Despite rapid progress in LLM agents, performance on long-horizon, tool-using tasks remains fragile. To better understand this fragility, we ask a simple question: \emph{do all actions contribute equally to failure?} Analyzing execution traces on $τ$-Bench (Airline/Retail) and SWE-Bench Verified, we decompose trajectories into \emph{mutating} (environment-changing) vs.\ non-mutating steps and formalize \emph{decisive deviations}, earliest action, level divergences that flip success to failure. A logistic regression reveals that each additional deviation in a mutating action reduces the odds of success by upto $92\%$ on Airline and upto $96\%$ on Retail for SoTA models. In contrast, deviations in non-mutating actions have little to no effect. Errors also grow with context length as agents drift from role and act on stale constraints. Motivated by these observations, we introduce \cm{}, a model-agnostic, gradient-free, test-time safeguard that (i) adds mutation-gated verification, (ii) injects \emph{Targeted Reflection} before mutating steps, and (iii) performs block-based context cleaning. \cm{} delivers consistent gains, e.g., Qwen3-Thinking: +28\% \emph{relative} on Airline, +11\% on Retail, and +7\% on SWE-Bench Verified; Claude: +9\%/+7\%. We further identify ceiling effects in $τ$-Bench, where annotation errors and underspecified tasks artificially cap model performance. To address this, we release $τ$-Bench Verified, which restores benchmark headroom through targeted revisions. Our results argue for action-level analysis, targeted safeguards, and reliable evaluations as prerequisites for robust multi-turn agents.

Access to multiple predictive models trained for the same task, whether in regression or classification, is increasingly common in many applications. Aggregating their predictive uncertainties to produce reliable and efficient uncertainty quantification is therefore a critical but still underexplored challenge, especially within the framework of conformal prediction (CP). While CP methods can generate individual prediction sets from each model, combining them into a single, more informative set remains a challenging problem. To address this, we propose SACP (Symmetric Aggregated Con-formal Prediction), a novel method that aggregates nonconformity scores from multiple predictors. SACP transforms these scores into e-values and combines them using any symmetric aggregation function. This flexible design enables a robust, data-driven framework for selecting aggregation strategies that yield sharper prediction sets. We also provide theoretical insights that help justify the validity and performance of the SACP approach. Extensive experiments on diverse datasets show that SACP consistently improves efficiency and often outperforms state-of-the-art model aggregation baselines.

Heterogeneous data are now ubiquitous in many applications in which correctly identifying the subgroups from a heterogeneous population is critical. Although there is an increasing body of literature on subgroup detection, existing methods mainly focus on the univariate response setting. In this paper, we propose a joint heterogeneity and reduced-rank learning framework to simultaneously identify the subgroup structure and estimate the covariate effects for heterogeneous multivariate response regression. In particular, our approach uses rank-constrained pairwise fusion penalization and conducts the subgroup analysis without requiring prior knowledge regarding the individual subgroup memberships. We implement the proposed approach by an alternating direction method of multipliers (ADMM) algorithm and show its convergence. We also establish the asymptotic properties for the resulting estimators under mild and interpretable conditions. A predictive information criterion is proposed to select the rank of the coefficient matrix with theoretical support. The effectiveness of the proposed approach is demonstrated through simulation studies and a real data application.

In this work, we study contextual strongly convex simulation optimization and adopt an "optimize then predict" (OTP) approach for real-time decision making. In the offline stage, simulation optimization is conducted across a set of covariates to approximate the optimal-solution function; in the online stage, decisions are obtained by evaluating this approximation at the observed covariate. The central theoretical challenge is to understand how the inexactness of solutions generated by simulation-optimization algorithms affects the optimality gap, which is overlooked in existing studies. To address this, we develop a unified analysis framework that explicitly accounts for both solution bias and variance. Using Polyak-Ruppert averaging SGD as an illustrative simulation-optimization algorithm, we analyze the optimality gap of OTP under four representative smoothing techniques: $k$ nearest neighbor, kernel smoothing, linear regression, and kernel ridge regression. We establish convergence rates, derive the optimal allocation of the computational budget $Γ$ between the number of design covariates and the per-covariate simulation effort, and demonstrate the convergence rate can approximately achieve $Γ^{-1}$ under appropriate smoothing technique and sample-allocation rule. Finally, through a numerical study, we validate the theoretical findings and demonstrate the effectiveness and practical value of the proposed approach.

