Görkem Akgül

Görkem Akgül

A neurojedi trained at the Great Library of Ossus, with outposts in Istanbul and Berlin. Trying to understand the Force by studying how biological and artificial neural networks make sense of the world.

Research Interest

“Nature considered rationally, that is to say, submitted to the process of thought, is a unity in diversity of phenomena; a harmony, blending together all created things, however dissimilar in form and attributes; one great whole (τὸ πᾶν) animated by the breath of life. The most important result of a rational inquiry into nature is, therefore, to establish the unity and harmony of this stupendous mass of force and matter, to determine with impartial justice what is due to the discoveries of the past and to those of the present, and to analyze the individual parts of natural phenomena without succumbing beneath the weight of the whole. Thus, and thus alone, is it permitted to man, while mindful of the high destiny of his race, to comprehend nature, to lift the veil that shrouds her phenomena, and, as it were, submit the results of observation to the test of reason and of intellect.”

— Alexander von Humboldt, Cosmos, Volume 1, page 26.

The Computational Engine of Reality

Nature is a fascinating phenomenon. From a single atom where symmetry and forces of attraction give rise to structure, to organisms and galaxies, it unfolds across an almost unimaginable range of scales. At the centre of this complexity lies a computational engine that shapes our reality: the brain.

The brain is made up of many different kinds of cells. At its centre are neurons: strangely shaped, highly specialised cells with the remarkable ability to generate and transmit electrical signals. What a fascinating phenomenon that the activity of these tiny entities, organised across billions of neurons and supported by many other cell types, gives rise to our ability to process information. Our sciences, our art, and every animal’s success in navigating a complex world on this pale blue dot depend entirely on this ability.

The brain is not just a passive filter waiting for stimuli. It is a deeply dynamic, nonlinear, and recurrent information-processing system. Brain waves, such as alpha and mu oscillations, desynchronise when we move, or even when we merely imagine moving (Pfurtscheller & Lopes da Silva, 1999). Blood flow in the cortex shifts in highly structured ways as we process stimuli (Logothetis et al., 2001). In the hippocampus, sharp-wave ripples help us consolidate memories and plan (Buzsáki, 2015), while recurrent circuits can create “ring-attractor” dynamics that act like an internal compass for tracking spatial position (Kim et al., 2017). The task of deciphering this system is challenging, involving a multitude of scales, mechanisms, and interactions but that is also what makes it worthwhile.

Biological and Artificial Information Processing

We have known for a long time that we can make sense of the complexity of nature. When Hubel and Wiesel (1959) discovered that neurons in the visual cortex respond selectively to oriented bars and edges, they showed once again that nature’s overwhelming complexity can be approached through simpler principles. Later work demonstrated that many simple-cell receptive fields can be approximated by mathematical Gabor functions (Jones & Palmer, 1987). This was a powerful example of how a seemingly complex biological system could be described using a model that the human mind can grasp.

This is not only scientifically exciting; it also touches on deep philosophical questions. David Hume was deeply concerned with how human beings come to understand the natural world. In his Treatise of Human Nature (1739), he argued that the mind connects ideas through resemblance, contiguity, and cause and effect. At the same time, Hume reminded us that our causal expectations come from experience and habit: we observe regularities in nature, but we do not directly observe a necessary connection between causes and their effects. For me, the search for mathematical principles in the brain is connected to this very human attempt to find stable structure in the complexity of experience.

Neuroscience has also deeply influenced another field concerned with information processing: Artificial Intelligence. Early artificial neural models drew inspiration from cortical hierarchies (Fukushima, 1980) and continuous neural dynamics (Amari, 1977). Today, this relationship has revealed something especially fascinating. Artificial and biological neural systems can sometimes arrive at related computational and representational solutions. For example, sparse-coding models trained on natural images can develop Gabor-like receptive fields resembling those found in the primary visual cortex (Olshausen & Field, 1996). In modern deep learning, performance-optimized hierarchical vision models can predict neural responses in higher visual cortex, even when they are not directly trained to match neural data (Yamins et al., 2014). In language, computational encoding models have also been used to predict and map distributed semantic representations across the human cortex during natural speech (Huth et al., 2016).

I find this parallel deeply compelling. Artificial networks lack many of the rich and messy properties of biological brains, including spiking dynamics, intricate dendritic computation, neuromodulation, and the continuous interaction of cells, circuits, bodies, and environments. They also typically learn through variants of backpropagation, whereas biological learning is thought to rely on local, time-extended, and biologically constrained mechanisms. Yet, despite these profound differences, artificial and biological systems can converge on related representational solutions. Understanding when this happens, why it happens, and where it fails is one of the main questions driving my research interest.

Symmetry, Geometry, and Representation

There is also a deep theoretical link between representation, symmetry, and invariance. A central problem for any intelligent system is learning which aspects of the world should remain stable when the sensory input changes. An object can move, rotate, appear under different lighting conditions, or be encountered in a new context, while still needing to be recognised as the same object. Symmetry and invariance provide a powerful mathematical language for describing this problem.

Historically, scholars such as Karl Pribram (1991) and David Bohm (1980) were drawn to the possibility that information processing might be distributed and relational rather than localized in single units. Pribram’s holonomic theory, inspired by holography and Fourier analysis, proposed that memory and perception could be understood through distributed patterns of transformation. Although these ideas remain speculative and should not be confused with contemporary accounts of neural computation, they point toward a question that still feels deeply relevant: how can distributed systems represent structured information in a stable and flexible way?

