Building generalist robot policies that can handle diverse tasks in open-ended environments is a central challenge in robotics. To leverage knowledge from large-scale pretraining, prior work (VLA) has typically built generalist policies either on top of vision-language models (VLMs) or generative models. However, both semantic understanding from vision-language pretraining and visual dynamics modeling from visual-generation pretraining are crucial for embodied robots. Recent unified models of generation and understanding have demonstrated strong capabilities in both comprehension and generation through large-scale pretraining. We posit that robotic policy learning can likewise benefit from the combined strengths of understanding, planning and continuous future representation learning. Building on this insight, we introduce UniCoD, which acquires the ability to dynamically model high-dimensional visual features through pretraining on over 1M internet-scale instructional manipulation videos. Subsequently, UniCoD is fine-tuned on data collected from the robot embodiment, enabling the learning of mappings from predictive representations to action tokens. Extensive experiments show our approach consistently outperforms baseline methods in terms of 9\% and 12\% across simulation environments and real-world out-of-distribution tasks.
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Applications · Chemistry, Physics, and Earth Sciences
High-fidelity solubility prediction is fundamental to pharmaceutical development and environmental partitioning, where accurate modeling must couple molecular structure with thermodynamic behavior across diverse chemical environments. However, recent advancements have been dominated by deep learning architectures that often sacrifice physical interpretability for predictive power. We challenge this trend by showing that state-of-the-art performance does not require such non-transparent architectures. To address this, we introduce $Dissolvr$, a transparent framework for molecular solubility prediction. In addition, we perform a comprehensive literature review and a benchmarking study against various methods. We show that $Dissolvr$ approaches the aleatoric limit of experimental uncertainty and achieves OOD generalization through structural invariance derived by mapping molecules to physically-grounded descriptors. Then, we present an LLM-assisted post-hoc explanation pipeline that bridges the gap between symbolic model artifacts and chemically grounded narratives. Finally, a comparative benchmark of a survey involving 22 expert chemists reveals that expert evaluators provide deep insights.
Applications · Everything Else
Statement autoformalization acts as a critical bridge between human mathematics and formal mathematics by translating natural language problems into formal language. While prior works have focused on data synthesis and diverse training paradigms to optimize end-to-end Large Language Models (LLMs), they typically treat formal code as flat sequences, neglecting the hierarchical logic inherent in mathematical statements. In this work, we introduce Decompose, Structure, and Repair (DSR), a neuro-symbolic framework that restructures autoformalization into a modular pipeline. DSR decomposes statements into logical components and maps them to structured operator trees, leveraging this topological blueprint to precisely localize and repair errors via sub-tree refinement. Furthermore, we introduce PRIME, a benchmark of 156 undergraduate and graduate-level theorems selected from canonical textbooks and expertly annotated in Lean 4. Experimental results demonstrate that DSR establishes a new state-of-the-art, consistently outperforming baselines under equivalent computational budgets. The benchmark, code, and detailed experimental results are available at https://anonymous.4open.science/r/DSR-4A51.
Applications · Health / Medicine
Protein language models (pLMs) have emerged as powerful predictors of protein structure and function. However, the computational circuits underlying their predictions remain poorly understood. Recent mechanistic interpretability methods decompose pLM representations into interpretable features, but they treat each layer independently and thus fail to capture cross-layer computation, limiting their ability to approximate the full model. We introduce ProtoMech, a framework for discovering computational circuits in pLMs using cross-layer transcoders that learn sparse latent representations jointly across layers to capture the model’s full computational circuitry. Applied to the pLM ESM2, ProtoMech recovers 82–89\% of the original performance on protein family classification and function prediction tasks. ProtoMech then identifies compressed circuits that use <1\% of the latent space while retaining up to 79\% of model accuracy, revealing correspondence with structural and functional motifs, including binding, signaling, and stability. Steering along these circuits enables high-fitness protein design, surpassing baseline methods in more than 70\% of cases. These results establish ProtoMech as a principled framework for protein circuit tracing.
