We study the topology of learned representations in predictive coding networks (PCNs), a neuro-inspired bidirectional architecture, using a quantitative layer-wise persistent homology analysis. We train well-performing PCNs on a synthetic classification dataset ($\geq 99.
arXiv:2608. 02816v1 Announce Type: new Abstract: We study the topology of learned representations in predictive coding networks (PCNs), a neuro-inspired bidirectional architecture, using a quantitative layer-wise persistent homology analysis.
arXiv:2606. 00073v1 Announce Type: cross Abstract: We investigate how internal representations emerge across hierarchical processing systems by introducing a neuroscience-inspired framework for analyzing deep spiking neural networks (SNN) through the lens of functional connectivity.
Predictive coding networks (PCNs) offer a biologically-plausible, local-learning alternative to back-propagation of errors (backprop). Nevertheless, they have remained largely confined to shallow architectures and evaluated on simple machine intelligence benchmarks.
We investigate how each component of the Transformer feedforward block architecture design determines how much rank survives across depth at initialization. We reinterpret skip connections and normalization, long understood as controlling magnitude, as mechanisms for preserving gradient rank across depth, since the very matrix multiplications and nonlinear activations that make the network expressive also reduce the rank.
arXiv:2607. 21366v1 Announce Type: cross Abstract: Deep neural networks encode complex representations, but deconstructing this internal knowledge remains a challenge.
arXiv:2604. 00208v2 Announce Type: replace Abstract: Comparing internal representations is a central goal in neuroscience and machine learning, but standard linear alignment metrics (Representational Similarity Analysis, Centered Kernel Alignment, and linear regression) are frequently applied to neural activity coordinates rather than on the underlying features.
arXiv:2607. 14018v1 Announce Type: cross Abstract: We investigate how each component of the Transformer feedforward block architecture design determines how much rank survives across depth at initialization.
arXiv:2602. 07697v3 Announce Type: replace-cross Abstract: Predictive coding (PC) is a biologically plausible alternative to standard backpropagation (BP) that minimises an energy function with respect to network activities before updating weights.
arXiv:2606. 31856v1 Announce Type: new Abstract: We study layered models, including feedforward networks, ResNets, and transformers, by limiting each layer to a width of $d = 3$, i.
arXiv:2606. 12138v1 Announce Type: cross Abstract: Sparse autoencoders (SAEs) are widely used to interpret neural network representations, but their utility depends on whether the learned features are reproducible across training runs.
arXiv:2604. 00230v2 Announce Type: replace Abstract: Neural collapse (NC) -- the convergence of penultimate-layer features to a simplex equiangular tight frame -- is well understood at equilibrium, but the dynamics governing its onset remain poorly characterised.
arXiv:2606. 21295v2 Announce Type: replace-cross Abstract: Existing sequence models, including RNNs, LSTMs, continuous-time networks, and Transformers, share a common structural principle: layer-wise dynamics, where all neurons in the same layer co-evolve through a shared parameterized operator, leaving individual neurons no freedom to evolve independently.