Single-Branch Neural Networks

• Single-branch neural networks are defined by a single shared processing stream that applies weight sharing across diverse inputs for efficient representation learning.
• They leverage mechanisms like temporal unfolding, gradient convergence analysis, and contrastive loss to ensure robust training and effective feature extraction.
• Empirical results show that these architectures offer competitive performance with fewer parameters, making them ideal for resource-constrained and multimodal applications.

Single-branch neural networks are neural architectures in which all inputs, possibly from diverse modalities, are processed through a single computational stream or set of shared network weights. This design paradigm is characterized by the use of weight sharing across different inputs or tasks, modal invariance enforced by training schemes, and a reduction in architectural modularity compared to traditional multi-branch models. Single-branch networks span from single neuron perceptrons and dendritic single-unit models to complex shared–encoder architectures for multimodal and collaborative filtering tasks, encompassing both biological inspiration and practical efficiency.

1. Architectural Principles and Taxonomy

Single-branch neural networks are defined by their use of one main feature extraction or processing pathway for all data, as opposed to architectures where each input modality or task is assigned a dedicated subnetwork. Major categories include:

• Single neuron or very sparse networks: Architectures utilizing a single hidden unit or a small population of parallel, independently trained minimal subnetworks for classification (Khalifa et al., 2019).
• Folded-in-time dynamic networks: Models where a single neuron is temporally unfolded via feedback delay loops to emulate deep architectures, as in the Fit-DNN approach (Stelzer et al., 2020).
• Single-branch multimodal encoders: Networks where embeddings from different modalities (e.g., image, text, audio, user/item features) are all projected through a shared set of weights, often for joint representation learning (Ganhör et al., 23 Sep 2025, Saeed et al., 2023, Moscati et al., 5 Aug 2025).
• Association and unified data-structure networks: Architectures leveraging tree-like or recursive structures, where heterogeneous data are mapped into common feature representations within a unified “neurotree” (Kim et al., 2021).

These designs share the following distinguishing architectural mechanisms:

• Weight sharing across inputs or tasks, enforcing an inductive bias toward modality-invariant or task-invariant representations.
• Unified embedding spaces in which disparate data types are brought into close proximity, enabling robust downstream prediction, retrieval, or classification.
• Reduced parameter count relative to multi-branch designs, conferring efficiency benefits in training, inference, and storage.

2. Theoretical Foundations and Convergence Properties

Theoretical studies of single-neuron–based networks and their trainability via gradient methods provide foundational guarantees relevant to broader single-branch systems. For a scalar-output neuron $y = \sigma(w^\top x + b)$ with activation $\sigma$, several key results hold (Yehudai et al., 2020):

• Gradient alignment: In the parameter regime where input distributions maintain sufficient density across all relevant projections and activations are monotonic with a lower-bounded derivative (e.g., ReLU, sigmoid), the gradient aligns with the error vector such that

$$\left\langle \nabla F(w),\, w - v \right\rangle \geq \frac{\alpha^4 \beta \gamma^2}{8\sqrt{2}\,\sin^3(\delta/4)}\|w - v\|^2$$

where $F(w)$ is the population risk, and $\alpha, \beta, \gamma, \delta$ are problem-dependent constants.

• Linear convergence: With appropriate initialization and step sizes, gradient methods (including stochastic variants) contract the distance to the target at an exponential or linear rate.
• Role of input distribution: Robust convergence relies on a “spread” condition—the lack of which (e.g., highly degenerate data) can lead to pathological non-convergence even in simple single-branch settings.

These principles extend, in modified form, to deeper or temporal single-branch systems when similar convexity-like properties and signal richness are preserved.

3. Sparse, Single-Neuron, and Minimalist Architectures for Recognition

Empirical studies show that, for a broad class of recognition tasks, single-neuron or extremely sparse networks can match or outperform dense deep networks under appropriate problem decompositions (Khalifa et al., 2019):

• Binary Classification: Single-neuron classifiers trained on synthetic Gaussian data or simple tasks can achieve accuracy similar to that of wider architectures (e.g., 69–73% vs. 10–100 neuron networks).
• Multi-Class Recognition via Decomposition: Decomposing recognition into multiple binary tasks (e.g., via one-vs-rest approaches) empowers a collection of single-neuron networks to reach or exceed the performance of single dense multi-class networks. For instance, on MNIST, a set of ten independent single-neuron binary classifiers yields 84.21% accuracy, outperforming a 16-neuron dense model.
• Redundancy Beyond Critical Network Size: Increasing hidden layer size beyond a threshold (e.g., 128 neurons in CNNs for MNIST, CIFAR-10) does not yield further accuracy gains, indicating redundancy inherent in dense configurations.

The operational advantages of this class include reduced risk of overfitting (due to a limited number of parameters), expeditious convergence, low memory consumption, and suitability for parallelization in resource-constrained settings.

