Daily Papers

Retrieval-Augmented Generation (RAG) has become a key paradigm for reducing factual hallucinations in large language models (LLMs), yet little is known about how the order of retrieved documents affects model behavior. We empirically show that under Top-5 retrieval with the gold document included, LLM answers vary substantially across permutations of the retrieved set, even when the gold document is fixed in the first position. This reveals a previously underexplored sensitivity to retrieval permutations. Although robust RAG methods primarily focus on enhancing LLM robustness to low-quality retrieval and mitigating positional bias to distribute attention fairly over long contexts, neither approach directly addresses permutation sensitivity. In this paper, we propose Stable-RAG, which exploits permutation sensitivity estimation to mitigate permutation-induced hallucinations. Stable-RAG runs the generator under multiple retrieval orders, clusters hidden states, and decodes from a cluster-center representation that captures the dominant reasoning pattern. It then uses these reasoning results to align hallucinated outputs toward the correct answer, encouraging the model to produce consistent and accurate predictions across document permutations. Experiments on three QA datasets show that Stable-RAG significantly improves answer accuracy, reasoning consistency and robust generalization across datasets, retrievers, and input lengths compared with baselines.

Graph generation has been dominated by autoregressive models due to their simplicity and effectiveness, despite their sensitivity to ordering. Yet diffusion models have garnered increasing attention, as they offer comparable performance while being permutation-invariant. Current graph diffusion models generate graphs in a one-shot fashion, but they require extra features and thousands of denoising steps to achieve optimal performance. We introduce PARD, a Permutation-invariant Auto Regressive Diffusion model that integrates diffusion models with autoregressive methods. PARD harnesses the effectiveness and efficiency of the autoregressive model while maintaining permutation invariance without ordering sensitivity. Specifically, we show that contrary to sets, elements in a graph are not entirely unordered and there is a unique partial order for nodes and edges. With this partial order, PARD generates a graph in a block-by-block, autoregressive fashion, where each block's probability is conditionally modeled by a shared diffusion model with an equivariant network. To ensure efficiency while being expressive, we further propose a higher-order graph transformer, which integrates transformer with PPGN. Like GPT, we extend the higher-order graph transformer to support parallel training of all blocks. Without any extra features, PARD achieves state-of-the-art performance on molecular and non-molecular datasets, and scales to large datasets like MOSES containing 1.9M molecules.

Integrating heterogeneous biomedical data including imaging, omics, and clinical records supports accurate diagnosis and personalised care. Graph-based models fuse such non-Euclidean data by capturing spatial and relational structure, yet clinical uptake requires regulator-ready interpretability. We present the first technical survey of interpretable graph based models for multimodal biomedical data, covering 26 studies published between Jan 2019 and Sep 2024. Most target disease classification, notably cancer and rely on static graphs from simple similarity measures, while graph-native explainers are rare; post-hoc methods adapted from non-graph domains such as gradient saliency, and SHAP predominate. We group existing approaches into four interpretability families, outline trends such as graph-in-graph hierarchies, knowledge-graph edges, and dynamic topology learning, and perform a practical benchmark. Using an Alzheimer disease cohort, we compare Sensitivity Analysis, Gradient Saliency, SHAP and Graph Masking. SHAP and Sensitivity Analysis recover the broadest set of known AD pathways and Gene-Ontology terms, whereas Gradient Saliency and Graph Masking surface complementary metabolic and transport signatures. Permutation tests show all four beat random gene sets, but with distinct trade-offs: SHAP and Graph Masking offer deeper biology at higher compute cost, while Gradient Saliency and Sensitivity Analysis are quicker though coarser. We also provide a step-by-step flowchart covering graph construction, explainer choice and resource budgeting to help researchers balance transparency and performance. This review synthesises the state of interpretable graph learning for multimodal medicine, benchmarks leading techniques, and charts future directions, from advanced XAI tools to under-studied diseases, serving as a concise reference for method developers and translational scientists.

Sequence models such as transformers require inputs to be represented as one-dimensional sequences. In vision, this typically involves flattening images using a fixed row-major (raster-scan) order. While full self-attention is permutation-equivariant, modern long-sequence transformers increasingly rely on architectural approximations that break this invariance and introduce sensitivity to patch ordering. We show that patch order significantly affects model performance in such settings, with simple alternatives like column-major or Hilbert curves yielding notable accuracy shifts. Motivated by this, we propose REOrder, a two-stage framework for discovering task-optimal patch orderings. First, we derive an information-theoretic prior by evaluating the compressibility of various patch sequences. Then, we learn a policy over permutations by optimizing a Plackett-Luce policy using REINFORCE. This approach enables efficient learning in a combinatorial permutation space. REOrder improves top-1 accuracy over row-major ordering on ImageNet-1K by up to 3.01% and Functional Map of the World by 13.35%.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

We propose Monte Carlo Permutation Search (MCPS), a general-purpose Monte Carlo Tree Search (MCTS) algorithm that improves upon the GRAVE algorithm. MCPS is relevant when deep reinforcement learning is not an option, or when the computing power available before play is not substantial, such as in General Game Playing, for example. The principle of MCPS is to include in the exploration term of a node the statistics on all the playouts that contain all the moves on the path from the root to the node. We extensively test MCPS on a variety of games: board games, wargame, investment game, video game and multi-player games. MCPS has better results than GRAVE in all the two-player games. It has equivalent results for multi-player games because these games are inherently balanced even when players have different strengths. We also show that using abstract codes for moves instead of exact codes can be beneficial to both MCPS and GRAVE, as they improve the permutation statistics and the AMAF statistics. We also provide a mathematical derivation of the formulas used for weighting the three sources of statistics. These formulas are an improvement on the GRAVE formula since they no longer use the bias hyperparameter of GRAVE. Moreover, MCPS is not sensitive to the ref hyperparameter.

We study the problem of detecting the correlation between two Gaussian databases XinR^{ntimes d} and Y^{ntimes d}, each composed of n users with d features. This problem is relevant in the analysis of social media, computational biology, etc. We formulate this as a hypothesis testing problem: under the null hypothesis, these two databases are statistically independent. Under the alternative, however, there exists an unknown permutation sigma over the set of n users (or, row permutation), such that X is rho-correlated with Y^sigma, a permuted version of Y. We determine sharp thresholds at which optimal testing exhibits a phase transition, depending on the asymptotic regime of n and d. Specifically, we prove that if rho^2dto0, as dtoinfty, then weak detection (performing slightly better than random guessing) is statistically impossible, irrespectively of the value of n. This compliments the performance of a simple test that thresholds the sum all entries of X^TY. Furthermore, when d is fixed, we prove that strong detection (vanishing error probability) is impossible for any rho<rho^star, where rho^star is an explicit function of d, while weak detection is again impossible as long as rho^2dto0. These results close significant gaps in current recent related studies.

Large language models (LLMs) now write code in settings where misreading a single word can break safety or cost money, yet we still expect them to overlook stray typos. To probe where useful robustness ends and harmful insensitivity begins, we compile 50 LeetCode problems and craft three minimal prompt perturbations that should vary in importance: (i) progressive underspecification deleting 10 % of words per step; (ii) lexical flip swapping a pivotal quantifier ("max" to "min"); and (iii) jargon inflation replacing a common noun with an obscure technical synonym. Six frontier models, including three "reasoning-tuned" versions, solve each mutated prompt, and their Python outputs are checked against the original test suites to reveal whether they reused the baseline solution or adapted. Among 11 853 generations we observe a sharp double asymmetry. Models remain correct in 85 % of cases even after 90 % of the prompt is missing, showing over-robustness to underspecification, yet only 54 % react to a single quantifier flip that reverses the task, with reasoning-tuned variants even less sensitive than their bases. Jargon edits lie in between, passing through 56 %. Current LLMs thus blur the line between harmless noise and meaning - changing edits, often treating both as ignorable. Masking salient anchors such as function names can force re - evaluation. We advocate evaluation and training protocols that reward differential sensitivity: stay steady under benign noise but adapt - or refuse - when semantics truly change.

