Context dependent adaptation in a neural computation (2509.01760v1)

Abstract: Brains adapt to the statistical structure of their input. In the visual system, local light intensities change rapidly, the variance of the intensity changes more slowly, and the dynamic range of contrast itself changes more slowly still. We use a motion-sensitive neuron in the fly visual system to probe this hierarchy of adaptation phenomena, delivering naturalistic stimuli that have been simplified to have a clear separation of time scales. We show that the neural response to visual motion depends on contrast, and this dependence itself varies with context. Using the spike-triggered average velocity trajectory as a response measure, we find that context dependence is confined to a low-dimensional space, with a single dominant dimension. Across a wide range of conditions this adaptation serves to match the integration time to the mean interval between spikes, reducing redundancy.

• The paper demonstrates that adaptation in H1 neurons is context-dependent, modulating responses based on both instantaneous contrast and its statistical distribution.
• It employs synthetic natural stimuli and singular value decomposition to reveal that adaptation is confined to a low-dimensional subspace dominated by a principal mode.
• It finds that the neuron's integration time is tightly coupled to the mean interspike interval, optimizing the neural code by reducing redundancy.

Context-Dependent Adaptation in Neural Computation: Analysis of Contrast and Context in Fly Visual Motion Processing

Introduction

This paper investigates the mechanisms of context-dependent adaptation in the motion-sensitive neuron H1 of the fly visual system, focusing on how neural responses to visual motion are modulated by both instantaneous contrast and the statistical context defined by the distribution of contrast values. The study leverages naturalistic, temporally structured stimuli to dissect the hierarchy of adaptation phenomena, providing quantitative evidence that adaptation is confined to a low-dimensional subspace and is dominated by a single principal mode. The work extends the efficient coding hypothesis to neural computation, demonstrating that adaptation serves to match the integration time of the neuron to the mean interspike interval, thereby reducing redundancy in the neural code.

Experimental Design and Stimulus Construction

The authors designed stimuli that mimic the statistical structure of natural visual inputs while allowing precise control over contrast and its distribution. The stimulus is a two-dimensional intensity field $I(x, y, t)$, constructed by translating a synthetic natural scene $F(x, y)$ along a velocity trajectory $v(t)$, with contrast $c(t)$ modulated as a temporally correlated random process. The dynamic range of contrast, $c_{\rm lim}$, is varied across experimental blocks, establishing different contexts for adaptation.

The contrast is defined as the fractional root-mean-square variation in intensity, and the spatial pattern $F(x, y)$ is generated in Fourier space to ensure scale invariance and binary structure, facilitating control over contrast while maintaining fixed spatial correlations. The velocity input $v(t)$ is Gaussian white noise, ensuring independence between velocity and contrast.

Measurement and Analysis of Neural Responses

Neural responses are characterized by the spike-triggered average (STA) of velocity, ${\rm STA}(\tau)$, and its contrast-conditioned variant ${\rm STA}(\tau; C)$, which quantifies the average velocity trajectory preceding a spike for a given contrast bin. The STA is computed as an $M \times L$ matrix, where $M$ is the number of contrast bins and $L$ is the number of time points sampled.

The central analytical approach involves comparing STAs across different contrast distributions (contexts) to assess context dependence. If adaptation were solely dependent on instantaneous contrast, ${\rm STA}(\tau; C)$ would be invariant across contexts. However, the results demonstrate that the response to a given contrast value is modulated by the context, indicating adaptation at the distributional level.

Figure 1: Contrast-dependent spike-triggered averages, ${\rm STA}(\tau; C)$, illustrating the modulation of neural response by contrast.

Figure 2: Contrast-dependent spike-triggered averages across six values of $c_{\rm lim}$, showing context-dependent adaptation.

Figure 3: The ${\rm STA}(\tau; C = 0.25)$ contour for each context, demonstrating non-invariance of response at fixed contrast across contexts.

Low-Rank Structure of Adaptation

A key finding is that the space of contrast-conditional STAs is low-rank, with the majority of variance explained by a single dominant mode and a secondary component. Singular value decomposition (SVD) of the stacked STA matrices across all contexts reveals that only two singular values are significant, indicating that adaptation operates within a two-dimensional subspace of possible velocity trajectories.

Figure 4: Singular values $S_n$ versus rank $n$ for the stacked STA matrix, confirming the low-rank structure of adaptation.

Figure 5: Significant components of the SVD decomposition: (a) $V_1(\tau)$, (b) $V_2(\tau)$, (c) $U_1(C, c_{\rm lim})$, (d) $U_2(C, c_{\rm lim})$.

The first mode, $V_1(\tau)$, captures the basic profile of the STA, while $V_2(\tau)$ adjusts the peak and width. The corresponding left singular vectors $U_1(C, c_{\rm lim})$ and $U_2(C, c_{\rm lim})$ encode the dependence on contrast and context. Notably, $U_1$ is well-approximated by a function of $C / c_{\rm lim}$, indicating normalization to the dynamic range, while $U_2$ depends primarily on absolute contrast.

Figure 6: The contribution of the dominant mode $U_1(C, c_{\rm lim})$ as a function of scaled contrast, showing normalization to context.

Temporal Dynamics and Redundancy Reduction

The study further analyzes the temporal integration properties of H1 by fitting the STA to an exponential decay model, extracting the integration time $\tau_{\rm int}$. Across all combinations of contrast and context, the integration time is tightly coupled to the mean interspike interval, with $\bar{r} \tau_{\rm int} \approx 1$. This relationship suggests that the neuron adapts its integration window to maintain independence between successive spikes, thereby minimizing redundancy in the neural code.

Figure 7: Integration time $\tau_{\rm int}$ versus mean spike rate $\bar{r}$, demonstrating the balance between integration and spike rate.

Figure 8: Example of contrast-conditional STAs and their exponential fits, illustrating the extraction of integration time.

Implications and Theoretical Significance

The results provide quantitative evidence for context-dependent adaptation in neural computation, extending the efficient coding hypothesis beyond coding to inference. The low-rank structure of adaptation implies that the neural system leverages a compact representation to modulate its response, facilitating rapid and efficient adjustment to changing input statistics. The normalization of response to the dynamic range of contrast is consistent with optimal coding strategies, while the tight coupling between integration time and spike rate supports the notion of redundancy reduction.

These findings have broad implications for understanding sensory adaptation in biological systems. The demonstration of adaptation to both instantaneous and distributional properties of stimuli suggests that neural circuits are equipped to track and respond to environmental statistics over multiple time scales. The low-dimensionality of adaptation mechanisms may reflect a general principle of neural computation, enabling efficient and robust processing in the face of complex, variable inputs.

Future Directions

Further research could explore the molecular and circuit-level mechanisms underlying context-dependent adaptation, as well as its generality across sensory modalities and species. The extension of these principles to artificial neural systems may inform the design of adaptive algorithms for dynamic environments. Additionally, the interplay between adaptation and information transmission warrants deeper investigation, particularly in regimes where noise and ambiguity introduce additional computational constraints.

Conclusion

This study elucidates the mechanisms of context-dependent adaptation in the fly visual system, demonstrating that neural responses to motion are modulated by both contrast and its statistical context. Adaptation is confined to a low-dimensional subspace, dominated by normalization to the dynamic range of contrast, and serves to balance integration time with spike rate, minimizing redundancy. These results advance the understanding of efficient coding and adaptive computation in neural systems, with implications for both biological and artificial intelligence.