Steering vectors (SVs) are widely used to influence the expression of concepts (e.g., truthfulness) in large language model outputs. A key assumption underpinning SVs is that they are linearly discriminative with respect to the concept: representations of texts that exhibit the concept are more aligned with the SV than those that do not, motivating shifts along the positive or negative SV direction to respectively promote or suppress the concept. In this work, we identify an inverted detection-control phenomenon in which some highly discriminative SVs that are aligned with positive representations can consistently promote the opposite behavior. We refer to such vectors as inverted-steering vectors (ISVs). We provide a geometric characterization of ISVs' effects, finding that steering along these directions systematically pushes representations in discriminative downstream heads as if the concept were absent, even prior to decoding. Motivated by this analysis, we propose an approach for distinguishing ISVs without requiring generation or associated response scoring. This enables targeted sign flips, which we use to improve a foundational detection-based steering pipeline via Inference Time Intervention (ITI). Our approach improves results in 27/30 experiments, ranging from +0.9

Chain-of-thought (CoT) reasoning enables large language models (LLMs) to solve complex problems by generating intermediate reasoning steps. While much attention has been paid to the length and content of these reasoning chains, far less is known about their internal geometry. We study the geometry of CoT trajectories in the hidden state space of transformer models, formalizing each reasoning chain as a discrete curve in ℝ^d and characterizing it through spectral, positional, and kinematic geometric functionals. We introduce the effective dimension d_ρ as a measure of trajectory complexity and show theoretically that trajectories with flatter eigenvalue spectra correspond to harder tasks, as they explore more of the hidden dimensions. Lastly, we explore how kinematic features of the trajectory, mean position, positional dispersion, initial and current hidden states, mean velocity, mean speed, and speed dispersion, can be used to predict solution correctness before generation is complete, and may inform future early-stopping strategies. Experimentally, on mathematical reasoning problems from the MATH500 dataset, d_ρ achieves 0.93 AUC in distinguishing easy from hard problems, while kinematic features potentially can predict correctness from only the first 20% of generated tokens. These correctness signatures transfer across questions of varying difficulty, establishing that the shape of a model's internal reasoning trajectory is a principled window into both task hardness and solution quality.

Explainability methods are often challenging to evaluate and compare. With a multitude of explainers available, practitioners must often compare and select explainers based on quantitative evaluation metrics. One particular differentiator between explainers is the diversity of explanations for a given dataset; i.e. whether all explanations are identical, unique and uniformly distributed, or somewhere between these two extremes. In this work, we define a complexity measure for explainers, globalness, which enables deeper understanding of the distribution of explanations produced by feature attribution and feature selection methods for a given dataset. We establish the axiomatic properties that any such measure should possess and prove that our proposed measure, Wasserstein Globalness, meets these criteria. We validate the utility of Wasserstein Globalness using image, tabular, and synthetic datasets, empirically showing that it both facilitates meaningful comparison between explainers and improves the selection process for explainability methods.

