arXiv subjects

Martin V. Butz

Publications and source records attributed to Martin V. Butz.

32 records · Page 2Linked to original sources

arXiv2022

Composing Partial Differential Equations with Physics-Aware Neural Networks

We introduce a compositional physics-aware FInite volume Neural Network (FINN) for learning spatiotemporal advection-diffusion processes. FINN implements a new way of combining the learning abilities of artificial neural networks with physical and structural knowledge from numerical simulation by modeling the constituents of partial differential equations (PDEs) in a compositional manner. Results on both one- and two-dimensional PDEs (Burgers', diffusion-sorption, diffusion-reaction, Allen--Cahn) demonstrate FINN's superior modeling accuracy and excellent out-of-distribution generalization ability beyond initial and boundary conditions. With only one tenth of the number of parameters on average, FINN outperforms pure machine learning and other state-of-the-art physics-aware models in all cases -- often even by multiple orders of magnitude. Moreover, FINN outperforms a calibrated physical model when approximating sparse real-world data in a diffusion-sorption scenario, confirming its generalization abilities and showing explanatory potential by revealing the unknown retardation factor of the observed process.

cs.LG↗

arXiv2022

Sparsely Changing Latent States for Prediction and Planning in Partially Observable Domains

A common approach to prediction and planning in partially observable domains is to use recurrent neural networks (RNNs), which ideally develop and maintain a latent memory about hidden, task-relevant factors. We hypothesize that many of these hidden factors in the physical world are constant over time, changing only sparsely. To study this hypothesis, we propose Gated $L_0$ Regularized Dynamics (GateL0RD), a novel recurrent architecture that incorporates the inductive bias to maintain stable, sparsely changing latent states. The bias is implemented by means of a novel internal gating function and a penalty on the $L_0$ norm of latent state changes. We demonstrate that GateL0RD can compete with or outperform state-of-the-art RNNs in a variety of partially observable prediction and control tasks. GateL0RD tends to encode the underlying generative factors of the environment, ignores spurious temporal dependencies, and generalizes better, improving sampling efficiency and overall performance in model-based planning and reinforcement learning tasks. Moreover, we show that the developing latent states can be easily interpreted, which is a step towards better explainability in RNNs.

cs.LG↗

arXiv2021

Latent State Inference in a Spatiotemporal Generative Model

Knowledge about the hidden factors that determine particular system dynamics is crucial for both explaining them and pursuing goal-directed interventions. Inferring these factors from time series data without supervision remains an open challenge. Here, we focus on spatiotemporal processes, including wave propagation and weather dynamics, for which we assume that universal causes (e.g. physics) apply throughout space and time. A recently introduced DIstributed SpatioTemporal graph Artificial Neural network Architecture (DISTANA) is used and enhanced to learn such processes, requiring fewer parameters and achieving significantly more accurate predictions compared to temporal convolutional neural networks and other related approaches. We show that DISTANA, when combined with a retrospective latent state inference principle called active tuning, can reliably derive location-respective hidden causal factors. In a current weather prediction benchmark, DISTANA infers our planet's land-sea mask solely by observing temperature dynamics and, meanwhile, uses the self inferred information to improve its own future temperature predictions.

cs.LG↗

arXiv2021

Latent Event-Predictive Encodings through Counterfactual Regularization

A critical challenge for any intelligent system is to infer structure from continuous data streams. Theories of event-predictive cognition suggest that the brain segments sensorimotor information into compact event encodings, which are used to anticipate and interpret environmental dynamics. Here, we introduce a SUrprise-GAted Recurrent neural network (SUGAR) using a novel form of counterfactual regularization. We test the model on a hierarchical sequence prediction task, where sequences are generated by alternating hidden graph structures. Our model learns to both compress the temporal dynamics of the task into latent event-predictive encodings and anticipate event transitions at the right moments, given noisy hidden signals about them. The addition of the counterfactual regularization term ensures fluid transitions from one latent code to the next, whereby the resulting latent codes exhibit compositional properties. The implemented mechanisms offer a host of useful applications in other domains, including hierarchical reasoning, planning, and decision making.

cs.LG↗

arXiv2021

Finite Volume Neural Network: Modeling Subsurface Contaminant Transport

Data-driven modeling of spatiotemporal physical processes with general deep learning methods is a highly challenging task. It is further exacerbated by the limited availability of data, leading to poor generalizations in standard neural network models. To tackle this issue, we introduce a new approach called the Finite Volume Neural Network (FINN). The FINN method adopts the numerical structure of the well-known Finite Volume Method for handling partial differential equations, so that each quantity of interest follows its own adaptable conservation law, while it concurrently accommodates learnable parameters. As a result, FINN enables better handling of fluxes between control volumes and therefore proper treatment of different types of numerical boundary conditions. We demonstrate the effectiveness of our approach with a subsurface contaminant transport problem, which is governed by a non-linear diffusion-sorption process. FINN does not only generalize better to differing boundary conditions compared to other methods, it is also capable to explicitly extract and learn the constitutive relationships (expressed by the retardation factor). More importantly, FINN shows excellent generalization ability when applied to both synthetic datasets and real, sparse experimental data, thus underlining its relevance as a data-driven modeling tool.