We study the problem of designing models for machine learning tasks defined on sets. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics poczos13aistats, to anomaly detection in piezometer data of embankment dams Jung15Exploration, to cosmology Ntampaka16Dynamical,Ravanbakhsh16ICML1. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

Prediction models can exhibit sensitivity with respect to training data: small changes in the training data can produce models that assign conflicting predictions to individual data points during test time. In this work, we study this sensitivity in recommender systems, where users' recommendations are drastically altered by minor perturbations in other unrelated users' interactions. We introduce a measure of stability for recommender systems, called Rank List Sensitivity (RLS), which measures how rank lists generated by a given recommender system at test time change as a result of a perturbation in the training data. We develop a method, CASPER, which uses cascading effect to identify the minimal and systematical perturbation to induce higher instability in a recommender system. Experiments on four datasets show that recommender models are overly sensitive to minor perturbations introduced randomly or via CASPER - even perturbing one random interaction of one user drastically changes the recommendation lists of all users. Importantly, with CASPER perturbation, the models generate more unstable recommendations for low-accuracy users (i.e., those who receive low-quality recommendations) than high-accuracy ones.

In complex systems, we often observe complex global behavior emerge from a collection of agents interacting with each other in their environment, with each individual agent acting only on locally available information, without knowing the full picture. Such systems have inspired development of artificial intelligence algorithms in areas such as swarm optimization and cellular automata. Motivated by the emergence of collective behavior from complex cellular systems, we build systems that feed each sensory input from the environment into distinct, but identical neural networks, each with no fixed relationship with one another. We show that these sensory networks can be trained to integrate information received locally, and through communication via an attention mechanism, can collectively produce a globally coherent policy. Moreover, the system can still perform its task even if the ordering of its inputs is randomly permuted several times during an episode. These permutation invariant systems also display useful robustness and generalization properties that are broadly applicable. Interactive demo and videos of our results: https://attentionneuron.github.io/

The ability of an architecture to realize permutations is quite fundamental. For example, Large Language Models need to be able to correctly copy (and perhaps rearrange) parts of the input prompt into the output. Classical universal approximation theorems guarantee the existence of parameter configurations that solve this task but offer no insights into whether gradient-based algorithms can find them. In this paper, we address this gap by focusing on two-layer fully connected feed-forward neural networks and the task of learning permutations on nonzero binary inputs. We show that in the infinite width Neural Tangent Kernel (NTK) regime, an ensemble of such networks independently trained with gradient descent on only the k standard basis vectors out of 2^k - 1 possible inputs successfully learns any fixed permutation of length k with arbitrarily high probability. By analyzing the exact training dynamics, we prove that the network's output converges to a Gaussian process whose mean captures the ground truth permutation via sign-based features. We then demonstrate how averaging these runs (an "ensemble" method) and applying a simple rounding step yields an arbitrarily accurate prediction on any possible input unseen during training. Notably, the number of models needed to achieve exact learning with high probability (which we refer to as ensemble complexity) exhibits a linearithmic dependence on the input size k for a single test input and a quadratic dependence when considering all test inputs simultaneously.

Many machine learning tasks such as multiple instance learning, 3D shape recognition, and few-shot image classification are defined on sets of instances. Since solutions to such problems do not depend on the order of elements of the set, models used to address them should be permutation invariant. We present an attention-based neural network module, the Set Transformer, specifically designed to model interactions among elements in the input set. The model consists of an encoder and a decoder, both of which rely on attention mechanisms. In an effort to reduce computational complexity, we introduce an attention scheme inspired by inducing point methods from sparse Gaussian process literature. It reduces the computation time of self-attention from quadratic to linear in the number of elements in the set. We show that our model is theoretically attractive and we evaluate it on a range of tasks, demonstrating the state-of-the-art performance compared to recent methods for set-structured data.

Mixed-precision quantization must decide which parts of a model to keep at higher precision. A common premise, shared by sensitivity-based methods such as HAWQ and CoopQ, is that the loss from quantizing a set of layers can be reconstructed from per-layer or pairwise sensitivities measured in isolation. We test this premise at the 4-bit weight-and-activation precisions now being deployed, treating the change in loss f(S) from quantizing a layer set S as a set function on the Boolean cube and analyzing it through two classical changes of basis. This analysis yields two findings. First, across configurations drawn from the deployment distribution, 85--93\% of the variance of f is explained by per-layer effects alone. Second, a monotone transform of a sum of per-layer terms reproduces f's ranking of configurations, misordering at most 2\% of pairs. We propose the coverage model f(S)=cbigl(1-prod_{iin S}(1-a_i)bigr), which reproduces the measured variance profile of f to within a few percent from its L fitted break-rates. This structure supports two predictors of a configuration's loss, each with L+1 parameters. The additive model is the optimal first-order predictor. By Parseval's identity its mean-squared error equals the variance of f left unexplained by per-layer effects, which we measure on full lattices, estimate out of sample at full-network scale, and report with every result as a certificate of how well any additive model can do. The coverage model itself is the second predictor. As allocators at matched memory, they attain the lowest KL divergence among the compared allocators on models from 30B to 355B parameters. Below four bits, the resulting allocations continue to solve code and reasoning tasks at budgets where allocations from gradient sensitivities no longer produce terminating generations.

Revolutionizing the field of deep learning, Transformer-based models have achieved remarkable performance in many tasks. Recent research has recognized these models are robust to shuffling but are limited to inter-token permutation in the forward propagation. In this work, we propose our definition of permutation equivariance, a broader concept covering both inter- and intra- token permutation in the forward and backward propagation of neural networks. We rigorously proved that such permutation equivariance property can be satisfied on most vanilla Transformer-based models with almost no adaptation. We examine the property over a range of state-of-the-art models including ViT, Bert, GPT, and others, with experimental validations. Further, as a proof-of-concept, we explore how real-world applications including privacy-enhancing split learning, and model authorization, could exploit the permutation equivariance property, which implicates wider, intriguing application scenarios.

Prompt sensitivity, which refers to how strongly the output of a large language model (LLM) depends on the exact wording of its input prompt, raises concerns among users about the LLM's stability and reliability. In this work, we consider LLMs as multivariate functions and perform a first-order Taylor expansion, thereby analyzing the relationship between meaning-preserving prompts, their gradients, and the log probabilities of the model's next token. We derive an upper bound on the difference between log probabilities using the Cauchy-Schwarz inequality. We show that LLMs do not internally cluster similar inputs like smaller neural networks do, but instead disperse them. This dispersing behavior leads to an excessively high upper bound on the difference of log probabilities between two meaning-preserving prompts, making it difficult to effectively reduce to 0. In our analysis, we also show which types of meaning-preserving prompt variants are more likely to introduce prompt sensitivity risks in LLMs. In addition, we demonstrate that the upper bound is strongly correlated with an existing prompt sensitivity metric, PromptSensiScore. Moreover, by analyzing the logit variance, we find that prompt templates typically exert a greater influence on logits than the questions themselves. Overall, our results provide a general interpretation for why current LLMs can be highly sensitive to prompts with the same meaning, offering crucial evidence for understanding the prompt sensitivity of LLMs. Code for experiments is available at https://github.com/ku-nlp/Understanding_the_Prompt_Sensitivity.