Importance:Obtaining spirometry requires repeated testing and using the maximal values based on quality control criteria. Whether the suboptimal efforts are useful for the prediction of respiratory outcomes is not clear. Objective:To determine whether a machine learning model could predict respiratory outcomes and mortality based on suboptimal spirometry. Design:Observational cohorts (UK Biobank and COPDGene). Setting:Multi-center; population, and disease-enriched. Participants:UK aged 40-69; US aged 45-80, >10 pack-years smoking, without respiratory diseases other than COPD or asthma. Exposures:Raw spirograms (volume-time). Main outcomes and measures:To create a combined representation of lung function we implemented a contrastive learning approach, Spirogram-based Contrastive Learning Framework (Spiro-CLF), which utilized all recorded volume-time curves per participant and applied different transformations (e.g. flow-volume, flow-time). We defined "maximal" efforts as those passing quality control (QC) with the maximum FVC; all other efforts, including submaximal and QC-failing efforts, were defined as "suboptimal". We trained the Spiro-CLF model using both maximal and suboptimal efforts from the UK Biobank. We tested the model in a held-out 20% testing UK Biobank subset and COPDGene, on 1) binary predictions of FEV 1 /FVC <0.7, and FEV 1 Percent Predicted (FEV 1 PP) <80%, 2) Cox regression for all-cause mortality, and 3) prediction of respiratory phenotypes. Results:We trained Spiro-CLF on 940,705 volume-time curves from 352,684 UKB participants with 2-3 spirometry efforts per individual (66.7% with 3 efforts) and at least one QC-passing spirometry effort. Of all spirometry efforts, 61.6% were suboptimal (37.5% submaximal and 24.1% QC-failing). In the UK Biobank, Spiro-CLF using QC-failing and submaximal efforts predicted FEV 1 /FVC < 0.7 with an Area under the Receiver Operating Characteristics (AUROC) of 0.956, mortality with a concordance index of 0.647, and asthma with a 9-42% improvement versus baseline models. In COPDGene (n=10,110 participants), adding QC-passing, submaximal efforts did not improve the prediction of lung function or mortality; however, Spiro-CLF representations predicted asthma and respiratory phenotypes (joint test P ≤ 2 × 10 -3 ). Conclusions and Relevance:A machine-learning model can predict respiratory phenotypes using suboptimal spirometry; results from all spirometry efforts may contain valuable data. Additional studies are required to determine performance and utility in specific clinical scenarios.

Sequential deep learning models excel in domains with temporal or sequential dependencies, but their complexity necessitates post-hoc feature attribution methods for understanding their predictions. While existing techniques quantify feature importance, they inherently assume fixed feature ordering - conflating the effects of (1) feature values and (2) their positions within input sequences. To address this gap, we introduce OrdShap, a novel attribution method that disentangles these effects by quantifying how a model's predictions change in response to permuting feature position. We establish a game-theoretic connection between OrdShap and Sanchez-Bergantiños values, providing a theoretically grounded approach to position-sensitive attribution. Empirical results from health, natural language, and synthetic datasets highlight OrdShap's effectiveness in capturing feature value and feature position attributions, and provide deeper insight into model behavior.

A variety of recent methods guide large language model outputs via the inference-time addition of *steering vectors* to residual-stream or attention-head representations. In contrast, we propose to inject steering vectors directly into the query and value representation spaces within attention heads. We provide evidence that a greater portion of these spaces exhibit high linear discriminability of concepts --a key property motivating the use of steering vectors-- than attention head outputs. We analytically characterize the effect of our method, which we term *DISentangled COmmunication (DISCO) Steering*, on attention head outputs. Our analysis reveals that DISCO disentangles a strong but underutilized baseline, steering attention head inputs, which implicitly modifies queries and values in a rigid manner. In contrast, DISCO's direct modulation of these components enables more granular control. We find that DISCO achieves superior performance over a number of steering vector baselines across multiple datasets on LLaMA 3.1 8B and Gemma 2 9B, with steering efficacy scoring up to $19.1$% higher than the runner-up. Our results support the conclusion that the query and value spaces are powerful building blocks for steering vector methods. Our code is publicly available at https://github.com/MaxTorop/DISCO.

