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arXiv1998

How to Implement A Priori Information: A Statistical Mechanics Approach

A new general framework is presented for implementing complex a priori knowledge, having in mind especially situations where the number of available training data is small compared to the complexity of the learning task. A priori information is hereby decomposed into simple components represented by quadratic building blocks (quadratic concepts) which are then combined by conjunctions and disjunctions to built more complex, problem specific error functionals. While conjunction of quadratic concepts leads to classical quadratic regularization functionals, disjunctions, representing ambiguous priors, result in non--convex error functionals. These go beyond classical quadratic regularization approaches and correspond, in Bayesian interpretation, to non--gaussian processes. Numerical examples show that the resulting stationarity equations, despite being in general nonlinear, inhomogeneous (integro--)differential equations, are not necessarily difficult to solve. Appendix A relates the formalism of statistical mechanics to statistics and Appendix B describes the framework of Bayesian decision theory.

cond-mat.dis-nn↗

arXiv1998

Thermodynamic Depth of Causal States: When Paddling around in Occam's Pool Shallowness Is a Virtue

Thermodynamic depth is an appealing but flawed structural complexity measure. It depends on a set of macroscopic states for a system, but neither its original introduction by Lloyd and Pagels nor any follow-up work has considered how to select these states. Depth, therefore, is at root arbitrary. Computational mechanics, an alternative approach to structural complexity, provides a definition for a system's minimal, necessary causal states and a procedure for finding them. We show that the rate of increase in thermodynamic depth, or {\it dive}, is the system's reverse-time Shannon entropy rate, and so depth only measures degrees of macroscopic randomness, not structure. To fix this we redefine the depth in terms of the causal state representation---$ε$-machines---and show that this representation gives the minimum dive consistent with accurate prediction. Thus, $ε$-machines are optimally shallow.

cond-mat.stat-mech↗

arXiv1998

Statistical Features in Learning

We study some features of learning models based on "delayed" and undifferentiated reinforcement and realized by simple algorithms which may be considered of a very elementary nature. We show that a modification of the Hebb-rule works well for this problem in a neural network realization and study numerically its convergence properties. An illustration for a more "concrete" situation is provided.

cond-mat↗

arXiv1998

Optimizing Traffic Flow

We present an economics-based method for deciding the optimal rates at which vehicles are allowed to enter a highway. The method exploits the naturally occuring fluctuations of traffic flow and is flexible enough to adapt in real time to the transient flow characteristics of road traffic. Simulations based on realistic parameter values show that this strategy is feasible for naturally occuring traffic, and that even far from optimality, injection policies can improve traffic flow. Our results also allow a better understanding of the high flows observed in ``synchronized'' congested traffic close to ramps.

cond-mat.stat-mech↗

arXiv1998

Gauge Physics of Finance: simple introduction

In this paper we state the fundamental principles of the gauge approach to financial economics and demonstrate the ways of its application. In particular, modelling of realistic price processes is considered for an example of S&P500 market index. Derivative pricing and portfolio theory are also briefly discussed.

cond-mat.stat-mech↗

arXiv1998

Crowd effects and volatility in a competitive market

We present analytic and numerical results for two models, namely the minority model and the bar-attendance model, which offer simple paradigms for a competitive marketplace. Both models feature heterogeneous agents with bounded rationality who act using inductive reasoning. We find that the effects of crowding are crucial to the understanding of the macroscopic fluctuations, or `volatility', in the resulting dynamics of these systems.

cond-mat↗

arXiv1999

Spontaneous coalition forming: a model from spin glass

In this paper a simple model is proposed to decribe the spontaneous formation of coalitions among a group of actors like countries. The basic ingredients are from the physics of disorder systems. It is the interplay of two different spin glass models with respectively random bond and random site disorders which is instrumental in the present approach. The cold war stabilty period is then given an explanation as well the instabilities produced by the Warsow pact dissolution. European and Chinese stabilities are also discussed.

cond-mat.dis-nn↗

arXiv1999

Comment on "A landscape theory of aggregation"

The problem of aggregation processes in alignments is the subject of a paper published in a Statistical Physics Journal (Physica A 230 (1996) 174-188). Two models are presented and discussed in that paper. First the energy landscape model proposed by Axelrod and Bennett (B. J. Pol. S. 23 (1993) 211-233) is analysed. The model is shown not to include most of its claimed results. Then a second model is presented to reformulate correctly the problem within statistical physics and to extend it beyond the initial Axelrod-Bennett analogy.

cond-mat.dis-nn↗

arXiv1999

Cortical Potential Distributions and Cognitive Information Processing

The use of cortical field potentials rather than the details of spike trains as the basis for cognitive information processing is proposed. This results in a space of cognitive elements with natural metrics. Sets of spike trains may also be considered to be points in a multidimensional metric space. The closeness of sets of spike trains in such a space implies the closeness of points in the resulting function space of potential distributions.

cond-mat.dis-nn↗

arXiv1999

Multiple Scales in Small-World Graphs

Small-world architectures may be implicated in a range of phenomena from disease propagation to networks of neurons in the cerebral cortex. While most of the recent attention on small-world networks has focussed on the effect of introducing disorder/randomness into a regular network, we show that that the fundamental mechanism behind the small-world phenomenon is not disorder/randomness, but the presence of connections of many different length scales. Consequently, in order to explain the small-world phenomenon, we introduce the concept of multiple scale graphs and then state the multiple length scale hypothesis. Multiple scale graphs form a unifying conceptual framework for the study of evolving graphs. Moreover, small-world behavior in randomly rewired graphs is a consequence of features common to all multiple scale graphs. To support the multiple length scale hypothesis, novel graph architectures are introduced that need not be a result of random rewiring of a regular graph. In each case it is shown that whenever the graph exhibits small-world behavior, it also has connections of diverse length scales. We also show that the distribution of the length scales of the new connections is significantly more important than whether the new connections are long range, medium range or short range connections.