Recent work found that LLMs are sensitive to a wide range of arbitrary prompt dimensions, including the type of delimiters, answer enumerators, instruction wording, and more. This throws into question popular single-prompt evaluation practices. We present DOVE (Dataset Of Variation Evaluation) a large-scale dataset containing prompt perturbations of various evaluation benchmarks. In contrast to previous work, we examine LLM sensitivity from an holistic perspective, and assess the joint effects of perturbations along various dimensions, resulting in thousands of perturbations per instance. We evaluate several model families against DOVE, leading to several findings, including efficient methods for choosing well-performing prompts, observing that few-shot examples reduce sensitivity, and identifying instances which are inherently hard across all perturbations. DOVE consists of more than 250M prompt perturbations and model outputs, which we make publicly available to spur a community-wide effort toward meaningful, robust, and efficient evaluation. Browse the data, contribute, and more: https://slab-nlp.github.io/DOVE/

Learning neural subset selection tasks, such as compound selection in AI-aided drug discovery, have become increasingly pivotal across diverse applications. The existing methodologies in the field primarily concentrate on constructing models that capture the relationship between utility function values and subsets within their respective supersets. However, these approaches tend to overlook the valuable information contained within the superset when utilizing neural networks to model set functions. In this work, we address this oversight by adopting a probabilistic perspective. Our theoretical findings demonstrate that when the target value is conditioned on both the input set and subset, it is essential to incorporate an invariant sufficient statistic of the superset into the subset of interest for effective learning. This ensures that the output value remains invariant to permutations of the subset and its corresponding superset, enabling identification of the specific superset from which the subset originated. Motivated by these insights, we propose a simple yet effective information aggregation module designed to merge the representations of subsets and supersets from a permutation invariance perspective. Comprehensive empirical evaluations across diverse tasks and datasets validate the enhanced efficacy of our approach over conventional methods, underscoring the practicality and potency of our proposed strategies in real-world contexts.

In this technical note, we study the problem of inverse permutation learning in decoder-only transformers. Given a permutation and a string to which that permutation has been applied, the model is tasked with producing the original (``canonical'') string. We argue that this task models a natural robustness property across a variety of reasoning tasks, including long-context retrieval, multiple choice QA and in-context learning. Our primary contribution is an impossibility result: we show that an arbitrary depth, decoder-only transformer cannot learn this task. This result concerns the expressive capacity of decoder-only transformer models and is agnostic to training dynamics or sample complexity. We give a pair of alternative constructions under which inverse permutation learning is feasible. The first of these highlights the fundamental role of the causal attention mask, and reveals a gap between the expressivity of encoder-decoder transformers and the more popular decoder-only architecture. The latter result is more surprising: we show that simply padding the input with ``scratch tokens" yields a construction under which inverse permutation learning is possible. We conjecture that this may suggest an alternative mechanism by which chain-of-thought prompting or, more generally, intermediate ``thinking'' tokens can enable reasoning in large language models, even when these tokens encode no meaningful semantic information (e.g., the results of intermediate computations).

Prompt sensitivity, referring to the phenomenon where paraphrasing (i.e., repeating something written or spoken using different words) leads to significant changes in large language model (LLM) performance, has been widely accepted as a core limitation of LLMs. In this work, we revisit this issue and ask: Is the widely reported high prompt sensitivity truly an inherent weakness of LLMs, or is it largely an artifact of evaluation processes? To answer this question, we systematically evaluate 7 LLMs (e.g., GPT and Gemini family) across 6 benchmarks, including both multiple-choice and open-ended tasks on 12 diverse prompt templates. We find that much of the prompt sensitivity stems from heuristic evaluation methods, including log-likelihood scoring and rigid answer matching, which often overlook semantically correct responses expressed through alternative phrasings, such as synonyms or paraphrases. When we adopt LLM-as-a-Judge evaluations, we observe a substantial reduction in performance variance and a consistently higher correlation in model rankings across prompts. Our findings suggest that modern LLMs are more robust to prompt templates than previously believed, and that prompt sensitivity may be more an artifact of evaluation than a flaw in the models.

Recently, Ainsworth et al. showed that using weight matching (WM) to minimize the L_2 distance in a permutation search of model parameters effectively identifies permutations that satisfy linear mode connectivity (LMC), in which the loss along a linear path between two independently trained models with different seeds remains nearly constant. This paper provides a theoretical analysis of LMC using WM, which is crucial for understanding stochastic gradient descent's effectiveness and its application in areas like model merging. We first experimentally and theoretically show that permutations found by WM do not significantly reduce the L_2 distance between two models and the occurrence of LMC is not merely due to distance reduction by WM in itself. We then provide theoretical insights showing that permutations can change the directions of the singular vectors, but not the singular values, of the weight matrices in each layer. This finding shows that permutations found by WM mainly align the directions of singular vectors associated with large singular values across models. This alignment brings the singular vectors with large singular values, which determine the model functionality, closer between pre-merged and post-merged models, so that the post-merged model retains functionality similar to the pre-merged models, making it easy to satisfy LMC. Finally, we analyze the difference between WM and straight-through estimator (STE), a dataset-dependent permutation search method, and show that WM outperforms STE, especially when merging three or more models.

We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model's performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.

Counterfactual prompting (i.e., perturbing a single factor and measuring output change) is widely used to evaluate things like LLM bias and CoT faithfulness. But in this work we argue that observed effects cannot be attributed to the targeted factor without accounting for baseline ``meaning-preserving'' modifications to text that establish general model sensitivity. This is because every counterfactual edit is a compound treatment that bundles the variable of interest with incidental surface-form variation; this violates treatment variation irrelevance. We observe prediction flip rates on MedQA of 14.9% when we surgically change patient gender. However, this is statistically indistinguishable from the flip rates induced by simply paraphrasing inputs (14.1%). In this case, it would therefore be unwarranted to conclude that the LLM is especially sensitive to patient gender. To account for this and robustly measure the effects of targeted interventions, we propose a framework in which we compare (via statistical testing) differences observed under target interventions to those induced by paraphrasing inputs. We then use this framework to revisit a analysis done on the MedPerturb dataset, which reported evidence of model sensitivity to patient demographics and stylistic cues. We find that these effects largely dissipate when we account for general model sensitivity, with only 5 of 120 tests reaching statistical significance. Applying the same framework to occupational biography classification, we detect clearly significant directional gender bias, showing that the framework identifies real directional effects even when they are small. We evaluate a range of metrics -- aggregate, per-sample distributional, and regression -- and find that per-sample metrics are dramatically more powerful than aggregate metrics and regression powerfully and uniquely characterizes effect direction and magnitude.

