Dialogue Systems

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear user-defined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Neural Differential Equations have become an important modeling framework due to their ability to adapt to new problems automatically. Training a neural differential equation is effectively a search over a space of plausible dynamical systems. Controlling the computational cost for these models is difficult since it relies on the number of steps the adaptive solver takes. Most prior works have used higher-order methods to reduce prediction timings while greatly increasing training time or reducing both training and prediction timings by relying on specific training algorithms, which are harder to use as a drop-in replacement. In this manuscript, *we use internal cost heuristics of adaptive differential equation solvers at stochastic time-points to guide the training towards learning a dynamical system that is easier to integrate*. We ``close the blackbox'' and allow the use of our method with any sensitivity method. We perform experimental studies to compare our method to global regularization to show that we attain similar performance numbers without compromising on the flexibility of implementation. *We develop two sampling strategies to trade-off between performance and training time*. Our method reduces the number of function evaluations to 0.556x - 0.733x and accelerates predictions by 1.3x - 2x.

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour in different regimes, or *modes*, each with simpler dynamics, and then learn the switching behaviour from one mode to another. To achieve this, Switching Dynamical Systems (SDS) are a powerful tool that automatically discovers these modes and mode-switching behaviour from time series data. While effective, these methods focus on *independent objects*, where the modes of one object are independent of the modes of the other objects. In this paper, we focus on the more general *interacting object* setting for switching dynamical systems, where the per-object dynamics also depend on an unknown and dynamically changing subset of other objects and their modes. To this end, we propose a novel graph-based approach for switching dynamical systems, GRAph Switching dynamical Systems (GRASS), in which we use a dynamic graph to characterize interactions between objects and learn both intra-object and inter-object mode-switching behaviour. For benchmarking, we create two new datasets, a synthesized ODE-driven particles dataset and a real-world Salsa-couple dancing dataset. Experiments show that GRASS can consistently outperforms previous state-of-the-art methods. We will release code and data after acceptance.

Recently Chen and Poor initiated the study of learning mixtures of linear dynamical systems. While linear dynamical systems already have wide-ranging applications in modeling time-series data, using mixture models can lead to a better fit or even a richer understanding of underlying subpopulations represented in the data. In this work we give a new approach to learning mixtures of linear dynamical systems that is based on tensor decompositions. As a result, our algorithm succeeds without strong separation conditions on the components, and can be used to compete with the Bayes optimal clustering of the trajectories. Moreover our algorithm works in the challenging partially-observed setting. Our starting point is the simple but powerful observation that the classic Ho-Kalman algorithm is a relative of modern tensor decomposition methods for learning latent variable models. This gives us a playbook for how to extend it to work with more complicated generative models.

Model-based reinforcement learning is a powerful tool, but collecting data to fit an accurate model of the system can be costly. Exploring an unknown environment in a sample-efficient manner is hence of great importance. However, the complexity of dynamics and the computational limitations of real systems make this task challenging. In this work, we introduce FLEX, an exploration algorithm for nonlinear dynamics based on optimal experimental design. Our policy maximizes the information of the next step and results in an adaptive exploration algorithm, compatible with arbitrary parametric learning models, and requiring minimal computing resources. We test our method on a number of nonlinear environments covering different settings, including time-varying dynamics. Keeping in mind that exploration is intended to serve an exploitation objective, we also test our algorithm on downstream model-based classical control tasks and compare it to other state-of-the-art model-based and model-free approaches. The performance achieved by FLEX is competitive and its computational cost is low.

Transfer operators provide a rich framework for representing the dynamics of very general, nonlinear dynamical systems. When interacting with reproducing kernel Hilbert spaces (RKHS), descriptions of dynamics often incur prohibitive data storage requirements, motivating dataset sparsification as a precursory step to computation. Further, in practice, data is available in the form of trajectories, introducing correlation between samples. In this work, we present a method for sparse learning of transfer operators from $\beta$-mixing stochastic processes, in both discrete and continuous time, and provide sample complexity analysis extending existing theoretical guarantees for learning from non-sparse, i.i.d. data. In addressing continuous-time settings, we develop precise descriptions using covariance-type operators for the infinitesimal generator that aids in the sample complexity analysis. We empirically illustrate the efficacy of our sparse embedding approach through deterministic and stochastic nonlinear system examples.

Decision-based attacks construct adversarial examples against a machine learning (ML) model by making only hard-label queries. These attacks have mainly been applied directly to standalone neural networks. However, in practice, ML models are just one component of a larger learning system. We find that by adding a single preprocessor in front of a classifier, state-of-the-art query-based attacks are up to seven× less effective at attacking a prediction pipeline than at attacking the model alone. We explain this discrepancy by the fact that most preprocessors introduce some notion of invariance to the input space. Hence, attacks that are unaware of this invariance inevitably waste a large number of queries to re-discover or overcome it. We, therefore, develop techniques to (i) reverse-engineer the preprocessor and then (ii) use this extracted information to attack the end-to-end system. Our preprocessors extraction method requires only a few hundred queries, and our preprocessor-aware attacks recover the same efficacy as when attacking the model alone. The code can be found at https://github.com/google-research/preprocessor-aware-black-box-attack.

A common training technique for language models is teacher forcing (TF). TF attempts to match human language exactly, even though identical meanings can be expressed in different ways. This motivates use of sequence-level objectives for dialogue response generation. In this paper, we study the efficacy of various offline reinforcement learning (RL) methods to maximize such objectives. We present a comprehensive evaluation across multiple datasets, models, and metrics. Offline RL shows a clear performance improvement over teacher forcing while not inducing training instability or sacrificing practical training budgets.

