Modern decision-making increasingly relies on contextual features (covariates) to improve optimization under uncertainty. In practice, however, such covariates are often only partially observed due to, e.g., data source heterogeneity or costly data collection. Nonetheless, most existing methods assume fully observed historical data and can become unreliable when this assumption is violated. We address this gap by proposing a distributionally robust optimization approach that exploits incomplete covariates to produce robust decisions without imputing a complete dataset. Our method builds ambiguity sets from the observed partial data and incorporates the general structure of the missingness mechanism, ensuring candidate distributions remain consistent with what is observed. Across settings with discrete or continuous covariates and outcomes, we derive tractable reformulations and establish finite-sample out-of-sample performance guarantees. Empirical results across a range of contextual decision-making tasks demonstrate that the proposed integrated approach consistently outperforms state-of-the-art baselines, including various impute-then-optimize pipelines, in both out-of-sample performance and reliability.
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Optimization · Stochastic
Modern decision-making increasingly relies on contextual features (covariates) to improve optimization under uncertainty. In practice, however, such covariates are often only partially observed due to, e.g., data source heterogeneity or costly data collection. Nonetheless, most existing methods assume fully observed historical data and can become unreliable when this assumption is violated. We address this gap by proposing a distributionally robust optimization approach that exploits incomplete covariates to produce robust decisions without imputing a complete dataset. Our method builds ambiguity sets from the observed partial data and incorporates the general structure of the missingness mechanism, ensuring candidate distributions remain consistent with what is observed. Across settings with discrete or continuous covariates and outcomes, we derive tractable reformulations and establish finite-sample out-of-sample performance guarantees. Empirical results across a range of contextual decision-making tasks demonstrate that the proposed integrated approach consistently outperforms state-of-the-art baselines, including various impute-then-optimize pipelines, in both out-of-sample performance and reliability.
Optimization · Discrete and Combinatorial Optimization
Learning models with categorical variables requires optimizing expectations over discrete distributions, a setting in which stochastic gradient-based optimization is challenging due to the non-differentiability of categorical sampling. A common workaround is to replace the discrete distribution with a continuous relaxation, yielding a smooth surrogate that admits reparameterized gradient estimates via the reparameterization trick. Building on this idea, we introduce ReDGE, a novel and efficient diffusion-based soft reparameterization method for categorical distributions. Our approach defines a flexible class of gradient estimators that includes the Straight-Through estimator as a special case. Experiments spanning latent variable models and inference-time reward guidance in discrete diffusion models demonstrate ReDGE consistently matches or outperforms existing gradient-based methods.
Applications · Health / Medicine
How do we map numeric values to representations in transformer-based sequence processing, particularly in electronic health record (EHR) data? We systematically compare discrete, continuous, and hybrid value embeddings using synthetic arithmetic tasks embedded within real-world EHR data, as well as real-world clinical prediction tasks. Our study reveals trade-offs between numeric precision, optimisation stability, and architectural flexibility. We find that representations that explicitly model value-concept interactions perform best on precision-sensitive arithmetic tasks when architectural constraints permit. Hybrid token-based approaches that retain numeric values but apply binning prior to projection provide a more robust and broadly applicable alternative, with the optimal number of bins following a simple empirically derived power-law in dataset size. Across tasks, models consistently exhibit reliable “good enough” numeric computation rather than exact arithmetic, while clinical gains from incorporating laboratory values are task-dependent. This suggests that robustness and deployability often outweigh maximal numeric precision in practice, motivating hybrid token-based approaches as a practical default.
