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At least 55 records · Page 3

Masked Symbol Modeling for Demodulation of Oversampled Baseband Communication Signals in Impulsive Noise-Dominated Channels

Recent breakthroughs in natural language processing show that attention mech- anism in Transformer networks, trained via masked-token prediction, enables models to capture the semantic context of the tokens and internalize the grammar of language. While the application of Transformers to communication systems is a burgeoning field, the notion of context within physical waveforms remains under-explored. This paper addresses that gap by re-examining inter-symbol con- tribution (ISC) caused by pulse-shaping overlap. Rather than treating ISC as a nuisance, we view it as a deterministic source of contextual information embedded in oversampled complex baseband signals. We propose Masked Symbol Model- ing (MSM), a framework for the physical (PHY) layer inspired by Bidirectional Encoder Representations from Transformers methodology. In MSM, a subset of symbol-aligned samples is randomly masked, and a Transformer predicts the missing symbol identifiers using the surrounding “in-between” samples. Through this objective, the model learns the latent syntax of complex baseband waveforms. We illustrate MSM’s potential by applying it to the task of demodulating sig- nals corrupted by impulsive noise, where the model infers corrupted segments by leveraging the learned context. Our results suggest a path toward receivers that interpret, rather than merely detect communication signals, opening new avenues for context-aware PHY layer design.

Bedir, Oguz↗

Approaches to the study of intelligence

A survey and an evaluation are conducted for the Rosenbloom et al. (1991) 'SOAR' model of intelligence, both as found in humans and in prospective AI systems, which views it as a representational system for goal-oriented symbolic activity based on a physical symbol system. Attention is given to SOAR's implications for semantic and episodic memory, symbol processing, and search within a uniform problem space; also noted are the relationships of SOAR to competing AI schemes, and its potential usefulness as a theoretical tool for cognitive psychology.

Norman, Donald A.↗

NEUROSPF: A Tool For the Symbolic Analysis of Neural Networks

This paper presents NEUROSPF, a tool for the symbolic analysis of neural networks. Given a trained neural network model, the tool extracts the architecture and model parameters and translates them into a Java representation that is amenable for analysis using the Symbolic PathFinder symbolic execution tool. Notably, NEUROSPF encodes specialized peer classes for parsing the model’s parameters, thereby enabling efficient analysis. With NEUROSPF the user has the flexibility to specify either the inputs or the network internal parameters as symbolic, promoting the application of program analysis and testing approaches from software engineering to the field of machine learning. For instance, NEUROSPF can be used for coverage-based testing and test generation, finding adversarial examples and also constraint-based repair of neural networks, thus improving the reliability of neural networks and of the applications that use them.

neural networks↗

Identifying stochastic dynamics via finite expression methods

Modeling stochastic differential equations (SDEs) is crucial for understanding complex dynamical systems in various scientific fields. Recent methods often employ neural network-based models, which typically represent SDEs through a combination of deterministic and stochastic terms. However, these models usually lack interpretability and have difficulty in generalizing beyond their training domain. Here, this paper introduces the Finite Expression Method (FEX), a symbolic learning approach designed to derive interpretable mathematical representations of the deterministic component of SDEs. For the stochastic component, we integrate FEX with advanced generative modeling techniques to provide a comprehensive representation of SDEs. The numerical experiments on linear, nonlinear, and multidimensional SDEs demonstrate that FEX generalizes well beyond the training domain and delivers more accurate long-term predictions compared to neural network-based methods. The symbolic expressions identified by FEX not only improve prediction accuracy but also offer valuable scientific insights into the underlying dynamics of the systems.

Complex dynamical systems↗

A two-loop four-point form factor at function level

Recently, the maximally-helicity-violating four-point form factor for the chiral stress-energy tensor in planar $\mathcal{N}$ = 4 super Yang-Mills was computed to three loops at the level of the symbol associated with multiple polylogarithms. It exhibits antipodal self-duality, or invariance under the combined action of a kinematic map and reversing the ordering of letters in the symbol. Here we lift the two-loop form factor from symbol level to function level. We provide an iterated representation of the function’s derivatives (coproducts). In order to do so, we find a three-parameter limit of the five-parameter phase space where the symbol’s letters are all rational. We also use function-level information about dihedral symmetries and the soft, collinear, and factorization limits, as well as limits governed by the form-factor operator product expansion (FFOPE). We provide plots of the remainder function on several kinematic slices, and show that the result is compatible with the FFOPE data. We further verify that antipodal self-duality is valid at two loops beyond the level of the symbol.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Closed-form solution of decomposable stochastic models

Markov and semi-Markov processes are increasingly being used in the modeling of complex reconfigurable systems (fault tolerant computers). The estimation of the reliability (or some measure of performance) of the system reduces to solving the process for its state probabilities. Such a model may exhibit numerous states and complicated transition distributions, contributing to an expensive and numerically delicate solution procedure. Thus, when a system exhibits a decomposition property, either structurally (autonomous subsystems), or behaviorally (component failure versus reconfiguration), it is desirable to exploit this decomposition in the reliability calculation. In interesting cases there can be failure states which arise from non-failure states of the subsystems. Equations are presented which allow the computation of failure probabilities of the total (combined) model without requiring a complete solution of the combined model. This material is presented within the context of closed-form functional representation of probabilities as utilized in the Symbolic Hierarchical Automated Reliability and Performance Evaluator (SHARPE) tool. The techniques adopted enable one to compute such probability functions for a much wider class of systems at a reduced computational cost. Several examples show how the method is used, especially in enhancing the versatility of the SHARPE tool.

