This paper reorganizes the current manuscript around the DPO versus DDO-RM preference-optimization project and focuses on two parts: the algorithmic view and the preliminary held-out benchmark. The benchmark asks a narrow question: even in a minimal pairwise chosen-versus-rejected setting, can a reward-guided decision-distribution update outperform a direct pairwise objective? We compare Direct Preference Optimization (DPO) against DDO-RM on EleutherAI/pythia-410m using HuggingFaceH4/ultrafeedback\_binarized, evaluate on the held-out test\_prefs split, and report results for seeds 42, 13, and 3407. Algorithmically, DDO-RM treats each prompt as a finite decision problem over candidate responses. Instead of optimizing only a binary chosen-rejected relation, it forms a policy distribution over candidates, centers reward-model scores under that distribution, and distills a reward-guided target distribution back into the policy. In the current public benchmark, DDO-RM improves mean pair accuracy from 0.5238 to 0.5602, AUC from 0.5315 to 0.5382, and mean margin from 0.1377 to 0.5353 relative to DPO. These are encouraging but still preliminary results: the study covers one model family, one dataset, one held-out evaluation split, and three seeds.

Converting an n-dimensional vector to a probability distribution over n objects is a commonly used component in many machine learning tasks like multiclass classification, multilabel classification, attention mechanisms etc. For this, several probability mapping functions have been proposed and employed in literature such as softmax, sum-normalization, spherical softmax, and sparsemax, but there is very little understanding in terms how they relate with each other. Further, none of the above formulations offer an explicit control over the degree of sparsity. To address this, we develop a unified framework that encompasses all these formulations as special cases. This framework ensures simple closed-form solutions and existence of sub-gradients suitable for learning via backpropagation. Within this framework, we propose two novel sparse formulations, sparsegen-lin and sparsehourglass, that seek to provide a control over the degree of desired sparsity. We further develop novel convex loss functions that help induce the behavior of aforementioned formulations in the multilabel classification setting, showing improved performance. We also demonstrate empirically that the proposed formulations, when used to compute attention weights, achieve better or comparable performance on standard seq2seq tasks like neural machine translation and abstractive summarization.

Learning to Defer (L2D) enables a classifier to abstain from predictions and defer to an expert, and has recently been extended to multi-expert settings. In this work, we show that multi-expert L2D is fundamentally more challenging than the single-expert case. With multiple experts, the classifier's underfitting becomes inherent, which seriously degrades prediction performance, whereas in the single-expert setting it arises only under specific conditions. We theoretically reveal that this stems from an intrinsic expert identifiability issue: learning which expert to trust from a diverse pool, a problem absent in the single-expert case and renders existing underfitting remedies failed. To tackle this issue, we propose PiCCE (Pick the Confident and Correct Expert), a surrogate-based method that adaptively identifies a reliable expert based on empirical evidence. PiCCE effectively reduces multi-expert L2D to a single-expert-like learning problem, thereby resolving multi expert underfitting. We further prove its statistical consistency and ability to recover class probabilities and expert accuracies. Extensive experiments across diverse settings, including real-world expert scenarios, validate our theoretical results and demonstrate improved performance.

Whilesomerecent works propose to distill an ensemble model into a single model to reduce such costs,thereisstillaperformance gapbetween theensemble anddistilledmodels.

Hopfield Boosting, a boosting approach, which leverages modern Hopfield energy to sharpen the decision boundary between the in-distribution and OOD data.

In particular, it aggregates multiple sub-models called experts based on a gating network. Here, experts can be formulated as neural networks, and they specialize in different aspects of the data.

Due to their size, the capability of these networks has increased tremendously, but this has come at the cost of a significant increase in necessary compute.