huashen218/convxai-cia-dataset huggingface dataset:
Estimating Lipschitz constants of monotone deep equilibrium models
Keywords: deep equilibrium models, Lipschitz constants

Several methods have been proposed in recent years to provide bounds on the Lipschitz constants of deep networks, which can be used to provide robustness guarantees, generalization bounds, and characterize the smoothness of decision boundaries. However, existing bounds get substantially weaker with increasing depth of the network, which makes it unclear how to apply such bounds to recently proposed models such as the deep equilibrium (DEQ) model, which can be viewed as representing an infinitely-deep network. In this paper, we show that monotone DEQs, a recently-proposed subclass of DEQs, have Lipschitz constants that can be bounded as a simple function of the strong monotonicity parameter of the network. We derive simple-yet-tight bounds on both the input-output mapping and the weight-output mapping defined by these networks, and demonstrate that they are small relative to those for comparable standard DNNs. We show that one can use these bounds to design monotone DEQ models, even with e.g. multi-scale convolutional structure, that still have constraints on the Lipschitz constant. We also highlight how to use these bounds to develop PAC-Bayes generalization bounds that do not depend on any depth of the network, and which avoid the exponential depth-dependence of comparable DNN bounds.
Implicit Gradient Regularization
Keywords: implicit regularization, deep learning, deep learning theory, theoretical issues in deep learning, theory, regularization

Gradient descent can be surprisingly good at optimizing deep neural networks without overfitting and without explicit regularization. We find that the discrete steps of gradient descent implicitly regularize models by penalizing gradient descent trajectories that have large loss gradients. We call this Implicit Gradient Regularization (IGR) and we use backward error analysis to calculate the size of this regularization. We confirm empirically that implicit gradient regularization biases gradient descent toward flat minima, where test errors are small and solutions are robust to noisy parameter perturbations. Furthermore, we demonstrate that the implicit gradient regularization term can be used as an explicit regularizer, allowing us to control this gradient regularization directly. More broadly, our work indicates that backward error analysis is a useful theoretical approach to the perennial question of how learning rate, model size, and parameter regularization interact to determine the properties of overparameterized models optimized with gradient descent.
Faster Binary Embeddings for Preserving Euclidean Distances
Keywords: Binary Embeddings, Johnson-Lindenstrauss Transforms, Sigma Delta Quantization

We propose a fast, distance-preserving, binary embedding algorithm to transform a high-dimensional dataset T⊆Rn into binary sequences in the cube {±1}m. When T consists of well-spread (i.e., non-sparse) vectors, our embedding method applies a stable noise-shaping quantization scheme to Ax where A∈Rm×n is a sparse Gaussian random matrix. This contrasts with most binary embedding methods, which usually use x↦sign(Ax) for the embedding. Moreover, we show that Euclidean distances among the elements of T are approximated by the ℓ1 norm on the images of {±1}m under a fast linear transformation. This again contrasts with standard methods, where the Hamming distance is used instead.  Our method is both fast and memory efficient, with time complexity  O(m) and space complexity O(m) on well-spread data. When the data is not well-spread, we show that the approach still works provided that data is transformed via a Walsh-Hadamard matrix, but now the cost is O(nlog⁡n) per data point.  Further, we prove that the method is accurate and its associated error is comparable to that of a continuous valued Johnson-Lindenstrauss embedding plus a quantization error that admits a polynomial decay as the embedding dimension m increases.
        	Thus the length of the binary codes required to achieve a desired accuracy is quite small, and we show it can even be compressed further without compromising the accuracy. To illustrate our results, we test the proposed method on natural images and show that it achieves strong performance.
Scalable Transfer Learning with Expert Models
Keywords: Transfer Learning, Expert Models, Few Shot

Transfer of pre-trained representations can improve sample efficiency and reduce computational requirements for new tasks. However, representations used for transfer are usually generic, and are not tailored to a particular distribution of downstream tasks. We explore the use of expert representations for transfer with a simple, yet effective, strategy. We train a diverse set of experts by exploiting existing label structures, and use cheap-to-compute performance proxies to select the relevant expert for each target task. This strategy scales the process of transferring to new tasks, since it does not revisit the pre-training data during transfer. Accordingly, it requires little extra compute per target task, and results in a speed-up of 2-3 orders of magnitude compared to competing approaches. Further, we provide an adapter-based architecture able to compress many experts into a single model. We evaluate our approach on two different data sources and demonstrate that it outperforms baselines on over 20 diverse vision tasks in both cases.
Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU
Keywords: signature, logsignature, gpu, library, open source

