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Jens-Bastian Eppler @j-b-eppler.bsky.social · 29/07/2026

Figure 6: does this matter for real networks? In deep neural networks, continued training produces representational drift with the same underlying geometry-preservation. So, a simple theoretical idea connects experiments, random networks, recurrent circuits and modern deep learning. 7/8 🧠🧪

Fig 6. A scientific figure. We show that also deep neural networks (DNN) preserve input topology. Toroidal inputs result in toroidal outputs. And we also quantify this through layers of the DNN.

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Jens-Bastian Eppler @j-b-eppler.bsky.social · 29/07/2026

Figures 4 & 5: how general is this? The phenomenon isn't specific to random rewiring in feedforward networks. We find the same behaviour with Hebbian plasticity, and it extends to recurrent networks. Preserving manifolds during drift is a surprisingly generic property of network dynamics. 6/8 🧠🧪

Fig 4. A scientific figure. If we use Hebbian plasticity instead of random changes, still response vectors change, but response angles don't.

Fig 5. A scientific figure. If we use a recurrent network instead of a feedforward one, still response vectors change, but response angles don't.

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Jens-Bastian Eppler @j-b-eppler.bsky.social · 29/07/2026

Figure 3: now let the network drift. We randomly rewire a fraction of synapses between sessions. The result looks strikingly like experimental representational drift: individual neurons change their tuning over time. At first glance, it looks as if the representation is falling apart... 4/8 🧠🧪

Fig 3. A scientific figure. We reproduce experimental data from Fig 1. And show that responses change substantially, whereas response similarities don't.

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Jens-Bastian Eppler @j-b-eppler.bsky.social · 29/07/2026

Figure 2: random networks preserve geometry. Before thinking about drift, we asked a simpler question: If similar stimuli enter a random network, are their outputs still similar? Well, yes. In fact, we show that output similarity is a simple monotonic function of input similarity. 3/8 🧠🧪

Fig 2. A scientific figure. Random networks preserve input similarities in their outputs. This is exemplified for linearly dependent inputs and inputs on a torus. And one plot showing the monotonic input-output relationship.

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Jens-Bastian Eppler @j-b-eppler.bsky.social · 29/07/2026

Figure 1: the puzzle. During representational drift, individual neurons change their tuning over days, yet the representational geometry is maintained. The figure illustrates exactly that. So... how can both be true? 2/8 🧠🧪

Fig 1. A scientific figure showing drift in experimental data. Activities change, but similarities are maintained. This is exemplified by a rotating manifold (torus).

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Jens-Bastian Eppler @j-b-eppler.bsky.social · 13/02/2026

Fig. 6: Modeling the mechanism Finally, the model! So, we see Hebbian structure in the data. But is a Hebbian mechanism enough to explain the observed drift? No. 🧠🧪 8/9

A scientific figure, showing that we can reproduce the described predictive effect of signal on noise correlations. But only via a combination of Hebbian plasticity and a stochastic process.

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Jens-Bastian Eppler @j-b-eppler.bsky.social · 13/02/2026

Fig. 5: Fear conditioning decreases Hebbian signature During fear conditioning, the signal correlation → noise correlation relationship is dampened. The Hebbian plasticity is weakened. During learning! Why might that be? 🧠🧪 6/9

A scientific figure, showing how during fear conditioning the stabilizing effect of signal correlation on noise correlation is diminished.

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Jens-Bastian Eppler @j-b-eppler.bsky.social · 13/02/2026

Fig. 4: Signal correlation stabilizes noise correlation Not only do signal correlations predict future noise correlation, they also predict noise correlation stability between t and t+1. Stronger signal correlation → more stable noise correlation. 🧠🧪 5/9

A scientific figure, showing how noise correlation stability between consecutive imaging time points is growing with noise correlation on the first imaging time point. Vice versa there is no such effect.

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Jens-Bastian Eppler @j-b-eppler.bsky.social · 13/02/2026

Fig. 3: Hebbian plasticity during drift Here’s the first big result: 👉 Signal correlations at time t predict noise correlations at time t+1. If two neurons co-activate now, their future functional coupling rises. This is the classic: “Fire together → wire together.” 🧠🧪 4/9

A scientific figure, showing that signal correlations at a given time point are predictive of noise correlations at a later time point (2 days apart). Vice versa this effect is very small.

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Jens-Bastian Eppler @j-b-eppler.bsky.social · 13/02/2026

Fig. 2: A volatile steady state Both signal and noise correlations appear to be in a stable distribution across days… BUT on the level of individual pairs, both are highly volatile. So at the population level it looks stable, yet at the pairwise level it’s highly dynamic. 🧠🧪 3/9

A scientific figure, showing stable distributions of signal and noise correlations, but volatility of individual signal and noise correlations between imaging days1 and 3.

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Jens-Bastian Eppler @j-b-eppler.bsky.social · 13/02/2026

Fig. 1: Defining SC and NC - Signal correlations (SC): co-active cells - Noise correlations (NC): functional connectivity For the SC/NC aficionados: We compute SC from the median response and estimate both SC and NC via bootstrapping. 👉 At a single time point, SC and NC are uncorrelated. 🧠🧪 2/9

A scientific figure, describing how we computed signal and noise correlations.

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