Jun Zhang


Email: junzhang _at_ simis.cn
Research Fields: Information Geometry, Computation Neuroscience, Cognitive Science and Artificial Intelligence.
Office No.:


Jun Zhang is a Professor at the Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS) and one of its co-founders. He is currently on leave from the University of Michigan, Ann Arbor, where he has worked since 1992 as an Assistant, Associate, and Full Professor in the Department of Psychology, with adjunct appointments in the Department of Mathematics, Department of Statistics, and Michigan Institute of Data Sciences. He received his PhD in Neuroscience from the University of California, Berkeley in 1991. During sabbatical years, he has held various visiting academic positions at the University of Melbourne (Australia), CNRS (France), University of Waterloo (Canada), RIKEN Brain Science Institute (Japan), CMSA at Harvard, etc. Professor Jun Zhang’s scholarly contributions have been in the various fields of computation neuroscience, cognition and behavior modeling, machine learning, statistical science, complex systems, etc, and is well known in the field of mathematical psychology. In recent years, his research has focused on the interdisciplinary subject of Information Geometry.

Education Experience

  • 1991    University of California, Berkeley    Neuroscience    PhD
  • 1985    Fudan University    Physics    Bachelor

Work Experience

  • 2024-            Shanghai Institute for Mathematics and Interdisciplinary Sciences    Professor
  • 1992-            University of Michigan    Assistant, Associate and Full Professor
  • 1991-1992    Salk Institute, San Diego    Postdoc

Honors and Awards

  • Member, Committee on Academic Affairs, Chinese Society for Cognitive Science (2019- )
  • Fellow, Psychonomic Society (2016- )
  • Fellow, Association for Psychological Sciences (2012-)
  • Governing Board Member-at-Large (elected), Federation of Associations in the Behavioral and Brain Sciences (2016-2018)
  • Council Member, Federation of Associations in the Behavioral & Brain Sciences (2010-2015) appointed on behalf of the Society for Mathematical Psychology
  • Elected to Executive Committee, Society for Mathematical Psychology (2005-2011)
  • Elected as President, Society for Mathematical Psychology (2007-2008)
  • Elected as Vice President, Society for Mathematical Psychology (2008-2009)
  • Invited 45-Minute Plenary Talk, Japan 58th Geometry Symposium, August 28, 2011
  • Invited Winer Memorial Lectures, Department of Psychology, Purdue University, 3-4/2003