Signatory is a library for calculating and performing functionality related to the signature and logsignature transforms. The focus is on machine learning, and as such includes features such as CPU parallelism, GPU support, and backpropagation. To our knowledge it is the first GPU-capable library for these operations. Signatory implements new features not available in previous libraries, such as efficient precomputation strategies. Furthermore, several novel algorithmic improvements are introduced, producing substantial real-world speedups even on the CPU without parallelism. The library operates as a Python wrapper around C++, and is compatible with the PyTorch ecosystem. It may be installed directly via \texttt{pip}. Source code, documentation, examples, benchmarks and tests may be found at \texttt{\url{https://github.com/patrick-kidger/signatory}}. The license is Apache-2.0.
Distance-Based Regularisation of Deep Networks for Fine-Tuning
Keywords: Deep Learning, Transfer Learning, Statistical Learning Theory

We investigate approaches to regularisation during fine-tuning of deep neural networks. First we provide a neural network generalisation bound based on Rademacher complexity that uses the distance the weights have moved from their initial values. This bound has no direct dependence on the number of weights and compares favourably to other bounds when applied to convolutional networks. Our bound is highly relevant for fine-tuning, because providing a network with a good initialisation based on transfer learning means that learning can modify the weights less, and hence achieve tighter generalisation. Inspired by this, we develop a simple yet effective fine-tuning algorithm that constrains the hypothesis class to a small sphere centred on the initial pre-trained weights, thus obtaining provably better generalisation performance than conventional transfer learning. Empirical evaluation shows that our algorithm works well, corroborating our theoretical results. It outperforms both state of the art fine-tuning competitors, and penalty-based alternatives that we show do not directly constrain the radius of the search space.
Decoupling Global and Local Representations via Invertible Generative Flows
Keywords: Generative Models, Generative Flow, Normalizing Flow, Image Generation, Representation Learning

In this work, we propose a new generative model that is capable of automatically decoupling global and local representations of images in an entirely unsupervised setting, by embedding a generative flow in the VAE framework to model the decoder.
        Specifically, the proposed model utilizes the variational auto-encoding framework to learn a (low-dimensional) vector of latent variables to capture the global information of an image, which is fed as a conditional input to a flow-based invertible decoder with architecture borrowed from style transfer literature.
        Experimental results on standard image benchmarks demonstrate the effectiveness of our model in terms of density estimation, image generation and unsupervised representation learning.
        Importantly, this work demonstrates that with only architectural inductive biases, a generative model with a likelihood-based objective is capable of learning decoupled representations, requiring no explicit supervision.
        The code for our model is available at \url{https://github.com/XuezheMax/wolf}.
Understanding Over-parameterization in Generative Adversarial Networks
Keywords: GAN, Over-parameterization, min-max optimization

A broad class of unsupervised deep learning methods such as Generative Adversarial Networks (GANs) involve training of overparameterized models where the number of parameters of the model exceeds a certain threshold. Indeed, most successful GANs used in practice are trained using overparameterized generator and discriminator networks, both in terms of depth and width. A large body of work in supervised learning have shown the importance of model overparameterization in the convergence of the gradient descent (GD) to globally optimal solutions. In contrast, the unsupervised setting and GANs in particular involve non-convex concave mini-max optimization problems that are often trained using Gradient Descent/Ascent (GDA).
        The role and benefits of model overparameterization in the convergence of GDA to a global saddle point in non-convex concave problems is far less understood. In this work, we present a comprehensive analysis of the importance of model overparameterization in GANs both theoretically and empirically. We theoretically show that in an overparameterized GAN model with a 1-layer neural network generator and a linear discriminator, GDA converges to a global saddle point of the underlying non-convex concave min-max problem. To the best of our knowledge, this is the first result for global convergence of GDA in such settings. Our theory is based on a more general result that holds for a broader class of nonlinear generators and discriminators that obey certain assumptions (including deeper generators and random feature discriminators). Our theory utilizes and builds upon a novel connection with the convergence analysis of linear time-varying dynamical systems which may have broader implications for understanding the convergence behavior of GDA for non-convex concave problems involving overparameterized models. We also empirically study the role of model overparameterization in GANs using several large-scale experiments on CIFAR-10 and Celeb-A datasets. Our experiments show that overparameterization improves the quality of generated samples across various model architectures and datasets. Remarkably, we observe that overparameterization leads to faster and more stable convergence behavior of GDA across the board.
Filtered Inner Product Projection for Crosslingual Embedding Alignment
Keywords: multilingual representations, word embeddings, natural language processing