Despite their remarkable capabilities, Large Language Models (LLMs) are found to be surprisingly sensitive to minor variations in prompts, often generating significantly divergent outputs in response to minor variations in the prompts, such as spelling errors, alteration of wording or the prompt template. However, while assessing the quality of an LLM, the focus often tends to be solely on its performance on downstream tasks, while very little to no attention is paid to prompt sensitivity. To fill this gap, we propose POSIX - a novel PrOmpt Sensitivity IndeX as a reliable measure of prompt sensitivity, thereby offering a more comprehensive evaluation of LLM performance. The key idea behind POSIX is to capture the relative change in loglikelihood of a given response upon replacing the corresponding prompt with a different intent-preserving prompt. We provide thorough empirical evidence demonstrating the efficacy of POSIX in capturing prompt sensitivity and subsequently use it to measure and thereby compare prompt sensitivity of various open-source LLMs. We find that merely increasing the parameter count or instruction tuning does not necessarily reduce prompt sensitivity whereas adding some few-shot exemplars, even just one, almost always leads to significant decrease in prompt sensitivity. We also find that alterations to prompt template lead to the highest sensitivity in the case of MCQ type tasks, whereas paraphrasing results in the highest sensitivity in open-ended generation tasks. The code for reproducing our results is open-sourced at https://github.com/kowndinya-renduchintala/POSIX.

As large language models (LLMs) are adopted as a fundamental component of language technologies, it is crucial to accurately characterize their performance. Because choices in prompt design can strongly influence model behavior, this design process is critical in effectively using any modern pre-trained generative language model. In this work, we focus on LLM sensitivity to a quintessential class of meaning-preserving design choices: prompt formatting. We find that several widely used open-source LLMs are extremely sensitive to subtle changes in prompt formatting in few-shot settings, with performance differences of up to 76 accuracy points when evaluated using LLaMA-2-13B. Sensitivity remains even when increasing model size, the number of few-shot examples, or performing instruction tuning. Our analysis suggests that work evaluating LLMs with prompting-based methods would benefit from reporting a range of performance across plausible prompt formats, instead of the currently-standard practice of reporting performance on a single format. We also show that format performance only weakly correlates between models, which puts into question the methodological validity of comparing models with an arbitrarily chosen, fixed prompt format. To facilitate systematic analysis we propose FormatSpread, an algorithm that rapidly evaluates a sampled set of plausible prompt formats for a given task, and reports the interval of expected performance without accessing model weights. Furthermore, we present a suite of analyses that characterize the nature of this sensitivity, including exploring the influence of particular atomic perturbations and the internal representation of particular formats.

Over the past few years, the acceleration of computing resources and research in deep learning has led to significant practical successes in a range of tasks, including in particular in computer vision. Building on these advances, reinforcement learning has also seen a leap forward with the emergence of agents capable of making decisions directly from visual observations. Despite these successes, the over-parametrization of neural architectures leads to memorization of the data used during training and thus to a lack of generalization. Reinforcement learning agents based on visual inputs also suffer from this phenomenon by erroneously correlating rewards with unrelated visual features such as background elements. To alleviate this problem, we introduce a new regularization technique consisting of channel-consistent local permutations (CLOP) of the feature maps. The proposed permutations induce robustness to spatial correlations and help prevent overfitting behaviors in RL. We demonstrate, on the OpenAI Procgen Benchmark, that RL agents trained with the CLOP method exhibit robustness to visual changes and better generalization properties than agents trained using other state-of-the-art regularization techniques. We also demonstrate the effectiveness of CLOP as a general regularization technique in supervised learning.

Recent machine learning papers often report 1-2 percentage point improvements from a single run on a benchmark. These gains are highly sensitive to random seeds, data ordering, and implementation details, yet are rarely accompanied by uncertainty estimates or significance tests. It is therefore unclear when a reported +1-2% reflects a real algorithmic advance versus noise. We revisit this problem under realistic compute budgets, where only a few runs are affordable. We propose a simple, PC-friendly evaluation protocol based on paired multi-seed runs, bias-corrected and accelerated (BCa) bootstrap confidence intervals, and a sign-flip permutation test on per-seed deltas. The protocol is intentionally conservative and is meant as a guardrail against over-claiming. We instantiate it on CIFAR-10, CIFAR-10N, and AG News using synthetic no-improvement, small-gain, and medium-gain scenarios. Single runs and unpaired t-tests often suggest significant gains for 0.6-2.0 point improvements, especially on text. With only three seeds, our paired protocol never declares significance in these settings. We argue that such conservative evaluation is a safer default for small gains under tight budgets.

Existing evaluation methods largely rely on clean, static benchmarks, which can overestimate true model performance by failing to capture the noise and variability inherent in real-world user inputs. This is especially true for language models, which can face human-generated text queries containing mistakes, typos, or alternative ways of phrasing the same question. In this work, we introduce a theoretical framework for quantifying model sensitivity to prompt variants, or brittleness, that can enable us to disentangle data-induced difficulty from prompt-related variability. Using this framework, we design a novel evaluation pipeline, Brittlebench, to holistically evaluate the sensitivity of frontier models. We apply semantics-preserving perturbations to a suite of popular benchmarks, and observe model performance to degrade as much as 12%. However, these perturbations do not affect all models equally: even a single perturbation alters the relative ranking of models in 63% of cases, impacting conclusions about comparative model performance. Decomposing the total variance of both state-of-the-art open-weight and commercial models, we find that semantics-preserving input perturbations can account for up to half of the performance variance for a given model. Brittlebench highlights the need for more robust evaluations and models, and allows us to systematically understand model brittleness.

Recent research has adopted a new experimental field centered around the concept of text perturbations which has revealed that shuffled word order has little to no impact on the downstream performance of Transformer-based language models across many NLP tasks. These findings contradict the common understanding of how the models encode hierarchical and structural information and even question if the word order is modeled with position embeddings. To this end, this paper proposes nine probing datasets organized by the type of controllable text perturbation for three Indo-European languages with a varying degree of word order flexibility: English, Swedish and Russian. Based on the probing analysis of the M-BERT and M-BART models, we report that the syntactic sensitivity depends on the language and model pre-training objectives. We also find that the sensitivity grows across layers together with the increase of the perturbation granularity. Last but not least, we show that the models barely use the positional information to induce syntactic trees from their intermediate self-attention and contextualized representations.

Neural network parameterizations exhibit inherent symmetries that yield multiple equivalent minima within the loss landscape. Scale Graph Metanetworks (ScaleGMNs) explicitly leverage these symmetries by proposing an architecture equivariant to both permutation and parameter scaling transformations. Previous work by Ainsworth et al. (2023) addressed permutation symmetries through a computationally intensive combinatorial assignment problem, demonstrating that leveraging permutation symmetries alone can map networks into a shared loss basin. In this work, we extend their approach by also incorporating scaling symmetries, presenting an autoencoder framework utilizing ScaleGMNs as invariant encoders. Experimental results demonstrate that our method aligns Implicit Neural Representations (INRs) and Convolutional Neural Networks (CNNs) under both permutation and scaling symmetries without explicitly solving the assignment problem. This approach ensures that similar networks naturally converge within the same basin, facilitating model merging, i.e., smooth linear interpolation while avoiding regions of high loss. The code is publicly available on our GitHub repository.