Classical supervised learning evaluates models primarily via predictive risk on hold-out data. Such evaluations quantify how well a function behaves on a distribution, but they do not address whether the internal decomposition of a model is uniquely determined by the data and evaluation design. In this paper, we introduce \emph{Modular Jets} for regression and classification pipelines. Given a task manifold (input space), a modular decomposition, and access to module-level representations, we estimate empirical jets, which are local linear response maps that describe how each module reacts to small structured perturbations of the input. We propose an empirical notion of \emph{mirage} regimes, where multiple distinct modular decompositions induce indistinguishable jets and thus remain observationally equivalent, and contrast this with an \emph{identifiable} regime, where the observed jets single out a decomposition up to natural symmetries. In the setting of two-module linear regression pipelines we prove a jet-identifiability theorem. Under mild rank assumptions and access to module-level jets, the internal factorisation is uniquely determined, whereas risk-only evaluation admits a large family of mirage decompositions that implement the same input-to-output map. We then present an algorithm (MoJet) for empirical jet estimation and mirage diagnostics, and illustrate the framework using linear and deep regression as well as pipeline classification.

With the increasing complexity of black-box machine learning models and their adoption in high-stakes areas, it is critical to provide explanations for their predictions. Local Interpretable Model-agnostic Explanation (LIME) is a widely used technique that explains the prediction of any classifier by learning an interpretable model locally around the predicted instance. However, it assumes that the local decision boundary is linear and fails to capture the non-linear relationships, leading to incorrect explanations. In this paper, we propose a novel method that can generate high-fidelity explanations. Multivariate adaptive regression splines (MARS) is used to model non-linear local boundaries that effectively captures the underlying behavior of the reference model, thereby enhancing the local fidelity of the explanation. Additionally, we utilize the N-ball sampling technique, which samples directly from the desired distribution instead of reweighting samples as done in LIME, further improving the faithfulness score. We evaluate our method on three UCI datasets across different classifiers and varying kernel widths. Experimental results show that our method yields more faithful explanations compared to baselines, achieving an average reduction of 37% in root mean square error, significantly improving local fidelity.

Sparse Autoencoders (SAEs) are widely employed for mechanistic interpretabil-ity and model steering. Within this context, steering is by design performed by means of decoding altered SAE intermediate representations. In contrast to existing literature, we forward an encoder-centric alternative to model steering which demonstrates a stronger cross-modal performance. We introduce S&P T op-K, a retraining-free and computationally lightweight Selection and Projection framework that identifies T op-K encoder features aligned with a sensitive attribute or behavior, optionally aggregates them into a single control axis, and computes an orthogonal projection to be subsequently applied directly in the model's native embedding space. In vision-language models, it improves fairness metrics on CelebA and FairFace by up to 3.2 times over conventional SAE usage, and in large language models, it substantially reduces aggressiveness and sycophancy in Llama-3 8B Instruct, achieving up to 3.6 times gains over masked reconstruction. These findings suggest that encoder-centric interventions provide a general, efficient, and more effective mechanism for shaping model behavior at inference time than the traditional decoder-centric use of SAEs.Figure 1: Sample generation demonstrating behavioral steering interventions on Llama 3 8B Instruct prompted to produce a sycophantic opinion. We apply two Sparse Autoencoder (SAE)-based methods to remove sycophancy: the conventional decoder-centric Masked Reconstruction approach and our proposed encoder-centric S&P Top-K protocol. Lower LLM-as-a-judge sycophancy scores indicate superior mitigation of the targeted behavioral pattern. The results illustrate that conventional Masked Reconstruction fails to suppress sycophantic behavior, while our S&P Top-K intervention successfully redirects the model's output, eliminating direct praise, repeatedly deferring endorsement, and leading the model to ultimately employ laudatory language in a sarcastic manner that subverts the original sycophantic intent. The main steps of our approach are highlighted in green. We first employ a selection mechanism to identify relevant SAE features.

