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The Computational Value of Sensory-Aligned Receptive Fields Depends on Neuronal Expressivity
Agnese Adorante, Aaron Spieler, Anna Levina
TL;DR
The paper asks whether receptive-field structure offers a computational advantage beyond resource efficiency and whether that value changes with neuronal expressivity. It tests task-aligned input structure in recurrent ELM networks across auditory and event-based visual classification. Task alignment improves generalization, but the advantage shrinks with neuronal expressivity, and generic sparsity only partly recovers it.
Problem
It remains unclear whether receptive-field structure offers computational value beyond resource constraints and how that value depends on neuronal complexity.
Source: §1 · p. 2Method
The authors compare sensory-coordinate-aligned and random feed-forward inputs in recurrent ELM networks while varying neuronal expressivity.
Source: §1 · p. 2Results
Task-aligned receptive fields improve generalization, but their advantage disappears with scrambled or task-irrelevant coordinates, decreases with neuronal expressivity, and is only partly recovered by sparsity regularization.
Source: §1 · p. 2, §4.2 · p. 6, §5 · pp. 8–9Takeaways & Limitations
Receptive-field structure can provide a computational prior beyond sparsity, with its value depending on neuronal expressivity.
Source: §1 · p. 2, §5 · p. 9The study tests only a small set of sensory geometries and tasks within one neuronal model family, and its imposed feed-forward structure does not identify biological mechanisms.
Source: §5 · p. 9
Abstract
from arXiv · showhide
Biological sensory neurons have selective receptive fields organized along meaningful stimulus coordinates, such as frequency, motion direction, or retinotopic position. Such structure may arise from efficient coding and biological constraints on activity, connectivity, and wiring, as computational studies of simple neurons have shown across modalities. This raises a question: do structured receptive fields confer a computational advantage beyond resource efficiency itself, and does this advantage persist when individual neurons are highly expressive? We address this question in recurrent networks of Expressive Leaky Memory neurons, where we can independently vary neuronal complexity and the organization of feed-forward receptive fields. Across auditory and event-based visual classification tasks, receptive fields aligned with a task-relevant sensory coordinate improve test accuracy relative to budget-matched random receptive fields. This advantage disappears when sensory coordinates are scrambled, or when receptive fields follow task-irrelevant coordinates, showing that the benefit comes from alignment with task geometry rather than restricted connectivity alone. Increasing neuronal complexity reduces the performance advantage of structured receptive fields. Finally, generic synaptic sparsity regularization induces input selectivity and partially recovers performance, but remains substantially below explicitly structured receptive fields, suggesting that sparsity alone is insufficient to recover the full computational benefit of task-aligned receptive fields. Together, our results show that appropriate receptive fields can serve as a computational prior beyond sparsity itself, and that their value depends on the computational expressivity of individual neurons.
1. Introduction
Receptive fields reflect meaningful sensory structure, but their computational value beyond resource efficiency—and how that value changes with neuronal complexity—remains an open question. The paper tests task-aligned input structure in recurrent ELM networks and finds that its benefit depends on task geometry and neuronal expressivity.
1. Introduction
- Receptive fields describe the sensory regions or features over which stimuli modulate a neuron’s response, including frequency ranges, visual-space regions, and motion direction.Examples include auditory frequency selectivity and visual selectivity.Source: §1 · p. 1
- The open question is whether receptive-field structure provides computational advantage beyond the resource constraints that can produce it.Prior efficient-coding and biological-constraint accounts explain how structure may emerge, but leave its separate functional value unresolved.Source: §1 · p. 2
- It is unclear how receptive-field value changes with neuronal complexity, since biological neurons can compute across timescales and computation can be distributed between neurons and networks.The paper varies neuronal complexity independently of feed-forward connectivity.Source: §1 · p. 2
- Convolutional networks combine local receptive fields with weight sharing and translation equivariance, leaving unclear how much sensory geometry alone benefits expressive units.The paper asks how computation should be divided between input structure and the capacity of individual neurons.Source: §1 · p. 2
- Task-aligned receptive fields improve generalization, but their advantage disappears with scrambled or task-irrelevant sensory coordinates and shrinks as neurons become more expressive.The study compares frequency, motion-direction, and retinotopic structure against matched random inputs.Source: §1 · p. 2
2. Related Work
Prior work treats receptive-field structure both as an outcome of resource constraints and as an architectural inductive bias. This paper instead tests whether its value depends on the expressivity of individual units and whether emergent selectivity can replace designed receptive fields.