Standard representation probing for visual models relies on mathematically permutation-invariant operations like Global Average Pooling (GAP) or CLS tokens, treating patch representations as an unstructured bag-of-words. We challenge this paradigm by demonstrating that token order is a critical, exploitable dimension in frozen visual representations (e.g., MAE, BEiT, DINOv2, and ViT as CLS-ablation extreme). We propose SSMProbe, a probing framework driven by a State Space Model (SSM). Operating as discrete Linear Time-Invariant (LTI) dynamical systems, SSMs act as permutation-sensitive probes where sequence order strictly dictates the final state due to inherent memory decay. Formulating token ordering as an information scheduling problem, we compare fixed scan heuristics against a differentiable soft permutation (Sinkhorn-based) learned from downstream supervision. Evaluations on standard and fine-grained classification benchmarks reveal a striking order gap: while fixed scans fail dramatically on highly localized patch features, our learned soft permutation successfully extracts highly competitive performance from otherwise heavily localized patch sequences. We find that pre-training objectives fundamentally shape token structure: DINOv2 concentrates global semantics in optimized CLS tokens leaving patches hyperspecialized, pure MAE preserves distributed representations with heterogeneous patch informativeness, and ViT represents a supervised CLS-dominated extreme. BEiT occupies middle ground. This heterogeneity is order-dependent -- meaning the SSM probe's performance depends critically on which tokens are placed at which temporal positions -- and is not merely a topological property of the spatial grid. SSMProbe's learned routing effectively discovers and exploits this heterogeneity, offering a powerful new diagnostic lens for visual representation analysis.

Set representation has become ubiquitous in deep learning for modeling the inductive bias of neural networks that are insensitive to the input order. DeepSets is the most widely used neural network architecture for set representation. It involves embedding each set element into a latent space with dimension L, followed by a sum pooling to obtain a whole-set embedding, and finally mapping the whole-set embedding to the output. In this work, we investigate the impact of the dimension L on the expressive power of DeepSets. Previous analyses either oversimplified high-dimensional features to be one-dimensional features or were limited to analytic activations, thereby diverging from practical use or resulting in L that grows exponentially with the set size N and feature dimension D. To investigate the minimal value of L that achieves sufficient expressive power, we present two set-element embedding layers: (a) linear + power activation (LP) and (b) linear + exponential activations (LE). We demonstrate that L being poly(N, D) is sufficient for set representation using both embedding layers. We also provide a lower bound of L for the LP embedding layer. Furthermore, we extend our results to permutation-equivariant set functions and the complex field.

The rapid proliferation of Large Language Models (LLMs) and diverse specialized benchmarks necessitates a shift from fragmented, task-specific metrics to a holistic, competitive ranking system that effectively aggregates performance across multiple ability dimensions. Primarily using static scoring, current evaluation methods are fundamentally limited. They struggle to determine the proper mix ratio across diverse benchmarks, and critically, they fail to capture a model's dynamic competitive fitness or its vulnerability when confronted with sequential, high-stakes tasks. To address this, we introduce the novel Competitive Swiss-System Dynamics (CSD) framework. CSD simulates a multi-round, sequential contest where models are dynamically paired across a curated sequence of benchmarks based on their accumulated win-loss record. And Monte Carlo Simulation (N=100,000 iterations) is used to approximate the statistically robust Expected Win Score (E[S_m]), which eliminates the noise of random pairing and early-round luck. Furthermore, we implement a Failure Sensitivity Analysis by parameterizing the per-round elimination quantity (T_k), which allows us to profile models based on their risk appetite--distinguishing between robust generalists and aggressive specialists. We demonstrate that CSD provides a more nuanced and context-aware ranking than traditional aggregate scoring and static pairwise models, representing a vital step towards risk-informed, next-generation LLM evaluation.

The assumption that response and predictor belong to the same statistical unit may be violated in practice. Unbiased estimation and recovery of true label ordering based on unlabeled data are challenging tasks and have attracted increasing attentions in the recent literature. In this paper, we present a relatively complete analysis of label permutation problem for the generalized linear model with multivariate responses. The theory is established under different scenarios, with knowledge of true parameters, with partial knowledge of underlying label permutation matrix and without any knowledge. Our results remove the stringent conditions required by the current literature and are further extended to the missing observation setting which has never been considered in the field of label permutation problem. On computational side, we propose two methods, "maximum likelihood estimation" algorithm and "two-step estimation" algorithm, to accommodate for different settings. When the proportion of permuted labels is moderate, both methods work effectively. Multiple numerical experiments are provided and corroborate our theoretical findings.

We study retrieval over catalogs of structured metadata, where each record is a small schema whose fields answer different kinds of query. Embedding a record with a text encoder first serializes its fields into a string, which forces a choice of field order. We show this choice, usually treated as an implementation detail, silently controls retrieval quality once the encoder is fine-tuned. A standard fine-tune loses 7.4 nDCG@10 points when the index is rebuilt under a different field order, because it reads absolute position instead of the field labels. We propose permutation-invariant fine-tuning (PI-FT), which serializes each record under a freshly sampled field order with random field dropout, so meaning binds to the labels rather than to position. The change is about two lines in the data loader; it costs negligible in-distribution accuracy and cuts the order-change penalty to 0.2 points. We study this in the discovery of development statistics, a catalog of nearly 10,000 indicators that should be searchable in many languages by a model small enough to self-host. As AI assistants and agents increasingly mediate access to public data and statistics, this retrieval step decides whether an answer is grounded in the right indicator or series, making discoverability a precondition for disseminating data through AI. Because usage logs cannot provide training signal for indicators no one has searched, we generate the queries instead. DevDataBench is a fully LLM-generated benchmark of grounded, facet-targeted queries across 15 languages, covering every indicator for both training and evaluation. A fine-tuned 118M-parameter CPU encoder outperforms every zero-shot baseline, including text-embedding-3-large (0.707 vs.\ 0.556 nDCG@10), with the largest gains in low-resource languages. We release the benchmark, pipeline, models, and a reusable PI-FT framework.

Pairwise Ranking Prompting (PRP) elicits pairwise preference judgments from an LLM, which are then aggregated into a ranking, usually via classical sorting algorithms. However, judgments are noisy, order-sensitive, and sometimes intransitive, so sorting assumptions do not match the setting. Because sorting aims to recover a full permutation, truncating it to meet a call budget does not produce a dependable top-K. We thus reframe PRP reranking as active learning from noisy pairwise comparisons and show that active rankers are drop-in replacements that improve NDCG@10 per call in the call-constrained regime. Our noise-robust framework also introduces a randomized-direction oracle that uses a single LLM call per pair. This approach converts systematic position bias into zero-mean noise, enabling unbiased aggregate ranking without the cost of bidirectional calls.

Instruction embedding models have become common among state-of-the-art models, however are evaluated using a single prompt per task. The single-point evaluation ignores a main problem of the instruction-based approach namely: sensitivity to the phrasing of the instruction. We present an empirical study of prompt sensitivity across 6 embedding models, 11 datasets, and 15 task-specific prompts per dataset, a total of 990. We show that reported scores misrepresent the distribution of scores over plausible prompts. The default prompt can both systematically understate or overstate performance. Furthermore, we show that the leaderboard ranking is not robust to prompt selection: by choosing prompts favorably, any model in our study can be promoted to first place. Our findings suggest that single-prompt evaluation is insufficient for instruction-tuned embedding models and that benchmarks should incorporate prompt robustness, either by evaluating over multiple prompts or by reporting sensitivity alongside point estimates.

Prior work evaluates code generation bias primarily through simple conditional statements, which represent only a narrow slice of real-world programming and reveal solely overt, explicitly encoded bias. We demonstrate that this approach dramatically underestimates bias in practice by examining a more realistic task: generating machine learning (ML) pipelines. Testing both code-specialized and general-instruction large language models, we find that generated pipelines exhibit significant bias during feature selection. Sensitive attributes appear in 87.7% of cases on average, despite models demonstrably excluding irrelevant features (e.g., including "race" while dropping "favorite color" for credit scoring). This bias is substantially more prevalent than that captured by conditional statements, where sensitive attributes appear in only 59.2% of cases. These findings are robust across prompt mitigation strategies, varying numbers of attributes, and different pipeline difficulty levels. Our results challenge simple conditionals as valid proxies for bias evaluation and suggest current benchmarks underestimate bias risk in practical deployments.