This thesis develops methods for causal inference and causal representation learning (CRL) in high-dimensional, time-varying data. The first contribution introduces the Causal Dynamic Variational Autoencoder (CDVAE), a model for estimating Individual Treatment Effects (ITEs) by capturing unobserved heterogeneity in treatment response driven by latent risk factors that affect only outcomes. CDVAE comes with theoretical guarantees on valid latent adjustment and generalization bounds for ITE error. Experiments on synthetic and real datasets show that CDVAE outperforms baselines, and that state-of-the-art models greatly improve when augmented with its latent substitutes, approaching oracle performance without access to true adjustment variables. The second contribution proposes an efficient framework for long-term counterfactual regression based on RNNs enhanced with Contrastive Predictive Coding (CPC) and InfoMax. It captures long-range dependencies under time-varying confounding while avoiding the computational cost of transformers, achieving state-of-the-art results and introducing CPC into causal inference. The third contribution advances CRL by addressing how latent causes manifest in observed variables. We introduce a model-agnostic interpretability layer based on the geometry of the decoder Jacobian. A sparse self-expression prior induces modular, possibly overlapping groups of observed features aligned with shared latent influences. We provide recovery guarantees in both disjoint and overlapping settings and show that meaningful latent-to-observed structure can be recovered without anchor features or single-parent assumptions. Scalable Jacobian-based regularization techniques are also developed.

Suicide remains a leading cause of death in Western countries. As social media becomes central to daily life, digital footprints offer valuable insight into suicidal behavior. Focusing on individuals who attempted suicide while uploading videos to their channels, we investigate: How do linguistic patterns on YouTube reflect suicidal behavior, and how do these patterns align with or differ from expert knowledge? We examined linguistic changes around suicide attempts and compared individuals who attempted suicide while actively uploading to their channel with three control groups: those with prior attempts, those experiencing major life events, and matched individuals from the broader cohort. Applying complementary bottom-up, hybrid, and expert-driven approaches, we analyzed a novel longitudinal dataset of 181 suicide-attempt channels and 134 controls. In the bottom-up analysis, LLM-based topic-modeling identified 166 topics; five were linked to suicide attempts, two also showed attempt-related temporal changes (Mental Health Struggles, $OR = 1.74$; YouTube Engagement, $OR = 1.67$; $p < .01$). In the hybrid approach, clinical experts reviewed LLM-derived topics and flagged 19 as suicide-related. However, none showed significant effects beyond those identified bottom-up. YouTube Engagement, a platform-specific indicator, was not flagged, underscoring the value of bottom-up discovery. A top-down psychological assessment of suicide narratives revealed differing motivations: individuals describing prior attempts aimed to help others ($β=-1.69$, $p<.01$), whereas those attempted during the uploading period emphasized personal recovery ($β=1.08$, $p<.01$). By integrating these approaches, we offer a nuanced understanding of suicidality, bridging digital behavior and clinical insights.

This work shows how human physical reasoning can guide machine-driven symbolic regression toward discovering empirical laws from observations. As an example, we derive a simple equation that classifies fast radio bursts (FRBs) into two distinct Gaussian distributions, indicating the existence of two physical classes. This human-AI workflow integrates feature selection, dimensional analysis, and symbolic regression: deep learning first analyzes CHIME Catalog 1 and identifies six independent parameters that collectively provide a complete description of FRBs; guided by Buckingham-$π$ analysis and correlation analysis, humans then construct dimensionless groups; finally, symbolic regression performed by the machine discovers the governing equation. When applied to the newer CHIME Catalog, the equation produces consistent results, demonstrating that it captures the underlying physics. This framework is applicable to a broad range of scientific domains.