ABSTRACTRationaleEmphysema is a COPD phenotype with important prognostic implications. Identifying blood-based biomarkers of emphysema will facilitate early diagnosis and development of targeted therapies.ObjectivesDiscover blood omics biomarkers for chest CT-quantified emphysema and develop predictive biomarker panels.MethodsEmphysema blood biomarker discovery was performed using differential gene expression, alternative splicing, and protein association analyses in a training set of 2,370 COPDGene participants with available whole blood RNA sequencing, plasma SomaScan proteomics, and clinical data. Validation was conducted in a testing set of 1,016 COPDGene subjects. Since low body mass index (BMI) and emphysema often co-occur, we performed a mediation analysis to quantify the effect of BMI on gene and protein associations with emphysema. Elastic net models were also developed in the training sample sequentially using clinical, complete blood count (CBC) cell proportions, RNA sequencing, and proteomic biomarkers to predict quantitative emphysema. Model accuracy was assessed in the testing sample by the area under the receiver-operator-characteristic-curves (AUROC) for subjects stratified into tertiles of emphysema severity.Measurements and Main Results4,913 genes, 1,478 isoforms, 386 exons, and 881 proteins were significantly associated with emphysema(FDR 10%)and yielded 109 biological pathways. 75% of the genes and 77% of the proteins associated with emphysema showed evidence of mediation by BMI. The highest-performing predictive model used clinical, CBC, and protein biomarkers, distinguishing the top from the bottom tertile of emphysema with an AUROC of 0.92.ConclusionsBlood transcriptome and proteome-wide analyses reveal key biological pathways of emphysema and enhance the prediction of emphysema.AT A GLANCE COMMENTARYScientific Knowledge on the SubjectDifferential gene expression and protein analyses have uncovered some of the molecular underpinnings of emphysema. However, no studies have assessed alternative splicing mechanisms and analyzed proteomic data from recently developed high-throughput panels. In addition, although emphysema has been associated with low body mass index (BMI), it is still unclear how BMI affects the transcriptome and proteome of the disease. Finally, the effectiveness of multi-omic biomarkers in determining the severity of emphysema has not yet been investigated.What This Study Adds to the FieldWe performed whole-blood genome-wide RNA sequencing and plasma SomaScan proteomic analyses in the large and well-phenotyped COPDGene study. In addition to confirming earlier findings, our differential gene expression, alternative splicing, and protein analyses identified novel biomarkers and pathways of chest CT-quantified emphysema. Our mediation analysis detected varying degrees of transcriptomic and proteomic mediation due to BMI. Our supervised machine learning modeling demonstrated the utility of incorporating multi-omics data in enhancing the prediction of emphysema.

Machine learning methods have significantly improved in their predictive capabilities, but at the same time they are becoming more complex and less transparent. As a result, explainers are often relied on to provide interpretability to these black-box prediction models. As crucial diagnostics tools, it is important that these explainers themselves are robust. In this paper we focus on one particular aspect of robustness, namely that an explainer should give similar explanations for similar data inputs. We formalize this notion by introducing and defining explainer astuteness, analogous to astuteness of prediction functions. Our formalism allows us to connect explainer robustness to the predictor's probabilistic Lipschitzness, which captures the probability of local smoothness of a function. We provide lower bound guarantees on the astuteness of a variety of explainers (e.g., SHAP, RISE, CXPlain) given the Lipschitzness of the prediction function. These theoretical results imply that locally smooth prediction functions lend themselves to locally robust explanations. We evaluate these results empirically on simulated as well as real datasets.

Transcranial magnetic stimulation (TMS) is often applied to the motor cortex to stimulate a collection of motor evoked potentials (MEPs) in groups of peripheral muscles. The causal interface between TMS and MEP is the selective activation of neurons in the motor cortex; moving around the TMS ‘spot’ over the motor cortex causes different MEP responses. A question of interest is whether a collection of MEP responses can be used to identify the stimulated locations on the cortex, which could potentially be used to then place the TMS coil to produce chosen sets of MEPs. In this work we leverage our previous report on a 3D convolutional neural network (CNN) architecture that predicted MEPs from the induced electric field, to tackle an inverse imaging task in which we start with the MEPs and estimate the stimulated regions on the motor cortex. We present and evaluate five different inverse imaging CNN architectures, both conventional and generative, in terms of several measures of reconstruction accuracy. We found that one architecture, which we propose as M2M-InvNet, consistently achieved the best performance.