Journal Publications

  1. Zhang, J. (1990). How to unconfound orientational and directional information in visual neuron’s response. Biological Cybernetics, 63: 135-142.
  2. Zhang, J. and Wu, S. (1990). Structure of visual perception. Proceedings of National Academy of Sciences, USA. 87: 7819-7823.
  3. Zhang, J. and Miller, J.P. (1991). A mathematical model for hyperacuity in sensory systems. Biological Cybernetics, 64: 357-364.
  4. Zhang, J. (1991). Dynamics and formation of self-organizing maps. Neural Computation, 3: 54-66.
  5. Zhang, J., Yeh, S.-L. and De Valois, K.K. (1993). Motion contrast and motion integration. Vision Research, 33: 2721-2732.
  6. Skottun, B., Zhang, J. and Grosof, D. (1994). On the direction selectivity of cortical neurons to drifting dot patterns. Visual Neuroscience, 11: 885-897.
  7. Zhang, J. (1995). Motion detectors and motion segregation. Spatial Vision, 9: 261-273.
  8. Zhang, J., Riehle, A., Requin, J. and Kornblum, S. (1997). Dynamics of single neuron activity in primary motor cortex related to sensorimotor transformation. Journal of Neuroscience, 17: 2227-2246.
  9. Zhang, J. and Kornblum, S. (1997). Distributional analysis, and De Jong et al.’s (1994) dual process model of the “Simon effect”. Journal of Experimental Psychology: Human Perception and Performance, 23: 1543-1551.
  10. Zhang, J., Riehle, A. and Requin, J. (1997). Locus of a neural process in stimulus-response association tasks. Journal of Mathematical Psychology, 41: 219-236.
  11. Zhang, J. (1998). Decomposing stimulus and response component waveforms in ERP. Journal of Neuroscience Methods, 80: 49-63.
  12. Zhang, H., Zhang, J. and Kornblum, S. (1999). An interactive activation model of stimulus-stimulus and stimulus-response compatibility. Cognitive Psychology, 38: 386-432.
  13. Hedden, T. and Zhang, J. (2002). What do you think I think you think? Theory of mind and strategic reasoning in matrix games. Cognition, 85: 1-36.
  14. Jones, M., Zhang, J. and Simpson, G. (2003). Aggregation of utility and social choice: A topological characterization. Journal of Mathematical Psychology, 47: 545-556.
  15. Zhang, J. (2004). Divergence function, duality, and convex analysis. Neural Computation, 16: 159-195.
  16. Zhang, J. (2004). Binary choice, subset choice, random utility, and ranking: A unified perspective using the permutahedron. Journal of Mathematical Psychology, 48: 107-134.
  17. Jones, M. and Zhang, J. (2004) Rationality and bounded information in repeated games, with application to the Iterated Prisoner’s Dilemma. Journal of Mathematical Psychology, 48: 334–354.
  18. Zhang, J. (2004). Dual scaling between comparison and reference stimuli in multidimensional psychological space. Journal of Mathematical Psychology, 48: 409-424.
  19. Zhang, J. and Mueller, S. (2005). A note on ROC analysis and non-parametric estimation of sensitivity. Psychometrika, 70: 203-212.
  20. Zhang. J. (2005). A method to unconfound orientation and direction tunings in neuronal response to moving bars and gratings. Journal of the Optical Society of America, A. 22: 2246-2256.
  21. Tindell, A.J., Berridge, K.C., Zhang, J., Peciña, S., and Aldridge, J.W. (2005) Ventral pallidal neurons code incentive motivation: effects of mesolimbic activation. European Journal of Neuroscience. 22, 2617-2634.
  22. Zhang, J. and Hasto, P. (2006). Statistical manifold as an affine space: A functional equation approach. Journal of Mathematical Psychology, 50: 60-65.
  23. Zhang, J. (2007). A note on curvature of α-connections on a statistical manifold. Annals of Institute of Statistical Mathematics, 59: 161-170.
  24. Wei, H., Zhang, J., Cousseau, F., Ozeki, T., and Amari, S. (2007). Dynamics of learning near singularities in layered network. Neural Computation, 20, 813-843.
  25. Zhou, T., Zhang, J. and Chen, L. (2008). Neural correlation of “global-first” topological perception: Anterior temporal lobe. Brain Imaging and Behavior. 2, 309-317.
  26. Yin, G., Zhang, J., Tian, Y. and Yao, D-Z. (2009). A multi-component decomposition algorithm for event-related potentials. Journal of Neuroscience Methods, 178, 219-227.
  27. He, L., Zhang, J., Zhou, T. and Chen, L. (2009). Connectedness affects dot numerosity judgment: implications for configural processing. Psychonomic Bulletin and Review 16, 509-517.
  28. Zhang, J. (2009). Adaptive learning via selectionism and Bayesianism. Part I: A connection. Neural Networks, 22, 220-228.
  29. Zhang, J. (2009). Adaptive learning via selectionism and Bayesianism Part II: The sequential case. Neural Networks, 22, 229-236.
  30. Zhang, J., Berridge, K.C., Tindell, A.J., Smith, K.S., and Aldridge, J.W. (2009). Modeling the neural computation of incentive salience. PLoS Computational Biology, 5: 1-14.
  31. Zhang, H., Xu, Y., and Zhang, J. (2009). Reproducing kernel Banach spaces for machine learning. Journal of Machine Learning Research 10: 2741-2775.
