State-space models (SSMs), particularly Mamba, emerge as an efficient Transformer alternative with linear complexity for long-sequence modeling. Recent empirical works demonstrate Mamba's in-context learning (ICL) capabilities competitive with Transformers, a critical capacity for large foundation models. However, theoretical understanding of Mamba's ICL remains limited, restricting deeper insights into its underlying mechanisms. Even fundamental tasks such as linear regression ICL, widely studied as a standard theoretical benchmark for Transformers, have not been thoroughly analyzed in the context of Mamba. To address this gap, we study the training dynamics of Mamba on the linear regression ICL task. By developing novel techniques tackling non-convex optimization with gradient descent related to Mamba's structure, we establish an exponential convergence rate to ICL solution, and derive a loss bound that is comparable to Transformer's. Importantly, our results reveal that Mamba can perform a variant of online gradient descent to learn the latent function in context. This mechanism is different from that of Transformer, which is typically understood to achieve ICL through gradient descent emulation. The theoretical results are verified by experimental simulation.

Machine learning models are often designed to maximize a primary goal, such as accuracy. However, as these models are increasingly used to inform decisions that affect people's lives or well-being, it is often unclear what the real-world repercussions of their deployment might be--making it crucial to understand and manage such repercussions effectively. Models maximizing user engagement on social media platforms, e.g., may inadvertently contribute to the spread of misinformation and content that deepens political polarization. This issue is not limited to social media--it extends to other applications where machine learning-informed decisions can have real-world repercussions, such as education, employment, and lending. Existing methods addressing this issue require prior knowledge or estimates of analytical models describing the relationship between a classifier's predictions and their corresponding repercussions. We introduce THEIA, a novel classification algorithm capable of optimizing a primary objective, such as accuracy, while providing high-confidence guarantees about its potential repercussions. Importantly, THEIA solves the open problem of providing such guarantees based solely on existing data with observations of previous repercussions. We prove that it satisfies constraints on a model's repercussions with high confidence and that it is guaranteed to identify a solution, if one exists, given sufficient data. We empirically demonstrate, using real-life data, that THEIA can identify models that achieve high accuracy while ensuring, with high confidence, that constraints on their repercussions are satisfied.

We introduce the Deep Value Benchmark (DVB), an evaluation framework that directly tests whether large language models (LLMs) learn fundamental human values or merely surface-level preferences. This distinction is critical for AI alignment: Systems that capture deeper values are likely to generalize human intentions robustly, while those that capture only superficial patterns in preference data risk producing misaligned behavior. The DVB uses a novel experimental design with controlled confounding between deep values (e.g., moral principles) and shallow features (e.g., superficial attributes). In the training phase, we expose LLMs to human preference data with deliberately correlated deep and shallow features--for instance, where a user consistently prefers (non-maleficence, formal language) options over (justice, informal language) alternatives. The testing phase then breaks these correlations, presenting choices between (justice, formal language) and (non-maleficence, informal language) options.

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Foundation models for time series analysis (TSA) have attracted significant attention. However, challenges such as training data scarcity and imbalance continue to hinder their development. Inspired by complex dynamic system theories, we design a series-symbol data generation mechanism, enabling the unrestricted creation of high-quality time series data paired with corresponding symbolic expressions. To leverage series-symbol data pairs with strong correlations, we develop SymTime, a pre-trained foundation model for enhancing time series representation using symbolic information. SymTime demonstrates competitive performance across five major TSA tasks when fine-tunes with downstream tasks, rivaling foundation models pre-trained on real-world datasets. This approach underscores the potential of series-symbol data generation and pretraining mechanisms in overcoming data scarcity and enhancing task performance.

Estimating treatment effects is crucial for personalized decision-making in medicine, but this task faces unique challenges in clinical practice. At training time, models for estimating treatment effects are typically trained on well-structured medical datasets that contain detailed patient information. However, at inference time, predictions are often made using textual descriptions (e.g., descriptions with self-reported symptoms), which are incomplete representations of the original patient information. In this work, we make three contributions.

