arXiv subjects

Hardik Rajpal

Publications and source records attributed to Hardik Rajpal.

11 recordsLinked to original sources

arXiv2026

Fisher Information Metric as a model-free measure of proximity to criticality in neural systems

Critical phenomena are widespread across many disciplines and have recently become a topic of deep interest in the study of biological and artificial neural networks. A distinct signature of criticality is the emergence of avalanches with power-law-distributed sizes and durations. However, empirically estimating the critical exponents remains challenging, and their interpretation is often model-dependent. In this work, we demonstrate how the Fisher Information Metric (FIM), a measure of generalized susceptibility, provides a comprehensive, model-agnostic characterization of the critical region in neural systems. We validate this approach across models of increasing biological complexity, from prototypical branching processes to spiking and whole-brain models, showing that FIM of each model's control parameter reliably tracks the system's degree of criticality. To emulate the study of real-world systems, where the control parameter is unknown, we additionally calculate FIM of the observed branching ratio of neural activity. The resulting FIM peaks where activity growth and decay balance, with the peak sharpening as the system approaches criticality. Hence, FIM peak width and height yield continuous, model-free readouts of proximity to criticality without requiring knowledge of the true control parameter, offering a robust tool for probing criticality in neural systems.

q-bio.NC↗

arXiv2026

Emergent Generalization by Representation Learning in Artificial Neural Networks

Dimensionality reduction has proven powerful for identifying neural manifolds, which are low-dimensional structures underlying high-dimensional neural activity. These low-dimensional representations have improved the interpretability of population-level coding. Yet whether such low-dimensional representations are biologically relevant and confer functional advantages in learning systems, or merely reflect neuron-level activity, remains contested in neuroscience. We show that an explicit information bottleneck forcing a recurrent neural network to learn a low-dimensional representation is necessary for rotational and out-of-distribution generalisation in a time-series prediction task. Using information-theoretic measures of causal emergence, we characterise the dynamics of this representation across the memorisation-to-generalisation transition, finding a non-monotonic trajectory which shows an initial decrease, a minimum, and a subsequent rise to a maximum, even as prediction loss falls monotonically. This trajectory scales with task complexity, and the magnitude of emergent structure reliably predicts generalisation performance. Analysis of CA1 hippocampal activity in mice learning an alternating maze task reveals analogous non-monotonic emergence dynamics that track behavioural performance. Together, these findings indicate that the ability of neural networks to learn compact, distributed and emergent representations confers a functional advantage for generalisation, supporting a causal role for learned representations in cognition.

q-bio.NC↗

arXiv2026

Collective Dynamics in Spiking Neural Networks Beyond Dale's Principle

Dale's Principle has historically guided neuroscience research as a valuable rule of thumb, namely that all synapses on each neuron release the same set of neurotransmitters. Most existing Spiking Neuron Network models share this dichotomous assumption that neurons are either excitatory or inhibitory; however, recent experimental evidence points towards co-release mechanisms that violate this assumption. Here, we introduce a minimal model of "Bilingual" neurons violating Dale's principle that can exert both excitatory and inhibitory effects. We identify parameter regimes in which this architecture exhibits transitions between synchronous and asynchronous dynamics that differ quantitatively from those observed in a matched monolingual control architecture. We report distinct information-processing signatures both at the level of neurons and higher-order interactions between them near the phase transitions. These results suggest that the population of neurons violating Dales principle may provide an alternative mechanism for regulating large-scale oscillatory activity in neural circuits.

q-bio.NC↗

arXiv2025

Improved estimators of causal emergence for large systems

A central challenge in the study of complex systems is the quantification of emergence -- understood as the ability of the system to exhibit collective behaviours that cannot be traced down to the individual components. While recent work has proposed practical measures to detect emergence, these approaches tend to double-count the contribution of shared components, which substantially hinders their capability to effectively study large systems. In this work, we introduce a family of improved information-theoretic measures of emergence that iteratively correct for double-counted terms. Our approach is computationally efficient and provides a controllable trade-off between computational load and sensitivity, leading to more accurate and versatile estimates of emergence. The benefits of the proposed approach are demonstrated by successfully detecting emergence in both simulated and real-world data related to flocking behaviour.

physics.soc-ph↗

arXiv2025

Directed Cycles as Higher-Order Units of Information Processing in Complex Networks

Directed cycles form the fundamental motifs in natural, social and artificial networks, yet their distinct computational roles remain under-explored, particularly in the context of higher-order structure and function. In this work, we investigate how two types of directed cycles - feedforward and feedback - can act as higher-order structures to facilitate the flow and integration of information in sparse random networks, and how these roles depend on the environment of the cycles. Using information-theoretic measures, we show that network size, sparsity and relative directionality critically impact the information-processing capacities of directed cycles. In a network with no-preferred global direction, a feedforward cycle enables greater information flow and a feedback cycle allows for increased information integration. The relative direction of a feedforward cycle as well as the structural incoherence it induces, determines its capacity to generate higher-order behaviour. Finally, we demonstrate that introducing feedback loops into otherwise feedforward architectures increases the diversity of network activity patterns. These findings suggest that directed cycles serve as computational motifs with local information processing capabilities that depend on the structure they are embedded. Using directed cycles, we highlight the interdependence between higher-order structures and the higher-order order behaviour they can induce in the network dynamics.

cond-mat.stat-mech↗

arXiv2025

Who is driving the conversation? Analysing the nodality of British MPs and journalists on social media