Social Aspects · Safety
Transferable jailbreaking attacks enable red-teaming of black-box large language models by optimizing adversarial prompts on open-source surrogates. A natural approach to improve transferability is multi-model training---optimizing against multiple source models simultaneously. Yet this approach has been largely abandoned, as it yields only marginal gains with standard optimizers. We argue the root cause is poor generalization: standard gradient descent lacks stability whenaggregating gradients from diverse models. Since GCG and its variants~\citep{zou2023universal, jia2024improved, yang2025guiding} mplicitly perform SGD in discrete token space, they inherit this instability in multi-model settings.We address this with \textbf{Lookahead-GCG}, which combines: (1) Stochastic Nesterov Accelerated Gradient (SNAG), whose lookahead mechanism reduces sensitivity to individual gradient updates, providing stability for multi-model optimization; (2) embedding-space momentum accumulation, which enables SNAG in discrete token optimization; and (3) maximally distant initialization, which exploits SNAG's improved generalization by starting from a universally beneficial point. Experiments show our method achieves 50.37\% ASR on open-source and 34.03\% on closed-source LLMs, outperforming GCG and TransferAttack with +11.78\% gains from multi-model optimization.
Deep Learning · Foundation Models
Static fine-tuning paradigms impose rigid structural constraints on foundation models like the Segment Anything Model 2 (SAM2), limiting their adaptability to the varying complexity of specialized downstream tasks. To overcome this limitation, we propose **ACO-MoE-LoRA**, a dynamic framework that introduces an "Evolving-while-Training" strategy by synergizing Ant Colony Optimization (ACO) with a Latent Space Mixture-of-Experts (MoE) architecture. Central to our method is the ACO-ConvLoRA module, which employs a pheromone-guided routing mechanism to actively govern expert selection and topological evolution. By formulating expert assignment as an evolutionary pathfinding problem, this module effectively mitigates the standard routing collapse issue and enables elastic adjustment of LoRA ranks via weight slicing, bridging discrete structural search with continuous parameter training. Extensive experiments across 16 challenging datasets demonstrate that our framework consistently outperforms leading static adapters, while effectively addressing the local optimality limitations of recent dynamic heuristics. This work presents a self-organizing solution that harmonizes swarm intelligence with gradient optimization for efficiently adapting foundation models to specialized domains.
Applications · Chemistry, Physics, and Earth Sciences
Identifying high-utility candidates from massive discrete spaces under expensive evaluations is a recurring challenge across the sciences, with structure-based drug discovery as a prominent example. While surrogate-based optimization can increase sample efficiency by reducing the number of expensive evaluations, modern molecular libraries have reached billions to trillions of compounds, making full-library surrogate inference itself a major computational bottleneck. We introduce BOBA, a bandit-guided surrogate optimization framework that eliminates full-library inference by adaptively allocating computation across partitions of the action space. By treating partitions as arms in a multi-armed bandit, BOBA concentrates inference and evaluations on empirically promising partitions while maintaining principled exploration. Experiments on real-world synthesis-on-demand libraries demonstrate that optimism-under-uncertainty bandits, combined with meaningful action space partitioning, are essential for effective allocation of inference and evaluations. Our findings reveal a tunable tradeoff between screening performance and surrogate inference cost, which supports practical optimization over current libraries, and establishes a viable route to ultra-large library virtual screening.
Applications · Time Series
Time series prototype learning is fundamentally challenged by observational ambiguity. Discrete architectures fail to resolve this, as they lack the capacity to decouple stochastic noise from continuous dynamics. Furthermore, rigid closed-set assumptions fail to capture unseen diversity. To address these limitations, we propose a hierarchical ordinary differential equation clustering network, which utilizes neural ordinary differential equation to model latent state evolution as a continuous integral curve. This formulation enforces temporal continuity to effectively disentangle smooth feature trends from stochastic noise, while our adaptive hierarchical mechanism autonomously identifies the optimal number of prototypes without rigid prior constraints. Validated on the early link failure detection task with irregularly sampled time series, the proposed method effectively extracts underlying physical prototypes, thereby enabling robust failure detection.