A central goal in systems biology and drug discovery is to predict the transcriptional response of cells to perturbations. This task is challenging due to the noisy and sparse nature of single-cell measurements, as well as the fact that perturbations often induce population-level shifts rather than changes in individual cells. Existing deep learning methods typically assume cell-level correspondences, limiting their ability to capture such global effects. We present scDFM, a generative framework based on conditional flow matching that models the full distribution of perturbed cells conditioned on control states. By incorporating a maximum mean discrepancy (MMD) objective, our method aligns perturbed and control populations beyond cell-level correspondences. To further improve robustness to sparsity and noise, we introduce the Perturbation-Aware Differential Transformer (PAD-Transformer), a backbone architecture that leverages gene interaction graphs and differential attention to capture context-specific expression changes. Across multiple genetic and drug perturbation benchmarks, scDFM consistently outperforms prior methods, demonstrating strong generalization in both unseen and combinatorial settings. In the combinatorial setting, it reduces mean squared error by 19.6% relative to the strongest baseline. These results highlight the importance of distribution-level generative modeling for robust in silico perturbation prediction. The code is available at https://github.com/AI4Science-WestlakeU/scDFM

We present a principled approach to uncover the structure of visual data by solving a novel deep learning task coined visual permutation learning. The goal of this task is to find the permutation that recovers the structure of data from shuffled versions of it. In the case of natural images, this task boils down to recovering the original image from patches shuffled by an unknown permutation matrix. Unfortunately, permutation matrices are discrete, thereby posing difficulties for gradient-based methods. To this end, we resort to a continuous approximation of these matrices using doubly-stochastic matrices which we generate from standard CNN predictions using Sinkhorn iterations. Unrolling these iterations in a Sinkhorn network layer, we propose DeepPermNet, an end-to-end CNN model for this task. The utility of DeepPermNet is demonstrated on two challenging computer vision problems, namely, (i) relative attributes learning and (ii) self-supervised representation learning. Our results show state-of-the-art performance on the Public Figures and OSR benchmarks for (i) and on the classification and segmentation tasks on the PASCAL VOC dataset for (ii).

Decoding methods play an indispensable role in converting language models from next-token predictors into practical task solvers. Prior research on decoding methods, primarily focusing on task-specific models, may not extend to the current era of general-purpose large language models (LLMs). Moreover, the recent influx of decoding strategies has further complicated this landscape. This paper provides a comprehensive and multifaceted analysis of various decoding methods within the context of LLMs, evaluating their performance, robustness to hyperparameter changes, and decoding speeds across a wide range of tasks, models, and deployment environments. Our findings reveal that decoding method performance is notably task-dependent and influenced by factors such as alignment, model size, and quantization. Intriguingly, sensitivity analysis exposes that certain methods achieve superior performance at the cost of extensive hyperparameter tuning, highlighting the trade-off between attaining optimal results and the practicality of implementation in varying contexts.

Large language models (LLMs) exhibit positional bias in how they use context, which especially complicates listwise ranking. To address this, we propose permutation self-consistency, a form of self-consistency over ranking list outputs of black-box LLMs. Our key idea is to marginalize out different list orders in the prompt to produce an order-independent ranking with less positional bias. First, given some input prompt, we repeatedly shuffle the list in the prompt and pass it through the LLM while holding the instructions the same. Next, we aggregate the resulting sample of rankings by computing the central ranking closest in distance to all of them, marginalizing out prompt order biases in the process. Theoretically, we prove the robustness of our method, showing convergence to the true ranking in the presence of random perturbations. Empirically, on five list-ranking datasets in sorting and passage reranking, our approach improves scores from conventional inference by up to 7-18% for GPT-3.5 and 8-16% for LLaMA v2 (70B), surpassing the previous state of the art in passage reranking. Our code is at https://github.com/castorini/perm-sc.

Causal sensitivity analysis aims to provide bounds for causal effect estimates in the presence of unobserved confounding. However, existing methods for causal sensitivity analysis are per-instance procedures, meaning that changes to the dataset, causal query, sensitivity level, or treatment require new computation. Here, we instead present an in-context learning approach. Specifically, we propose an amortized approach to causal sensitivity analysis based on prior-data fitted networks. A key challenge is that the sensitivity bounds are not directly available when sampling training data. To address this, we develop a general prior-data construction that is applicable across the class of generalized treatment sensitivity models. Our construction involves a Lagrangian scalarization of the objective to generate training labels for the bounds through a tradeoff between causal effect min/max-imization and sensitivity model violation, which avoids model-specific analytical derivations. We further show that, under standard convexity and linearity conditions, our objective recovers the full Pareto frontier of solutions. Empirically, we demonstrate our amortized approach across various datasets, causal queries, and sensitivity levels, where our approach achieves a test-time computation that is orders of magnitude faster than per-instance methods. To the best of our knowledge, ours is the first foundation model for in-context learning for causal sensitivity analysis.

Attribution methods can provide powerful insights into the reasons for a classifier's decision. We argue that a key desideratum of an explanation method is its robustness to input hyperparameters which are often randomly set or empirically tuned. High sensitivity to arbitrary hyperparameter choices does not only impede reproducibility but also questions the correctness of an explanation and impairs the trust of end-users. In this paper, we provide a thorough empirical study on the sensitivity of existing attribution methods. We found an alarming trend that many methods are highly sensitive to changes in their common hyperparameters e.g. even changing a random seed can yield a different explanation! Interestingly, such sensitivity is not reflected in the average explanation accuracy scores over the dataset as commonly reported in the literature. In addition, explanations generated for robust classifiers (i.e. which are trained to be invariant to pixel-wise perturbations) are surprisingly more robust than those generated for regular classifiers.

Large language models (LLMs) have demonstrated impressive capabilities across various tasks, but their performance is highly sensitive to the prompts utilized. This variability poses challenges for accurate assessment and user satisfaction. Current research frequently overlooks instance-level prompt variations and their implications on subjective evaluations. To address these shortcomings, we introduce ProSA, a framework designed to evaluate and comprehend prompt sensitivity in LLMs. ProSA incorporates a novel sensitivity metric, PromptSensiScore, and leverages decoding confidence to elucidate underlying mechanisms. Our extensive study, spanning multiple tasks, uncovers that prompt sensitivity fluctuates across datasets and models, with larger models exhibiting enhanced robustness. We observe that few-shot examples can alleviate this sensitivity issue, and subjective evaluations are also susceptible to prompt sensitivities, particularly in complex, reasoning-oriented tasks. Furthermore, our findings indicate that higher model confidence correlates with increased prompt robustness. We believe this work will serve as a helpful tool in studying prompt sensitivity of LLMs. The project is released at: https://github.com/open-compass/ProSA .