Deep Learning · Graph Neural Networks
In recent advances, to enable a fully data-driven learning paradigm on relational databases (RDB), relational deep learning (RDL) is proposed to structure the RDB as a heterogeneous entity graph and adopt the graph neural network (GNN) as the predictive model. However, existing RDL methods neglect the imbalance problem of relational data in RDBs and risk under-representing the minority entities, leading to an unusable model in practice. In this work, we investigate, for the first time, class imbalance problem in RDB entity classification and design the relation-centric minority synthetic over-sampling GNN (**Rel-MOSS**), in order to fill a critical void in the current literature. Specifically, to mitigate the issue of minority-related information being submerged by majority counterparts, we design the relation-wise gating controller to modulate neighborhood messages from each individual relation type. Based on the relational-gated representations, we further propose the relation-guided minority synthesizer for over-sampling, which integrates the entity relational signatures to maintain relational consistency. Extensive experiments on 12 entity classification datasets provide compelling evidence for the superiority of Rel-MOSS, yielding an average improvement of up to 2.46% and 4.00% in terms of *Balanced Accuracy* and *G-Mean*, compared with SOTA RDL methods and classic methods for handling class imbalance.
Theory · Learning Theory
Sparse PCA is one of the most well-studied problems in high-dimensional statistics. In this problem, we are given samples from a distribution with covariance $\\mathbf{\Sigma}$, whose top eigenvector $\\mathbf{v} \in \\mathbb{R}^d$ is $s$-sparse. Existing sparse PCA algorithms can be broadly categorized into (1) combinatorial algorithms (e.g., diagonal or elementwise covariance thresholding) and (2) SDP-based algorithms. While combinatorial algorithms are much simpler, they are typically only analyzed under the spiked identity model (where $\\mathbf{\Sigma} \propto \\mathbf{I}_d + \gamma \\mathbf{v}\\mathbf{v}^\top$ for some $\gamma > 0$), whereas SDP-based algorithms require no additional assumptions on $\\mathbf{\Sigma}$. We demonstrate explicit counterexample covariances $\\mathbf{\Sigma}$ against the success of standard combinatorial algorithms for sparse PCA, when moving beyond the spiked identity model. In light of this discrepancy, we give the first combinatorial method for sparse PCA that provably succeeds for general $\\mathbf{\Sigma}$ using $\\mathsf{poly}(s, \log(d))$ samples and $d^2 \cdot \\mathsf{poly}(s, \log(d))$ time, by providing a global convergence guarantee on the truncated power method of Yuan and Zhang (JMLR, 2013). We provide a natural generalization of our method to recovering $k$ sparse principal components. Finally, we evaluate our method on synthetic and real-world sparse PCA datasets.
Deep Learning · Large Language Models
Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a key ingredient for unlocking complex reasoning capabilities in large language models. Recent work ProRL \citep{liu2025prorl} has shown promise in scaling RL by increasing the number of training steps. However, performance plateaus after thousands of steps, with clear diminishing returns from allocating more computation to additional training. In this work, we investigate a complementary paradigm for scaling RL: \textbf{BroRL}—increasing the number of rollouts per example to hundreds to exhaustively \textbf{Bro}aden exploration, which yields continuous performance gains beyond the saturation point observed in ProRL when scaling the number of training steps. Our approach is motivated by a mass balance equation analysis allowing us to characterize the rate of change in probability mass for correct and incorrect tokens during the reinforcement process. We show that under a one-step RL assumption, sampled rollout tokens contribute to correct-mass expansion, while unsampled tokens outside rollouts may lead to gains or losses depending on their distribution and the net reward balance. Importantly, as the number of rollouts per example $N$ increases, the effect of unsampled terms diminishes, making overall correct-mass expansion more likely. To validate our theoretical analysis, we conduct simulations under more relaxed conditions and find that a sufficiently large rollout size $N$—corresponding to ample exploration—can increase the probability mass of correct tokens broadly, and in our simulator it increases all correct-token probabilities and eliminates knowledge shrinkage. Empirically, BroRL revives models saturated after 3K ProRL training steps and demonstrates robust, continuous improvement, achieving strong results for the 1.5B model across diverse benchmarks. Notably, under the same training time, BroRL is both more data- and compute-efficient: large-$N$ rollouts reduce the number of filtered samples during dynamic sampling at the algorithmic level and nearly double generation throughput compared to ProRL in our hardware setup; this throughput increase is consistent with shifting generation from a more memory-bound regime toward a more compute-bound one.
