# TIGER

DINGO-TGR infers binary parameters and six post-Newtonian phase-deformation parameters jointly with neural posterior estimation, then reweights the network's approximate posterior by importance sampling. For GW150914 the inference takes about 38 minutes against roughly 177 hours for bilby-tgr with dynesty, and about 4.4 hours against 238 hours for the higher signal-to-noise GW250114. GW150914 shows a mild offset from general relativity in the leading principal-component mode, but 115 of 1,000 general-relativity injections resembling GW150914 reach or exceed that offset, an empirical upper-tail p-value of about 0.115 that does not reject the general-relativity null at the 5% level.

DINGO-TGR infers binary parameters and six post-Newtonian phase-deformation parameters jointly with neural posterior estimation, then reweights the network's approximate posterior by importance sampling. For GW150914 the inference takes about 38 minutes against roughly 177 hours for bilby-tgr with dynesty, and about 4.4 hours against 238 hours for the higher signal-to-noise GW250114. GW150914 shows a mild offset from general relativity in the leading principal-component mode, but 115 of 1,000 general-relativity injections resembling GW150914 reach or exceed that offset, an empirical upper-tail p-value of about 0.115 that does not reject the general-relativity null at the 5% level.

Multimodal large language models can read text in an image accurately yet still fail to reason over the same problem as well as they do over plain text, a shortfall the authors call a modality reasoning-access gap. TIGER renders text-only math problems as images, mines cases the model solves from text but fails from the image, and post-trains on those image inputs with GRPO and related objectives. Trained only on synthetic rendered-text images, Qwen3-VL-8B rises from 54.5 to 65.8 on MathVerse, while Qwen2.5-VL-7B rises from 43.9 to 47.5 on MathVerse and from 22.2 to 25.7 on EMMA.

Multimodal large language models can read text in an image accurately yet still fail to reason over the same problem as well as they do over plain text, a shortfall the authors call a modality reasoning-access gap. TIGER renders text-only math problems as images, mines cases the model solves from text but fails from the image, and post-trains on those image inputs with GRPO and related objectives. Trained only on synthetic rendered-text images, Qwen3-VL-8B rises from 54.5 to 65.8 on MathVerse, while Qwen2.5-VL-7B rises from 43.9 to 47.5 on MathVerse and from 22.2 to 25.7 on EMMA.