Evolutionary Feature Engineering for Structured Data

Large language models are increasingly used as open-ended search operators in evolutionary optimization. We introduce Evolutionary Feature Engineering (EFE), a framework for using LLM-based evolution to discover preprocessing transformations for structured data. EFE represents transformations as Python programs with a standardized fit/transform interface, allowing them to be inserted directly into existing machine learning pipelines. During evolution, candidate programs are refined using dataset context, summary statistics, and downstream performance feedback on validation set. We instantiate EFE in two settings. For time-series forecasting, EFE-Time learns invertible, dataset-specific normalizations that improve off-the-shelf time-series foundation models. It reduces forecasting errors (MASE, WQL, MAE) 3% or more when averaged across datasets and improvements are as much as 19% on the COVID-Deaths dataset. Notably, these improvements occur with recent TSFMs such as Chronos-2. For tabular prediction, EFE-Tab evolves compact feature programs that add useful interpretable features and remove redundant ones, improving or matching existing LLM-based feature-engineering methods. We found EFE-Tab to be particularly effective on classical decision trees, where small sets of evolved features yield competitive accuracy while preserving interpretability. Overall, EFE demonstrates that LLM-based evolution can improve both accuracy and interpretability when automatically tackling structured data.

Evolutionary Multi-Task Optimization for LLM-Guided Program Discovery

Recent LLM-guided evolutionary search methods have shown that iterative program mutation can discover strong algorithms, but they typically optimize each task independently, even when related tasks share reusable structure. We introduce Evolutionary Multi-Task Optimization (EMO) for LLM-guided program discovery, and propose EMO-STA (Shared-Then-Adapt), a two-stage framework that first evolves a shared archive of executable programs across a task family and then adapts selected shared candidates to each target task. Within EMO-STA, we explore multiple adaptation strategies, including warm-starting from the shared archive, adapting the best average shared program, and adapting the shared program that performs best on each target task. Across eight task families spanning continuous optimization, geometric construction, modeling, and algorithmic optimization, EMO-STA improves over matched-compute single-task evolution in most settings, with STA Best-Local providing the strongest in-distribution adaptation and STA Best-Shared yielding robust transfer to unseen tasks. Compute-allocation experiments show that allocating a substantial fraction of the family-level budget to shared evolution is consistently beneficial, with roughly balanced shared and adaptation budgets often being optimal. Beyond compute efficiency, we show that shared evolution can mitigate overfitting in low-evidence settings (e.g. few training data), including ARC tasks and time-series feature engineering, by favoring programs that generalize across all tasks rather than exploiting task-specific brittle artifacts.

Stochastic Sparse Attention for Memory-Bound Inference

Autoregressive decoding becomes bandwidth-limited at long contexts, as generating each token requires reading all $n_k$ key and value vectors from KV cache. We present Stochastic Additive No-mulT Attention (SANTA), a method that sparsifies value-cache access by sampling $S \ll n_k$ indices from the post-softmax distribution and aggregates only those value rows. This yields an unbiased estimator of the post-softmax value aggregation while replacing value-stage multiply-accumulates with gather-and-add. We introduce stratified sampling to design variance-reduced, GPU-friendly variants, demonstrating $1.5\times$ decode-step attention kernel speedup over FlashInfer and FlashDecoding on an NVIDIA RTX 6000 Ada while matching baseline accuracy at 32k-token contexts. Finally, we propose Bernoulli $qK^\mathsf{T}$ sampling as a complementary technique to sparsify the score stage, reducing key-feature access through stochastic ternary queries. Both methods are orthogonal to upstream techniques such as ternary quantization, low-rank projections, and KV-cache compression. Together, they point toward sparse, multiplier-free, and energy-efficient inference. We open-source our kernels at: https://github.com/OPUSLab/SANTA.git

Learning to Correct: Calibrated Reinforcement Learning for Multi-Attempt Chain-of-Thought