Deep Learning · Generative Models and Autoencoders
Diffusion Language Models (DLMs) have recently achieved strong results in text generation. However, their multi-step sampling leads to slow inference, limiting practical use. To address this, we extend Inverse Distillation, a technique originally developed to accelerate continuous diffusion models, to the discrete setting. Nonetheless, this extension introduces both theoretical and practical challenges. From a theoretical perspective, the inverse distillation objective lacks uniqueness guarantees, which may lead to suboptimal solutions. From a practical standpoint, backpropagation in the discrete space is non-trivial and often unstable. To overcome these challenges, we first provide a theoretical result demonstrating that our inverse formulation admits a unique solution, thereby ensuring valid optimization. We then introduce gradient-stable relaxations to support effective training. As a result, experiments on multiple DLMs show that our method, *Inverse-distilled Diffusion Language Models (IDLM)*, reduces the number of inference steps by $4 \times$-$64 \times$, while preserving the teacher model’s entropy and generative perplexity.
Deep Learning · Large Language Models
The scaling of Large Language Models (LLMs) has driven significant performance gains but created substantial challenges in inference efficiency. While Mixture of Experts (MoEs) architectures address this by decoupling model size from inference cost, training MoEs from scratch is often unstable and compute intensive. Conversion of pre-trained dense models into sparse MoEs has emerged as an alternative solution; however, existing methods typically rely on heuristic neuron clustering or random splitting to partition Feed-Forward Networks (FFNs) into experts. In this work, we propose DOT-MoE, a novel framework that formulates the decomposition of dense layers as a Differentiable Optimal Transport (DOT) problem. Instead of static heuristics, we model neuron assignment as a balanced transport problem, utilizing differentiable Sinkhorn-Knopp iterations to enforce strict expert capacity constraints. Furthermore, we utilize Straight-Through Estimators (STE) to jointly learn the discrete neuron-to-expert assignment and the token-to-expert routing policy end-to-end. Extensive experiments across multiple architectures and benchmarks demonstrate that DOT-MoE significantly outperforms structured pruning, heuristic clustering, and random-split baselines, retaining 90% of the original dense model's performance while reducing active parameters by 50%.
Optimization · Discrete and Combinatorial Optimization
Many combinatorial optimization problems admit quadratic unconstrained binary formulations (QUBO) which can often be relaxed to the box $[0,1]^n$ and optimized using scalable gradient-based methods. However, the resulting non-convex landscape can often contain local optima that are spurious or infeasible. In this paper, we establish sufficient structural conditions on quadratic penalties that rule out these failures, guaranteeing that every local minimizer of the relax problem is both binary and feasible. For each problem we study, we examine existing QUBO formulations when available, identify why they fail when they do, and propose alternative relaxed QUBOs that satisfy our conditions. We show for several common combinatorial problems, including open-pit mining, knapsack, and traveling salesman formulations, that these constructions allow gradient-based methods such as projected gradient descent and Adam to be safely applied to obtain valid binary solutions. Our results clarify when differentiable optimization is a reliable local solver for quadratic combinatorial objectives.
Applications · Everything Else
State-space language models such as Mamba match Transformer quality while permitting linear complexity inference, yet still comprise billions of parameters that hinder deployment. While existing one-shot pruning methods are effective for generic linear and attention blocks, they are not designed with the overall Mamba architecture in mind and fail to account for the time-shared and discretized state-transition matrix at the heart of the selective state-space module (SSM). In this paper, we introduce SparseSSM, the first training-free pruning framework that extends the classic optimal brain surgeon (OBS) framework to state space architectures. Our layer-wise algorithm (i) derives an approximate second-order saliency score that aggregates Hessian-trace information across time steps, (ii) incorporates a component sensitivity analysis to guide feed-forward network (FFN) pruning, which also sheds light on where redundancy resides in mamba architecture, (iii) can be easily extended to semi-structured and structured sparsity, and generalized to other SSM-based architectures. Empirically, we prune 50% of SSM weights without fine-tuning and observe no zero-shot accuracy loss, achieving the current state-of-the-art pruning algorithm for Mamba-based LLMs.
