arXiv subjects

Prakhar Godara

Publications and source records attributed to Prakhar Godara.

7 recordsLinked to original sources

arXiv2026

Beyond DSA: Conjugacy-based Comparison of Dynamical Systems

Comparing whether two dynamical systems implement the same computation despite differences in coordinates or measurements is a central problem in neuroscience and machine learning. Dynamical Similarity Analysis [DSA; Ostrow et al., 2023] addresses this problem by aligning finite-dimensional Koopman approximations through an orthogonal similarity transformation. Here we show that orthogonal alignment is neither necessary nor sufficient for topological conjugacy: conjugate systems may require a non-orthogonal basis-transfer matrix that DSA cannot capture, while non-conjugate systems may have orthogonally equivalent Koopman operators that DSA fails to distinguish. We use this observation to formulate Conjugacy-based Similarity Analysis (CSA), which restricts alignments to those induced by candidate state-space bijections rather than arbitrary orthogonal matrices. We prove that CSA's fitted alignment is the finite-data projection of the composition operator associated with the candidate bijection, and use controlled examples to show why this distinction matters when observable dictionaries are chosen explicitly or implicitly from data. These results clarify what Koopman-based similarity measures must ensure to support claims of identifying conjugacies between computational systems.

q-bio.NC↗

arXiv2026

Metareasoning in uncertain environments: a meta-BAMDP framework

\textit{Reasoning} may be viewed as an algorithm $P$ that makes a choice of an action $a^* \in \mathcal{A}$, aiming to optimize some outcome. However, executing $P$ itself bears costs (time, energy, limited capacity, etc.) and needs to be considered alongside explicit utility obtained by making the choice in the underlying decision problem. Finding the right $P$ can itself be framed as an optimization problem over the space of reasoning processes $P$, generally referred to as \textit{metareasoning}. Conventionally, human metareasoning models assume that the agent knows the transition and reward distributions of the underlying MDP. This paper generalizes such models by proposing a meta Bayes-Adaptive MDP (meta-BAMDP) framework to handle metareasoning in environments with unknown reward/transition distributions, which encompasses a far larger and more realistic set of planning problems that humans and AI systems face. As a first step, we apply the framework to Bernoulli bandit tasks. Owing to the meta problem's complexity, our solutions are necessarily approximate. However, we introduce two novel theorems that significantly enhance the tractability of the problem, enabling stronger approximations that are robust within a range of assumptions grounded in realistic human decision-making scenarios. These results offer a resource-rational perspective and a normative framework for understanding human exploration under cognitive constraints, as well as providing experimentally testable predictions about human behavior in Bernoulli Bandit tasks.

cs.AI↗

arXiv2026

Adversarial construction as a potential solution to the experiment design problem in large task spaces

Despite decades of work, we still lack a robust, task-general theory of human behavior even in the simplest domains. In this paper we tackle the generality problem head-on, by aiming to develop a unified model for all tasks embedded in a task-space. In particular we consider the space of binary sequence prediction tasks where the observations are generated by the space parameterized by hidden Markov models (HMM). As the space of tasks is large, experimental exploration of the entire space is infeasible. To solve this problem we propose the adversarial construction approach, which helps identify tasks that are most likely to elicit a qualitatively novel behavior. Our results suggest that adversarial construction significantly outperforms random sampling of environments and therefore could be used as a proxy for optimal experimental design in high-dimensional task spaces.

cs.LG↗

arXiv2025

Bias or Optimality? Disentangling Bayesian Inference and Learning Biases in Human Decision-Making

Recent studies claim that human behavior in a two-armed Bernoulli bandit (TABB) task is described by positivity and confirmation biases, implying that humans do not integrate new information objectively. However, we find that even if the agent updates its belief via objective Bayesian inference, fitting the standard Q-learning model with asymmetric learning rates still recovers both biases. Bayesian inference cast as an effective Q-learning algorithm has symmetric, though decreasing, learning rates. We explain this by analyzing the stochastic dynamics of these learning systems using master equations. We find that both confirmation bias and unbiased but decreasing learning rates yield the same behavioral signatures. Finally, we propose experimental protocols to disentangle true cognitive biases from artifacts of decreasing learning rates.

cs.AI↗

arXiv2023

Emergent Organization and Polarization due to Active Fluctuations

We introduce and study a model of active Brownian motion with multiplicative noise describing fluctuations in the self-propulsion or activity. We find that the standard picture of density accumulation in slow regions is qualitatively modified by active fluctuations, as stationary density profiles are generally not determined only by the mean self-propulsion speed landscape. As a result, activity gradients generically correlate the particle self-propulsion speed and orientation, leading to emergent polarization at interfaces pointing either towards dense or dilute regions depending on the amount of noise in the system. We discuss how active noise affects the emergence of motility induced phase separation. Our work provides a foundation for systematic studies of active matter self-organization in the presence of activity landscapes and active fluctuations.

cond-mat.soft↗

arXiv2021

A control theory approach to optimal pandemic mitigation

In the framework of homogeneous susceptible-infected-recovered (SIR) models, we use a control theory approach to identify optimal pandemic mitigation strategies. We derive rather general conditions for reaching herd immunity while minimizing the costs incurred by the introduction of societal control measures (such as closing schools, social distancing, lockdowns, etc.), under the constraint that the infected fraction of the population does never exceed a certain maximum corresponding to public health system capacity. Optimality is derived and verified by variational and numerical methods for a number of model cost functions. The effects of immune response decay after recovery are taken into account and discussed in terms of the feasibility of strategies based on herd immunity.

q-bio.PE↗

arXiv2018

Understanding transient uncoupling induced synchronization through modified dynamic coupling

An important aspect of the recently introduced transient uncoupling scheme is that it induces synchronization for large values of coupling strength at which the coupled chaotic systems resist synchronization when continu- ously coupled. However, why this is so is an open problem. To answer this question, we recall the conventional wisdom that the eigenvalues of the Jacobian of the transverse dynamics measure whether a trajectory at a phase point is locally contracting or diverging with respect to another nearby trajectory. Subsequently, we go on to highlight a lesser appreciated fact that even when, under the corresponding linearised flow, the nearby trajectory asymptotically diverges away, its distance from the reference trajectory may still be contracting for some intermediate period. We term this phenomenon transient decay in line with the phenomenon of the transient growth. Using these facts, we show that an optimal coupling region, i.e., a region of the phase space where coupling is on, should ideally be such that at any of the constituent phase point either the maximum of the real parts of the eigenvalues is negative or the magnitude of the positive maximum is lesser than that of the negative minimum. We also invent and employ modified dynamics coupling scheme---a significant improvement over the well-known dynamic coupling scheme---as a decisive tool to justify our results.

nlin.CD↗