State-of-the-art reasoning models utilize long chain-of-thought (CoT) to solve increasingly complex problems using more test-time computation. In this work, we explore a long CoT setting where the model makes up to K successive attempts at solving a problem, in which each attempt is allowed to build on earlier ones after the model receives a hard verifier feedback. This motivates RL methods that can harness per-attempt rewards by carefully weighting individual attempts. We study optimizing the Verification@K reward (the model succeeds by the K-th attempt) and show that naively weighing the attempts by their pass/fail results in biased gradients. We introduce Calibrated Attempt-Level (CAL) GRPO by devising a weighing strategy to obtain unbiased gradients while maintaining small variance. Our theory reveals how incorporating per-attempt rewards influence the training and the eventual Verification@K performance. Experiments, baselines, and ablations on synthetic and real data corroborate our theory and the benefits of CAL-GRPO over vanilla GRPO as well as naive weighting.

Enabling Intrinsic Reasoning over Dense Geospatial Embeddings with DFR-Gemma

Representation learning for geospatial and spatio-temporal data plays a critical role in enabling general-purpose geospatial intelligence. Recent geospatial foundation models, such as the Population Dynamics Foundation Model (PDFM), encode complex population and mobility dynamics into compact embeddings. However, their integration with Large Language Models (LLMs) remains limited. Existing approaches to LLM integration treat these embeddings as retrieval indices or convert them into textual descriptions for reasoning, introducing redundancy, token inefficiency, and numerical inaccuracies. We propose Direct Feature Reasoning-Gemma (DFR-Gemma), a novel framework that enables LLMs to reason directly over dense geospatial embeddings. DFR aligns high-dimensional embeddings with the latent space of an LLM via a lightweight projector, allowing embeddings to be injected as semantic tokens alongside natural language instructions. This design eliminates the need for intermediate textual representations and enables intrinsic reasoning over spatial features. To evaluate this paradigm, we introduce a multi-task geospatial benchmark that pairs embeddings with diverse question-answer tasks, including feature querying, comparison, and semantic description. Experimental results show that DFR allows LLMs to decode latent spatial patterns and perform accurate zero-shot reasoning across tasks, while significantly improving efficiency compared to text-based baselines. Our results demonstrate that treating embeddings as primary data inputs, provides a more direct, efficient, and scalable approach to multimodal geospatial intelligence.

Learning to Bet for Horizon-Aware Anytime-Valid Testing

We develop horizon-aware anytime-valid tests and confidence sequences for bounded means under a strict deadline $N$. Using the betting/e-process framework, we cast horizon-aware betting as a finite-horizon optimal control problem with state space $(t, \log W_t)$, where $t$ is the time and $W_t$ is the test martingale value. We first show that in certain interior regions of the state space, policies that deviate significantly from Kelly betting are provably suboptimal, while Kelly betting reaches the threshold with high probability. We then identify sufficient conditions showing that outside this region, more aggressive betting than Kelly can be better if the bettor is behind schedule, and less aggressive can be better if the bettor is ahead. Taken together these results suggest a simple phase diagram in the $(t, \log W_t)$ plane, delineating regions where Kelly, fractional Kelly, and aggressive betting may be preferable. Guided by this phase diagram, we introduce a Deep Reinforcement Learning approach based on a universal Deep Q-Network (DQN) agent that learns a single policy from synthetic experience and maps simple statistics of past observations to bets across horizons and null values. In limited-horizon experiments, the learned DQN policy yields state-of-the-art results.

Covariance-Aware Transformers for Quadratic Programming and Decision Making

We explore the use of transformers for solving quadratic programs and how this capability benefits decision-making problems that involve covariance matrices. We first show that the linear attention mechanism can provably solve unconstrained QPs by tokenizing the matrix variables (e.g.~$A$ of the objective $\frac{1}{2}x^\top Ax+b^\top x$) row-by-row and emulating gradient descent iterations. Furthermore, by incorporating MLPs, a transformer block can solve (i) $\ell_1$-penalized QPs by emulating iterative soft-thresholding and (ii) $\ell_1$-constrained QPs when equipped with an additional feedback loop. Our theory motivates us to introduce Time2Decide: a generic method that enhances a time series foundation model (TSFM) by explicitly feeding the covariance matrix between the variates. We empirically find that Time2Decide uniformly outperforms the base TSFM model for the classical portfolio optimization problem that admits an $\ell_1$-constrained QP formulation. Remarkably, Time2Decide also outperforms the classical "Predict-then-Optimize (PtO)" procedure, where we first forecast the returns and then explicitly solve a constrained QP, in suitable settings. Our results demonstrate that transformers benefit from explicit use of second-order statistics, and this can enable them to effectively solve complex decision-making problems, like portfolio construction, in one forward pass.

