arXiv subjects

Mathias Lechner

Publications and source records attributed to Mathias Lechner.

43 records · Page 3Linked to original sources

arXiv2020

Lagrangian Reachtubes: The Next Generation

We introduce LRT-NG, a set of techniques and an associated toolset that computes a reachtube (an over-approximation of the set of reachable states over a given time horizon) of a nonlinear dynamical system. LRT-NG significantly advances the state-of-the-art Langrangian Reachability and its associated tool LRT. From a theoretical perspective, LRT-NG is superior to LRT in three ways. First, it uses for the first time an analytically computed metric for the propagated ball which is proven to minimize the ball's volume. We emphasize that the metric computation is the centerpiece of all bloating-based techniques. Secondly, it computes the next reachset as the intersection of two balls: one based on the Cartesian metric and the other on the new metric. While the two metrics were previously considered opposing approaches, their joint use considerably tightens the reachtubes. Thirdly, it avoids the "wrapping effect" associated with the validated integration of the center of the reachset, by optimally absorbing the interval approximation in the radius of the next ball. From a tool-development perspective, LRT-NG is superior to LRT in two ways. First, it is a standalone tool that no longer relies on CAPD. This required the implementation of the Lohner method and a Runge-Kutta time-propagation method. Secondly, it has an improved interface, allowing the input model and initial conditions to be provided as external input files. Our experiments on a comprehensive set of benchmarks, including two Neural ODEs, demonstrates LRT-NG's superior performance compared to LRT, CAPD, and Flow*.

eess.SY↗

arXiv2020

Learning Long-Term Dependencies in Irregularly-Sampled Time Series

Recurrent neural networks (RNNs) with continuous-time hidden states are a natural fit for modeling irregularly-sampled time series. These models, however, face difficulties when the input data possess long-term dependencies. We prove that similar to standard RNNs, the underlying reason for this issue is the vanishing or exploding of the gradient during training. This phenomenon is expressed by the ordinary differential equation (ODE) representation of the hidden state, regardless of the ODE solver's choice. We provide a solution by designing a new algorithm based on the long short-term memory (LSTM) that separates its memory from its time-continuous state. This way, we encode a continuous-time dynamical flow within the RNN, allowing it to respond to inputs arriving at arbitrary time-lags while ensuring a constant error propagation through the memory path. We call these RNN models ODE-LSTMs. We experimentally show that ODE-LSTMs outperform advanced RNN-based counterparts on non-uniformly sampled data with long-term dependencies. All code and data is available at https://github.com/mlech26l/ode-lstms.

cs.LG↗

arXiv2019

Can a Compact Neuronal Circuit Policy be Re-purposed to Learn Simple Robotic Control?

We propose a neural information processing system which is obtained by re-purposing the function of a biological neural circuit model, to govern simulated and real-world control tasks. Inspired by the structure of the nervous system of the soil-worm, C. elegans, we introduce Neuronal Circuit Policies (NCPs), defined as the model of biological neural circuits reparameterized for the control of an alternative task. We learn instances of NCPs to control a series of robotic tasks, including the autonomous parking of a real-world rover robot. For reconfiguration of the purpose of the neural circuit, we adopt a search-based optimization algorithm. Neuronal circuit policies perform on par and in some cases surpass the performance of contemporary deep learning models with the advantage leveraging significantly fewer learnable parameters and realizing interpretable dynamics at the cell-level.

cs.LG↗

arXiv2018

Liquid Time-constant Recurrent Neural Networks as Universal Approximators

In this paper, we introduce the notion of liquid time-constant (LTC) recurrent neural networks (RNN)s, a subclass of continuous-time RNNs, with varying neuronal time-constant realized by their nonlinear synaptic transmission model. This feature is inspired by the communication principles in the nervous system of small species. It enables the model to approximate continuous mapping with a small number of computational units. We show that any finite trajectory of an $n$-dimensional continuous dynamical system can be approximated by the internal state of the hidden units and $n$ output units of an LTC network. Here, we also theoretically find bounds on their neuronal states and varying time-constant.

cs.LG↗

arXiv2018

Response Characterization for Auditing Cell Dynamics in Long Short-term Memory Networks

In this paper, we introduce a novel method to interpret recurrent neural networks (RNNs), particularly long short-term memory networks (LSTMs) at the cellular level. We propose a systematic pipeline for interpreting individual hidden state dynamics within the network using response characterization methods. The ranked contribution of individual cells to the network's output is computed by analyzing a set of interpretable metrics of their decoupled step and sinusoidal responses. As a result, our method is able to uniquely identify neurons with insightful dynamics, quantify relationships between dynamical properties and test accuracy through ablation analysis, and interpret the impact of network capacity on a network's dynamical distribution. Finally, we demonstrate generalizability and scalability of our method by evaluating a series of different benchmark sequential datasets.

cs.LG↗

arXiv2018

Neuronal Circuit Policies

We propose an effective way to create interpretable control agents, by re-purposing the function of a biological neural circuit model, to govern simulated and real world reinforcement learning (RL) test-beds. We model the tap-withdrawal (TW) neural circuit of the nematode, C. elegans, a circuit responsible for the worm's reflexive response to external mechanical touch stimulations, and learn its synaptic and neuronal parameters as a policy for controlling basic RL tasks. We also autonomously park a real rover robot on a pre-defined trajectory, by deploying such neuronal circuit policies learned in a simulated environment. For reconfiguration of the purpose of the TW neural circuit, we adopt a search-based RL algorithm. We show that our neuronal policies perform as good as deep neural network policies with the advantage of realizing interpretable dynamics at the cell level.

q-bio.NC↗

arXiv2017

Worm-level Control through Search-based Reinforcement Learning

Through natural evolution, nervous systems of organisms formed near-optimal structures to express behavior. Here, we propose an effective way to create control agents, by \textit{re-purposing} the function of biological neural circuit models, to govern similar real world applications. We model the tap-withdrawal (TW) neural circuit of the nematode, \textit{C. elegans}, a circuit responsible for the worm's reflexive response to external mechanical touch stimulations, and learn its synaptic and neural parameters as a policy for controlling the inverted pendulum problem. For reconfiguration of the purpose of the TW neural circuit, we manipulate a search-based reinforcement learning. We show that our neural policy performs as good as existing traditional control theory and machine learning approaches. A video demonstration of the performance of our method can be accessed at \url{https://youtu.be/o-Ia5IVyff8}.

cs.NE↗