cs.LG↗

arXiv2020

Binding and Perspective Taking as Inference in a Generative Neural Network Model

The ability to flexibly bind features into coherent wholes from different perspectives is a hallmark of cognition and intelligence. Importantly, the binding problem is not only relevant for vision but also for general intelligence, sensorimotor integration, event processing, and language. Various artificial neural network models have tackled this problem with dynamic neural fields and related approaches. Here we focus on a generative encoder-decoder architecture that adapts its perspective and binds features by means of retrospective inference. We first train a model to learn sufficiently accurate generative models of dynamic biological motion or other harmonic motion patterns, such as a pendulum. We then scramble the input to a certain extent, possibly vary the perspective onto it, and propagate the prediction error back onto a binding matrix, that is, hidden neural states that determine feature binding. Moreover, we propagate the error further back onto perspective taking neurons, which rotate and translate the input features onto a known frame of reference. Evaluations show that the resulting gradient-based inference process solves the perspective taking and binding problem for known biological motion patterns, essentially yielding a Gestalt perception mechanism. In addition, redundant feature properties and population encodings are shown to be highly useful. While we evaluate the algorithm on biological motion patterns, the principled approach should be applicable to binding and Gestalt perception problems in other domains.

cs.LG↗

arXiv2020

Active Tuning

We introduce Active Tuning, a novel paradigm for optimizing the internal dynamics of recurrent neural networks (RNNs) on the fly. In contrast to the conventional sequence-to-sequence mapping scheme, Active Tuning decouples the RNN's recurrent neural activities from the input stream, using the unfolding temporal gradient signal to tune the internal dynamics into the data stream. As a consequence, the model output depends only on its internal hidden dynamics and the closed-loop feedback of its own predictions; its hidden state is continuously adapted by means of the temporal gradient resulting from backpropagating the discrepancy between the signal observations and the model outputs through time. In this way, Active Tuning infers the signal actively but indirectly based on the originally learned temporal patterns, fitting the most plausible hidden state sequence into the observations. We demonstrate the effectiveness of Active Tuning on several time series prediction benchmarks, including multiple super-imposed sine waves, a chaotic double pendulum, and spatiotemporal wave dynamics. Active Tuning consistently improves the robustness, accuracy, and generalization abilities of all evaluated models. Moreover, networks trained for signal prediction and denoising can be successfully applied to a much larger range of noise conditions with the help of Active Tuning. Thus, given a capable time series predictor, Active Tuning enhances its online signal filtering, denoising, and reconstruction abilities without the need for additional training.

cs.LG↗

arXiv2020

Investigating Efficient Learning and Compositionality in Generative LSTM Networks

When comparing human with artificial intelligence, one major difference is apparent: Humans can generalize very broadly from sparse data sets because they are able to recombine and reintegrate data components in compositional manners. To investigate differences in efficient learning, Joshua B. Tenenbaum and colleagues developed the character challenge: First an algorithm is trained in generating handwritten characters. In a next step, one version of a new type of character is presented. An efficient learning algorithm is expected to be able to re-generate this new character, to identify similar versions of this character, to generate new variants of it, and to create completely new character types. In the past, the character challenge was only met by complex algorithms that were provided with stochastic primitives. Here, we tackle the challenge without providing primitives. We apply a minimal recurrent neural network (RNN) model with one feedforward layer and one LSTM layer and train it to generate sequential handwritten character trajectories from one-hot encoded inputs. To manage the re-generation of untrained characters, when presented with only one example of them, we introduce a one-shot inference mechanism: the gradient signal is backpropagated to the feedforward layer weights only, leaving the LSTM layer untouched. We show that our model is able to meet the character challenge by recombining previously learned dynamic substructures, which are visible in the hidden LSTM states. Making use of the compositional abilities of RNNs in this way might be an important step towards bridging the gap between human and artificial intelligence.

cs.LG↗

arXiv2020

Inferring, Predicting, and Denoising Causal Wave Dynamics

The novel DISTributed Artificial neural Network Architecture (DISTANA) is a generative, recurrent graph convolution neural network. It implements a grid or mesh of locally parameterizable laterally connected network modules. DISTANA is specifically designed to identify the causality behind spatially distributed, non-linear dynamical processes. We show that DISTANA is very well-suited to denoise data streams, given that re-occurring patterns are observed, significantly outperforming alternative approaches, such as temporal convolution networks and ConvLSTMs, on a complex spatial wave propagation benchmark. It produces stable and accurate closed-loop predictions even over hundreds of time steps. Moreover, it is able to effectively filter noise -- an ability that can be improved further by applying denoising autoencoder principles or by actively tuning latent neural state activities retrospectively. Results confirm that DISTANA is ready to model real-world spatio-temporal dynamics such as brain imaging, supply networks, water flow, or soil and weather data patterns.

