Strong Attractors of Hopfield Neural Networks to Model Attachment Types and Behavioural Patterns

Abstract — We study the notion of a strong attractor of a Hopfield neural model as a pattern that has been stored multiple times in the network, and examine its properties using basic mathematical techniques as well as a variety of simulations. It is proposed that strong attractors can be used to model attachment types in developmental psychology as well as behavioural patterns in psychology and psychotherapy. We study the stability and basins of attraction of strong attractors in the presence of other simple attractors and show that they are indeed more stable with a larger basin of attraction compared with simple attractors. We also show that the perturbation of a strong attractor by random noise results in a cluster of attractors near the original strong attractor measured by the Hamming distance. We investigate the stability and basins of attraction of such clusters as the noise increases and establish that the unfolding of the strong attractor, leading to its breakup, goes through three different stages. Finally the relation between strong attractors of different multiplicity and their influence on each other are studied and we show how the impact of a strong attractor can be replaced with that of a new strong attractor. This retraining of the network is proposed as a model of how attachment types and behavioural patterns can undergo change. I

Self-attachment: A self-administrable intervention for chronic anxiety and depression

There has been increasing evidence to suggest that the root cause of much mental illness lies in a sub-optimal capacity for affect regulation. Cognition and emotion are intricately linked and cognitive deficits, which are characteristic of many psychiatric conditions, are often driven by affect dysregulation, which itself can usually be traced back to sub-optimal childhood development as supported by Attachment Theory. Individuals with insecure attachment types in their childhoods are prone to a variety of mental illness, whereas a secure attachment type in childhood provides a secure base in life. We therefore propose a holistic approach to tackle chronic anxiety and depression, typical of Axis II clinical disorders, which is informed by the development of the infant brain in social interaction with its primary care-givers. We formulate, in a self-administrable way, the protocols governing the interaction of a securely attached child with its primary care-givers that produce the capacity for affect regulation in the child. We posit that these protocols construct, by neuroplasticity and long term potentiation, new optimal neural pathways in the brains of adults with insecure childhood attachment that suffer from mental disorder. This procedure is called self-attachment and aims to help the individuals to create their own attachment objects in the form of their adult self looking after their inner child

A pilot study to evaluate the efficacy of self-attachment to treat chronic anxiety and/or depression in Iranian women

The aim of this pilot study was to evaluate the efficacy of the new Self-Attachment Technique (SAT) in treating resistant anxiety and depression, lasting at least three years, among Iranian women from different social backgrounds. In this intervention, the participant, using their childhood photos, imaginatively creates an affectional bond with their childhood self, vows to consistently support and lovingly re-raise this child to emotional well-being. We conducted a longitudinal study with repeated measurement to evaluate the efficacy of SAT using ANOVA. Thirty-eight women (N=30) satisfying the inclusion and exclusion criteria were recruited from different parts of Tehran. To describe the SAT protocols, a total of eight one-to-one sessions were offered to the recruits, the first four were weekly while the last four were fortnightly. The participants were expected to practice the protocols for twenty minutes twice a day. Two questionnaires, GAD-7 and PHQ-9, were used to measure anxiety and depression levels before and after the intervention and in a three-month follow-up. Thirty women completed the course. The change in the anxiety level between the pre-test and the post-test was significant at p<0.001 with effect size 2.6. The change in anxiety between pre-test and follow-up test was also significant at p<0.001 with effect size 3.0 respectively. The change in anxiety between the post-test and the follow-up was significant at p<0.05 with effect size 0.6. For depression, the change between the pre-test and the post-test or the follow-up was significant at p<0.001 with effect size 2.5 for each

