Here are a few recent papers from the field of computational and theoretical neuroscience that I think are worth the time to read them. All of them are close to what I have been working on or what I am planning to work on in the future, but there is not tight connection among them.

The Neuron as a Direct Data-Driven Controller

In their preprint, Moore et al. (2024) provide an interesting perspective on how to think about neurons: rather than input-output devices, neurons are described as control units. In their framework, these neuronal control units receive input as feedback about their own output in a feedback loop which may involve the environment. In turn, the neurons try to control this feedback loop by adapting their output according to a neuron-specific objective function. To use the authors’ words, this scheme is “enabling neurons to evaluate the effectiveness of their control via synaptic feedback”.

These are ideas that have been fascinating for me since quite some time. For example, I have described similar ideas about the single-neuron perspective and the objective function of single neurons in a previous blog post. The work of Moore et al. (2024) is an interesting new perspective, not only because it clearly states the main ideas of their approach, but also because the ideas are shaped by a mathematical perspective of linear control theoretical approaches (see: control theory).

To probe the framework, the paper shows how several disconnected observations in neurophysiology emerge in such a framework, like STDP (spike time-dependent plasticity). STDP is a learning rule that has been found in slice work and had a huge impact on theoretical ideas about neuronal plasticity. STDP can be dissected into a “causal” part (postsynaptic activity comes after presynaptic activity) and an “a-causal” part (presynaptic after postsynaptic). The a-causal part of STDP makes a lot of sense in the framework of Moore et al. (2024) since the pre-synaptic activity could in this case be interpreted as a meaningful feedback signal for the neuron. These conceptual ideas that do not require a lot of math to understand them are – in my opinion – the main strength of the paper.

The proposed theoretical framework however also comes with limitations. It is based on a linear system; and I feel that the paper is too focused on mathematics and linear algebra, while the interesting aspects are rather conveyed in the non-mathematical part of the study. I found Figure 3 with a dissection of feedback and feedforward contributions in experimental data quite unclear and confusing. And the mathematical or algorithmic procedure how a neuron computes the ideal control signal given its objective function did not sound very biologically plausible to me (it included quite a lot complex linear algebra transformations).

Overall, I think it is a very interesting and inspiring paper. I highly recommend reading the Discussion. This discussion includes a nice sentence that summarizes this framework and distinguishes it from other frameworks like predictive coding: “[In this framework,] the controller neuron does not just predict the future input but aims to influence it through its output”. Check it out!

A Learning Algorithm beyond Backpropagation

This study by Song et al. (2024) includes several bold claims in the title and abstract. The promise is to provide a learning algorithm that is “more efficient and effective” than backpropagation. Backpropagation is the foundation of almost all “AI” systems, so this would be no small feat.

The main idea of the algorithm is to clamp the activity of input and output neurons with the teaching signals and wait until the activity of all layers in the middle converge (in a “relaxation” process), and then fix this configuration by weight changes. This is quite different conceptually from backpropagation, where the activity of output neurons is not clamped but compared to target activities, and differences are mathematically propagated back to middle layer neurons. Song et al. (2024) describe this relaxation process in their algorithm, which they term “prospective configuration” learning, as akin to relaxation of masses connected via springs. They also highlight a conceptual and mathematical relation to “energy-based networks” such as Hopfield networks (Hopfield, 1982). This is an aspect that I found surprising because such networks are well-known and less efficient than standard deep learning; so why is the proposed method here better than traditional energy-based methods? I did not find a satisfying answer to this question.

One aspect that I found particularly compelling about prospective configuration was that weights are updated not independently from each other but all together simultaneously, as opposed to backpropagation. Intuitively, this sounds like a very compelling idea. Thinking of it, it is surprising that backpropagation works so well although errors for each neuron are updated independently from each other. But as a consequence, learning rates need to be incremental to prevent a scenario where weight changes in input layers make the simultaneously applied weight changes in deeper layers meaningless, which is a limitation of backpropagation. It seems that prospective configuration does not have this limitation.

Is this algorithm biologically plausible? The authors seem to suggest this between the lines, but I found it hard to judge. The authors do not match the bits and pieces of their algorithm to biological entities, so I found it not easy to judge the potential correspondences. Given the physical analogies (“relaxation”, “springs”), I would expect that weights in these energy-based networks are symmetric (which is not biologically realistic). The energy function (Equation 6) seems to be almost symmetric, and I find it hard to imagine this algorithm to work properly without symmetric weights. The authors discuss this issue briefly in the Discussion, but I would have loved to hear the opinion of experts on this topic. One big disadvantage of the journal Nature Neuroscience is that it does not provide open reviews. Apparently, the paper was reviewed by Friedeman Zenke, Karl Friston, Walter Senn and Joel Zylberberg, all of whom are highly reputed theoreticians. It would have added a lot to read the opinions of these reviewers from relatively diverse backgrounds.

Putting these considerations aside, do these prospective configuration networks really deliver what they promise? It’s hard to say. In every single figure of this extensive paper, prospective configuration seems to outcompete standard deep learning in basically all aspects – catastrophic forgetting, faster target alignment, et cetera. In the end, however, the algorithm seems to be computationally too demanding to be an efficient competitor for backpropagation as of now (see last part of Discussion). The potential solutions to circumvent this difficulty do not sound too convincing at this stage yet. I would have been really glad to read a second opinion on these points that are rather difficult to judge just from reading the paper. Again, it would have been very helpful to have open reviews.