4. Folded-in-Time and Dynamically Unfolded Single-Neuron Networks

The “Folded-in-Time Deep Neural Network” (Fit-DNN) architecture generalizes the single-branch concept via temporal multiplexing with time-delayed feedback (Stelzer et al., 2020):

• Temporal Unfolding: A single nonlinear node, with appropriately modulated multipath feedback (delay loops), generates a virtual deep network in the time domain. Each discrete time point encodes a virtual node in an unfolded multilayer perceptron.
• Connection Weight Encoding: The weights of the virtual layers and nodes are mapped onto modulation functions and delay intervals, with precise formulas controlling both inter-layer and intra-layer connections.
• Training via Modified Backpropagation: Weight adaptation requires a four-step backpropagation process that explicitly accounts for both standard delay-induced connections and additional local (“intra-layer”) couplings. Formulas for gradient updates must be adjusted to include exponential decay factors and readout timing.
• Task Generality and Hardware Implications: This architecture reproduces the behavior of standard dense networks in the “map limit” (large node separation) and maintains computational capacity in sparse/dense or slow/fast operation regimes. Fit-DNN is thus naturally suited for neuromorphic photonic or optoelectronic implementations, promising substantial hardware savings.

5. Unified and Multimodal Single-Branch Encoders

Single-branch networks for multimodal and hybrid recommendation tasks integrate diverse modalities or data sources through a common encoder pathway (Ganhör et al., 23 Sep 2025, Saeed et al., 2023, Moscati et al., 5 Aug 2025):

• Weight Sharing and Modality Sampling: A shared encoder (e.g., $g$) processes all available modalities, with modalities randomly sampled during training (modality dropout). This not only forces the network to develop representations that are robust to missing or incomplete modalities but also narrows the modality gap, ensuring that embeddings from different sources for the same item coalesce in the latent space.
• Contrastive Loss Integration: Addition of a symmetric InfoNCE contrastive loss aligns intra-item modality representations by maximizing their similarity while minimizing similarity to other items, thereby enhancing robustness to cold start and missing data.
• Performance and Embedding Proximity: Quantitative and qualitative analyses (e.g., t-SNE plots, cosine similarity) reveal that single-branch designs achieve close proximity for same-item modalities in the embedding space and outperform multi-branch baselines in cold or partial data settings.
• Beyond-Accuracy Metrics: Single-branch models can offer improved catalog coverage and lower popularity bias in recommendations, according to ARP, APLT, and other measures.

In recommendation and multimodal fusion, this architecture supports parameter efficiency, system simplicity, and superior robustness when side information is variable or incomplete.

6. Biological Inspiration and Computational Power of Single-Branch Systems

Analyses inspired by biological neural systems demonstrate that the computational capacity of a single neuron, augmented with nonlinear dendritic branches, substantially exceeds that of the standard linear–nonlinear unit in artificial neural networks (Jones et al., 2020):

• Dendritic Nonlinearity Model: Each branch performs a thresholded linear transformation, and outputs are aggregated ($f(x) = \sum_i \Theta(w_i^\top x + b_i)$), imparting the neuron with piecewise linear modeling power.
• Distributed Processing and Shared Inputs: Multiple branches process identical input, greatly expanding the space of representable functions and blurring the distinction between network depth and “internal neuronal depth.”
• Empirical Results: These dendritic neurons can solve complex learning tasks (e.g., MNIST, CIFAR-10) traditionally requiring multi-layer architectures, challenging the assumption that computational power is strictly a function of depth and number of units.
• Implications: Popular artificial neuron models may severely underestimate the computational efficiency accessible via biologically inspired, internally structured single-unit architectures.

7. Practical Implications, Limitations, and Future Research

Single-branch neural networks offer multiple practical advantages including ease of training, rapid convergence, high parameter efficiency, and resilience to input incompleteness. However, certain limitations and operational caveats are observed:

• Trade-offs vs. Multi-Branch Architectures: While effective for invariant or semantically aligned modalities, single-branch networks may underperform when modality-specific features are critical or sensor channels have distinct noise dynamics (Tian et al., 23 Aug 2025).
• Hyperparameter Tuning Complexity: The use of advanced techniques such as contrastive loss or modality sampling increases the hyperparameter landscape and introduces sensitivity to training regimens.
• Hardware and Parallelization: Sequential operation (as in folded-in-time systems) trades off resource savings for processing latency unless multiple copies are operated in parallel.
• Theoretical Gaps: Guarantees established for single-neuron systems may not generalize straightforwardly to highly asymmetric input distributions or deep architectures, and further research is needed for broad theoretical characterization (Yehudai et al., 2020).

In summary, single-branch neural networks represent a paradigm that leverages biological inspiration, decomposition strategies, and architectural streamlining to achieve robustness, computational efficiency, and strong generalization for both simple and complex tasks. Ongoing research seeks to further delineate the conditions under which they offer advantages and to generalize their application to a wider class of problems in modern machine learning.