# A space of goals: the cognitive geometry of informationally bounded agents

arXiv: https://arxiv.org/abs/2111.03699 · HTML: https://mlsanity.com/paper/2111.03699/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 74 references that are in the map.
- First posted on arXiv 5 Nov 2021.

## Builds on (most cited first, 12 of 12)

- [A Generalized Algorithm for Multi-Objective Reinforcement Learning and Policy Adaptation](https://mlsanity.com/paper/1908.08342/) (2019)
- [Neural population geometry: An approach for understanding biological and artificial neural networks](https://mlsanity.com/paper/2104.07059/) (2021)
- [People construct simplified mental representations to plan](https://mlsanity.com/paper/2105.06948/) (2021)
- [On the Complexity of Solving Markov Decision Problems](https://mlsanity.com/paper/1302.4971/) (2013)
- [Neural tuning and representational geometry](https://mlsanity.com/paper/2104.09743/) (2021)
- [Cognitive science as a source of forward and inverse models of human decisions for robotics and control](https://mlsanity.com/paper/2109.00127/) (2021)
- [Information-Theoretic Bounded Rationality](https://mlsanity.com/paper/1512.06789/) (2015)
- [Mutual-Information Regularization in Markov Decision Processes and Actor-Critic Learning](https://mlsanity.com/paper/1909.05950/) (2019)
- [Towards a Quantum-Like Cognitive Architecture for Decision-Making](https://mlsanity.com/paper/1905.05176/) (2019)
- [Resource-rational Task Decomposition to Minimize Planning Costs](https://mlsanity.com/paper/2007.13862/) (2020)
- [The evolution of lossy compression](https://mlsanity.com/paper/1506.06138/) (2015)
- [Hierarchical State Abstractions for Decision-Making Problems with Computational Constraints](https://mlsanity.com/paper/1710.07990/) (2017)

## Built on by (most cited first, 1 of 1)

- [Detecting danger in gridworlds using Gromov's Link Condition](https://mlsanity.com/paper/2201.06274/) (2022)

## Abstract (arXiv)

Traditionally, Euclidean geometry is treated by scientists as a priori and objective. However, when we take the position of an agent, the problem of selecting a best route should also factor in the abilities of the agent, its embodiment and particularly its cognitive effort. In this paper we consider geometry in terms of travel between states within a world by incorporating information processing costs with the appropriate spatial distances. This induces a geometry that increasingly differs from the original geometry of the given world as information costs become increasingly important. We visualise this "cognitive geometry" by projecting it onto 2- and 3-dimensional spaces showing distinct distortions reflecting the emergence of epistemic and information-saving strategies as well as pivot states. The analogies between traditional cost-based geometries and those induced by additional informational costs invite a generalisation of the notion of geodesics as cheapest routes towards the notion of infodesics. In this perspective, the concept of infodesics is inspired by the property of geodesics that, travelling from a given start location to a given goal location along a geodesic, not only the goal, but all points along the way are visited at optimal cost from the start.