In neuroscience: Resource constraints shape receptive fields
- Resource constraints can produce receptive fields: retinal information optimization recovers ganglion-cell-like fields, while downstream depth changes whether filters are general-purpose or task-specialized.Related effects are also reported for color processing.Source: §2 · p. 3
Related-work distinction
- This study varies individual-unit expressivity to test how it changes the value of structured input connectivity, rather than varying bandwidth or network depth.The question is motivated by evidence that single neurons can implement substantial computation (Spieler et al., 2026).Source: §2 · p. 3
In machine learning: locality as an inductive bias
- Architectural priors can reduce data needs, while weaker locality priors can perform comparably with sufficient capacity and data; prior studies vary network- or training-level capacity, not individual-unit capacity.The cited comparisons include local versus convolutional networks and vision transformers (Lahoti et al., 2024; Dosovitskiy et al., 2021; d’Ascoli et al., 2021).Source: §2 · p. 3
Selectivity can emerge without prescribed structure
- Selectivity can emerge under generic sparsity, nonnegativity, energy-efficiency, wiring-cost, or smoothness constraints, but prior studies do not test whether it replaces deliberately designed receptive fields.The paper directly makes that comparison.Source: §2 · p. 3
3. Methods
The methods vary sensory-coordinate input organization and ELM neuronal complexity while matching synaptic budgets across structured and random conditions. Experiments span auditory and event-based visual tasks, with repeated-seed evaluation and a separate sparsity-regularization condition.
3.1. Datasets and Sensory Coordinates
- Three classification datasets use task-relevant coordinates: frequency for SHD, motion direction for DVS-Gesture, and retinotopic axes for CIFAR10-DVS.DVS-Gesture motion channels are derived with a direction-selective correlator; event-camera data are accumulated into binarized frames.Source: §3.1 · p. 4
3.2. The Expressive Leaky Memory Network
- ELM neurons maintain M memory units with fixed decay timescales, and an MLP updates their states and output; increasing M raises single-neuron expressivity, while increasing N widens the network.The experiments vary M at fixed N and N at fixed M.Source: §3.2 · p. 4
3.3. Experimental Conditions
- Structured units sample restricted sensory-coordinate regions, while random units sample across the full input array; the figure depicts both wirings and their shared random recurrent connections.Conditions are parameter-count matched, and only feed-forward wiring differs; full input is an additional SHD-only condition.Source: §3.3 · pp. 4–5, Figure 1 · p. 5
3.4. Statistical Analysis
- Each condition uses 10 independently initialized seeds, and test accuracy is compared with two-sided Welch’s t-tests and Benjamini–Hochberg correction.The analysis unit is a trained network, with n = 10 per condition.Source: §3.4 · p. 5
3.5. Sparsity Regularization
- A subset of full-input experiments applies a gradually introduced ℓ1 penalty to feed-forward weights while leaving recurrent weights and other hyperparameters unchanged.The penalty reaches its maximum halfway through training.Source: §3.5 · p. 5
4. Results
Across auditory and event-based visual tasks, sensory-aligned structured input improves accuracy over random wiring, but its advantage shrinks as neuronal complexity rises. The benefit depends on alignment with task geometry, while generic sparsity regularization recovers only part of it.