We consider the task of interpolating a k-sparse band-limited signal from a small collection of noisy time-domain samples. Exploiting a new analytic framework for hierarchical frequency decomposition that performs systematic noise cancellation, we give the first polynomial-time algorithm with a provable (3+ 2+ε)approximation guarantee for continuous interpolation. Our method breaks the long-standing C > 100 barrier set by the best previous algorithms, sharply reducing the gap to optimal recovery and establishing a new state of the art for high-accuracy band-limited interpolation. We also give a refined "shrinking-range" variant that achieves a ( 2+ε+c)-approximation on any sub-interval (1 c)T for some c (0,1), which gives even higher interpolation accuracy.

With the development of biotechnology, RNA therapies have shown great potential. However, different from proteins, the sequences corresponding to a single RNA three-dimensional structure are more abundant. Most of the existing RNA design methods merely take into account the secondary structure of RNA, or are only capable of generating a limited number of candidate sequences. To address these limitations, we propose a geometric-algebra-enhanced Bayesian Flow Network for the inverse design of RNA, called RBFN. RBFN uses a Bayesian Flow Network to model the distribution of nucleotide sequences in RNA, enabling the generation of more reasonable RNA sequences. Meanwhile, considering the more flexible characteristics of RNA conformations, we utilize geometric algebra to enhance the modeling ability of the RNA three-dimensional structure, facilitating a better understanding of RNA structural properties. In addition, due to the scarcity of RNA structures and the limitation that there are only four types of nucleic acids, we propose a new time-step distribution sampling to address the scarcity of RNA structure data and the relatively small number of nucleic acid types. Evaluation on the single-state fixed-backbone re-design benchmark and multi-state fixedbackbone benchmark indicates that RBFN can outperform existing RNA design methods in various RNA design tasks, enabling effective RNA sequence design.

Differentially private (DP) machine learning often relies on the availability of public data for tasks like privacy-utility trade-off estimation, hyperparameter tuning, and pretraining. While public data assumptions may be reasonable in text and image data, they are less likely to hold for tabular data due to tabular data heterogeneity across domains. We propose leveraging powerful priors to address this limitation; specifically, we synthesize realistic tabular data directly from schemalevel specifications - such as variable names, types, and permissible ranges - without ever accessing sensitive records. To that end, this work introduces the notion of "surrogate" public data - datasets generated independently of sensitive data, which consume no privacy loss budget and are constructed solely from publicly available schema or metadata. Surrogate public data are intended to encode plausible statistical assumptions (informed by publicly available information) into a dataset with many downstream uses in private mechanisms. We automate the process of generating surrogate public data with large language models (LLMs); in particular, we propose two methods: direct record generation as CSV files, and automated structural causal model (SCM) construction for sampling records. Through extensive experiments, we demonstrate that surrogate public tabular data can effectively replace traditional public data when pretraining differentially private tabular classifiers. To a lesser extent, surrogate public data are also useful for hyperparameter tuning of DP synthetic data generators, and for estimating the privacy-utility tradeoff.

Large language models (LLMs) excel in tasks like question answering and dialogue, but complex tasks requiring interaction, such as negotiation and persuasion, require additional long-horizon reasoning and planning. Reinforcement learning (RL) fine-tuning can enable such planning in principle, but suffers from drawbacks that hinder scalability. In particular, multi-turn RL training incurs high memory and computational costs, which are exacerbated when training LLMs as policies. Furthermore, the largest LLMs do not expose the APIs necessary to be trained in such manner. As a result, modern methods to improve the reasoning of LLMs rely on sophisticated prompting mechanisms rather than RL fine-tuning. To remedy this, we propose a novel approach that uses goal-conditioned value functions to guide the reasoning of LLM agents, that scales even to large API-based models. These value functions predict how a task will unfold given an action, allowing the LLM agent to evaluate multiple possible outcomes, both positive and negative, to plan effectively. In addition, these value functions are trained over reasoning steps rather than full actions, to be a concise and light-weight module that facilitates decisionmaking in multi-turn interactions.