Market microstructure has long classified trading activity by its informational role: an informed trader demands liquidity by trading in the direction of private information, while a market maker supplies liquidity by absorbing that order flow and earning the spread in compensation Kyle (1985); Glosten and Milgrom (1985). This classification is typically recovered from the data the classifier requires: signed order flow, quote revisions, or the sequential-trade structure of the market. The classification is harder to apply to an algorithmic strategy whose internal logic is unobservable. However, the signals or optimization problems generating the decisions of a typical quantitative fund are not visible, even though the trades and reported positions may be available. This paper shows that the liquidity role of such a strategy (consumer or provider) can be recovered from realized portfolio costs and trade decisions alone, without observing quotes, order flow, or any other microstructure-specific signal.

Neural networks are known to be susceptible to over-reliance on spurious correlations. However, the precise mechanism by which models exploit shortcut features is not fully understood, and algorithms to mitigate this behavior rely on as yet unjustified assumptions about the learned representations. In this work, we provide the first end-to-end theoretical characterization of spurious feature learning for two-layer ReLU neural networks trained by online minibatch SGD on the logistic loss. We consider data drawn from the high-dimensional Boolean hypercube with a quadratic signal function (namely XOR) and a linear spurious correlation. We show that SGD learns the spurious feature first, and exponentially fast. Moreover, the optimization dynamics couple the spurious and signal features, with a stronger spurious component inhibiting signal feature learning. Our analysis reveals precise phase transitions in the learning dynamics. In the first phase, alignment between the signs of the spurious feature and second-layer weight drives rapid growth of the spurious feature. In the second phase, large majority group margin slows learning and the signal feature remains suppressed. When the spurious correlation is maximally strong, we show theoretically that the spurious feature dominates even at the sample complexity threshold where XOR would be learned in isolation (i.e., if the spurious feature was absent). In contrast, when the correlation strength is constant, we provide preliminary empirical evidence that the model can eventually learn the XOR signal, although the spurious feature is not forgotten.

Contrastive embedding models trained with scale-invariant losses are typically paired with distance metrics like cosine similarity, effectively ignoring embedding magnitudes. However, surprisingly, empirical studies reveal that despite this, these "discarded" norms seem to correlate with semantic properties such as concept specificity, token frequency, and human uncertainty. In this work, we provide a formal theoretical framework explaining this phenomenon. By analyzing the optimization dynamics, we derive an analytic formula demonstrating that embedding length naturally encodes this information as a byproduct of the training process. We also show how this gives rise to signals that can serve as "free" calibration tools in specific models and retrieval tasks, providing a grounded explanation for a previously heuristic observation.

Binary classification from positive-only samples is a variant of PAC learning in which the learner receives i.i.d. samples from the positive region of an unknown target concept, but is evaluated under the original distribution (which places mass on both positive and negative regions). This model dates back to Natarajan [1987, STOC], and the characterization of improper learning is well-known -- it even appears in textbooks. The characterization of proper positive-only learning, however, has long remained open. In this work, we revisit and settle this question: a concept class is properly learnable from positive-only samples if and only if it has finite VC dimension and satisfies a new combinatorial condition, which we call uniform exterior separability. Together with several separation results, this characterization reveals a surprisingly rich landscape that differs sharply from standard PAC learning: proper and improper learning are separated, randomized and deterministic proper learning are separated, there are classes for which no ERM is a learner, and finite VC dimension does not suffice even for non-uniform learning. Along the way, we introduce new combinatorial dimensions that we believe can be of broader interest in learning theory.

We study safe linear bandits (SLBs), where an agent selects actions from a convex set to maximize an unknown linear objective subject to unknown linear constraints in each round. Existing methods for SLBs provide strong regret guarantees, but require solving expensive optimization problems. To address this, we propose Constrained Linear Thompson Sampling (COLTS), a sampling-based framework that selects actions by solving perturbed linear programs, which significantly reduces computational costs while matching the regret and risk of prior methods. We develop two main variants: S-COLTS, which ensures zero risk and eO( d3T) regret given a safe action, and R-COLTS, which achieves eO( d3T)regret and risk with no instance information. In simulations, these methods match or outperform state of the art SLB approaches while substantially improving scalability. On the technical front, we introduce a novel coupled noise design that ensures frequent'local optimism' about the true optimum, and a scaling-based analysis to handle the per-round variability of constraints.