cond-mat.dis-nn↗

arXiv1999

Learning, competition and cooperation in simple games

The minority model was introduced to study the competition between agents with limited information. It has the remarkable feature that, as the amount of information available increases, the collective gain made by the agents is reduced. This crowd effect arises from the fact that only a minority can profit at each moment, while all agents make their choices using the same input. We show that the properties of the model change drastically if the agents make choices based on their individual stories, keeping all remaining rules unaltered. This variation reduces the intrinsic frustration of the model, and improves the tendency towards cooperation and self organization. We finally study the stable mixing of individual and collective behavior.

cond-mat.stat-mech↗

arXiv1999

Algorithmic Complexity in Minority Game

In this paper we introduce a new approach for the study of the complex behavior of Minority Game using the tools of algorithmic complexity, physical entropy and information theory. We show that physical complexity and mutual information function strongly depend on memory size of the agents and yields more information about the complex features of the stream of binary outcomes of the game than volatility itself.

cond-mat.stat-mech↗

arXiv1999

Effective potential for the reaction-diffusion-decay system

In previous work [cond-mat/9904207,cond-mat/9904215] we have developed a general method for casting stochastic partial differential equations (SPDEs) into a functional integral formalism, and have derived the one-loop effective potential for these systems. In this paper we apply the same formalism to a specific field theory of considerable interest, the reaction-diffusion-decay system. When this field theory is subject to white noise we can calculate the one-loop effective potential (for arbitrary polynomial reaction kinetics) and show that it is one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions. For specific choices of interaction terms the one-loop renormalizability can be extended to higher dimensions. We also show how to include the effects of fluctuations in the study of pattern formation away from equilibrium, and conclude that noise affects the stability of the system in a way which is calculable.

cond-mat.stat-mech↗

arXiv1999

Cosmology in a Test Tube: Theory of Domain Walls Formation in Binary Fluids

Formation of domain walls during a rapid phase transition in a quasi one dimensional Cahn-Hiliard equation describing binary fluids in a thin tube is studied. Density of kinks scales like a sixth root of quench rate for equal concentrations and like a square root of quench rate for unequal concentrations of fluids. For a slow inhomogeneous transition the density is linear in velocity of temperature front. This paper is first theoretical study of topological defects formation in a system with conserved order parameter.

cond-mat↗

arXiv1999

Autocatalytic Theory of Meaning

Recently it has been argued that autocatalytic theory could be applied to the origin of culture. Here possible application to a theory of meaning in the philosophy of language, called radical interpretation, is commented upon and compared to previous applications.

cs.CL↗

arXiv1999

Using Collective Intelligence to Route Internet Traffic

A COllective INtelligence (COIN) is a set of interacting reinforcement learning (RL) algorithms designed in an automated fashion so that their collective behavior optimizes a global utility function. We summarize the theory of COINs, then present experiments using that theory to design COINs to control internet traffic routing. These experiments indicate that COINs outperform all previously investigated RL-based, shortest path routing algorithms.

cs.LG↗

arXiv1999

General Principles of Learning-Based Multi-Agent Systems

We consider the problem of how to design large decentralized multi-agent systems (MAS's) in an automated fashion, with little or no hand-tuning. Our approach has each agent run a reinforcement learning algorithm. This converts the problem into one of how to automatically set/update the reward functions for each of the agents so that the global goal is achieved. In particular we do not want the agents to ``work at cross-purposes'' as far as the global goal is concerned. We use the term artificial COllective INtelligence (COIN) to refer to systems that embody solutions to this problem. In this paper we present a summary of a mathematical framework for COINs. We then investigate the real-world applicability of the core concepts of that framework via two computer experiments: we show that our COINs perform near optimally in a difficult variant of Arthur's bar problem (and in particular avoid the tragedy of the commons for that problem), and we also illustrate optimal performance for our COINs in the leader-follower problem.

cs.MA↗

arXiv1999

An Introduction to Collective Intelligence

This paper surveys the emerging science of how to design a ``COllective INtelligence'' (COIN). A COIN is a large multi-agent system where: (i) There is little to no centralized communication or control; and (ii) There is a provided world utility function that rates the possible histories of the full system. In particular, we are interested in COINs in which each agent runs a reinforcement learning (RL) algorithm. Rather than use a conventional modeling approach (e.g., model the system dynamics, and hand-tune agents to cooperate), we aim to solve the COIN design problem implicitly, via the ``adaptive'' character of the RL algorithms of each of the agents. This approach introduces an entirely new, profound design problem: Assuming the RL algorithms are able to achieve high rewards, what reward functions for the individual agents will, when pursued by those agents, result in high world utility? In other words, what reward functions will best ensure that we do not have phenomena like the tragedy of the commons, Braess's paradox, or the liquidity trap? Although still very young, research specifically concentrating on the COIN design problem has already resulted in successes in artificial domains, in particular in packet-routing, the leader-follower problem, and in variants of Arthur's El Farol bar problem. It is expected that as it matures and draws upon other disciplines related to COINs, this research will greatly expand the range of tasks addressable by human engineers. Moreover, in addition to drawing on them, such a fully developed scie nce of COIN design may provide much insight into other already established scientific fields, such as economics, game theory, and population biology.

cs.LG↗