Computing with traceable tensor networks

What the math gives to ML

The paper provides a constructive SVD decomposition for tensor networks on arbitrary graph topologies, together with graph-aware addition and rounding operations that preserve a prescribed relative Frobenius error. The transferable asset is the ability to choose connectivity and rank per pair of tensorized modes rather than being restricted to a chain or tree. This suggests tensorized neural layers whose weight tensors use learned or hand-designed sparse graph topologies, with SVD truncation controlling parameter count and approximation error. The traceable addition rule also offers a way to accumulate residual adapters or expert updates while preventing rank growth from becoming proportional to the number of additions.