When and How Unlabeled Data Provably Improve In-Context Learning

Recent research shows that in-context learning (ICL) can be effective even when demonstrations have missing or incorrect labels. To shed light on this capability, we examine a canonical setting where the demonstrations are drawn according to a binary Gaussian mixture model (GMM) and a certain fraction of the demonstrations have missing labels. We provide a comprehensive theoretical study to show that: (1) The loss landscape of one-layer linear attention models recover the optimal fully-supervised estimator but completely fail to exploit unlabeled data; (2) In contrast, multilayer or looped transformers can effectively leverage unlabeled data by implicitly constructing estimators of the form $\sum_{i\ge 0} a_i (X^\top X)^iX^\top y$ with $X$ and $y$ denoting features and partially-observed labels (with missing entries set to zero). We characterize the class of polynomials that can be expressed as a function of depth and draw connections to Expectation Maximization, an iterative pseudo-labeling algorithm commonly used in semi-supervised learning. Importantly, the leading polynomial power is exponential in depth, so mild amount of depth/looping suffices. As an application of theory, we propose looping off-the-shelf tabular foundation models to enhance their semi-supervision capabilities. Extensive evaluations on real-world datasets show that our method significantly improves the semisupervised tabular learning performance over the standard single pass inference.

Extrapolation by Association: Length Generalization Transfer in Transformers

Transformer language models have demonstrated impressive generalization capabilities in natural language domains, yet we lack a fine-grained understanding of how such generalization arises. In this paper, we investigate length generalization--the ability to extrapolate from shorter to longer inputs--through the lens of \textit{task association}. We find that length generalization can be \textit{transferred} across related tasks. That is, training a model with a longer and related auxiliary task can lead it to generalize to unseen and longer inputs from some other target task. We demonstrate this length generalization transfer across diverse algorithmic tasks, including arithmetic operations, string transformations, and maze navigation. Our results show that transformer models can inherit generalization capabilities from similar tasks when trained jointly. Moreover, we observe similar transfer effects in pretrained language models, suggesting that pretraining equips models with reusable computational scaffolding that facilitates extrapolation in downstream settings. Finally, we provide initial mechanistic evidence that length generalization transfer correlates with the re-use of the same attention heads between the tasks. Together, our findings deepen our understanding of how transformers generalize to out-of-distribution inputs and highlight the compositional reuse of inductive structure across tasks.

Continuous Chain of Thought Enables Parallel Exploration and Reasoning

Current language models generate chain-of-thought traces by autoregressively sampling tokens from a finite vocabulary. While this discrete sampling has achieved remarkable success, conducting chain-of-thought with continuously-valued tokens (CoT2) offers a richer and more expressive alternative. Our work examines the benefits of CoT2 through logical reasoning tasks that inherently require search capabilities and provide optimization and exploration methods for CoT2. Theoretically, we show that CoT2 allows the model to track multiple traces in parallel and quantify its benefits for inference efficiency. Notably, one layer transformer equipped with CoT2 can provably solve the combinatorial "subset sum problem" given sufficient embedding dimension. These insights lead to a novel and effective supervision strategy where we match the softmax outputs to the empirical token distributions of a set of target traces. Complementing this, we introduce sampling strategies that unlock policy optimization and self-improvement for CoT2. Our first strategy samples and composes $K$ discrete tokens at each decoding step to control the level of parallelism, and reduces to standard CoT when $K=1$. Our second strategy relies on continuous exploration over the probability simplex. Experiments confirm that policy optimization with CoT2 indeed improves the performance of the model beyond its initial discrete or continuous supervision.