Stephan POHL§, Department of Philosophy, New York University, stephan.pohl@nyu.eduEdgar Y WALKER, Department of Physiology and Biophysics, Computational NeuroscienceCenter, University of Washington, Seattle, WA, eywalker@uw.eduDavid L BARACK, Departments of Neuroscience and Philosophy, University of Pennsylvania,Philadelphia, PA, dbarack@gmail.comJennifer LEE, Center for Neural Science, New York University, jll616@nyu.eduRachel N DENISON, Department of Psychological & Brain Sciences, Boston University, Boston,MA, rdenison@bu.eduNed BLOCK, Department of Philosophy, New York University, ned.block@nyu.eduFlorent MEYNIEL#, Cognitive Neuroimaging Unit, INSERM, CEA, CNRS, UniversitéParis-Saclay, NeuroSpin center, Gif/Yvette, France & Institute for Neuromodulation, GHU Parispsychiatrie et neuroscience, Sainte Anne Hospital, Paris, France, florent.meyniel@cea.frWei Ji MA# Center for Neural Science and Department of Psychology, New York University,weijima@nyu.edu#: co-senior authors; §: corresponding authorWhen claiming that a neural response represents a feature of the world, scientists try to establish that the neural response is (1) sensitive and (2) specific to the feature, (3) invariant to other features, and (4) functional downstream in the brain. We formalize these desiderata in information-theoretic terms, permitting their precise statement while unifying the different analysis methods used in neuroscience under one framework, thereby providing a common terminology to researchers. We discuss how common analysis methods are used to evaluate the desiderata and present canonical examples to illustrate the desiderata at work in research practice.This paper develops a systematic framework for the evidence neuroscientists use to establish whether a neural response represents a feature. Researchers try to establish that the neural response is (1) sensitive and (2) specific to the feature, (3) invariant to other features, and (4) functional, which means that it is used downstream in the brain. We formalize these desiderata in information-theoretic terms. This formalism allows us to precisely state the desiderata while unifying the different analysis methods used in neuroscience under one framework. We discuss how common methods such as correlational analyses, decoding and encoding models, representational similarity analysis, and tests of statistical dependence are used to evaluate the desiderata. In doing so, we provide a common terminology to researchers that helps to clarify disagreements, to compare and integrate results across studies and research groups, and to identify when evidence might be missing and when evidence for some representational conclusion is strong. We illustrate the framework with several canonical examples, including the representation of orientation, numerosity, faces, and spatial location. We end by discussing how the framework can be extended to cover models of the neural code, multi-stage models, and other domains.