arXiv subjects

Jonathan D. Cohen

Publications and source records attributed to Jonathan D. Cohen.

45 records · Page 3Linked to original sources

arXiv2020

Efficiency of learning vs. processing: Towards a normative theory of multitasking

A striking limitation of human cognition is our inability to execute some tasks simultaneously. Recent work suggests that such limitations can arise from a fundamental tradeoff in network architectures that is driven by the sharing of representations between tasks: sharing promotes quicker learning, at the expense of interference while multitasking. From this perspective, multitasking failures might reflect a preference for learning efficiency over multitasking capability. We explore this hypothesis by formulating an ideal Bayesian agent that maximizes expected reward by learning either shared or separate representations for a task set. We investigate the agent's behavior and show that over a large space of parameters the agent sacrifices long-run optimality (higher multitasking capacity) for short-term reward (faster learning). Furthermore, we construct a general mathematical framework in which rational choices between learning speed and processing efficiency can be examined for a variety of different task environments.

q-bio.NC↗

arXiv2020

The Efficiency of Human Cognition Reflects Planned Information Processing

Planning is useful. It lets people take actions that have desirable long-term consequences. But, planning is hard. It requires thinking about consequences, which consumes limited computational and cognitive resources. Thus, people should plan their actions, but they should also be smart about how they deploy resources used for planning their actions. Put another way, people should also "plan their plans". Here, we formulate this aspect of planning as a meta-reasoning problem and formalize it in terms of a recursive Bellman objective that incorporates both task rewards and information-theoretic planning costs. Our account makes quantitative predictions about how people should plan and meta-plan as a function of the overall structure of a task, which we test in two experiments with human participants. We find that people's reaction times reflect a planned use of information processing, consistent with our account. This formulation of planning to plan provides new insight into the function of hierarchical planning, state abstraction, and cognitive control in both humans and machines.

cs.AI↗

arXiv2019

Trusses and Trapezes: Easily-Interpreted Communities in Social Networks

The truss, a relaxation of the clique based on triangles, serves to identify clusters of actors in a way that is easy to interpret and is computationally attractive. This paper introduces the 4-cycle-based relative to the truss, called the trapeze, presents a weighted extension of both the truss and trapeze, and offers the refinements of strong trusses and trapezes and summit trusses and trapezes. Use of trapezes permits the application to bipartite graphs, while the weighted versions permit variation of support due to natural edge weights without increasing computational complexity. Finally, strong and summit versions make for easy determination of communities across graphs of varying density. Each of these structures offers guaranteed computation in polynomial time, is motivated by a natural observation of social cohesion, and is related nicely to other standard structures.

cs.SI↗

arXiv2018

Multitasking Capacity: Hardness Results and Improved Constructions

We consider the problem of determining the maximal $α\in (0,1]$ such that every matching $M$ of size $k$ (or at most $k$) in a bipartite graph $G$ contains an induced matching of size at least $α|M|$. This measure was recently introduced in Alon et al. (NIPS 2018) and is motivated by connectionist models of cognition as well as modeling interference in wireless and communication networks. We prove various hardness results for computing $α$ either exactly or approximately. En route to our results, we also consider the maximum connected matching problem: determining the largest matching $N$ in a graph $G$ such that every two edges in $N$ are connected by an edge. We prove a nearly optimal $n^{1-ε}$ hardness of approximation result (under randomized reductions) for connected matching in bipartite graphs (with both sides of cardinality $n$). Towards this end we define bipartite half-covers: A new combinatorial object that may be of independent interest. To the best of our knowledge, the best previous hardness result for the connected matching problem was some constant $β>1$. Finally, we demonstrate the existence of bipartite graphs with $n$ vertices on each side of average degree $d$, that achieve $α=1/2-ε$ for matchings of size sufficiently smaller than $n/poly(d)$. This nearly matches the trivial upper bound of $1/2$ on $α$ which holds for any graph containing a path of length 3.

cs.DS↗

arXiv2017

Matrix-normal models for fMRI analysis

Multivariate analysis of fMRI data has benefited substantially from advances in machine learning. Most recently, a range of probabilistic latent variable models applied to fMRI data have been successful in a variety of tasks, including identifying similarity patterns in neural data (Representational Similarity Analysis and its empirical Bayes variant, RSA and BRSA; Intersubject Functional Connectivity, ISFC), combining multi-subject datasets (Shared Response Mapping; SRM), and mapping between brain and behavior (Joint Modeling). Although these methods share some underpinnings, they have been developed as distinct methods, with distinct algorithms and software tools. We show how the matrix-variate normal (MN) formalism can unify some of these methods into a single framework. In doing so, we gain the ability to reuse noise modeling assumptions, algorithms, and code across models. Our primary theoretical contribution shows how some of these methods can be written as instantiations of the same model, allowing us to generalize them to flexibly modeling structured noise covariances. Our formalism permits novel model variants and improved estimation strategies: in contrast to SRM, the number of parameters for MN-SRM does not scale with the number of voxels or subjects; in contrast to BRSA, the number of parameters for MN-RSA scales additively rather than multiplicatively in the number of voxels. We empirically demonstrate advantages of two new methods derived in the formalism: for MN-RSA, we show up to 10x improvement in runtime, up to 6x improvement in RMSE, and more conservative behavior under the null. For MN-SRM, our method grants a modest improvement to out-of-sample reconstruction while relaxing an orthonormality constraint of SRM. We also provide a software prototyping tool for MN models that can flexibly reuse noise covariance assumptions and algorithms across models.

