A Network of Biologically Inspired Rectified Spectral Units (ReSUs) Learns Hierarchical Features Without Error Backpropagation

Abstract: We introduce a biologically inspired, multilayer neural architecture composed of Rectified Spectral Units (ReSUs). Each ReSU projects a recent window of its input history onto a canonical direction obtained via canonical correlation analysis (CCA) of previously observed past-future input pairs, and then rectifies either its positive or negative component. By encoding canonical directions in synaptic weights and temporal filters, ReSUs implement a local, self-supervised algorithm for progressively constructing increasingly complex features. To evaluate both computational power and biological fidelity, we trained a two-layer ReSU network in a self-supervised regime on translating natural scenes. First-layer units, each driven by a single pixel, developed temporal filters resembling those of Drosophila post-photoreceptor neurons (L1/L2 and L3), including their empirically observed adaptation to signal-to-noise ratio (SNR). Second-layer units, which pooled spatially over the first layer, became direction-selective -- analogous to T4 motion-detecting cells -- with learned synaptic weight patterns approximating those derived from connectomic reconstructions. Together, these results suggest that ReSUs offer (i) a principled framework for modeling sensory circuits and (ii) a biologically grounded, backpropagation-free paradigm for constructing deep self-supervised neural networks.

• The paper introduces a biologically inspired network using ReSUs that learns hierarchical features via local past-future CCA, omitting error backpropagation.
• The methodology leverages dynamic rectification and predictive coding to emulate sensory circuits, matching neuronal dynamics observed in Drosophila.
• Results demonstrate ReSUs achieve adaptive temporal filtering and direction selectivity, with synaptic patterns aligned with experimental connectomics.

Rectified Spectral Units: Biologically-Inspired Hierarchical Feature Learning without Backpropagation

Introduction

The challenge of bridging the gap between artificial and biological intelligence remains central to neuroscience and AI. Predominant deep learning systems rely on static ReLU units trained by nonlocal error backpropagation, diverging markedly from known biological mechanisms. This paper introduces Rectified Spectral Units (ReSUs), a dynamic, biologically inspired neuron model: each ReSU projects recent temporal input windows onto canonical directions obtained from past–future canonical correlation analysis (CCA), then applies rectification. Consequently, ReSUs implement a local and self-supervised framework for hierarchical feature extraction, emulating essential aspects of biological sensory circuits and learning without error backpropagation.

Figure 1: Drosophila-inspired two-layer ReSU architecture mirroring the ON motion pathway, with photoreceptors (PR), temporally filtering first-layer (L1/L3), and direction-selective second-layer (T4) analogs.

Framework: CCA-Based Predictive Coding and ReSU Dynamics

ReSU networks formalize the hypothesis that sensory circuits function as predictive encoders, extracting low-dimensional latent variables $\mathbf{z}_t$ from input history $\mathbf{p}_t$ that maximize mutual information with the future $\mathbf{f}_t$. For linear-Gaussian processes (e.g., the Ornstein–Uhlenbeck process), this reduces to a past–future CCA, where canonical projections preserve the most predictable aspects of sensory signals. The resulting singular vectors and values directly yield temporal filters and quantification of information transmission.

Figure 2: CCA as a computational primitive—past/future lag vectors (A), CCA on OU, non-OU, and natural image sequences (B–D) with associated canonical correlations (second column) and canonical directions (third column).

The architecture generalizes to other stationary Gaussian processes with translation-invariant kernels, retaining optimality for a broad class of stimulus statistics. Filter structure—including adaptation to signal-to-noise ratio (SNR)—emerges directly from maximizing predictive information, paralleling empirical findings in sensory neurons. As SNR declines, filters transition from multi-lobed to monotonic shapes.

Figure 3: SNR dependence in CCA: responses to noise (A), correlation/mutual information decay (B), shape transition of canonical filters with SNR (C), and adaptation in biological retinal ganglion cells (D).

From Temporal Filtering to Hierarchical Feature Construction

First-layer ReSU units, driven by single-pixel inputs, reproduce the temporal filter diversity and adaptation properties of Drosophila L1/L2 (differentiator-like, ON-selective) and L3 (integrator-like, luminance coding) post-photoreceptor neurons. The nonlinear rectification (positive/negative) is not merely an artifact but computationally essential—permitting selective encoding of change and supporting switching-system representations of more complex dynamics.