  32. Stevens, G. and Zhang, J. (2009). A dynamic systems model of infant attachment. IEEE Transaction of Autonomous Mental Development. 1: 196-207.
  33. Stern, E., Liu, Y., Gehring, W., Lister, J., Yin, G., Zhang, J., Fitzgerald, K., Himle, J., Abelson, J., Taylor, S. (2010). Chronic medication does not affect hyperactive error responses in obsessive-compulsive disorder. Psychophysiology 47: 913-920.
  34. Park, J and Zhang, J. (2010). Sensorimotor locus of the buildup activity in monkey LIP neurons. Journal of Neurophysiology. 103: 2664-2674.
  35. Zhang, H. and Zhang, J. (2010). Generalized semi-inner products with application to regularized learning. Journal of Mathematical Analysis and Application. 372: 181-196.
  36. Zhang, H. and Zhang, J. (2011). Frames, Riesz bases, and sampling expansions in Banach spaces via semi-inner products. Applied and Computational Harmonic Analysis. 31:1-25.
  37. Yin, G. and Zhang J. (2011). On decomposing stimulus and response waveforms in event-related potentials (ERP) recordings. IEEE Transactions on Biomedical Engineering, 58: 1534-1545 (DOI:10.1109/TBME.2010.2090152).
  38. Zhang, J., Hedden, T and Chia, A. (2012) Perspective-taking and depth of theory-of-mind reasoning in sequential-move games. Cognitive Science, 36: 560-573.
  39. Zhang, H. and Zhang, J. (2012). Regularized learning in Banach space as an optimization problem: Representer theorems. Journal of Global Optimization, 54: 235-250 (e-print published 11 July 2010).
  40. Zhang, H. and Zhang, J. (2013). Vector-valued Reproducing Kernel Banach Spaces with applications to multi-task learning, Journal of Complexity, 29: 195-215.
  41. Zhang, J. (2013). Nonparametric information geometry: From divergence function to referential-representational biduality on statistical manifolds. Entropy, 15: 5384-5418.
  42. Ilin, R., Zhang, J., Perlovsky, L., and Kozma, R. (2014). Vague-to-crisp dynamics of percept formation modeled as operant (selectionist) process. Cognitive Neurodynamics, 8: 71-80.
  43. Zhang, J. (2015). On monotone embedding in information geometry. Entropy, 17: 4485-4489.
  44. Tao, J. and Zhang, J. (2016). Transformations and coupling relations for affine connections. Journal of Differential Geometry and Applications. 49: 111-130.
  45. Fei, T. and Zhang, J. (2017). Interaction of Codazzi couplings with (para)-Kahler geometry. Results in Mathematics. 72: 2037-2056
  46. Leok, M. and Zhang, J. (2017). Connecting information geometry to geometric mechanics. Entropy, 19: 518; doi:10.3390/e19100518
  47. Greenfield M. and Zhang, J (2018) Resolution to the topological social choice paradox. Mathematical Social Sciences. 93: 47-51.
  48. Naudts, J. and Zhang, J. (2018) Rho-tau embedding and gauge freedom in information geometry. Information Geometry. 1: 79-115.
  49. Zhang, J. (2019) Characterizing projective geometry of binocular visual space through Mobius transformation. Journal of Mathematical Psychology. 88: 15-26.
  50. Grigorian, S. and Zhang, J. (2019). (Para)-holomorphic and conjugate on (para-)Hermitian and (para-)Kahler manifolds. Results in Mathematics, 74: 150.
  51. Zhang, J. and Khan, G. (2019). From Hessian to Weitzenbock: Manifolds with torsion-carrying connections. Information Geometry, 2: 77-98.
  52. Qian, N. and Zhang, J. (2020). Neuronal firing rate as code length: a hypothesis. Computation Brain and Behavior, 3(1), 34-53
  53. Zhang, J. and Shi Z. (2020). Bayesian inference as probability transfer across sample spaces. Decision 7(2), 121-136.
  54. Khan, G. and Zhang, J. (2020). The Kahler geometry of certain optimal transport problems. Pure and Applied Analysis. 2(2), 397-426.
  55. Kim, D.Y., Jung, E.K., Zhang, J., Lee, S.Y., and Lee, J.H. (2020). Functional magnetic resonance imaging multivoxel pattern analysis reveals neuronal substrates for collaboration and competition with myopic and predictive strategic reasoning. Human Brain Mapping. 41(15) 4314-4331.
  56. Zhang, J. and Khan, G. (2020). Statistical mirror symmetry. Differential Geometry and Applications. 73, 101678.
  57. Zhang, J. and Matsuzoe, H. (2021). Entropy, cross-entropy, relative entropy: Deformation theory. European Journal of Physics. 134(1), 18001.
  58. Lei, Y. and Zhang, J. (2021). Closure system and its semantics. Axiom, 10(3), 198.
  59. Zhang, J. and Wong, T.K. L. (2022). λ-Deformation: A canonical framework for statistical manifolds of constant curvature. Entropy, 24, 193.
  60. Lin, R., Zhang, J. and Zhang, H. (2022). On Reproducing Kernel Banach Spaces: Generic definitions and unified framework of construction. Acta Mathematica Sinica, English series, 38, 1459-1483.
  61. Wong, T.K. L. and Zhang, J. (2022). Tsallis and Renyi deformations linked via a new λ-duality. Transaction of IEEE Information Theory, 68, 5353-5373.
  62. Khan, G. and Zhang, J. (2022). When optimal transport meets information geometry. Information Geometry. In press.
  63. Khan, G. and Zhang, J. (2023). A hall of statistical mirrors. Asian Journal of Mathematics.