Due to widespread interest in machine translation and transfer learning, there are numerous algorithms for mapping multiple embeddings to a shared representation space. Recently, these algorithms have been studied in the setting of bilingual lexicon induction where one seeks to align the embeddings of a source and a target language such that translated word pairs lie close to one another in a common representation space. In this paper, we propose a method, Filtered Inner Product Projection (FIPP), for mapping embeddings to a common representation space. As semantic shifts are pervasive across languages and domains, FIPP first identifies the common geometric structure in both embeddings and then, only on the common structure, aligns the Gram matrices of these embeddings. FIPP is applicable even when the source and target embeddings are of differing dimensionalities. Additionally, FIPP provides computational benefits in ease of implementation and is faster to compute than current approaches. Following the baselines in Glavas et al. 2019, we evaluate FIPP both in the context of bilingual lexicon induction and downstream language tasks. We show that FIPP outperforms existing methods on the XLING BLI dataset for most language pairs while also providing robust performance across downstream tasks.
Deep Partition Aggregation: Provable Defenses against General Poisoning Attacks
Keywords: bagging, ensemble, robustness, certificate, poisoning, smoothing

Adversarial poisoning attacks distort training data in order to corrupt the test-time behavior of a classifier. A provable defense provides a certificate for each test sample, which is a lower bound on the magnitude of any adversarial distortion of the training set that can corrupt the test sample's classification.
        We propose two novel provable defenses against poisoning attacks: (i) Deep Partition Aggregation (DPA), a certified defense against a general poisoning threat model, defined as the insertion or deletion of a bounded number of samples to the training set --- by implication, this threat model also includes arbitrary distortions to a bounded number of images and/or labels; and (ii) Semi-Supervised DPA (SS-DPA), a certified defense against label-flipping poisoning attacks. DPA is an ensemble method where base models are trained on partitions of the training set determined by a hash function. DPA is related to both subset aggregation, a well-studied ensemble method in classical machine learning, as well as to randomized smoothing, a popular provable defense against evasion (inference) attacks. Our defense against label-flipping poison attacks, SS-DPA, uses a semi-supervised learning algorithm as its base classifier model: each base classifier is trained using the entire unlabeled training set in addition to the labels for a partition. SS-DPA significantly outperforms the existing certified defense for label-flipping attacks (Rosenfeld et al., 2020) on both MNIST and CIFAR-10: provably tolerating, for at least half of test images, over 600 label flips (vs. < 200 label flips) on MNIST and over 300 label flips (vs. 175 label flips) on CIFAR-10. Against general poisoning attacks where no prior certified defenses exists, DPA can certify ≥ 50% of test images against over 500 poison image insertions on MNIST, and nine insertions on CIFAR-10. These results establish new state-of-the-art provable defenses against general and label-flipping poison attacks. Code is available at https://github.com/alevine0/DPA
HalentNet: Multimodal Trajectory Forecasting with Hallucinative Intents

Motion forecasting is essential for making intelligent decisions in robotic navigation. As a result, the multi-agent behavioral prediction has become a core component of modern human-robot interaction applications such as autonomous driving. Due to various intentions and interactions among agents, agent trajectories can have multiple possible futures. Hence, the motion forecasting model's ability to cover possible modes becomes essential to enable accurate prediction. Towards this goal, we introduce HalentNet to better model the future motion distribution in addition to a traditional trajectory regression learning objective by incorporating generative augmentation losses. We model intents with unsupervised discrete random variables whose training is guided by a collaboration between two key signals: A discriminative loss that encourages intents' diversity and a hallucinative loss that explores intent transitions (i.e., mixed intents) and encourages their smoothness. This regulates the neural network behavior to be more accurately predictive on uncertain scenarios due to the active yet careful exploration of possible future agent behavior. Our model's learned representation leads to better and more semantically meaningful coverage of the trajectory distribution. Our experiments show that our method can improve over the state-of-the-art trajectory forecasting benchmarks, including vehicles and pedestrians, for about 20% on average FDE and 50% on road boundary violation rate when predicting 6 seconds future. We also conducted human experiments to show that our predicted trajectories received 39.6% more votes than the runner-up approach and 32.2% more votes than our variant without hallucinative mixed intent loss. The code will be released soon.
INT: An Inequality Benchmark for Evaluating Generalization in Theorem Proving
Keywords: Theorem proving, Synthetic benchmark dataset, Generalization, Transformers, Graph neural networks, Monte Carlo Tree Search

In learning-assisted theorem proving, one of the most critical challenges is to generalize to theorems unlike those seen at training time. In this paper, we introduce INT, an INequality Theorem proving benchmark designed to test agents’ generalization ability. INT is based on a theorem generator, which provides theoretically infinite data and allows us to measure 6 different types of generalization, each reflecting a distinct challenge, characteristic of automated theorem proving. In addition, provides a fast theorem proving environment with sequence-based and graph-based interfaces, conducive to performing learning-based research. We introduce base-lines with architectures including transformers and graph neural networks (GNNs)for INT. Using INT, we find that transformer-based agents achieve stronger test performance for most of the generalization tasks, despite having much larger out-of-distribution generalization gaps than GNNs. We further find that the addition of Monte Carlo Tree Search (MCTS) at test time helps to prove new theorems.
Bayesian Few-Shot Classification with One-vs-Each Pólya-Gamma Augmented Gaussian Processes
Keywords: few-shot learning, gaussian processes, bayesian deep learning, uncertainty estimation