stat.ML↗

arXiv2017

A Graph-Theoretic Approach to Multitasking

A key feature of neural network architectures is their ability to support the simultaneous interaction among large numbers of units in the learning and processing of representations. However, how the richness of such interactions trades off against the ability of a network to simultaneously carry out multiple independent processes -- a salient limitation in many domains of human cognition -- remains largely unexplored. In this paper we use a graph-theoretic analysis of network architecture to address this question, where tasks are represented as edges in a bipartite graph $G=(A \cup B, E)$. We define a new measure of multitasking capacity of such networks, based on the assumptions that tasks that \emph{need} to be multitasked rely on independent resources, i.e., form a matching, and that tasks \emph{can} be multitasked without interference if they form an induced matching. Our main result is an inherent tradeoff between the multitasking capacity and the average degree of the network that holds \emph{regardless of the network architecture}. These results are also extended to networks of depth greater than $2$. On the positive side, we demonstrate that networks that are random-like (e.g., locally sparse) can have desirable multitasking properties. Our results shed light into the parallel-processing limitations of neural systems and provide insights that may be useful for the analysis and design of parallel architectures.

cs.DM↗

arXiv2017

A Formal Approach to Modeling the Cost of Cognitive Control

This paper introduces a formal method to model the level of demand on control when executing cognitive processes. The cost of cognitive control is parsed into an intensity cost which encapsulates how much additional input information is required so as to get the specified response, and an interaction cost which encapsulates the level of interference between individual processes in a network. We develop a formal relationship between the probability of successful execution of desired processes and the control signals (additive control biases). This relationship is also used to specify optimal control policies to achieve a desired probability of activation for processes. We observe that there are boundary cases when finding such control policies which leads us to introduce the interaction cost. We show that the interaction cost is influenced by the relative strengths of individual processes, as well as the directionality of the underlying competition between processes.

q-bio.NC↗

arXiv2016

A martingale analysis of first passage times of time-dependent Wiener diffusion models

Research in psychology and neuroscience has successfully modeled decision making as a process of noisy evidence accumulation to a decision bound. While there are several variants and implementations of this idea, the majority of these models make use of a noisy accumulation between two absorbing boundaries. A common assumption of these models is that decision parameters, e.g., the rate of accumulation (drift rate), remain fixed over the course of a decision, allowing the derivation of analytic formulas for the probabilities of hitting the upper or lower decision threshold, and the mean decision time. There is reason to believe, however, that many types of behavior would be better described by a model in which the parameters were allowed to vary over the course of the decision process. In this paper, we use martingale theory to derive formulas for the mean decision time, hitting probabilities, and first passage time (FPT) densities of a Wiener process with time-varying drift between two time-varying absorbing boundaries. This model was first studied by Ratcliff (1980) in the two-stage form, and here we consider the same model for an arbitrary number of stages (i.e. intervals of time during which parameters are constant). Our calculations enable direct computation of mean decision times and hitting probabilities for the associated multistage process. We also provide a review of how martingale theory may be used to analyze similar models employing Wiener processes by re-deriving some classical results. In concert with a variety of numerical tools already available, the current derivations should encourage mathematical analysis of more complex models of decision making with time-varying evidence.

math.PR↗

arXiv2015

Evolutionary game dynamics of controlled and automatic decision-making

We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model where agents who make decisions using either automatic or controlled processing compete with each other for survival. Agents using automatic processing act quickly and so are more likely to acquire resources, but agents using controlled processing are better planners and so make more effective use of the resources they have. Using the replicator equation, we characterize the conditions under which automatic or controlled agents dominate, when coexistence is possible, and when bistability occurs. We then extend the replicator equation to consider feedback between the state of the population and the environment. Under conditions where having a greater proportion of controlled agents either enriches the environment or enhances the competitive advantage of automatic agents, we find that limit cycles can occur, leading to persistent oscillations in the population dynamics. Critically, however, these limit cycles only emerge when feedback occurs on a sufficiently long time scale. Our results shed light on the connection between evolution and human cognition, and demonstrate necessary conditions for the rise and fall of rationality.

math.DS↗