Reinforcement Learning · Batch/Offline
Hierarchical policies in offline goal-conditioned reinforcement learning (GCRL) addresses long-horizon tasks by decomposing control into high-level subgoal planning and low-level action execution. A critical design choice in such architectures is the goal representation—the compressed encoding of goals that serves as the interface between these levels. Existing approaches commonly derive goal representations while learning value functions, implicitly assuming that preserving information sufficient for value estimation is adequate for optimal control. We show that this assumption can fail, even when the value estimation is exact, as such representations may collapse goal states that need to be differentiated for action learning. To address this, we introduce an information-theoretic framework that defines *action sufficiency*, a condition on goal representations necessary for optimal action selection. We prove that value sufficiency does not imply action sufficiency and empirically verify that the latter is more strongly associated with control success in a discrete environment. We further demonstrate that standard log-loss training of low-level policies naturally induces action-sufficient representations. Our experimental results a popular benchmark demonstrate that our actor-derived representations consistently outperform representations learned via value estimation.
Reinforcement Learning · Everything Else
Multi-objective reinforcement learning (MORL) must often support preferences that change online or are specified only after data collection. We study finite-horizon MORL with vector feedback in linear MDPs under two protocols: (i) predictable adversarial preferences revealed before each episode, and (ii) reward-free preference-free exploration (PFE), where exploration observes only transitions and must later answer arbitrary preference queries. Standard reductions are protocol-unsafe: re-scalarizing past stochastic rewards with future weights breaks the martingale structure needed for self-normalized confidence bounds, and hypervolume evaluation must account for episode-start randomization, which yields a deployable convex hull of return vectors. We propose a protocol-safe reward interface that estimates each reward coordinate via regression and performs scalarization only at query time, and we formalize deployable hypervolume semantics with a stability chain from support-function error to hypervolume error. Consequently, we obtain filtration-safe regret bounds for any predictable preference sequence without discretizing the simplex (only $\log m$ dependence) and matching near-minimax rates in linear MDPs, as well as sharp reward-free PFE guarantees: a (near-)minimax decision-optimal query answering rate $\tilde{O}(d^2 U_{\mathrm{ret}}^2/\varepsilon^2)$ and a tight separation from explicit transition-model recovery $\Theta(d(|\mathcal{S}|-1)/\varepsilon_P^2)$. These results connect online learning, preference-free deployment, and hypervolume-aware evaluation through a single protocol-aligned theory.
Deep Learning · Generative Models and Autoencoders
In many domains generating variable length sequences through insertions provides greater flexibility over autoregressive models. However, the action space of insertion models is much larger than that of autoregressive models (ARMs) making the learning challenging. To address this, we incorporate trainable order dynamics into the target rates for discrete flow matching, and show that with suitable choices of parameterizations, joint training of the target order dynamics and the generator is tractable without the need for numerical simulation. As the generative insertion model, we use a variable length masked diffusion model, which generates by inserting and filling mask tokens. On graph traversal tasks for which a locally optimal insertion order is known, we explore the choices of parameterization empirically and demonstrate the trade-offs between flexibility, training stability and generation quality. On de novo small molecule generation, we find that the learned order dynamics leads to a significant increase in validity and quality of the generated molecules, when compared to uniform order dynamics.
Applications · Language, Speech and Dialog
Continuous diffusion for categorical data is a framework belonging to the diffusion family and aiming at generating discrete data. The scientific interest to such models has been constantly increasing these days because researchers try to achieve a challenging goal of finding reasonable alternatives to autoregressive large language models. In this paper, we study the properties of the structure of the latent space corresponding to discrete tokens expressed in terms of Kullback-Leibler divergence on diffusion path measures and accuracy of the correct token prediction by the optimally trained diffusion model. We find that FSQ tokenization scheme has the latent space structure with the properties that make it best suited for continuous diffusion for categorical data as verified through rigorous theoretical analysis and extensive numerical experiments. To validate our findings in real-life scenario, we train several text-to-speech diffusion models having speech tokens as intermediate acoustic features, and show that the one based on FSQ tokens indeed performs the best, and, moreover, it outperforms its strong LLM-based counterpart, at the same time being significantly smaller and faster.