cs.LG↗

arXiv2020

Fostering Event Compression using Gated Surprise

Our brain receives a dynamically changing stream of sensorimotor data. Yet, we perceive a rather organized world, which we segment into and perceive as events. Computational theories of cognitive science on event-predictive cognition suggest that our brain forms generative, event-predictive models by segmenting sensorimotor data into suitable chunks of contextual experiences. Here, we introduce a hierarchical, surprise-gated recurrent neural network architecture, which models this process and develops compact compressions of distinct event-like contexts. The architecture contains a contextual LSTM layer, which develops generative compressions of ongoing and subsequent contexts. These compressions are passed into a GRU-like layer, which uses surprise signals to update its recurrent latent state. The latent state is passed forward into another LSTM layer, which processes actual dynamic sensory flow in the light of the provided latent, contextual compression signals. Our model shows to develop distinct event compressions and achieves the best performance on multiple event processing tasks. The architecture may be very useful for the further development of resource-efficient learning, hierarchical model-based reinforcement learning, as well as the development of artificial event-predictive cognition and intelligence.

cs.LG↗

arXiv2020

Learning Precise Spike Timings with Eligibility Traces

Recent research in the field of spiking neural networks (SNNs) has shown that recurrent variants of SNNs, namely long short-term SNNs (LSNNs), can be trained via error gradients just as effective as LSTMs. The underlying learning method (e-prop) is based on a formalization of eligibility traces applied to leaky integrate and fire (LIF) neurons. Here, we show that the proposed approach cannot fully unfold spike timing dependent plasticity (STDP). As a consequence, this limits in principle the inherent advantage of SNNs, that is, the potential to develop codes that rely on precise relative spike timings. We show that STDP-aware synaptic gradients naturally emerge within the eligibility equations of e-prop when derived for a slightly more complex spiking neuron model, here at the example of the Izhikevich model. We also present a simple extension of the LIF model that provides similar gradients. In a simple experiment we demonstrate that the STDP-aware LIF neurons can learn precise spike timings from an e-prop-based gradient signal.

cs.NE↗

arXiv2019

A Distributed Neural Network Architecture for Robust Non-Linear Spatio-Temporal Prediction

We introduce a distributed spatio-temporal artificial neural network architecture (DISTANA). It encodes mesh nodes using recurrent, neural prediction kernels (PKs), while neural transition kernels (TKs) transfer information between neighboring PKs, together modeling and predicting spatio-temporal time series dynamics. As a consequence, DISTANA assumes that generally applicable causes, which may be locally modified, generate the observed data. DISTANA learns in a parallel, spatially distributed manner, scales to large problem spaces, is capable of approximating complex dynamics, and is particularly robust to overfitting when compared to other competitive ANN models. Moreover, it is applicable to heterogeneously structured meshes.

cs.LG↗

arXiv2019

Autonomous Identification and Goal-Directed Invocation of Event-Predictive Behavioral Primitives

Voluntary behavior of humans appears to be composed of small, elementary building blocks or behavioral primitives. While this modular organization seems crucial for the learning of complex motor skills and the flexible adaption of behavior to new circumstances, the problem of learning meaningful, compositional abstractions from sensorimotor experiences remains an open challenge. Here, we introduce a computational learning architecture, termed surprise-based behavioral modularization into event-predictive structures (SUBMODES), that explores behavior and identifies the underlying behavioral units completely from scratch. The SUBMODES architecture bootstraps sensorimotor exploration using a self-organizing neural controller. While exploring the behavioral capabilities of its own body, the system learns modular structures that predict the sensorimotor dynamics and generate the associated behavior. In line with recent theories of event perception, the system uses unexpected prediction error signals, i.e., surprise, to detect transitions between successive behavioral primitives. We show that, when applied to two robotic systems with completely different body kinematics, the system manages to learn a variety of complex and realistic behavioral primitives. Moreover, after initial self-exploration the system can use its learned predictive models progressively more effectively for invoking model predictive planning and goal-directed control in different tasks and environments.

cs.AI↗

arXiv2019

Learning, Planning, and Control in a Monolithic Neural Event Inference Architecture

We introduce REPRISE, a REtrospective and PRospective Inference SchEme, which learns temporal event-predictive models of dynamical systems. REPRISE infers the unobservable contextual event state and accompanying temporal predictive models that best explain the recently encountered sensorimotor experiences retrospectively. Meanwhile, it optimizes upcoming motor activities prospectively in a goal-directed manner. Here, REPRISE is implemented by a recurrent neural network (RNN), which learns temporal forward models of the sensorimotor contingencies generated by different simulated dynamic vehicles. The RNN is augmented with contextual neurons, which enable the encoding of distinct, but related, sensorimotor dynamics as compact event codes. We show that REPRISE concurrently learns to separate and approximate the encountered sensorimotor dynamics: it analyzes sensorimotor error signals adapting both internal contextual neural activities and connection weight values. Moreover, we show that REPRISE can exploit the learned model to induce goal-directed, model-predictive control, that is, approximate active inference: Given a goal state, the system imagines a motor command sequence optimizing it with the prospective objective to minimize the distance to the goal. The RNN activities thus continuously imagine the upcoming future and reflect on the recent past, optimizing the predictive model, the hidden neural state activities, and the upcoming motor activities. As a result, event-predictive neural encodings develop, which allow the invocation of highly effective and adaptive goal-directed sensorimotor control.

cs.LG↗