Book Chapters

  1. Zhang, J. (1994) Image representation using affine covariant coordinates. In O, Y.-L., Toet, A., Foster, D., Heijmans, H.J.A.M., and Meer, P. (Eds.) Shape in Picture: Mathematical Description of Shape in Grey-Level Images, Springer-Verlag, Berlin (pp.353-362).
  2. Zhang, J. (1999) A game-theoretic analysis of the political situation across Taiwan Strait. In J. Zhang and Y. Yu (Eds), Taiwan in the 21st Century: the Mainland Chinese Scholars Looking Ahead, Global Publishing Co., River Edge, New Jersey (pp 217-236). In Chinese.
  3. Zhang, J. (2006) Referential duality and representational duality in the scaling of multidimensional and infinite-dimensional stimulus space. In Dzhafarov, E. and Colonius, H. (Eds.) Measurement and representation of sensations: Recent progress in psychological theory. Lawrence Erlbaum Associates, Mahwah, NJ (pp. 131-157).
  4. Chavez, A. and Zhang, J. (2008). Metagame strategies of nation-states, with application to Cross-Strait relations. In Liu, H., Salerno, J. and Young, M. (Eds.) Social computing, behavioral modeling, and prediction. Springer (pp.229-238).
  5. Zhang, J. and Matsuzoe, H. (2009). Dualistic differential geometry associated with a convex function. In Gao D.Y. and Sherali, H.D. (Eds) Advances in Applied Mathematics and Global Optimization (Dedicated to Gilbert Strang on the Occasion of His 70th Birthday), Advances in Mechanics and Mathematics, Vol. III, Chapter 13, Springer (pp 437-464).
  6. Zhang, J., Berridge, K., Tindell, A., and Aldridge, J.A. (2011). Computational models of incentive-sensitization in addiction: Dynamic limbic transformation of learning into motivation. In Gutkin, B. and Ahmed, S.H. (Eds.) Computational Neuroscience of Drug Addition. Springer (pp.189-203).
  7. Zhang, J. (2011). Model selection with informative normalized maximum likelihood: Data prior and model prior. In Dzhafarov, E.N and Perry, L. (Eds) Descriptive and Normative Approaches to Human Behavior. World Scientific, New Jersey (pp. 303-319).
  8. Zhang, J. and Yin, G. (2013). A method to decompose stimulus and response components in event-related potential (ERP) recordings. In Z. Lu and Y. Luo (Eds). Progress in Cognitive Science: From Cellular Mechanisms to Computational Theories. Peking University Press (pp.378-413).
  9. Zhang, J. (2014) Divergence functions and geometric structures they induce on a manifold. In F. Nielsen (Ed). Geometric Theory of Information, Springer (pp.1-30).
  10. Zhang, J. and Ilin, R. (2015). Modeling uncertainty, context, and information fusion via lattice-based probability. In Chichilnisky G. and Rezai A. (Eds). The Economics of the Global Environment – Catastrophic Risks in Theory and Practice. Springer. (pp. 89-116)
  11. Zhang, J. and Sun, Y. (2016). Subset systems: Mathematical abstraction of object and context. In Houpt and Blaha (Eds.).Mathematical Models of Perception and Cognition, Volume I: A Festschrift for James T. Townsend. Psychological Press. (pp. 47-64).
  12. Zhang, H. and Zhang, J. (2017). Learning with reproducing kernel Banach spaces. New Trends in Analysis and Interdisciplinary Applications. (pp.417-423). Birkhauser, Cham.
  13. Zhang, J. and Zhang, H. (2018). Categorization based on similarity and features: The reproducing kernel Banach space (RKBS) approach. In W. Batchelder, H. Colonius, E.N. Dzhafarov, J. Myung (Eds.) New Handbook of Mathematical Psychology, Volume 2, Springer.
  14. Naudts, J. and Zhang, J. (2019). Rho-tau embedding of statistical models. Geometric Structures of Information, Springer, Cham (pp.1-13).
  15. Lei, Y. and Zhang, J. (2019). Generalizing topological set operators. Electronic Notes in Computer Science, Vol 345: 63-76.
  16. Zhang, J. and Khan, G. (2021). Affine connections with torsion in (para-)complexified structures. In Nielsen, F. (Ed) Progress in Information Geometry, Springer Nature.
  17. Zhang, J. and Wong, T.K.L. (2021). λ-Deformed probability families with subtractive and divisive normalizations. In Rao, A.S.R.R. (Ed) Handbook of Statistics, Vol 45.