4.1. Structured input improves performance but becomes less beneficial for expressive neurons.
- Structured input improves test accuracy across tested network sizes, but its advantage shrinks with more memory units, disappearing on SHD and remaining smaller on DVS-Gesture.The comparison uses structured and random wiring across network sizes and neuronal complexities.Source: Figure 2 · p. 6, §4.1 · p. 6
4.2. Structured input helps only when aligned with task geometry.
- Motion-aligned input benefits DVS-Gesture but not CIFAR10-DVS, while spatial structure shows the reverse; scrambling sensory coordinates removes the advantage on SHD and DVS-Gesture.The task-relevant coordinate differs: motion direction for DVS-Gesture and spatial structure for CIFAR10-DVS.Source: §4.2 · pp. 6–7, Figure 3 · p. 7
4.3. Sparsity regularization partially recovers performance in full input networks.
- Full-input networks have lower test accuracy and a larger train–test gap than structured-input networks; ℓ1 regularization improves both but does not close the performance gap.The full-input comparison is on SHD; full input supplies substantially more feed-forward connections.Source: §4.3 · pp. 7–8, Figure 4 · p. 8
4.4. Sparsity regularization promotes input selectivity
- ℓ1 regularization drives many input weights to zero and creates neuron-specific restricted frequency bands, but these fields remain broad and overlapping rather than recovering the explicit organization.The emerging fields concentrate where SHD has substantial input activity and are largely absent where it has few spikes.Source: §4.4 · p. 8
5. Discussion
Task-aligned receptive fields improve generalization, but their advantage shrinks as neurons become more expressive. Generic sparsity induces input selectivity but does not fully recover the benefit, and the imposed structure does not identify biological mechanisms.
5. Discussion
- Increasing neuronal complexity reduces the advantage of structured input, with convergence on SHD and a smaller gap on DVS-Gesture.The benefit of this bias depends on neuronal expressivity.Source: §5 · pp. 8–9
- ℓ1 regularization induces coarse frequency-selective input fields but does not fully recover the benefit of explicitly structured receptive fields.Most weights are driven to zero, but the remaining inputs do not recover the explicit organization.Source: §5 · p. 9, Figure 5 · p. 9
- The imposed feed-forward structure is an abstraction of functional receptive fields and does not identify their biological mechanisms.Source: §5 · p. 9
- The study covers only a small set of sensory geometries and tasks, with neuronal expressivity varied within one model family.Testing other geometric priors and architectures is needed to determine how general the trade-off is.Source: §5 · p. 9
Appendix A. Datasets, Preprocessing, and Network Configuration
SHD uses spike-encoded spoken digits converted through an inner-ear model into 700 frequency-ordered channels and 500 time steps; all wiring conditions share the same train-validation split.
Appendix A. Datasets, Preprocessing, and Network Configuration
- SHD recordings are converted to 700 cochlear-frequency-ordered binary channels over 500 time steps, with a shared fixed-seed validation split and an official test set holding out two speakers.The official train and test files contain 8156 and 2264 recordings; no augmentation is applied.Source: §A.1 · p. 13
A.2. Event-Camera Datasets: DVS-Gesture and CIFAR10-DVS
Event-camera streams are converted into fixed-size frame tensors by integrating events over time or event-count intervals. DVS-Gesture uses time-based frames, while CIFAR10-DVS uses event-count frames because its recording path makes event count more stable.
A.2. Event-Camera Datasets: DVS-Gesture and CIFAR10-DVS
- Event streams are variable-length event lists that must be converted to fixed-size tensors; integration produces frames of event counts for each pixel and polarity.Time-based splitting preserves temporal scale, whereas event-count splitting equalizes evidence per frame and adapts to varying event rates.Source: §A.2 · p. 13
- DVS-Gesture uses 100 time-split frames on a 64 × 64 grid, with a standard subject-wise split and training-only random spatial translation.The dataset contains recordings of 29 subjects performing 11 gestures under three lighting conditions.Source: §A.2 · pp. 13–14
- CIFAR10-DVS uses 20 event-count-split frames because its repeating stimulus path makes event count more stable, and its class-relevant structure is spatial.Its 8:1:1 train-validation-test partition uses a fixed random seed; the study focuses on relative performance and compares each structured condition only with its own budget-matched random control.Source: §A.2 · p. 14
A.3. Motion Preprocessing: The Direction-Selective Correlator
The appendix describes direction-selective motion preprocessing, the ELM network, feed-forward wiring conditions, and regularization used in the experiments.