Proof autoformalization aims to translate a mathematical informal proof written in natural language into a formal proof in a formal language such as Lean~4. Several works have developed LLM-based models for proof autoformalization. However, existing evaluations have typically focused on translating well-formed informal proofs from curated datasets. We argue that a robust proof autoformalizer must remain faithful even for informal proofs that diverge from these idealized ones, and we present the first study on the robustness of proof autoformalization models. We formulate two categories of perturbations and evaluate robustness under each: a global perturbation paraphrases the informal proof in a different style, under which the formalization should remain consistent; a local perturbation alters a value, symbol, or proof step, possibly in a counterfactual way, and a robust formalization should faithfully reflect the perturbation rather than reverting to the original one or inferring a different one on its own. We build a benchmark with both perturbations on miniF2F and MATH-500, and automatically measure how stable a proof autoformalization's correctness is under global perturbations and how faithfully its output reflects local perturbations. We evaluate seven recent models, all of which are sensitive to global perturbations and mostly fail to remain faithful under local perturbations. Code and data are available via https://github.com/ucr-rai/robust-proof-autoformalization.

Large language models have demonstrated impressive performance on challenging mathematical reasoning tasks, which has triggered the discussion of whether the performance is achieved by true reasoning capability or memorization. To investigate this question, prior work has constructed mathematical benchmarks when questions undergo simple perturbations -- modifications that still preserve the underlying reasoning patterns of the solutions. However, no work has explored hard perturbations, which fundamentally change the nature of the problem so that the original solution steps do not apply. To bridge the gap, we construct MATH-P-Simple and MATH-P-Hard via simple perturbation and hard perturbation, respectively. Each consists of 279 perturbed math problems derived from level-5 (hardest) problems in the MATH dataset (Hendrycksmath et. al., 2021). We observe significant performance drops on MATH-P-Hard across various models, including o1-mini (-16.49%) and gemini-2.0-flash-thinking (-12.9%). We also raise concerns about a novel form of memorization where models blindly apply learned problem-solving skills without assessing their applicability to modified contexts. This issue is amplified when using original problems for in-context learning. We call for research efforts to address this challenge, which is critical for developing more robust and reliable reasoning models.

While large language models (LLMs) have achieved impressive performance across diverse tasks, recent studies showcase that causal LLMs suffer from the "reversal curse". It is a typical example that the model knows "A's father is B", but is unable to reason "B's child is A". This limitation poses a challenge to the advancement of artificial general intelligence (AGI), as it suggests a gap in the models' ability to comprehend and apply bidirectional reasoning. In this paper, we first conduct substantial evaluation and identify that the root cause of the reversal curse lies in the different word order between the training and inference stage, namely, the poor ability of causal language models to predict antecedent words within the training data. Accordingly, permutation on the training data is considered as a potential solution, since this can make the model predict antecedent words or tokens. However, previous permutation methods may disrupt complete phrases or entities, thereby posing challenges for the model to comprehend and learn from training data. To address this issue, we propose Semantic-aware Permutation Training (SPT), which addresses this issue by segmenting the training sentences into semantic units (i.e., entities or phrases) with an assistant language model and permuting these units before feeding into the model. Extensive experiments demonstrate that SPT effectively mitigates the reversal curse since the performance on reversed questions approximates that on the forward ones, and significantly advances the performance of existing works.

Large Language Models (LLMs) changed the way we design and interact with software systems. Their ability to process and extract information from text has drastically improved productivity in a number of routine tasks. Developers that want to include these models in their software stack, however, face a dreadful challenge: debugging LLMs' inconsistent behavior across minor variations of the prompt. We therefore introduce two metrics for classification tasks, namely sensitivity and consistency, which are complementary to task performance. First, sensitivity measures changes of predictions across rephrasings of the prompt, and does not require access to ground truth labels. Instead, consistency measures how predictions vary across rephrasings for elements of the same class. We perform an empirical comparison of these metrics on text classification tasks, using them as guideline for understanding failure modes of the LLM. Our hope is that sensitivity and consistency will be helpful to guide prompt engineering and obtain LLMs that balance robustness with performance.

Modern industrial recommender systems rely on thousands of heterogeneous features -- ranging from low-dimensional scalars (e.g., statistical value) to high-dimensional embeddings (e.g., user-id embeddings, MLP representations) -- to achieve high-precision predictions. Given the immense computational costs associated with training, efficient feature selection is critical. However, existing methods encounter three primary bottlenecks: (1) they typically assume uniform feature dimensions or require costly mapping to a fixed size; (2) they struggle with extreme sparsity, where the majority of features (e.g., 99%+) remain at default values; and (3) traditional permutation-based approaches are computationally prohibitive in large-scale settings. To address these challenges, we propose LeAP (Learnable Adaptive Permutation), a novel, model-agnostic plug-in module for feature selection. LeAP transforms the inefficient random permutation process into a learnable mechanism, significantly accelerating the evaluation of feature importance. In addition, we introduce an adaptive regularization strategy tailored for heterogeneous dimensions and extreme sparsity, enabling superior feature importance ranking results across asymmetric input spaces. Experiments on four public recommendation datasets demonstrate that LeAP achieves state-of-the-art performance. Furthermore, LeAP has been deployed in a large-scale industrial search ranking model with over a billion daily requests and a 2TB model parameter scale. In this real-world scenario involving 12,000+ total feature dimensions, LeAP successfully identified and removed over 3,600 redundant dimensions without performance degradation, which is 2 to 10 times the ability of compared baseline methods.

Large language models are increasingly deployed as automated judges for evaluating other models, yet the stability of their verdicts under semantically equivalent prompt paraphrases remains unmeasured. We introduce JudgeSense, a framework and benchmark for quantifying this property via the Judge Sensitivity Score (JSS), defined as the fraction of paraphrase pairs on which a judge returns an identical decision. Evaluating nine judge models on 494 validated paraphrase pairs, we find that coherence is the only task where judges meaningfully differ, with JSS ranging from 0.389 to 0.992. On factuality, all judges cluster near JSS about 0.63, driven by a polarity-inverted prompt artifact; after correction, factuality JSS rises to about 0.9. Pairwise tasks (preference and relevance) exhibit degenerate always-A behavior in 8 of 9 judges, indicating strong position bias. Model scale does not predict consistency. We release code, decision logs, and a validated paraphrase dataset to support standardized JSS reporting.

LLMs are highly sensitive to prompt phrasing, yet standard benchmarks typically report performance using a single prompt, raising concerns about the reliability of such evaluations. In this work, we argue for a stochastic method of moments evaluation over the space of meaning-preserving prompt perturbations. We introduce a formal definition of reliable evaluation that accounts for prompt sensitivity, and suggest ReliableEval - a method for estimating the number of prompt resamplings needed to obtain meaningful results. Using our framework, we stochastically evaluate five frontier LLMs and find that even top-performing models like GPT-4o and Claude-3.7-Sonnet exhibit substantial prompt sensitivity. Our approach is model-, task-, and metric-agnostic, offering a recipe for meaningful and robust LLM evaluation.

Randomized controlled trials are susceptible to imbalance on covariates predictive of the outcome. Rerandomization and deterministic treatment assignment are two proposed solutions. This paper explores the relationship between rerandomization and deterministic assignment, showing how deterministic assignment is an extreme case of rerandomization. The paper argues that in small experiments, both fully randomized and fully deterministic assignment have limitations. Instead, the researcher should consider setting the rerandomization acceptance probability based on an analysis of covariates and assumptions about the data structure to achieve an optimal alignment between randomness and balance. This allows for the calculation of minimum p-values along with valid permutation tests and fiducial intervals. The paper also introduces tools, including a new, open-source R package named fastrerandomize, to implement rerandomization and explore options for optimal rerandomization acceptance thresholds.