Conference Proceedings, Commentaries, and Reviews

  1. Zhang, J. and Miller, J.P. (1989). A model for resolution enhancement (hyperacuity) in sensory representation. In Touretzky, D. (Ed.) Advances in Neural Network Information Processing System. I. pp.444-450. Morgan-Kaufmann Publishers, San Mateo, CA.
  2. Zhang, J. (1990). Dynamical self-organization and formation of cortical maps. In Proceedings of International Joint Conference on Neural Networks, San Diego, 1990, Vol. III, pp. 487-492.
  3. Zhang, J. (1990). Review of “Theory of self-organization of cortical maps” by Shigeru Tanaka. Neural Network Review, 4.
  4. Zhang, H., Kornblum, S. and Zhang, J. (1995). Utilization of stimulus-response and stimulus-stimulus compatibility principles in machine design. In K. Cox, J. Marsh, and B. Anderson (Eds.) Proceedings of the First International Cognitive Technology Conference, Hong Kong: City University of Hong Kong (pp. 151-157).
  5. Zhang, J. (1999). A note on Lefebvre’s reflexive function. In V.A. Lefebvre (Ed.) Proceedings of the Workshop on Multi-Reflexive Models of Agent Behavior, ARL-SR-64, U.S. Army Research Lab (pp.109-110).
  6. Zhang, J. (2001). Dimension overlap and S-S and S-R compatibility: a structural model. In L. Chen and Y. Zhuo (Eds.) Proceedings of the Third International Conference on Cognitive Science (ICCS2001), Heifei, China: Press of University of Science and Technology of China (pp 377-381).
  7. Zhang, J. and Hedden, T. (2003). Two paradigms for depth of strategic reasoning in games: Response to Colman. Trends in Cognitive Sciences, 7, 4-5.
  8. Jones, M. and Zhang, J. (2003). Which is to blame: Instrumental rationality or common knowledge? Comments to “Cooperation, psychological games theory, and limitations of rationality in social interaction” by A. Colman. Brain and Behavioral Science, 26: 166-167.
  9. Zhang, J. (2005). Object oneness: the essence of the topological approach to perception. Visual Cognition, 12: 683-690.
  10. Zhang, J. (2005). Referential duality and representational duality on statistical manifolds. Proceedings of the Second International Symposium on Information Geometry and Its Applications, Tokyo (pp 58-67).
  11. Mueller, S. and Zhang, J. (2006). Upper and lower bounds of area under ROC curves and index of discriminability of classifier performance. Proceedings of ICML2006 Workshop on ROC Analysis in Machine Learning, Pittsburgh, PA, 2006 (pp.41-46).
  12. Berridge, K., Zhang, J., and Aldridge, W. (2008). Computing motivation: Incentive salience boosts of drug or appetite states. Behavioral Brain Science 31:440-441. 
  13. Zhang, H., Xu, Y, and Zhang, J. (2009). Reproducing kernel Banach spaces for Machine Learning. Proceedings of the 2009 International Joint Conference on Neural Networks, IJCNN2009, Atlanta, Georgia, USA (pp.3520-3527).
  14. Calin, O., Matsuzoe, H., and Zhang, J. (2009). Generalization of conjugate connections. Proceedings of 9th International Workshop on Complex Structures, Integrability, and Vector Fields. (pp.26-34).
  15. Yenduri, P.K., Zhang, J., and Gilbert, A. (2012). Integrate-and-fire neuron modeled as a low-rate sparse time-encoding device. Proceedings of the Third International Conference on Intelligent Control and Information Processing, ICICIP 2012 (pp507-512).   
  16. Jung, E. K., Zhang, J, Lee, S-Y, and Lee, J-H (2013). A preliminary study on neural basis of collaboration as mediated by the level of reasoning. Neural Information Processing, Proceedings of the 20th International Conference on Neural Information Processing (ICONIP2013), Daegu, Korea. Springer, Berlin Heidelberg (pp.50-56).