Deep Learning · Generative Models and Autoencoders
Unpaired domain translation remains a challenging task due to the need of finding a balance between faithfulness and realism. In this paper, we propose a method called Regularized Distribution Matching Distillation (RDMD) that combines the best properties of Optimal Transport (OT) and diffusion-based domain translation methods. Instead of the conventional adversarial training, RDMD utilizes diffusion-based distribution matching, addressing the common shortcomings of OT methods and providing a strong initialization for the trained models. RDMD provides efficient one-step inference, explicitly controls the input-output alignment via regularization of the transport cost and maintains high faithfulness similar to the OT methods. We prove that in theory RDMD approximates the OT map and demonstrate its empirical performance on several tasks, including unpaired image-to-image translation in pixel and latent space and unpaired text detoxification. Empirical results show that RDMD achieves a comparable or better faithfulness-realism trade-off compared to the diffusion and OT baselines.
Probabilistic Methods · Bayesian Models and Methods
Bayesian experimental design (BED) is a principled framework for data-efficient design of sequential experiments. However, existing BED methods are unable to adapt to dynamic constraints inherent in real-world tasks due to budget limitations, varying costs, or physical constraints that restrict how designs evolve over time. In this paper, we introduce a novel approach to BED that enables constrained optimization of experimental designs by combining offline pre-training of an amortized policy and a posterior network with online multi-step lookahead planning using scenario trees. We empirically demonstrate that our method yields substantially more informative design sequences than existing methods across a range of constrained BED tasks, while incurring only a modest additional computational overhead.
Deep Learning · Large Language Models
Group Relative Policy Optimization (GRPO) is effective for training language models on complex reasoning. However, since the objective is defined relative to a group of sampled trajectories, extended deliberation can create more chances to realize relative gains, leading to inefficient reasoning and overthinking, and complicating the trade-off between correctness and rollout efficiency. Controlling this behavior is difficult in practice, considering (i) Length penalties are hard to calibrate because longer rollouts may reflect harder problems that require longer reasoning, penalizing tokens risks truncating useful reasoning along with redundant continuation; and (ii) supervision that directly indicates when to continue or stop is typically unavailable beyond final answer correctness. We propose Weakly Supervised GRPO (WS-GRPO), which improves rollout efficiency by converting terminal rewards into correctness-aware guidance over partial trajectories. Unlike global length penalties that are hard to calibrate, WS-GRPO trains a preference model from outcome-only correctness to produce prefix-level signals that indicate when additional continuation is beneficial. Thus, WS-GRPO supplies outcome-derived continue/stop guidance, reducing redundant deliberation while maintaining accuracy. We provide theoretical results and empirically show on reasoning benchmarks that WS-GRPO substantially reduces rollout length while remaining competitive with GRPO baselines.
Applications · Time Series
Time series imputation benefits from leveraging cross-feature correlations, yet existing attention based methods re-discover feature relationships at each layer, lacking persistent anchors to maintain consistent representations. To address this, we propose HELIX, which assigns each feature a learnable feature identity, a persistent embedding that captures intrinsic semantic properties throughout the network. Unlike graph-based methods that rely on predefined topology and assume homogeneous spatial relationships, HELIX learns arbitrary feature dependencies end-to-end from temporal co-variation, naturally handling datasets where features mix spatial locations with semantic variables. Integrated with hybrid temporal-feature attention, HELIX achieves the state-of-the-art performance, ranking first among 17 methods across 21 experimental settings. Furthermore, our mechanistic analysis reveals that feature attention progressively aligns with underlying physical structure across layers, demonstrating more effectively exploits cross-feature dependencies for imputation.