Post-hoc explanation methods have become a critical tool for understanding black-box classifiers in high-stakes applications. However, high-performing classifiers are often highly nonlinear and can exhibit complex behavior around the decision boundary, leading to brittle or misleading local explanations. Therefore there is an impending need to quantify the uncertainty of such explanation methods in order to understand when explanations are trustworthy. In this work we propose the Gaussian Process Explanation UnCertainty (GPEC) framework, which generates a unified uncertainty estimate combining decision boundary-aware uncertainty with explanation function approximation uncertainty. We introduce a novel geodesic-based kernel, which captures the complexity of the target black-box decision boundary. We show theoretically that the proposed kernel similarity increases with decision boundary complexity. The proposed framework is highly flexible; it can be used with any black-box classifier and feature attribution method. Empirical results on multiple tabular and image datasets show that the GPEC uncertainty estimate improves understanding of explanations as compared to existing methods.

Subspace clustering algorithms are used for understanding the cluster structure that explains the patterns prevalent in the dataset well. These methods are extensively used for data-exploration tasks in various areas of Natural Sciences. However, most of these methods fail to handle confounding attributes in the dataset. For datasets where a data sample represent multiple attributes, naively applying any clustering approach can result in undesired output. To this end, we propose a novel framework for jointly removing confounding attributes while learning to cluster data points in individual subspaces. Assuming we have label information about these confounding attributes, we regularize the clustering method by adversarially learning to minimize the mutual information between the data representation and the confounding attribute labels. Our experimental result on synthetic and real-world datasets demonstrate the effectiveness of our approach.

Explainability methods have been notoriously difficult to evaluate and compare. Because of this, practitioners are often left guessing as to which explainer they should use for their task. Locality is one critical property of explainers which grants insight into the diversity of produced explanations. In this paper, we define a set of axioms which align with natural intuition regarding globalness, the inverse of locality. We then introduce a novel measure of globalness, Wasserstein Globalness, which uses optimal transport to quantify how local or global a given explainer is. Finally, we provide theoretical results describing the sample complexity of Wasserstein Globalness, and experimentally demonstrate how globalness can be used to effectively compare explainers. These results illustrate connections between both explainer fidelity and explainer robustness.

Machine learning methods are getting increasingly better at making predictions, but at the same time they are also becoming more complicated and less transparent. As a result, explainers are often relied on to provide interpretability to these \textit{black-box} prediction models. As crucial diagnostics tools, it is important that these explainers themselves are reliable. In this paper we focus on one particular aspect of reliability, namely that an explainer should give similar explanations for similar data inputs. We formalize this notion by introducing and defining \textit{explainer astuteness}, analogous to astuteness of classifiers. Our formalism is inspired by the concept of \textit{probabilistic Lipschitzness}, which captures the probability of local smoothness of a function. For a variety of explainers (e.g., SHAP, RISE, CXPlain), we provide lower bound guarantees on the astuteness of these explainers given the Lipschitzness of the prediction function. These theoretical results imply that locally smooth prediction functions lend themselves to locally robust explanations. We evaluate these results empirically on simulated as well as real datasets.

Several recent methods for interpretability model feature interactions by looking at the Hessian of a neural network. This poses a challenge for ReLU networks, which are piecewise-linear and thus have a zero Hessian almost everywhere. We propose SmoothHess, a method of estimating second-order interactions through Stein's Lemma. In particular, we estimate the Hessian of the network convolved with a Gaussian through an efficient sampling algorithm, requiring only network gradient calls. SmoothHess is applied post-hoc, requires no modifications to the ReLU network architecture, and the extent of smoothing can be controlled explicitly. We provide a non-asymptotic bound on the sample complexity of our estimation procedure. We validate the superior ability of SmoothHess to capture interactions on benchmark datasets and a real-world medical spirometry dataset.