  17. Zhang, J. and Li, F. (2013). Symplectic and Kahler structures on statistical manifolds induced from divergence functions. In Nielson, F. and Barbaresco, F. (Eds), Geometric Science of Information, 1st International Conference GSI2013, Springer LNCS8085(pp. 595-603).
  18. Ilin, R. and Zhang, J. (2014). Information fusion with uncertainty modeled on topological event spaces. In Symposium on Foundations of Computational Intelligence, FOCI’2014, IEEE (pp.1-8).
  19. Ilin, R. and Zhang, J. (2015). Information fusion with topological event spaces. In Proceedings of International Conference on Information Fusion FUSION’2015, IEEE (pp. 2092-2099).
  20. Zhang, J. (2015). Reference duality and representation duality in information geometry. In Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt2014), Vol. 1641 (pp130-146). AIP Publishing.
  21. Tao, J. and Zhang, J. (2015). Transformation and coupling of relations for affine connections. In Nielson, F. and Barbaresco, F. (Eds), Geometric Science of Information, 2nd International Conference GSI2015, Springer LNCS 9389(pp. 326-339).
  22. Zhang, J. and Naudts, J. (2017). Information geometry under monotone embedding.Part I: divergence functions. In Nielson, F. and Barbaresco, F. (Eds), Geometric Science of Information, 3rd International Conference GSI2017 Springer LNCS 10589 (pp. 205-214).
  23. Naudts, J. and Zhang, J. (2017). Information geometry under monotone embedding.Part II: geometry. In Nielson, F. and Barbaresco, F. (Eds), Geometric Science of Information, 3rd International Conference GSI2017 Springer LNCS 10589 (pp. 215-222).
  24. Grigorian, S. and Zhang, J. (2017). (Para)-holomorphic connections for information geometry. In Nielson, F. and Barbaresco, F. (Eds), Geometric Science of Information, GSI2017 (pp. 186-194).
  25. Zhang, J. and Fei, T. (2018). (Para-)Kahler structure in information geometry. In Ay, N., Gibilisco, P., Matus, F. (Eds) Information Geometry and Its Applications, IGAIA4 Proceedings. Springer Proceedings in Mathematics & Statistics Vol 252 (pp 297-321).
  26. Zhang, J. and Khan, G. (2019). New geometry of parametric statistical models. In Nielson, F. and Barbaresco, F. (Eds), Geometric Science of Information,4th International Conference GSI2019 Springer LNCS 11712 (pp. 288-296).
  27. Khan, G. and Zhang, J. (2019). Hessian curvature and optimal transport. In Nielson, F. and Barbaresco, F. (Eds), Geometric Science of Information, 4th International Conference GSI2019 Springer LNCS 11712(pp. 423-430).
  28. Khan, G. Zhang, J. and Zheng, F. (2020). The geometry of positively curved Kahler metrics on tube domains. arXiv preprint arXiv:2001.06155
  29. Han, T., Zhang, J. and Wu Y. (2020). From em-projection to variational auto-encoder. Workshop on deep-learning through information geometry. NeuRIPS’2020.  
  30. Khan, G. and Zhang, J. (2021). Recent development on the MTW tensor. In Nielson, F. and Barbaresco, F. (Eds), Geometric Science of Information,5th International Conference GSI2021 Springer.
  31. Zhang, J. (2021). Constructing rationals through conjoint measurement of numerator and denominator as approximate integer magnitudes in tradeoff relations. Comments to “The number sense represents (rational) numbers” by S. Clark and J. Beck. Brain and Behavioral Science, 44: 51-53.
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