Sjogren, Jon A.↗

Demonstration of Detection and Ranging Using Solvable Chaos

Acoustic experiments demonstrate a novel approach to ranging and detection that exploits the properties of a solvable chaotic oscillator. This nonlinear oscillator includes an ordinary differential equation and a discrete switching condition. The chaotic waveform generated by this hybrid system is used as the transmitted waveform. The oscillator admits an exact analytic solution that can be written as the linear convolution of binary symbols and a single basis function. This linear representation enables coherent reception using a simple analog matched filter and without need for digital sampling or signal processing. An audio frequency implementation of the transmitter and receiver is described. Successful acoustic ranging measurements are presented to demonstrate the viability of the approach.

Corron, Ned J.↗

Language model-accelerated deep symbolic optimization

Symbolic optimization methods have been used to solve varied challenging and relevant problems such as symbolic regression and neural architecture search. However, the current state of the art typically learns each problem from scratch and is unable to leverage pre-existing knowledge and datasets that are available for many applications. Here, inspired by the similarity between sequence representations learned in natural language processing and the formulation of symbolic optimization as a discrete sequence optimization problem, we propose language model-accelerated deep symbolic optimization (LA-DSO), a method that leverages language models to learn symbolic optimization solutions more efficiently. We demonstrate LA-DSO in two tasks: symbolic regression, which allows us to perform extensive experimentation due to its low computation requirements, and computational antibody optimization, which shows that our proposal accelerates learning in challenging real-world problems.

97 MATHEMATICS AND COMPUTING↗

Computers for symbolic processing

A detailed survey on the motivations, design, applications, current status, and limitations of computers designed for symbolic processing is provided. Symbolic processing computations are performed at the word, relation, or meaning levels, and the knowledge used in symbolic applications may be fuzzy, uncertain, indeterminate, and ill represented. Various techniques for knowledge representation and processing are discussed from both the designers' and users' points of view. The design and choice of a suitable language for symbolic processing and the mapping of applications into a software architecture are then considered. The process of refining the application requirements into hardware and software architectures is treated, and state-of-the-art sequential and parallel computers designed for symbolic processing are discussed.

Wah, Benjamin W.↗

The scheme machine: A case study in progress in design derivation at system levels

The Scheme Machine is one of several design projects of the Digital Design Derivation group at Indiana University. It differs from the other projects in its focus on issues of system design and its connection to surrounding research in programming language semantics, compiler construction, and programming methodology underway at Indiana and elsewhere. The genesis of the project dates to the early 1980's, when digital design derivation research branched from the surrounding research effort in programming languages. Both branches have continued to develop in parallel, with this particular project serving as a bridge. However, by 1990 there remained little real interaction between the branches and recently we have undertaken to reintegrate them. On the software side, researchers have refined a mathematically rigorous (but not mechanized) treatment starting with the fully abstract semantic definition of Scheme and resulting in an efficient implementation consisting of a compiler and virtual machine model, the latter typically realized with a general purpose microprocessor. The derivation includes a number of sophisticated factorizations and representations and is also deep example of the underlying engineering methodology. The hardware research has created a mechanized algebra supporting the tedious and massive transformations often seen at lower levels of design. This work has progressed to the point that large scale devices, such as processors, can be derived from first-order finite state machine specifications. This is roughly where the language oriented research stops; thus, together, the two efforts establish a thread from the highest levels of abstract specification to detailed digital implementation. The Scheme Machine project challenges hardware derivation research in several ways, although the individual components of the system are of a similar scale to those we have worked with before. The machine has a custom dual-ported memory to support garbage collection. It consists of four tightly coupled processes--processor, collector, allocator, memory--with a very non-trivial synchronization relationship. Finally, there are deep issues of representation for the run-time objects of a symbolic processing language. The research centers on verification through integrated formal reasoning systems, but is also involved with modeling and prototyping environments. Since the derivation algebra is basd on an executable modeling language, there is opportunity to incorporate design animation in the design process. We are looking for ways to move smoothly and incrementally from executable specifications into hardware realization. For example, we can run the garbage collector specification, a Scheme program, directly against the physical memory prototype, and similarly, the instruction processor model against the heap implementation.

