The paper proposes projecting continual updates away from old-task spatial directions in hyperbolic multimodal models, claims this is theoretically required to prevent forgetting, but the necessity claim is unproven and the experiments are confounded by a step-pullback.
The interplay of the polar decomposition theorem and the Lorentz group
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abstract
It is shown that the polar decomposition theorem of operators in (real) Hilbert spaces gives rise to the known decomposition in boost and spatial rotation part of any matrix of the orthochronous proper Lorentz group $SO(1,3)\uparrow$. This result is not trivial because the polar decomposition theorem is referred to a positive defined scalar product while the Lorentz-group decomposition theorem deals with the indefinite Lorentz metric. A generalization to infinite dimensional spaces can be given. It is finally shown that the polar decomposition of $SL(2,\bC)$ is preserved by the covering homomorphism of $SL(2,\bC)$ onto $SO(1,3)\spa\uparrow$
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Hyperbolic Multimodal Continual Learning
The paper proposes projecting continual updates away from old-task spatial directions in hyperbolic multimodal models, claims this is theoretically required to prevent forgetting, but the necessity claim is unproven and the experiments are confounded by a step-pullback.