Cutting planes (cuts) are essential for solving mixed-integer linear programming (MILP) problems, as they tighten the feasible solution space and accelerate the solving process. Modern MILP solvers offer diverse cutting plane separators to generate cuts, enabling users to leverage their potential complementary strengths to tackle problems with different structures. Recent machine learning approaches learn to configure separators based on problem-specific features, selecting effective separators and deactivating ineffective ones to save unnecessary computing time. However, they ignore the dynamics of separator efficacy at different stages of cut generation and struggle to adapt the configurations for the evolving problems after multiple rounds of cut generation. To address this challenge, we propose a novel dyn amic sep arator configuration ( DynSep ) method that models separator configuration in different rounds as a reinforcement learning task, making decisions based on an incremental triplet graph updated by iteratively added cuts. Specifically, we tokenize the incremental subgraphs and utilize a decoder-only Transformer as our policy to autoregressively predict when to halt separation and which separators to activate at each round. Evaluated on synthetic and large-scale real-world MILP problems, DynSep speeds up average solving time by 64% on easy and medium datasets, and reduces primal-dual gap integral within the given time limit by 16% on hard datasets
Mingxuan Ye, Jie Wang, Fangzhou Zhu et al.· Neural Information Processin...· 0 citations
Scaling Large Language Models (LLMs) has been driven mainly by enlarging the Transformer backbone, but for an already-strong model this requires another round of costly pretraining. We study whether an existing backbone can keep improving by allocating more computation to each token while leaving the Transformer backbone fixed. Depth-recurrent (looped) Transformers pursue this goal but are hard to scale, because looped computation does not fit naturally with the pipeline parallelism used to train the largest models. We add computation along the sequence-length dimension, where the extra computation is simply a longer input and stays compatible with standard large-model training. We propose Hidden Decoding, a sequence-length scaling method applied during continued pretraining (CPT). It expands each token into n streams with independent embedding tables and keeps the intermediate streams'key-value cache as context, so each token performs more internal computation without adding or widening Transformer layers. To keep this affordable at scale, we introduce Stream-Factorized Attention, in which most layers attend only within each stream and only a few layers mix across streams, reducing the attention cost from quadratic to roughly linear in n. Experiments support two scaling results. At frontier scale, we train WeLM-HD4-80B and WeLM-HD4-617B at n=4 and improve their matched non-HD baselines, making Hidden Decoding the first demonstrated sequence-length scaling method at the 100B+ MoE scale. Across expansion factors, the gains grow as n increases, showing that sequence-length expansion is a practical fixed-backbone scaling path for frontier-scale LLMs.
Aiwei Liu, Cheng Shi, Chuhan Wu et al.· 2 citations