigms in the geosciences. Here we present differentiable geoscientific modeling as a powerful pathway toward dissolving the perceived barrier between them and ushering in a paradigm shift. For decades, PBM offered benefits in interpretability and physical consistency but struggled to efficiently leverage large datasets. ML methods, especially deep networks, presented strong predictive skills yet lacked the ability to answer specific scientific questions. While various methods have been proposed for ML-physics integration, an important underlying theme -- differentiable modeling -- is not sufficiently recognized. Here we outline the concepts, applicability, and significance of differentiable geoscientific modeling (DG). "Differentiable" refers to accurately and efficiently calculating gradients with respect to model variables, critically enabling the learning of high-dimensional unknown relationships. DG refers to a range of methods connecting varying amounts of prior knowledge to neural networks and training them together, capturing a different scope than physics-guided machine learning and emphasizing first principles. Preliminary evidence suggests DG offers better interpretability and causality than ML, improved generalizability and extrapolation capability, and strong potential for knowledge discovery, while approaching the performance of purely data-driven ML. DG models require less training data while scaling favorably in performance and efficiency with increasing amounts of data. With DG, geoscientists may be better able to frame and investigate questions, test hypotheses, and discover unrecognized linkages.

Answering Private Linear Queries Adaptively using the Common Mechanism

When analyzing confidential data through a privacy filter, a data scientist often needs to decide which queries will best support their intended analysis. For example, an analyst may wish to study noisy two-way marginals in a dataset produced by a mechanism M1. But, if the data are relatively sparse, the analyst may choose to examine noisy one-way marginals, produced by a mechanism M2 instead. Since the choice of whether to use M1 or M2 is data-dependent, a typical differentially private workflow is to first split the privacy loss budget rho into two parts: rho1 and rho2, then use the first part rho1 to determine which mechanism to use, and the remainder rho2 to obtain noisy answers from the chosen mechanism. In a sense, the first step seems wasteful because it takes away part of the privacy loss budget that could have been used to make the query answers more accurate. In this paper, we consider the question of whether the choice between M1 and M2 can be performed without wasting any privacy loss budget. For linear queries, we propose a method for decomposing M1 and M2 into three parts: (1) a mechanism M* that captures their shared information, (2) a mechanism M1' that captures information that is specific to M1, (3) a mechanism M2' that captures information that is specific to M2. Running M* and M1' together is completely equivalent to running M1 (both in terms of query answer accuracy and total privacy cost rho). Similarly, running M* and M2' together is completely equivalent to running M2. Since M* will be used no matter what, the analyst can use its output to decide whether to subsequently run M1'(thus recreating the analysis supported by M1) or M2'(recreating the analysis supported by M2), without wasting privacy loss budget.

ThreshNet: Segmentation Refinement Inspired by Region-Specific Thresholding

We present ThreshNet, a post-processing method to refine the output of neural networks designed for binary segmentation tasks. ThreshNet uses the confidence map produced by a base network along with global and local patch information to significantly improve the performance of even state-of-the-art methods. Binary segmentation models typically convert confidence maps into predictions by thresholding the confidence scores at 0.5 (or some other fixed number). However, we observe that the best threshold is image-dependent and often even region-specific -- different parts of the image benefit from using different thresholds. Thus ThreshNet takes a trained segmentation model and learns to correct its predictions by using a memory-efficient post-processing architecture that incorporates region-specific thresholds as part of the training mechanism. Our experiments show that ThreshNet consistently improves over current the state-of-the-art methods in binary segmentation and saliency detection, typically by 3 to 5% in mIoU and mBA.

Neural JPEG: End-to-End Image Compression Leveraging a Standard JPEG Encoder-Decoder

Recent advances in deep learning have led to superhuman performance across a variety of applications. Recently, these methods have been successfully employed to improve the rate-distortion performance in the task of image compression. However, current methods either use additional post-processing blocks on the decoder end to improve compression or propose an end-to-end compression scheme based on heuristics. For the majority of these, the trained deep neural networks (DNNs) are not compatible with standard encoders and would be difficult to deply on personal computers and cellphones. In light of this, we propose a system that learns to improve the encoding performance by enhancing its internal neural representations on both the encoder and decoder ends, an approach we call Neural JPEG. We propose frequency domain pre-editing and post-editing methods to optimize the distribution of the DCT coefficients at both encoder and decoder ends in order to improve the standard compression (JPEG) method. Moreover, we design and integrate a scheme for jointly learning quantization tables within this hybrid neural compression framework.Experiments demonstrate that our approach successfully improves the rate-distortion performance over JPEG across various quality metrics, such as PSNR and MS-SSIM, and generates visually appealing images with better color retention quality.

An Empirical Analysis of Recurrent Learning Algorithms In Neural Lossy Image Compression Systems

Recent advances in deep learning have resulted in image compression algorithms that outperform JPEG and JPEG 2000 on the standard Kodak benchmark. However, they are slow to train (due to backprop-through-time) and, to the best of our knowledge, have not been systematically evaluated on a large variety of datasets. In this paper, we perform the first large-scale comparison of recent state-of-the-art hybrid neural compression algorithms, while exploring the effects of alternative training strategies (when applicable). The hybrid recurrent neural decoder is a former state-of-the-art model (recently overtaken by a Google model) that can be trained using backprop-through-time (BPTT) or with alternative algorithms like sparse attentive backtracking (SAB), unbiased online recurrent optimization (UORO), and real-time recurrent learning (RTRL). We compare these training alternatives along with the Google models (GOOG and E2E) on 6 benchmark datasets. Surprisingly, we found that the model trained with SAB performs better (outperforming even BPTT), resulting in faster convergence and a better peak signal-to-noise ratio.

OmniLayout: Room Layout Reconstruction from Indoor Spherical Panoramas

Given a single RGB panorama, the goal of 3D layout reconstruction is to estimate the room layout by predicting the corners, floor boundary, and ceiling boundary. A common approach has been to use standard convolutional networks to predict the corners and boundaries, followed by post-processing to generate the 3D layout. However, the space-varying distortions in panoramic images are not compatible with the translational equivariance property of standard convolutions, thus degrading performance. Instead, we propose to use spherical convolutions. The resulting network, which we call OmniLayout performs convolutions directly on the sphere surface, sampling according to inverse equirectangular projection and hence invariant to equirectangular distortions. Using a new evaluation metric, we show that our network reduces the error in the heavily distorted regions (near the poles) by approx 25 % when compared to standard convolutional networks. Experimental results show that OmniLayout outperforms the state-of-the-art by approx 4% on two different benchmark datasets (PanoContext and Stanford 2D-3D). Code is available at https://github.com/rshivansh/OmniLayout.