Related papers: State-space fading memory
In this paper, we investigate the long-term memory learning capabilities of state-space models (SSMs) from the perspective of parameterization. We prove that state-space models without any reparameterization exhibit a memory limitation…
This position paper explores the rapid development of Foundation Models (FMs) in AI and their implications for intelligence and reasoning. It examines the characteristics of FMs, including their training on vast datasets and use of…
Several topological and analytical notions of continuity and fading memory for causal and time-invariant filters are introduced, and the relations between them are analyzed. A significant generalization of the convolution theorem that…
This paper addresses characterizations of Integral Input-to-State Stability (iISS) for hybrid systems with memory. Based on the Krasovskii approach, a novel Lyapunov characterization of iISS is established to extend the hybrid system theory…
A new class of non-homogeneous state-affine systems is introduced for use in reservoir computing. Sufficient conditions are identified that guarantee first, that the associated reservoir computers with linear readouts are causal,…
Knowledge workers face an ever increasing flood of information in their daily lives. To counter this and provide better support for information management and knowledge work in general, we have been investigating solutions inspired by human…
Much effort has been devoted in the last two decades to characterize the situations in which a reservoir computing system exhibits the so-called echo state (ESP) and fading memory (FMP) properties. These important features amount, in…
With the explosive growth of data, long-sequence modeling has become increasingly important in tasks such as natural language processing and bioinformatics. However, existing methods face inherent trade-offs between efficiency and memory.…
We present a method for incremental modeling and time-varying control of unknown nonlinear systems. The method combines elements of evolving intelligence, granular machine learning, and multi-variable control. We propose a State-Space…
This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The definition of output-input stability does not rely on a…
A key capability of intelligent agents is operating under partial observability: reasoning and acting effectively despite missing or incomplete state observations. While recurrent (memory-based) policies learned via reinforcement learning…
Deep Feedback Models (DFMs) are a new class of stateful neural networks that combine bottom up input with high level representations over time. This feedback mechanism introduces dynamics into otherwise static architectures, enabling DFMs…
A dynamic mean field theory is developed for finite state and action Bayesian reinforcement learning in the large state space limit. In an analogy with statistical physics, the Bellman equation is studied as a disordered dynamical system;…
Extended finite state machines (EFSMs) model stateful systems with internal data variables and have numerous applications in software engineering. A major advantage of this type of model lies in its ability to model both the data flow and…
Many important tasks are defined in terms of object. To generalize across these tasks, a reinforcement learning (RL) agent needs to exploit the structure that the objects induce. Prior work has either hard-coded object-centric features,…
This paper introduces the extension of Finite-Time Stability (FTS) to the input-output case, namely the Input-Output FTS (IO-FTS). The main differences between classic IO stability and IO-FTS are that the latter involves signals defined…
State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the…
In this paper, we extend the notion of finite-time input-to-state stability (FTISS) for finite-dimensional systems to infinite-dimensional systems. More specifically, we first prove an FTISS Lyapunov theorem for a class of…
A key question in reinforcement learning is how an intelligent agent can generalize knowledge across different inputs. By generalizing across different inputs, information learned for one input can be immediately reused for improving…
State-space models have gained popularity in sequence modelling due to their simple and efficient network structures. However, the absence of nonlinear activation along the temporal direction limits the model's capacity. In this paper, we…