Recommenders aim to rank items from a discrete item corpus in line with user interests, yet suffer from extremely sparse user preference data. Recent advances in diffusion models have inspired diffusion-based recommenders, which alleviate sparsity by injecting noise during a forward process to prevent the collapse of perturbed preference distributions. However, current diffusion-based recommenders predominantly rely on continuous Gaussian noise, which is intrinsically mismatched with the discrete nature of user preference data in recommendation. In this paper, building upon recent advances in discrete diffusion, we propose PreferGrow, a discrete diffusion-based recommender system that models preference ratios by fading and growing user preferences over the discrete item corpus. PreferGrow differs from existing diffusion-based recommenders in three core aspects: (1) Discrete modeling of preference ratios: PreferGrow models relative preference ratios between item pairs, rather than operating in the item representation or raw score simplex.

Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology. Existing convergence theory, however, exhibits fundamental limitations. KL-based analyses diverge under singular priors such as the masked distribution, while bounds in total variation (TV) depend on the state space size $S$ and become vacuous for modern language tasks, where vocabularies contain hundreds of thousands of tokens. We develop a unified adjoint-equation-based framework that establishes dimension-free convergence guarantees in any integral probability metric (IPM). To the best of our knowledge, our bounds are the first to be entirely free of $S$ and applicable to both masked and uniform priors. Importantly, our theory relies only on a single standard rate-matrix regularity assumption and is compatible with time-inhomogeneous schedules. Four novel techniques drive our improvements: working in the space of observables via adjoint equations rather than directly with probability measures, a regularity analysis that yields bounds on any IPM, a coupling argument that removes $S$-dependence under uniform transitions, and a score-marginal cancellation technique that removes $S$-dependence under masked transitions. Our framework thus sharply departs from prior analyses and avoids the shortcomings of pathspace-KL and existing TV-based approaches. Beyond convergence bounds, our framework provides a versatile toolkit for further theoretical study of discrete diffusion models.

Neural Information Processing Systems http://nips.cc/

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

From[BorkarandMeyn,2000],weknowthatthestochastic approximation (18) converges to the fixed point ofT, i.e., Q . Finally, to show Theorem 3, we only need to show each term in(56) is smaller than . In this section we develop the finite-time analysis of the robust TDC algorithm. We note that recently there are several works [Srikant and Ying, 2019, Xu and Liang, 2021, Kaledin et al., 2020] on finite-time analysis of RL algorithms that do not need theprojection. Specifically, the problem in [Srikant and Ying, 2019] is for one time scalelinear stochastic approximation.

While attention has been empirically shown to improve model performance, it lacks a rigorous mathematical justification. This short paper establishes a novel connection between attention mechanisms and multinomial regression. Specifically, we show that in a fixed multinomial regression setting, optimizing over latent features yields solutions that align with the dynamics induced on features by attention blocks. In other words, the evolution of representations through a transformer can be interpreted as a trajectory that recovers the optimal features for classification.

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

In our notation, the model in Dasgupta et al. [4] would have score function F As presented in Dasgupta et al. Although the model was proposed and analyzed in Dasgupta et al. Remark 2. Note that the mean of The proof is by direct calculation. The following lemma will be helpful in proving the next part. Given a threshold T, temperature hyperparameters,, there exists and a bijection on the set of parameterizations {V!