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. Motivated by the conjugate gradients algorithm that iteratively selects search directions for minimizing the matrix norm of the approximation error, we design an approach that utilizes a deep neural network to accelerate convergence via data-driven improvement of the search direction at each iteration. Our method leverages a carefully chosen convolutional network to approximate the action of the inverse of the linear operator up to an arbitrary constant. We demonstrate the efficacy of our approach on spatially discretized Poisson equations, which arise in computational fluid dynamics applications, with millions of degrees of freedom. Unlike state-of-the-art learning approaches, our algorithm is capable of reducing the linear system residual to a given tolerance in a small number of iterations, independent of the problem size. Moreover, our method generalizes effectively to various systems beyond those encountered during training.

A complex system with cluttered observations may be a coupled mixture of multiple simple sub-systems corresponding to latent entities. Such sub-systems may hold distinct dynamics in the continuous-time domain; therein, complicated interactions between sub-systems also evolve over time. This setting is fairly common in the real world but has been less considered. In this paper, we propose a sequential learning approach under this setting by decoupling a complex system for handling irregularly sampled and cluttered sequential observations. Such decoupling brings about not only subsystems describing the dynamics of each latent entity but also a meta-system capturing the interaction between entities over time. Specifically, we argue that the meta-system evolving within a simplex is governed by projected differential equations (ProjDEs). We further analyze and provide neural-friendly projection operators in the context of Bregman divergence. Experimental results on synthetic and real-world datasets show the advantages of our approach when facing complex and cluttered sequential data compared to the state-of-the-art.

It has previously been reported that the representation that is learned in the first layer of deep Convolutional Neural Networks (CNNs) is highly consistent across initializations and architectures. In this work, we quantify this consistency by considering the first layer as a filter bank and measuring its energy distribution. We find that the energy distribution is very different from that of the initial weights and is remarkably consistent across random initializations, datasets, architectures and even when the CNNs are trained with *random labels*. In order to explain this consistency, we derive an analytical formula for the energy profile of linear CNNs and show that this profile is mostly dictated by the second order statistics of image patches in the training set and it will approach a whitening transformation when the number of iterations goes to infinity. Finally, we show that this formula for linear CNNs also gives an excellent fit for the energy profiles learned by commonly used *nonlinear* CNNs such as ResNet and VGG, and that the first layer of these CNNs indeed performs approximate whitening of their inputs.

Artificial neural networks are being proposed as models of parts of the brain. The networks are compared to recordings of biological neurons, and good performance in reproducing neural responses is considered to support the model's validity. A key question is how much this system identification approach tells us about brain computation. Does it validate one model architecture over another? We evaluate the most commonly used comparison techniques, such as a linear encoding model and centered kernel alignment, to correctly identify a model by replacing brain recordings with known ground truth models. System identification performance is quite variable; it also depends significantly on factors independent of the ground truth architecture, such as stimuli images. In addition, we show the limitations of using functional similarity scores in identifying higher-level architectural motifs.

Systems consisting of interacting agents are prevalent in the world, ranging from dynamical systems in physics to complex biological networks. To build systems which can interact robustly in the real world, it is thus important to be able to infer the precise interactions governing such systems. Existing approaches typically discover such interactions by explicitly modeling the feed-forward dynamics of the trajectories. In this work, we propose Neural Interaction Inference with Potentials (NIIP) as an alternative approach to discover such interactions that enables greater flexibility in trajectory modeling: it discovers a set of relational potentials, represented as energy functions, which when minimized reconstruct the original trajectory. NIIP assigns low energy to the subset of trajectories which respect the relational constraints observed. We illustrate that with these representations NIIP displays unique capabilities in test-time. First, it allows trajectory manipulation, such as interchanging interaction types across separately trained models, as well as trajectory forecasting. Additionally, it allows adding external hand-crafted potentials at test-time. Finally, NIIP enables the detection of out-of-distribution samples and anomalies without explicit training.

The capability to generate responses with diversity and faithfulness using factual knowledge is paramount for creating a human-like, trustworthy dialogue system. Common strategies either adopt a two-step paradigm, which optimizes knowledge selection and response generation separately, and may overlook the inherent correlation between these two tasks, or leverage conditional variational method to jointly optimize knowledge selection and response generation by employing an inference network. In this paper, we present an end-to-end learning framework, termed Sequential Posterior Inference (SPI), capable of selecting knowledge and generating dialogues by approximately sampling from the posterior distribution. Unlike other methods, SPI does not require the inference network or assume a simple geometry of the posterior distribution. This straightforward and intuitive inference procedure of SPI directly queries the response generation model, allowing for accurate knowledge selection and generation of faithful responses. In addition to modeling contributions, our experimental results on two common dialogue datasets (Wizard of Wikipedia and Holl-E) demonstrate that SPI outperforms previous strong baselines according to both automatic and human evaluation metrics.

Partial differential equations (PDEs) are important tools to model physical systems and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant coefficients, we propose a family of Gaussian process (GP) priors, which we call EPGP, such that all realizations are exact solutions of this system. We apply the Ehrenpreis-Palamodov fundamental principle, which works as a non-linear Fourier transform, to construct GP kernels mirroring standard spectral methods for GPs. Our approach can infer probable solutions of linear PDE systems from any data such as noisy measurements, or pointwise defined initial and boundary conditions. Constructing EPGP-priors is algorithmic, generally applicable, and comes with a sparse version (S-EPGP) that learns the relevant spectral frequencies and works better for big data sets. We demonstrate our approach on three families of systems of PDEs, the heat equation, wave equation, and Maxwell's equations, where we improve upon the state of the art in computation time and precision, in some experiments by several orders of magnitude.