Second-layer ReSUs pool spatially over adjacent first-layer outputs (L1/L3 analogs from neighboring pixels) and learn via past–future CCA on this expanded channel set. These units develop robust direction selectivity—the hallmark of T4 motion cells in Drosophila—revealed by strong, polarity-dependent responses to moving ON edges and by the emergent structure of synaptic weights.

Figure 4: Comparison of experimentally observed and model-learned ON motion detection circuits (A), direction-selective T4-like responses to stimuli (B), spatially weighted first-layer contributions (C), and correspondence of learned/model synaptic weights with connectomic data (D).

Critically, the pattern and sign of learned synapses approximates connectomic reconstructions, capturing both the functional connectivity and spatial logic underlying insect motion detection.

Biophysical and Algorithmic Implications

By fusing CCA-based predictive coding with physiologically grounded rectification, ReSU networks yield several key outcomes:

• Biological Fidelity: Spatiotemporal filters in the model closely match measured neuronal dynamics, including adaptive responses to contrast and noise.
• Canonical Self-Supervision: Learning is fully local and directly leverages the statistical structure of unlabelled natural stimuli, eschewing propagating errors or reliance on annotated ground truth.
• Stackability: ReSU composition supports the emergence of increasingly complex, hierarchical features, as shown in both two-layer and extended three-layer versions capturing motion selectivity at multiple scales.
• Interpretability and Parsimony: Learned weights and activations remain tightly aligned with biological circuits, enabling direct mechanistic explanations often missing in deep, nonlocal models.

Numerical evaluations highlight the ability of two-layer ReSU networks to recapitulate motion direction selectivity and achieve temporal filter shapes that dynamically adapt to changes in input SNR, in agreement with experimental measurements for multiple neuron classes. The synaptic weight patterns in higher layers correspond to direction-selective circuits as reconstructed by electron microscopy.

Relations to Prior Art

The study delineates ReSUs from comparator frameworks:

• Unsupervised Hebbian/Anti-Hebbian and SFA: While these can extract low-rank representations and sparse codes, their static or overdemanding nonlinear extensions have difficulty producing hierarchical, composable features comparable to cortex.
• Predictive Coding: Though powerful for modeling hierarchical inference, predictive coding architectures encode error signals rather than features per se; their temporal dynamics further diverge from biological early sensory circuits.
• Backpropagation-Based Deep Networks and Feedback Alignment: These achieve hierarchical representations, but at the cost of unwieldy labeled datasets, brittle generalization, and biologically implausible credit assignment.

ReSUs, by contrast, instantiate both the predictive principle and local, mechanistically plausible learning, leveraging only synaptic covariances observed through experience.

Limitations and Future Directions

While the ReSU model exhibits strong alignment with Drosophila, several critical questions remain. The memory and prediction horizons are currently set a priori; auto-tuning these based on input statistics remains to be developed. Theoretical generalization to more complex, recurrent, or nonstationary stimuli—such as those involving top-down feedback or rich motor interactions—represents a further extension. Additionally, experimental validation with higher temporal resolution or via targeted perturbations (e.g., cell ablation, optogenetics) could further substantiate the mechanistic predictions of the framework.

Future extensions include integrating robust local learning rules for past–future CCA, stacking ReSU networks for deeper hierarchical modeling, and transplantation into mammalian-like or engineered sensory domains. There is also a clear pathway toward modeling the role of feedback in sensory prediction, either via recurrent ReSU architectures or integration with biologically grounded controller models.

Conclusion

ReSU networks represent a biologically grounded synthesis of predictive coding and hierarchical feature learning. By leveraging local past–future CCA projections with rectified outputs, ReSUs unify data-driven, self-supervised abstraction with the structural and adaptive logic of real sensory circuits. This self-supervised, stackable architecture stands as a compelling alternative to contemporary backpropagation-based models—both as a plausible explanatory framework for neural computation and as a blueprint for future deep artificial networks aimed at closing the gap with biological intelligence.

(2512.23146)