A.3. Motion Preprocessing: The Direction-Selective Correlator
- A correlator compares activity at a pixel with recent activity from opposite neighbors, then rectifies the opponent difference to select motion direction.Preferred-direction motion makes the difference positive; null-direction motion makes it negative and is set to zero.Source: §A.3 · p. 15
A.4. The Expressive Leaky Memory Network
- The ELM network concatenates current input with prior layer activity, and each independently parameterized unit reads a fixed subset of channels.The input subset is varied while synapse budget and recurrent-connection fraction are held fixed across wiring conditions.Source: §A.4 · pp. 15–16
A.5. Wiring Conditions
- Wiring conditions vary feed-forward source assignment; structured options organize inputs by frequency, motion direction, or spatial position, while scrambling removes sensory-coordinate correspondence.Random input samples sensory or recurrent sources independently; structured conditions use frequency windows, direction channels, or spatial patches, and the scrambled control preserves source counts and overlap.Source: §A.5 · pp. 16–17
A.6. Regularization
- All networks use neuron-weight and activity regularizers; a feed-forward weight penalty is added only in selected full-input experiments.The feed-forward penalty is introduced gradually and reaches its maximum halfway through training.Source: §A.6 · p. 17
A.7. Training and Optimization Settings
Training uses the full input sequence and predicts from final-timestep logits; the network-size and memory sweeps use different stopping protocols.
A.7. Training and Optimization Settings
- Each dataset is processed as a full sequence, with class prediction from final-timestep logits using cross-entropy loss.Optimization settings are identical across wiring conditions and, except for epoch count, across datasets.Source: §A.7 · p. 18, Table 3 · p. 18
- The size sweep uses validation-based early stopping, whereas the memory sweep runs for the full epoch budget to isolate memory capacity from training duration.Early stopping occurs after 20 epochs without a validation-accuracy improvement of at least 0.01.Source: §A.7 · p. 18
Appendix B. Statistical Analysis of the results
The appendix reports Welch tests on independent network accuracies and applies Benjamini–Hochberg correction across the reported comparisons.
Appendix B. Statistical Analysis of the results
- Each comparison uses test accuracies from two independent sets of 10 networks and a two-sided Welch’s t-test.The reported difference is in test-accuracy points, signed to favor the first-named condition.Source: Appendix B · p. 18
- Significance requires q < 0.05 after Benjamini–Hochberg correction across 39 reported tests; correction across 36 unique comparisons yields the same 25 significant results.Correction within each of six predefined subsets also yields the same significant comparisons.Source: Appendix B · p. 18, Table 4 · p. 19
Appendix C. Recurrent Wiring Experiments
The appendix tests whether structuring recurrent connections adds to the feed-forward receptive-field organization. It reports no consistent performance improvement over uniform recurrence across datasets and network sizes.
Appendix C. Recurrent Wiring Experiments
- The recurrent samplers leave feed-forward connections and total synapse count unchanged, replacing only the distribution of recurrent sources.The alternatives are strict modular, flexible modular, and small-world recurrence.Source: Appendix C · p. 20
- Structured recurrent connectivity shows no consistent performance improvement relative to uniform recurrence across datasets and network sizes.The imposed recurrent patterns add a constraint without a wiring-cost objective or spatial embedding to make that constraint beneficial.Source: Appendix C · p. 20
- The authors attribute the main benefit to aligning feed-forward inputs with task sensory geometry, which supplies inputs that expressive units can otherwise compensate for lacking.The claim concerns sensory inputs to units, not the arrangement of units relative to one another.Source: Appendix C · pp. 20–21