With the rise of social media, political conversations now take place in more diffuse environments. In this context, it is not always clear why some actors, more than others, have greater influence on how discussions are shaped. To investigate the factors behind such influence, we build on nodality, a concept in political science which describes the capacity of an actor to exchange information within discourse networks. This concept goes beyond traditional network metrics that describe the position of an actor in the network to include exogenous drivers of influence (e.g. factors relating to organisational hierarchies). We study online discourse on Twitter (now X) in the UK to measure the relative nodality of two sets of policy actors - Members of Parliament (MPs) and accredited journalists - on four policy topics. We find that influence on the platform is driven by two key factors: (i) active nodality, derived from the actor's level of topic-related engagement, and (ii) inherent nodality, which is independent of the platform discourse and reflects the actor's institutional position. These findings significantly further our understanding of the origins of influence on social media platforms and suggest in which contexts influence is transferable across topics.

cs.SI↗

arXiv2025

A scalable estimator of higher-order information in complex dynamical systems

Our understanding of complex systems rests on our ability to characterise how they perform distributed computation and integrate information. Advances in information theory have introduced several quantities to describe complex information structures, where collective patterns of coordination emerge from higher-order (i.e. beyond-pairwise) interdependencies. Unfortunately, the use of these approaches to study large complex systems is severely hindered by the poor scalability of existing techniques. Moreover, there are relatively few measures specifically designed for multivariate time series data. Here we introduce a novel measure of information about macroscopic structures, termed M-information, which quantifies the higher-order integration of information in complex dynamical systems. We show that M-information can be calculated via a convex optimisation problem, and we derive a robust and efficient algorithm that scales gracefully with system size. Our analyses show that M-information is resilient to noise, indexes critical behaviour in artificial neuronal populations, and reflects states of consciousness and task performance in real-world macaque and mouse neuroimaging data. Furthermore, M-information can be incorporated into existing information decomposition frameworks to reveal a comprehensive taxonomy of information dynamics. Taken together, these results help us unravel collective computation in large complex systems.

cs.IT↗

arXiv2023

Quantifying Hierarchical Selection

At what level does selective pressure effectively act? When considering the reproductive dynamics of interacting and mutating agents, it has long been debated whether selection is better understood by focusing on the individual or if hierarchical selection emerges as a consequence of joint adaptation. Despite longstanding efforts in theoretical ecology there is still no consensus on this fundamental issue, most likely due to the difficulty in obtaining adequate data spanning sufficient number of generations and the lack of adequate tools to quantify the effect of hierarchical selection. Here we capitalise on recent advances in information-theoretic data analysis to advance this state of affairs by investigating the emergence of high-order structures -- such as groups of species -- in the collective dynamics of the Tangled Nature model of evolutionary ecology. Our results show that evolutionary dynamics can lead to clusters of species that act as a selective group, that acquire information-theoretic agency. Overall, our findings provide quantitative evidence supporting the relevance of high-order structures in evolutionary ecology, which can emerge even from relatively simple processes of adaptation and selection.

q-bio.PE↗

arXiv2023

Synergistic Small Worlds that Drive Technological Sophistication

Advanced economies exhibit a high degree of sophistication in the creation of various products. While critical to such sophistication, the nature and underlying structure of the interactions taking place inside production processes remain opaque when studying large systems such as industries or entire economies. Using partial information decomposition, we quantify the nature of these interactions, allowing us to infer how much innovation stems form specific input interactions and how they are structured. These estimates yield a novel picture of the nuanced interactions underpinning technological sophistication. By analyzing networks of synergistic interactions, we find that more sophisticated industries tend to exhibit highly modular small-world topologies; with the tertiary sector as its central connective core. Countries and industries that have a well-established connective core and specialized modules exhibit higher economic complexity and output efficiency. Similar modular networks have been found to be responsible for maintaining a balance between integration and segregation of information in the human brain, suggesting a universal principle underlying the organization of sophisticated production processes.

econ.GN↗

arXiv2019

Tangled Worldview Model of Opinion Dynamics

We study the joint evolution of worldviews by proposing a model of opinion dynamics, which is inspired in notions from evolutionary ecology. Agents update their opinion on a specific issue based on their propensity to change -- asserted by the social neighbours -- weighted by their mutual similarity on other issues. Agents are, therefore, more influenced by neighbours with similar worldviews (set of opinions on various issues), resulting in a complex co-evolution of each opinion. Simulations show that the worldview evolution exhibits events of intermittent polarization when the social network is scale-free. This, in turn, trigger extreme crashes and surges in the popularity of various opinions. Using the proposed model, we highlight the role of network structure, bounded rationality of agents, and the role of key influential agents in causing polarization and intermittent reformation of worldviews on scale-free networks.

physics.soc-ph↗

arXiv2018

Achieving perfect coordination amongst agents in the co-action minority game

We discuss the strategy that rational agents can use to maximize their expected long-term payoff in the co-action minority game. We argue that the agents will try to get into a cyclic state, where each of the $(2N +1)$ agent wins exactly $N$ times in any continuous stretch of $(2N+1)$ days. We propose and analyse a strategy for reaching such a cyclic state quickly, when any direct communication between agents is not allowed, and only the publicly available common information is the record of total number of people choosing the first restaurant in the past. We determine exactly the average time required to reach the periodic state for this strategy. We show that it varies as $(N/\ln 2) [1 + \alpha \cos (2 \pi \log_2 N)$], for large $N$, where the amplitude $\alpha$ of the leading term in the log-periodic oscillations is found be $\frac{8 \pi^2}{(\ln 2)^2} \exp{(- 2 \pi^2/\ln 2)} \approx {\color{blue}7 \times 10^{-11}}$.

econ.EM↗