Deep Learning · Large Language Models
Masked Diffusion Models (MDMs) have emerged as a promising approach for generative modeling in discrete spaces. By generating sequences in any order and allowing for parallel decoding, they enable fast inference and strong performance on non-causal tasks. However, this flexibility comes with a *training complexity* trade-off: MDMs train on an exponentially large set of masking patterns, which is not only computationally expensive, but also creates a train--test mismatch between the random masks used in training and the highly structured masks induced by inference-time unmasking. In this work, we propose Progressive UnMAsking (PUMA), a simple modification of the forward masking process that aligns training-time and inference-time masking patterns, thereby focusing optimization on *inference-aligned masks* and speeding up training. Empirically, PUMA speeds up pretraining at the 125M scale by $\approx 2.5 \times$ and offers complementary advantages on top of common recipes like autoregressive initialization.
Applications · Health / Medicine
Protein function is often controlled by ligands that bias the direction of state transitions, such as agonists and antagonists, rather than stabilizing a single conformation. This is especially important for clinically relevant G protein-coupled receptors (GPCRs), where therapeutic efficacy depends on functional directionality. Structure-based design methods optimize binding to static conformations and cannot represent non-reversible, directional effects or systematically distinguish agonist from antagonist behavior. To address this gap, we introduce **T**ransition-**D**irected **D**iscrete **D**iffusion for allosteric **B**inder design (**TD3B**), a sequence-based generative framework that designs binders with specified agonist or antagonist behavior via a directional transition control objective. TD3B combines a target-aware Direction Oracle, a soft binding-affinity gate, and amortized fine-tuning of a pre-trained discrete diffusion model, enabling targeted agonist and antagonist generation decoupled from binding affinity and unattainable by equilibrium-based or inference-only guidance baselines.
Theory · Deep Learning
Softmax attention is increasingly treated as a reusable inference primitive in transformers. Much prior theory covers Gaussian/linear models or assumes one shared quadratic query--key metric, which can fail for non-Gaussian exponential-family likelihoods with varying curvature. This risks overreading learned similarities as a global metric or as proof of Bayes-optimality. For discrete latent symbols with exponential-family observations, we show a single head can implement Bayes posteriors (and posterior means) by setting logits to log prior plus log likelihood, and we characterize single-head posteriors as exactly the log-linear (exponential-family) class. Using convex duality, we rewrite log-likelihoods as negative Bregman divergences on mean/sufficient-statistic space, making Bayes rule a soft nearest-neighbor computation; this yields a sharp boundary for globally shared quadratic metrics and a multi-head curvature-atlas approximation with head-count scaling, and we extend these guarantees to in-context estimation with consistency and finite-sample stability bounds. In synthetic Gaussian and Bernoulli in-context estimation, trained minimal attention models validate these predictions: performance approaches a Bayes-oracle baseline as prompt length grows; learned metrics align with noise precision in the Gaussian case, while Bernoulli retains a gap consistent with curvature variation. Together, these results explain when Fisher geometry should emerge, when a single metric is justified, and when multiple heads are necessary for Bayes-like in-context estimators beyond Gaussians.
Deep Learning · Large Language Models
Current chemical large language models (LLMs) predominantly rely on explicit Chain-of-Thought (CoT) to solve complex reasoning problems. However, forcing nonverbal tacit chemical logic into discrete natural language imposes a fundamental ``modality mismatch,'' creating an artificial bottleneck for reasoning. To investigate this, we introduce LatentChem, a reasoning interface that decouples chemical logic from linguistic generation, enabling the model to process information via continuous thought vectors and dynamic perception. Our investigation reveals a pivotal emergent behavior: spontaneous internalization. When optimized for task success, the model voluntarily abandons verbose textual derivations in favor of implicit latent computation, suggesting that it autonomously identifies the continuous manifold as a more native substrate for chemical logic. This paradigm shift also proves to be a superior computational strategy: LatentChem achieves a 59.88\% non-tie win rate against the strong CoT baseline on the rigorous ChemCoTBench, while delivering a broad 10.84$\times$ average speedup across all evaluated benchmarks. This empirically validates that chemical logic is inherently better modeled by continuous latent dynamics than by linear linguistic approximations.