Computational models of attachment and self-attachment

We explore, using a variety of models grounded in computational neuroscience, the dynamics of attachment formation and change. In the first part of the thesis we consider the formation of the traditional organised forms of attachment (as defined by Mary Ainsworth) within the context of the free energy principle, showing how each type of attachment might arise in infant agents who minimise free energy over interoceptive states while interacting with caregivers with varying responsiveness. We show how exteroceptive cues (in the form of disrupted affective communication from the caregiver) can result in disorganised forms of attachment (as first uncovered by Mary Main) in infants of caregivers who consistently increase stress on approach, but can have an organising (towards ambivalence) effect in infants of inconsistent caregivers. The second part of the thesis concerns Self-Attachment: a new self-administrable attachment-based psychotherapy recently introduced by Abbas Edalat, which aims to induce neural plasticity in order to retrain an individual's suboptimal attachment schema. We begin with a model of the hypothesised neurobiological underpinnings of the Self-Attachment bonding protocols, which are concerned with the formation of an abstract, self-directed bond. Finally, using neuroscientific findings related to empathy and the self-other distinction within the context of pain, we propose a simple spiking neural model for how empathic states might serve to motivate application of the aforementioned bonding protocols.Open Acces

The attachment control system and computational modeling: Origins and prospects

From his first attempts to explain attachment phenomena in the 1940s through his Attachment and Loss trilogy (Bowlby, 1969/1982, 1973, 1980), John Bowlby reformulated the theoretical underpinnings of attachment theory several times. He initially attempted to explain attachment phenomena in psychoanalytic terms. Then he invoked ethological theory in the explanation of how and why people behave as they do in close personal relationships. The mature theoretical framework that he presented between 1969 and 1982 in the attachment and loss trilogy retained strengths and insights, ultimately situating them within an overarching control systems framework. This article describes key stages in Bowlby's theoretical development, with particular emphasis placed on the emergence of control systems theory as a cornerstone of the mature theory. It also compares Bowlby's control systems approach to contemporary cognitive science approaches. It concludes by suggesting how Bowlby's control systems formulation could evolve along the path opened up by contemporary work in computational modeling and how it could benefit by doing so

A complex systems approach to education in Switzerland

The insights gained from the study of complex systems in biological, social, and engineered systems enables us not only to observe and understand, but also to actively design systems which will be capable of successfully coping with complex and dynamically changing situations. The methods and mindset required for this approach have been applied to educational systems with their diverse levels of scale and complexity. Based on the general case made by Yaneer Bar-Yam, this paper applies the complex systems approach to the educational system in Switzerland. It confirms that the complex systems approach is valid. Indeed, many recommendations made for the general case have already been implemented in the Swiss education system. To address existing problems and difficulties, further steps are recommended. This paper contributes to the further establishment complex systems approach by shedding light on an area which concerns us all, which is a frequent topic of discussion and dispute among politicians and the public, where billions of dollars have been spent without achieving the desired results, and where it is difficult to directly derive consequences from actions taken. The analysis of the education system's different levels, their complexity and scale will clarify how such a dynamic system should be approached, and how it can be guided towards the desired performance

Whole Brain Network Dynamics of Epileptic Seizures at Single Cell Resolution

Epileptic seizures are characterised by abnormal brain dynamics at multiple scales, engaging single neurons, neuronal ensembles and coarse brain regions. Key to understanding the cause of such emergent population dynamics, is capturing the collective behaviour of neuronal activity at multiple brain scales. In this thesis I make use of the larval zebrafish to capture single cell neuronal activity across the whole brain during epileptic seizures. Firstly, I make use of statistical physics methods to quantify the collective behaviour of single neuron dynamics during epileptic seizures. Here, I demonstrate a population mechanism through which single neuron dynamics organise into seizures: brain dynamics deviate from a phase transition. Secondly, I make use of single neuron network models to identify the synaptic mechanisms that actually cause this shift to occur. Here, I show that the density of neuronal connections in the network is key for driving generalised seizure dynamics. Interestingly, such changes also disrupt network response properties and flexible dynamics in brain networks, thus linking microscale neuronal changes with emergent brain dysfunction during seizures. Thirdly, I make use of non-linear causal inference methods to study the nature of the underlying neuronal interactions that enable seizures to occur. Here I show that seizures are driven by high synchrony but also by highly non-linear interactions between neurons. Interestingly, these non-linear signatures are filtered out at the macroscale, and therefore may represent a neuronal signature that could be used for microscale interventional strategies. This thesis demonstrates the utility of studying multi-scale dynamics in the larval zebrafish, to link neuronal activity at the microscale with emergent properties during seizures