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Recent advances in large pretrained models have led to their widespread integration as core components in modern software systems. The trend is expected to continue in the foreseeable future. Unlike traditional software systems governed by…

Two high-level "pictures" of probability theory have emerged: one that takes as central the notion of random variable, and one that focuses on distributions and probability channels (Markov kernels). While the channel-based picture has been…

The nature of abstract reasoning is a matter of debate. Modern artificial neural network (ANN) models, like large language models, demonstrate impressive success when tested on abstract reasoning problems. However, it has been argued that…

State-space models (SSMs) have recently attention as an efficient alternative to computationally expensive attention-based models for sequence modeling. They rely on linear recurrences to integrate information over time, enabling fast…

Epidemic propagation on networks represents an important departure from traditional massaction models. However, the high-dimensionality of the exact models poses a challenge to both mathematical analysis and parameter inference. By using…

Though quite challenging, leveraging large-scale unlabeled or partially labeled data in learning systems (e.g., model/classifier training) has attracted increasing attentions due to its fundamental importance. To address this problem, many…

We prove that Moore machines can be exactly realized as state-space models (SSMs), establishing a formal correspondence between symbolic automata and these continuous machine learning architectures. These Moore-SSMs preserve both the…

State Space Models (SSMs) have become the leading alternative to Transformers for sequence modeling. Their primary advantage is efficiency in long-context and long-form generation, enabled by fixed-size memory and linear scaling of…

A structured variable selection problem is considered in which the covariates, divided into predefined groups, activate according to sparse patterns with few nonzero entries per group. Capitalizing on the concept of atomic norm, a composite…

State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series…

Artificial intelligence systems are increasingly embedded as persistent, closed-loop components within cyber-physical, social, and institutional processes. Rather than producing isolated outputs, such systems operate continuously under…

Agent-based modeling (ABM) is a well-established paradigm for simulating complex systems via interactions between constituent entities. Machine learning (ML) refers to approaches whereby statistical algorithms 'learn' from data on their…

Software systems are complex, and behavioral comprehension with the increasing amount of AI components challenges traditional testing and maintenance strategies.The lack of tools and methodologies for behavioral software comprehension…

Latent state space models are a fundamental and widely used tool for modeling dynamical systems. However, they are difficult to learn from data and learned models often lack performance guarantees on inference tasks such as filtering and…

Testing of autonomous systems is extremely important as many of them are both safety-critical and security-critical. The architecture and mechanism of such systems are fundamentally different from traditional control software, which appears…

State-Space Models (SSMs) have re-emerged as a powerful tool for online function approximation, and as the backbone of machine learning models for long-range dependent data. However, to date, only a few polynomial bases have been explored…

With the increasing ubiquity of safety-critical autonomous systems operating in uncertain environments, there is a need for mathematical methods for formal verification of stochastic models. Towards formally verifying properties of…

There have been many proposals for access control models and authorization policy languages, which are used to inform the design of access control systems. Most, if not all, of these proposals impose restrictions on the implementation of…

This paper discusses the letter entitled "Network analysis of the state space of discrete dynamical systems" by A. Shreim et al. [Physical Review Letters, 98, 198701 (2007)]. We found that some theoretical analyses are wrong and the…

Stochastic models that predict adaptive filtering algorithms performance usually employ several assumptions in order to simplify the analysis. Although these simplifications facilitate the recursive update of the statistical quantities of…