More recently, work in machine learning has made parts of the relationship between symmetry and representation mathematically explicit. Marchetti et al. (2024) showed that, under specific conditions, neural networks invariant to a finite symmetry group recover weights closely related to the Fourier transform of that group. In other words, when a learning system must respect particular transformations, the structure of those transformations can shape the features it learns.

This does not mean that the brain literally implements the same mechanism. However, it suggests a compelling direction: the symmetries and invariances present in an organism’s environment, task, and body may place important constraints on the representations that neural systems develop. Understanding these constraints and testing whether similar principles appear in biological and artificial neural networks is one of the questions that I find particularly interesting.

The Field of NeuroAI

It is an exciting period to be in interested in such research directions. Driven by many developments, the field of NeuroAI has grown rapidly. We are no longer using neural networks only as engineering tools; we can also use them as explicit, testable models of biological cognition. This approach, known as the neuroconnectionist research programme (Doerig et al., 2023), treats artificial neural networks as a computational language for expressing and testing falsifiable theories about brain computation. It allows us to ask not only whether a model can predict neural responses or behaviour, but also whether it offers explanatory insight into how the brain computes (Doerig et al., 2023). This is where I locate myself: interested in the many questions surrounding neural information processing, including the roles of symmetry, geometry, dynamics, stochasticity, learning, and representation in both biological and artificial neural systems.

Core Research Questions

Ultimately, my central interest is understanding biological neural information processing. I am specifically driven by questions like:

My goal is to contribute to a deeper understanding of how neural systems transform sensory input into stable, flexible, and meaningful representations. By studying how dynamics and learning shape these representations, I hope to use computational models to move our understanding of the brain from mere prediction to true explanation.

References

  1. Amari, S. (1977). Dynamics of pattern formation in lateral-inhibition type neural fields. Biological Cybernetics, 27, 77–87. https://doi.org/10.1007/BF00337259
  2. Bohm, D. (1980). Wholeness and the implicate order. Routledge & Kegan Paul.
  3. Buzsáki, G. (2015). Hippocampal sharp wave-ripple: A cognitive biomarker for episodic memory and planning. Hippocampus, 25(10), 1073–1188. https://doi.org/10.1002/hipo.22488
  4. Doerig, A., Sommers, R. P., Seeliger, K., Richards, B., Ismael, J., Lindsay, G. W., Kording, K. P., Konkle, T., van Gerven, M. A. J., Kriegeskorte, N., & Kietzmann, T. C. (2023). The neuroconnectionist research programme. Nature Reviews Neuroscience, 24(7), 431–450. https://doi.org/10.1038/s41583-023-00705-w
  5. Fukushima, K. (1980). Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position. Biological Cybernetics, 36, 193–202. https://doi.org/10.1007/BF00344251
  6. Hubel, D. H., & Wiesel, T. N. (1959). Receptive fields of single neurones in the cat’s striate cortex. The Journal of Physiology, 148(3), 574–591. https://doi.org/10.1113/jphysiol.1959.sp006308
  7. Hume, D. (1739/2000). A treatise of human nature (D. F. Norton & M. J. Norton, Eds.). Oxford University Press.
  8. Huth, A. G., de Heer, W. A., Griffiths, T. L., Theunissen, F. E., & Gallant, J. L. (2016). Natural speech reveals the semantic maps that tile human cerebral cortex. Nature, 532, 453–458. https://doi.org/10.1038/nature17637
  9. Kim, S. S., Rouault, H., Druckmann, S., & Jayaraman, V. (2017). Ring attractor dynamics in the Drosophila central brain. Science, 356(6340), 849–853. https://doi.org/10.1126/science.aal4835
  10. Logothetis, N. K., Pauls, J., Augath, M., Trinath, T., & Oeltermann, A. (2001). Neurophysiological investigation of the basis of the fMRI signal. Nature, 412, 150–157. https://doi.org/10.1038/35084005
  11. Marchetti, G. L., Hillar, C., Kragic, D., & Sanborn, S. (2024). Harmonics of learning: Universal Fourier features emerge in invariant networks. In Proceedings of the Thirty-Seventh Conference on Learning Theory (Proceedings of Machine Learning Research, Vol. 247, pp. 3775–3797). https://proceedings.mlr.press/v247/marchetti24a.html
  12. Olshausen, B. A., & Field, D. J. (1996). Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature, 381, 607–609. https://doi.org/10.1038/381607a0
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  14. Pribram, K. H. (1991). Brain and perception: Holonomy and structure in figural processing. Lawrence Erlbaum Associates.
  15. Sucholutsky, I., Muttenthaler, L., Weller, A., Peng, A., Bobu, A., Kim, B., Love, B. C., Cueva, C. J., Grant, E., Groen, I., Achterberg, J., Tenenbaum, J. B., Collins, K. M., Hermann, K. L., Kriegeskorte, N., Konkle, T., Griffiths, T. L., et al. (2023). Getting aligned on representational alignment. arXiv. https://arxiv.org/abs/2310.13018
  16. von Humboldt, A. (1849). Cosmos: A sketch of a physical description of the universe (Vol. 1, E. C. Otté, Trans.). Longman, Brown, Green, and Longmans. (Original work published 1845.)
  17. Yamins, D. L. K., Hong, H., Cadieu, C. F., Solomon, E. A., Seibert, D., & DiCarlo, J. J. (2014). Performance-optimized hierarchical models predict neural responses in higher visual cortex. Proceedings of the National Academy of Sciences, 111(23), 8619–8624. https://doi.org/10.1073/pnas.1403112111
  18. Jones, J. P., & Palmer, L. A. (1987). An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex. Journal of Neurophysiology, 58(6), 1233–1258. https://doi.org/10.1152/jn.1987.58.6.1233