Wayne State University

The work proposes a Nonmonotone Coderivative-based Newton (NCN) method that builds generalized Hessians from Mordukhovich coderivatives of the gradient mapping and combines a Hybrid Adaptive Nonmonotone (HAN) line search with two adaptive regularization schemes; under standard assumptions it proves global convergence and local superlinear convergence for exact and inexact second-order information, and experiments on Lasso, SVM, and logistic Lasso show competitive iteration counts and CPU times.

The work proposes a Nonmonotone Coderivative-based Newton (NCN) method that builds generalized Hessians from Mordukhovich coderivatives of the gradient mapping and combines a Hybrid Adaptive Nonmonotone (HAN) line search with two adaptive regularization schemes; under standard assumptions it proves global convergence and local superlinear convergence for exact and inexact second-order information, and experiments on Lasso, SVM, and logistic Lasso show competitive iteration counts and CPU times.

The work proposes Soft Spatial Reasoning, a post-training framework in which a large vision-language model forms a continuous soft state at each chain-of-thought step by mixing token embeddings instead of committing to a single token, with an AdaptSoft controller that adapts the degree of softness from the current hidden state and predictive uncertainty and is trained by a gradient-alignment objective; across OmniSpatial, SpatiaLab, and MindCube it reaches higher weighted-average accuracy than same-backbone hard-thinking and fixed-soft chain-of-thought baselines and the compared existing models.

The work proposes Soft Spatial Reasoning, a post-training framework in which a large vision-language model forms a continuous soft state at each chain-of-thought step by mixing token embeddings instead of committing to a single token, with an AdaptSoft controller that adapts the degree of softness from the current hidden state and predictive uncertainty and is trained by a gradient-alignment objective; across OmniSpatial, SpatiaLab, and MindCube it reaches higher weighted-average accuracy than same-backbone hard-thinking and fixed-soft chain-of-thought baselines and the compared existing models.

SpatialCORE is a GRPO-based post-training framework that weights the geometric matching quality of each predicted bounding box by the model's own coordinate-token uncertainty in generating that grounding, and uses an answer gate to tie grounding optimization to final-answer correctness, so the model learns to reason from task-relevant objects that are both accurately and confidently localized; on the held-out OmniSpatial test set SpatialCORE-8B reaches the highest weighted-average accuracy among open-source and specialized spatial-reasoning models and leads zero-shot on the unseen SpatiaLab, while ablations show that removing confidence weighting drops accuracy from 56.33% to 52.33%.

SpatialCORE is a GRPO-based post-training framework that weights the geometric matching quality of each predicted bounding box by the model's own coordinate-token uncertainty in generating that grounding, and uses an answer gate to tie grounding optimization to final-answer correctness, so the model learns to reason from task-relevant objects that are both accurately and confidently localized; on the held-out OmniSpatial test set SpatialCORE-8B reaches the highest weighted-average accuracy among open-source and specialized spatial-reasoning models and leads zero-shot on the unseen SpatiaLab, while ablations show that removing confidence weighting drops accuracy from 56.33% to 52.33%.