Knowledge distillation improves large language model (LLM) reasoning by compressing the knowledge of a teacher LLM to train smaller LLMs. On-policy distillation advances this approach by having the student sample its own trajectories while a teacher LLM provides dense token-level supervision, addressing the distribution mismatch between training and inference in off-policy distillation methods. However, on-policy distillation typically requires a separate, often larger, teacher LLM and does not explicitly leverage ground-truth solutions available in reasoning datasets. Inspired by the intuition that a sufficiently capable LLM can rationalize external privileged reasoning traces and teach its weaker self (i.e., the version without access to privileged information), we introduce On-Policy Self-Distillation (OPSD), a framework where a single model acts as both teacher and student by conditioning on different contexts. The teacher policy conditions on privileged information (e.g., verified reasoning traces) while the student policy sees only the question; training minimizes the per-token divergence between these distributions over the student's own rollouts. We demonstrate the efficacy of our method on multiple mathematical reasoning benchmarks, achieving 4-8× token efficiency compared to reinforcement learning methods such as GRPO and superior performance over off-policy distillation methods.
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.
Applications · Social Sciences
This position paper argues that **LLM-based social simulations require clear boundaries to make meaningful contributions to social science**. While Large Language Models (LLMs) offer promising capabilities for simulating human behavior, their tendency to produce homogeneous outputs, acting as an "average persona", fundamentally limits their ability to capture the behavioral diversity essential for complex social dynamics. We examine why heterogeneity matters for social simulations and how current LLMs fall short, analyzing the relationship between mean alignment and variance in LLM-generated behaviors. Through a systematic review of representative studies, we find that validation practices often fail to match the heterogeneity requirements of research questions: while most papers include ground truth comparisons, fewer than half explicitly assess behavioral variance, and most that do report lower variance than human populations. We propose that researchers should: (1) match validation depth to the heterogeneity demands of their research questions, (2) explicitly report variance alongside mean alignment, and (3) constrain claims to collective-level qualitative patterns when variance is insufficient. Rather than dismissing LLM-based simulation, we advocate for a boundary-aware approach that ensures these methods contribute genuine insights to social science.
Deep Learning · Generative Models and Autoencoders
Diffusion models have become a dominant paradigm for high-quality generative modeling, while post-training is essential for adapting them to diverse downstream applications. However, post-training of large diffusion models is still challenging due to the prohibitive memory footprints and slow training speed, which existing parameter-efficient fine-tuning methods only partially address. To overcome these limitations, we propose FourTune, an efficient post-training framework for diffusion models based on an end-to-end W4A4G4 paradigm. FourTune introduces a triple-branch hybrid pipeline that augments the standard LoRA architecture with a frozen numerical stabilizer to isolate quantization-sensitive outliers, enabling stable training under native 4-bit computation. In addition, FourTune employs hardware-efficient block-wise quantization and customized fused kernels to support efficient quantized backpropagation and reduce memory bandwidth overhead. Across customization, reinforcement learning, and distillation tasks, FourTune matches the quality of full-precision fine-tuning. On FLUX.1-dev (12B), FourTune reduces memory overhead by $2.25\times$ and increases end-to-end training throughput by $2.27\times$ compared to BF16 LoRA.
General Machine Learning · Evaluation
Tool-use agents that address day-to-day digital tasks such as ordering groceries must not only operate applications, but also interact with the user, e.g., to ask clarification questions, prompt for confirmation, and inform the user when the instruction is infeasible. However, current benchmarks for evaluating agent-user interactions do not capture the diversity of such interactions. Further, they operate in small environments with few, often non-state-changing, APIs. To address this gap, we introduce AppWorld-UL, a ``user-in-the-loop'' benchmark of 306 challenging tasks requiring diverse agent-user interactions. Building upon the AppWorld framework with 9 popular simulated apps like Amazon and Spotify, we systematically modify original tasks to introduce ambiguities and constraints that necessitate various types of agent-user interaction. User behavior is simulated by an LLM prompted to respond with carefully designed knowledge boundaries, offering more reliable simulation than the unconstrained or overly rigid alternatives used in prior work. Our evaluation reveals that a state-of-the-art LLM, GPT-5, achieves only 38.2\% success on AppWorld-UL and that correct user-interaction is crucial for success. This demonstrates the benchmark's difficulty and its potential to advance research on user-in-the-loop tool-use agents.
