Can an MLP Absorb Its Own Skip Connection?
Researchers have proven fundamental limits on when skip connections in neural networks can be mathematically absorbed into residual-free architectures. The work establishes that for common gated activations like SwiGLU and GeGLU, and nonlinear functions like ReLU squared, skip connections cannot be eliminated through architectural redesign, even across deep compositions. This constrains the design space for efficient model compression and informs why certain architectural patterns persist across modern transformers and large language models, suggesting practitioners cannot simplify these structures without functional loss.
Modelwire context
ExplainerThe paper's contribution isn't just negative: by formally bounding which activation families permit absorption, it implicitly maps the design space where compression *is* theoretically permissible, which is the more actionable result for practitioners.
This connects directly to the 'Transformer as an Euler Discretization of Score-based Variational Flow' paper from the same day, which proved that standard Transformer layers emerge from a continuous dynamical system. That work gave a principled account of *why* certain architectural components appear; this paper adds a complementary constraint, showing that skip connections in gated-activation networks aren't removable artifacts but load-bearing structures. Together they push against the same informal assumption that modern transformer components are interchangeable or collapsible under reparameterization. The quasi-equivariant metanetworks paper is also relevant at the margin: if weight-space models are to faithfully represent functional identity across architectures, knowing which structural features are mathematically non-eliminable tightens what those models must preserve.
Watch whether compression-focused teams at major labs cite these impossibility bounds when justifying residual retention in distilled or pruned model variants over the next six months. Silence there would suggest the result is not yet reaching practitioners.
Coverage we drew on
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MentionsSwiGLU · GeGLU · ReLU · ReGLU
Modelwire Editorial
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