Few-shot classification (FSC), the task of adapting a classifier to unseen classes given a small labeled dataset, is an important step on the path toward human-like machine learning. Bayesian methods are well-suited to tackling the fundamental issue of overfitting in the few-shot scenario because they allow practitioners to specify prior beliefs and update those beliefs in light of observed data. Contemporary approaches to Bayesian few-shot classification maintain a posterior distribution over model parameters, which is slow and requires storage that scales with model size. Instead, we propose a Gaussian process classifier based on a novel combination of Pólya-Gamma augmentation and the one-vs-each softmax approximation that allows us to efficiently marginalize over functions rather than model parameters. We demonstrate improved accuracy and uncertainty quantification on both standard few-shot classification benchmarks and few-shot domain transfer tasks.
A Hypergradient Approach to Robust Regression without Correspondence
Keywords: Regression without correspondence, differentiable programming, first-order optimization, Sinkhorn algorithm

We consider a regression problem, where the correspondence between the input and output data is not available. Such shuffled data are commonly observed in many real world problems. Take flow cytometry as an example: the measuring instruments are unable to preserve the correspondence between the samples and the measurements. Due to the combinatorial nature of the problem, most of the existing methods are only applicable when the sample size is small, and are limited to linear regression models. To overcome such bottlenecks, we propose a new computational framework --- ROBOT --- for the shuffled regression problem, which is applicable to large data and complex models. Specifically, we propose to formulate regression without correspondence as a continuous optimization problem. Then by exploiting the interaction between the regression model and the data correspondence, we propose to develop a hypergradient approach based on differentiable programming techniques. Such a hypergradient approach essentially views the data correspondence as an operator of the regression model, and therefore it allows us to find a better descent direction for the model parameters by differentiating through the data correspondence. ROBOT is quite general, and can be further extended to an inexact correspondence setting, where the input and output data are not necessarily exactly aligned. Thorough numerical experiments show that ROBOT achieves better performance than existing methods in both linear and nonlinear regression tasks, including real-world applications such as flow cytometry and multi-object tracking.
C-Learning: Horizon-Aware Cumulative Accessibility Estimation
Keywords: reinforcement learning, goal reaching, Q-learning

Multi-goal reaching is an important problem in reinforcement learning needed to achieve algorithmic generalization. Despite recent advances in this field, current algorithms suffer from three major challenges: high sample complexity, learning only a single way of reaching the goals,  and difficulties in solving complex motion planning tasks. In order to address these limitations, we introduce the concept of cumulative accessibility functions, which measure the reachability of a goal from a given state within a specified horizon. We show that these functions obey a recurrence relation, which enables learning from offline interactions. We also prove that optimal cumulative accessibility functions are monotonic in the planning horizon. Additionally, our method can trade off speed and reliability in goal-reaching by suggesting multiple paths to a single goal depending on the provided horizon. We evaluate our approach on a set of multi-goal discrete and continuous control tasks. We show that our method outperforms state-of-the-art goal-reaching algorithms in success rate, sample complexity, and path optimality. Our code is available at https://github.com/layer6ai-labs/CAE, and additional visualizations can be found at https://sites.google.com/view/learning-cae/.
MIROSTAT: A NEURAL TEXT DECODING ALGORITHM THAT DIRECTLY CONTROLS PERPLEXITY
Keywords: Neural text decoding, sampling algorithms, cross-entropy, repetitions, incoherence

Neural text decoding algorithms strongly influence the quality of texts generated using language models, but popular algorithms like top-k, top-p (nucleus), and temperature-based sampling may yield texts that have objectionable repetition or incoherence. Although these methods generate high-quality text after ad hoc parameter tuning that depends on the language model and the length of generated text, not much is known about the control they provide over the statistics of the output. This is important, however, since recent reports show that humans prefer when perplexity is neither too much nor too little and since we experimentally show that cross-entropy (log of perplexity) has a near-linear relation with repetition. First, we provide a theoretical analysis of perplexity in top-k, top-p, and temperature sampling, under Zipfian statistics. Then, we use this analysis to design a feedback-based adaptive top-k text decoding algorithm called mirostat that generates text (of any length) with a predetermined target value of perplexity without any tuning. Experiments show that for low values of k and p, perplexity drops significantly with generated text length and leads to excessive repetitions (the boredom trap). Contrarily, for large values of k and p, perplexity increases with generated text length and leads to incoherence (confusion trap). Mirostat avoids both traps. Specifically, we show that setting target perplexity value beyond a threshold yields negligible sentence-level repetitions. Experiments with
        human raters for fluency, coherence, and quality further verify our findings.