While score based generative models, or diffusion models, have found success in image synthesis, they are often coupled with text data or image label to be able to manipulate and conditionally generate images. Even though manipulation of images by changing the text prompt is possible, our understanding of the text embedding and our ability to modify it to edit images is quite limited. Towards the direction of having more control over image manipulation and conditional generation, we propose to learn image components in an unsupervised manner so that we can compose those components to generate and manipulate images in informed manner. Taking inspiration from energy based models, we interpret different score components as the gradient of different energy functions. We show how score based learning allows us to learn interesting components and we can visualize them through generation. We also show how this novel decomposition allows us to compose, generate and modify images in interesting ways akin to dreaming. We make our code available at https://github.com/sandeshgh/Score-based-disentanglement

Post-hoc explanation methods have become increasingly depended upon for understanding black-box classifiers in high-stakes applications, precipitating a need for reliable explanations. While numerous explanation methods have been proposed, recent works have shown that many existing methods can be inconsistent or unstable. In addition, high-performing classifiers are often highly nonlinear and can exhibit complex behavior around the decision boundary, leading to brittle or misleading local explanations. Therefore, there is an impending need to quantify the uncertainty of such explanation methods in order to understand when explanations are trustworthy. We introduce a novel uncertainty quantification method parameterized by a Gaussian Process model, which combines the uncertainty approximation of existing methods with a novel geodesic-based similarity which captures the complexity of the target black-box decision boundary. The proposed framework is highly flexible—it can be used with any black-box classifier and feature attribution method to amortize uncertainty estimates for explanations. We show theoretically that our proposed geodesic-based kernel similarity increases with the complexity of the decision boundary. Empirical results on multiple tabular and image datasets show that our decision boundary-aware uncertainty estimate improves understanding of explanations as compared to existing methods

In this work, we look at Score-based generative models (also called diffusion generative models) from a geometric perspective. From a new view point, we prove that both the forward and backward process of adding noise and generating from noise are Wasserstein gradient flow in the space of probability measures. We are the first to prove this connection. Our understanding of Score-based (and Diffusion) generative models have matured and become more complete by drawing ideas from different fields like Bayesian inference, control theory, stochastic differential equation and Schrodinger bridge. However, many open questions and challenges remain. One problem, for example, is how to decrease the sampling time? We demonstrate that looking from geometric perspective enables us to answer many of these questions and provide new interpretations to some known results. Furthermore, geometric perspective enables us to devise an intuitive geometric solution to the problem of faster sampling. By augmenting traditional score-based generative models with a projection step, we show that we can generate high quality images with significantly fewer sampling-steps.

There is currently a debate within the neuroscience community over the likelihood of the brain performing backpropagation (BP). To better mimic the brain, training a network one layer at a time with only a "single forward pass" has been proposed as an alternative to bypass BP; we refer to these networks as "layer-wise" networks. We continue the work on layer-wise networks by answering two outstanding questions. First, do they have a closed-form solution? Second, how do we know when to stop adding more layers? This work proves that the kernel Mean Embedding is the closed-form weight that achieves the network global optimum while driving these networks to converge towards a highly desirable kernel for classification; we call it the Neural Indicator Kernel.

As machine learning algorithms are deployed ubiquitously to a variety of domains, it is imperative to make these often black-box models transparent. Several recent works explain black-box models by capturing the most influential features for prediction per instance; such explanation methods are univariate, as they characterize importance per feature. We extend univariate explanation to a higher-order; this enhances explainability, as bivariate methods can capture feature interactions in black-box models, represented as a directed graph. Analyzing this graph enables us to discover groups of features that are equally important (i.e., interchangeable), while the notion of directionality allows us to identify the most influential features. We apply our bivariate method on Shapley value explanations, and experimentally demonstrate the ability of directional explanations to discover feature interactions. We show the superiority of our method against state-of-the-art on CIFAR10, IMDB, Census, Divorce, Drug, and gene data.

2022), fidelity to the black-box model (Yeh et al., 2019), or combinations of these metrics et al., 2020).