Training-free guided generation is a widely used and powerful technique that allows the end user to exert further control over the generative process of flow/diffusion models. Generally speaking, two families of techniques have emerged for solving this problem for gradient-based guidance: namely, posterior guidance (i.e., guidance by projecting the current sample to the target distribution via the target prediction model) and end-to-end guidance (i.e., guidance by performing backpropagation throughout the entire ODE solve). In this work, we show that these two seemingly separate families can actually be unified by looking at the posterior guidance as a greedy strategy of end-to-end guidance. We explore the theoretical connections between these two families and provide an in-depth theoretical understanding of these two techniques relative to the continuous ideal gradients. Motivated by this analysis, we then show a method for interpolating between these two families enabling a trade-off between compute and accuracy of the guidance gradients.

We introduce a novel framework for differentially private (DP) statistical estimation via data truncation, addressing a key challenge in DP estimation when the data support is unbounded. Traditional approaches rely on problem-specific sensitivity analysis, limiting their applicability. By leveraging techniques from truncated statistics, we develop computationally efficient DP estimators for exponential family distributions, including Gaussian mean and covariance estimation, achieving near-optimal sample complexity. Previous works on exponential families only consider bounded or one-dimensional families. Our approach mitigates sensitivity through truncation while carefully correcting for the introduced bias using maximum likelihood estimation and DP stochastic gradient descent. Along the way, we establish improved uniform convergence guarantees for the log-likelihood function of exponential families, which may be of independent interest. Our results provide a general blueprint for DP algorithm design via truncated statistics.

Recently, Large Language Models (LLMs) have been increasingly used to support various decision-making tasks, assisting humans in making informed decisions. However, when LLMs confidently provide incorrect information, it can lead humans to make suboptimal decisions. To prevent LLMs from generating incorrect information on topics they are unsure of and to improve the accuracy of generated content, prior works have proposed Retrieval Augmented Generation (RAG), where external documents are referenced to generate responses. However, previous RAG methods focus only on retrieving documents most relevant to the input query, without specifically aiming to ensure that the human user's decisions are well-calibrated. To address this limitation, we propose a novel retrieval method called Calibrated Retrieval-Augmented Generation (CalibRAG), which ensures that decisions informed by RAG are well-calibrated. Then we empirically validate that CalibRAG improves calibration performance as well as accuracy, compared to other baselines across various datasets.

Generative models for structure-based drug design are often limited to a specific modality, restricting their broader applicability. To address this challenge, we introduce FuncBind, a framework based on computer vision to generate targetconditioned, all-atom molecules across atomic systems. FuncBind uses neural fields to represent molecules as continuous atomic densities and employs scorebased generative models with modern architectures adapted from the computer vision literature. This modality-agnostic representation allows a single unified model to be trained on diverse atomic systems, from small to large molecules, and handle variable atom/residue counts, including non-canonical amino acids. FuncBind achieves competitive in silico performance in generating small molecules, macrocyclic peptides, and antibody complementarity-determining region loops, conditioned on target structures. FuncBind also generated in vitro novel antibody binders via de novo redesign of the complementarity-determining region H3 loop of two chosen co-crystal structures. As a final contribution, we introduce a new dataset and benchmark for structure-conditioned macrocyclic peptide generation*.

We show how to use low-quality, synthetic, and out-of-distribution images to improve the quality of a diffusion model. Typically, diffusion models are trained on curated datasets that emerge from highly filtered data pools from the Web and other sources. We show that there is immense value in the lower-quality images that are often discarded. We present Ambient Diffusion Omni, a simple, principled framework to train diffusion models that can extract signal from all available images during training. Our framework exploits two properties of natural images - spectral power law decay and locality. We first validate our framework by successfully training diffusion models with images synthetically corrupted by Gaussian blur, JPEG compression, and motion blur. We then use our framework to achieve stateof-the-art ImageNet FID and we show significant improvements in both image quality and diversity for text-to-image generative modeling. The core insight is that noise dampens the initial skew between the desired high-quality distribution and the mixed distribution we actually observe. We provide rigorous theoretical justification for our approach by analyzing the trade-off between learning from biased data versus limited unbiased data across diffusion times.