Johnson, Steven D.↗

Research on knowledge representation, machine learning, and knowledge acquisition

Research in knowledge representation, machine learning, and knowledge acquisition performed at Knowledge Systems Lab. is summarized. The major goal of the research was to develop flexible, effective methods for representing the qualitative knowledge necessary for solving large problems that require symbolic reasoning as well as numerical computation. The research focused on integrating different representation methods to describe different kinds of knowledge more effectively than any one method can alone. In particular, emphasis was placed on representing and using spatial information about three dimensional objects and constraints on the arrangement of these objects in space. Another major theme is the development of robust machine learning programs that can be integrated with a variety of intelligent systems. To achieve this goal, learning methods were designed, implemented and experimented within several different problem solving environments.

Buchanan, Bruce G.↗

Hybrid Symbolic-Numerical Modeling and Parametric Stability Analysis of DC–AC Power Systems

Hybrid DC-AC power systems integrating diverse inverter-based resources (IBRs) and multi-terminal high-voltage direct current (MTDC) networks represent a promising architecture for future power grids, while introducing challenges for modeling, stability analysis, and control design. This paper develops a hybrid symbolic-numerical modeling framework and tool to characterize the parametric small-signal stability of DC-AC coupled power systems. The proposed approach constructs parametric state-space models to enable efficient representation of system dynamics under varying control parameters and network configurations, with target parameters retained as symbolic variables and the remainder treated numerically. The stability analysis framework covers eigenvalue, sensitivity, and stability boundary and region characterization. Enhanced linear matrix inequality (LMI) techniques are proposed to directly certify small-signal stability over regions of parameter space while also reducing the conservativeness and computational burden. The resulting tools and frameworks enable rapid parametric model construction across diverse grid conditions, thereby facilitating stability-informed control and operation in complex DC–AC power systems.

DC–AC power systems↗

Statechart Analysis with Symbolic PathFinder

We report here on our on-going work that addresses the automated analysis and test case generation for software systems modeled using multiple Statechart formalisms. The work is motivated by large programs such as NASA Exploration, that involve multiple systems that interact via safety-critical protocols and are designed with different Statechart variants. To verify these safety-critical systems, we have developed Polyglot, a framework for modeling and analysis of model-based software written using different Statechart formalisms. Polyglot uses a common intermediate representation with customizable Statechart semantics and leverages the analysis and test generation capabilities of the Symbolic PathFinder tool. Polyglot is used as follows: First, the structure of the Statechart model (expressed in Matlab Stateflow or Rational Rhapsody) is translated into a common intermediate representation (IR). The IR is then translated into Java code that represents the structure of the model. The semantics are provided as "pluggable" modules.

Pasareanu, Corina S.↗

Structured programming: Principles, notation, procedure

Structured programs are best represented using a notation which gives a clear representation of the block encapsulation. In this report, a set of symbols which can be used until binding directives are republished is suggested. Structured programming also allows a new method of procedure for design and testing. Programs can be designed top down, that is, they can start at the highest program plane and can penetrate to the lowest plane by step-wise refinements. The testing methodology also is adapted to this procedure. First, the highest program plane is tested, and the programs which are not yet finished in the next lower plane are represented by so-called dummies. They are gradually replaced by the real programs.

JOST↗

A Natural Language Interface to Databases

The development of a Natural Language Interface (NLI) is presented which is semantic-based and uses Conceptual Dependency representation. The system was developed using Lisp and currently runs on a Symbolics Lisp machine.

Ford, D. R.↗

Predit: A temporal predictive framework for scheduling systems

Scheduling can be formalized as a Constraint Satisfaction Problem (CSP). Within this framework activities belonging to a plan are interconnected via temporal constraints that account for slack among them. Temporal representation must include methods for constraints propagation and provide a logic for symbolic and numerical deductions. In this paper we describe a support framework for opportunistic reasoning in constraint directed scheduling. In order to focus the attention of an incremental scheduler on critical problem aspects, some discrete temporal indexes are presented. They are also useful for the prediction of the degree of resources contention. The predictive method expressed through our indexes can be seen as a Knowledge Source for an opportunistic scheduler with a blackboard architecture.

Paolucci, E.↗

Model Based Analysis and Test Generation for Flight Software

We describe a framework for model-based analysis and test case generation in the context of a heterogeneous model-based development paradigm that uses and combines Math- Works and UML 2.0 models and the associated code generation tools. This paradigm poses novel challenges to analysis and test case generation that, to the best of our knowledge, have not been addressed before. The framework is based on a common intermediate representation for different modeling formalisms and leverages and extends model checking and symbolic execution tools for model analysis and test case generation, respectively. We discuss the application of our framework to software models for a NASA flight mission.

Pasareanu, Corina S.↗

On triality defects in 2d CFT

We consider the triality fusion category discovered in the c = 1 Kosterlitz-Thouless theory. We analyze this fusion category using the tools from the group theoretical fusion category and compute the simple lines, fusion rules and F-symbols. We then studied the physical implication of this fusion category including deriving the spin selection rule, computing the asymptotic density of states of irreducible representations of the fusion category symmetries, and analyzing its anomaly and constraints under the renormalization group flow. There is another set of F-symbols for the fusion categories with the same fusion rule known in the literature. We find these two solutions are different as they lead to different spin selection rules. This gives a complete list of the fusion categories with the same fusion rule by the classification result in.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