Deep Learning · Everything Else
Test-Time Scaling (TTS) improves LLM reasoning by exploring multiple candidate responses and then operating over this set to find the best output. A tacit premise behind TTS is that sufficiently diverse candidate pools enhance reliability. In this work, we show that this assumption in TTS introduces a previously unrecognized failure mode. When candidate diversity is curtailed, even by a modest amount, TTS becomes much more likely to produce unsafe outputs. We present a reference-guided diversity reduction protocol (RefDiv) that serves as a diagnostic attack to stress test TTS pipelines. Through extensive experiments across open-source models (e.g. Qwen3, Mistral, Llama3.1, Gemma3) and two widely used TTS strategies (Monte Carlo Tree Search and Best-of-N), constraining diversity consistently signifies the rate at which TTS produces unsafe results. The effect is often stronger than that produced by prompts directly with high adversarial intent scores. This observed phenomenon also transfers across TTS strategies and to closed-source models (e.g. OpenAI o3-mini and Gemini-2.5-Pro), thus indicating that this is a general and extant property of TTS rather than a model-specific artifact. Additionally, we find that numerous widely used safety guardrail classifiers (e.g. Llama-Guard), are unable to flag the adversarial input prompts generated by RefDiv, demonstrating that existing defenses offer limited protection against this diversity-driven failure mode.
Theory · Reinforcement Learning and Planning
We study the problem of learning the optimal policy in a discounted, infinite-horizon reinforcement learning (RL) setting in the presence of adversarially corrupted rewards. To address this problem, we develop a novel robust variant of the Q-learning algorithm and analyze it under the challenging asynchronous sampling model with time-correlated data. Despite corruption, we prove that the finite-time guarantees of our approach match existing bounds, up to an additive term that scales with the fraction of corrupted samples. We also establish an information-theoretic lower bound, revealing that our guarantees are near-optimal. Notably, our algorithm is agnostic to the underlying reward distribution and provides the first finite-time robustness guarantees for asynchronous Q-learning. A key element of our analysis is a refined Azuma-Hoeffding inequality for almost-martingales, which may have broader applicability in the study of RL algorithms.
Deep Learning · Theory
Recent work describes what transformers can and cannot compute through connections to boolean circuits, but existing results lack exact characterizations and are sensitive to modeling choices. Padded transformers---whose input is padded with filler symbols such as ``...''---emerge as a useful gadget for establishing equivalences to circuit classes by providing polynomial space for adaptive parallel computation. However, only a limited set of padded transformer idealizations has been studied, leaving open how robust these equivalences are to choices such as attention type, model width, and uniformity. We find that, under practical assumptions, padded transformers are surprisingly robust to all of these, and identify numeric precision and model depth as the main factors affecting expressivity. Concretely, we prove that polynomially-padded L-uniform constant-precision transformers with growing width equal L-uniform $\text{AC}^{0}$, while growing-precision ones achieve L-uniform $\text{TC}^{0}$ regardless of width. Furthermore, looping enables sequential processing analogous to circuits: $\log^d N$-looped constant-precision transformers reach FO-uniform $\text{AC}^{d}$, and growing-precision ones reach FO-uniform $\text{TC}^{d}$. Interestingly, growing width or precision beyond logarithmic does not increase expressivity, and all our results hold for both softmax and average hard attention transformers.
Applications · Chemistry, Physics, and Earth Sciences
Structured scientific spectra encode rich physical information while satisfying hard constraints such as conservation and spectral geometry. We study a canonical example, the electronic density of states (eDOS), whose accurate prediction is central to materials discovery. Prior methods often (i) decouple band gaps from eDOS, (ii) violate total-state conservation, or (iii) collapse crystals into global embeddings that obscure atom-projected contributions. We introduce \textbf{DeepSciReasoner}, a design paradigm for deep scientific reasoning under physical constraints. Instantiated for eDOS prediction, DeepSciReasoner combines structure-aware spectrum decoding with constraint-preserving physical reasoning, in this case, mass-conserving iterative refinement. It substantially improves eDOS accuracy while maintaining physical validity, enabling reliable high-throughput screening. Beyond eDOS, DeepSciReasoner offers a reusable blueprint for predicting structured scientific spectra under hard physical constraints.