Overall, I found the paper interesting and worth the read. Without second opinions, I found it however difficult to properly judge novelty (in comparison to related algorithms such as “target propagation” mentioned briefly, by Bengio (2014)) and potential impact relative to standard deep learning (possibility to speed up the algorithm; ability to generalize). Let me know if you have an opinion on this paper!

Continuous vs. Discrete Representations in a Recurrent Network                                           

In this study, Meissner-Bernard et al. (2024) investigate a specific biological circuit that has been thought of as a good model for attractor networks, the zebrafish homologue of the olfactory cortex. The concept of discrete attractors mediated by recurrent connections has been highly influential for more than 40 years (Hopfield, 1982) and has been early-on thought of as a good model for circuits like the olfactory cortex that exhibit strong recurrent connections (Hasselmo and Barkai, 1995). Here, Meissner-Bernard et al. (2024) investigate how such a recurrent network model is affected by the implementation of precise synaptic balance. What is precise balance?

Individual neurons receive both excitatory and inhibitory synaptic inputs. In a precisely balanced network, these inputs of opposite influence are balanced for each neuron and also precisely in time. To some surprise, Meissner-Bernard et al. (2024) find that a recurrent network that implements such a precise balance does not exhibit discrete attractor dynamics but locally constrained dynamics that result in continuous rather than discrete sensory representations. The authors include a nice control by showing that the same network without this precise balance and a globally tuned inhibition instead does indeed exhibit discrete attractor dynamics.

One interesting feature of this study is that the model is constrained by a lot of detailed results from neurophysiological experiments. For example, the experimental results of my PhD work on precise synaptic balance – (Rupprecht and Friedrich, 2018) – have been one of the main starting points for this modeling approach. Not only this but also other experimental evidence specific used to constrain the model had been acquired in the same lab where also the theoretical study by Meissner-Bernard et al. (2024) was conducted. Moreover, the authors suggest in the outlook section of the Discussion to use EM-based connectomics to dissect the neuronal ensembles in this balanced recurrent circuit. The lab of Rainer Friedrich is working on EM-connectomics with synaptic resolution for longer than a decade (Wanner and Friedrich, 2020). It is interesting to see this line of research that spans not only several decades of work with various techniques such as calcium imaging (Frank et al., 2019), whole-cell patch clamp (Blumhagen et al., 2011; Rupprecht and Friedrich, 2018) and EM-based connectomics, but also attempts to connect all perspectives using modeling approaches.

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References

Bengio, Y., 2014. How Auto-Encoders Could Provide Credit Assignment in Deep Networks via Target Propagation. https://doi.org/10.48550/arXiv.1407.7906

Blumhagen, F., Zhu, P., Shum, J., Schärer, Y.-P.Z., Yaksi, E., Deisseroth, K., Friedrich, R.W., 2011. Neuronal filtering of multiplexed odour representations. Nature 479, 493–498. https://doi.org/10.1038/nature10633

Frank, T., Mönig, N.R., Satou, C., Higashijima, S., Friedrich, R.W., 2019. Associative conditioning remaps odor representations and modifies inhibition in a higher olfactory brain area. Nat. Neurosci. 22, 1844–1856. https://doi.org/10.1038/s41593-019-0495-z

Hasselmo, M.E., Barkai, E., 1995. Cholinergic modulation of activity-dependent synaptic plasticity in the piriform cortex and associative memory function in a network biophysical simulation. J. Neurosci. 15, 6592–6604. https://doi.org/10.1523/JNEUROSCI.15-10-06592.1995

Hopfield, J.J., 1982. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. 79, 2554–2558. https://doi.org/10.1073/pnas.79.8.2554

Meissner-Bernard, C., Zenke, F., Friedrich, R.W., 2024. Geometry and dynamics of representations in a precisely balanced memory network related to olfactory cortex. https://doi.org/10.1101/2023.12.12.571272

Moore, J., Genkin, A., Tournoy, M., Pughe-Sanford, J., Steveninck, R.R. de R. van, Chklovskii, D.B., 2024. The Neuron as a Direct Data-Driven Controller. https://doi.org/10.1101/2024.01.02.573843

Rupprecht, P., Friedrich, R.W., 2018. Precise Synaptic Balance in the Zebrafish Homolog of Olfactory Cortex. Neuron 100, 669-683.e5. https://doi.org/10.1016/j.neuron.2018.09.013

Song, Y., Millidge, B., Salvatori, T., Lukasiewicz, T., Xu, Z., Bogacz, R., 2024. Inferring neural activity before plasticity as a foundation for learning beyond backpropagation. Nat. Neurosci. 27, 348–358. https://doi.org/10.1038/s41593-023-01514-1

Wanner, A.A., Friedrich, R.W., 2020. Whitening of odor representations by the wiring diagram of the olfactory bulb. Nat. Neurosci. 23, 433–442. https://doi.org/10.1038/s41593-019-0576-z