Perturbative availability poisons (PAPs) add small changes to images to prevent their use for model training. Current research adopts the belief that practical and effective approaches to countering PAPs do not exist. In this paper, we argue that it is time to abandon this belief. We present extensive experiments showing that 12 state-of-the-art PAP methods are vulnerable to Image Shortcut Squeezing (ISS), which is based on simple compression. For example, on average, ISS restores the CIFAR-10 model accuracy to 81.73%, surpassing the previous best preprocessing-based countermeasures by 37.97% absolute. ISS also (slightly) outperforms adversarial training and has higher generalizability to unseen perturbation norms and also higher efficiency. Our investigation reveals that the property of PAP perturbations depends on the type of surrogate model used for poison generation, and it explains why a specific ISS compression yields the best performance for a specific type of PAP perturbation. We further test stronger, adaptive poisoning, and show it falls short of being an ideal defense against ISS. Overall, our results demonstrate the importance of considering various (simple) countermeasures to ensure the meaningfulness of analysis carried out during the development of PAP methods.

Neural networks have a number of shortcomings. Amongst the severest ones is the sensitivity to distribution shifts which allows models to be easily fooled into wrong predictions by small perturbations to inputs that are often imperceivable to humans and do not have to carry semantic meaning. Adversarial training poses a partial solution to address this issue by training models on worst-case perturbations. Yet, recent work has also pointed out that the reasoning in neural networks is different from humans. Humans identify objects by shape, while neural nets mainly employ texture cues. Exemplarily, a model trained on photographs will likely fail to generalize to datasets containing sketches. Interestingly, it was also shown that adversarial training seems to favorably increase the shift toward shape bias. In this work, we revisit this observation and provide an extensive analysis of this effect on various architectures, the common ell_2- and ell_infty-training, and Transformer-based models. Further, we provide a possible explanation for this phenomenon from a frequency perspective.

The study of adversarial robustness has so far largely focused on perturbations bound in p-norms. However, state-of-the-art models turn out to be also vulnerable to other, more natural classes of perturbations such as translations and rotations. In this work, we thoroughly investigate the vulnerability of neural network--based classifiers to rotations and translations. While data augmentation offers relatively small robustness, we use ideas from robust optimization and test-time input aggregation to significantly improve robustness. Finally we find that, in contrast to the p-norm case, first-order methods cannot reliably find worst-case perturbations. This highlights spatial robustness as a fundamentally different setting requiring additional study. Code available at https://github.com/MadryLab/adversarial_spatial and https://github.com/MadryLab/spatial-pytorch.

Large language models (LLMs) are now widely used to evaluate the quality of text, a field commonly referred to as LLM-as-a-judge. While prior works mainly focus on point-wise and pair-wise evaluation paradigms. Rubric-based evaluation, where LLMs select a score from multiple rubrics, has received less analysis. In this work, we show that rubric-based evaluation implicitly resembles a multi-choice setting and therefore has position bias: LLMs prefer score options appearing at specific positions in the rubric list. Through controlled experiments across multiple models and datasets, we demonstrate consistent position bias. To mitigate this bias, we propose a balanced permutation strategy that evenly distributes each score option across positions. We show that aggregating scores across balanced permutations not only reveals latent position bias, but also improves correlation between the LLM-as-a-Judge and human. Our results suggest that rubric-based LLM-as-a-Judge is not inherently point-wise and that simple permutation-based calibration can substantially improve its reliability.

Overconfidence and underconfidence in machine learning classifiers is measured by calibration: the degree to which the probabilities predicted for each class match the accuracy of the classifier on that prediction. How one measures calibration remains a challenge: expected calibration error, the most popular metric, has numerous flaws which we outline, and there is no clear empirical understanding of how its choices affect conclusions in practice, and what recommendations there are to counteract its flaws. In this paper, we perform a comprehensive empirical study of choices in calibration measures including measuring all probabilities rather than just the maximum prediction, thresholding probability values, class conditionality, number of bins, bins that are adaptive to the datapoint density, and the norm used to compare accuracies to confidences. To analyze the sensitivity of calibration measures, we study the impact of optimizing directly for each variant with recalibration techniques. Across MNIST, Fashion MNIST, CIFAR-10/100, and ImageNet, we find that conclusions on the rank ordering of recalibration methods is drastically impacted by the choice of calibration measure. We find that conditioning on the class leads to more effective calibration evaluations, and that using the L2 norm rather than the L1 norm improves both optimization for calibration metrics and the rank correlation measuring metric consistency. Adaptive binning schemes lead to more stablity of metric rank ordering when the number of bins vary, and is also recommended. We open source a library for the use of our calibration measures.

With the rapid growth in language processing applications, fairness has emerged as an important consideration in data-driven solutions. Although various fairness definitions have been explored in the recent literature, there is lack of consensus on which metrics most accurately reflect the fairness of a system. In this work, we propose a new formulation : ACCUMULATED PREDICTION SENSITIVITY, which measures fairness in machine learning models based on the model's prediction sensitivity to perturbations in input features. The metric attempts to quantify the extent to which a single prediction depends on a protected attribute, where the protected attribute encodes the membership status of an individual in a protected group. We show that the metric can be theoretically linked with a specific notion of group fairness (statistical parity) and individual fairness. It also correlates well with humans' perception of fairness. We conduct experiments on two text classification datasets : JIGSAW TOXICITY, and BIAS IN BIOS, and evaluate the correlations between metrics and manual annotations on whether the model produced a fair outcome. We observe that the proposed fairness metric based on prediction sensitivity is statistically significantly more correlated with human annotation than the existing counterfactual fairness metric.

Perturbation probing generates task-specific causal hypotheses for FFN neurons in large language models using two forward passes per prompt and no backpropagation, followed by a one-time intervention sweep of about 150 passes amortized across all identified neurons. Across eight behavioral circuits, 13 models, and four architecture families, we identify two circuit structures that organize LLM behavior. Opposition circuits appear when RLHF suppresses a pre-training tendency. In safety refusal, about 50 neurons, or 0.014 percent of all neurons, control the refusal template; ablating them changes 80 percent of response formats on 520 AdvBench prompts while producing near-zero harmful compliance, 3 of 520 cases, all with disclaimers. Routing circuits appear for pre-training behaviors distributed through attention. For language selection, residual-stream direction injection switches English to Chinese output on 99.1 percent of 580 benchmark prompts in the 3 of 19 tested models that satisfy three observed conditions: bilingual training, FFN-to-skip signal ratio between 0.3 and 1.1, and linear representability. The same intervention fails on the other 16 models and on math, code, and factual circuits, defining the limits of directional steering. The FFN-to-skip signal ratio, computed from the same two forward passes, distinguishes the two structures and predicts the appropriate intervention. Circuit topology varies by architecture, from Qwen's concentrated FFN bottleneck to Gemma's normalization-shielded circuit. In Qwen3.5-2B, ablating 20 neurons eliminates multi-turn sycophantic capitulation, while amplifying 10 related neurons improves factual correction from 52 percent to 88 percent on 200 TruthfulQA prompts. These results show that perturbation probing offers mechanistic insight into RLHF-organized behavior and a practical toolkit for precision template-layer editing.

In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees on the quality of approximation, while reducing the number of examples to the product of the VC dimension d and the total sensitivity mathfrak S in remarkably general settings. However, guarantees going beyond this general bound of mathfrak S d are known in perhaps only one setting, for ell_2 subspace embeddings, despite intense study of sensitivity sampling in prior work. In this work, we show the first bounds for sensitivity sampling for ell_p subspace embeddings for pneq 2 that improve over the general mathfrak S d bound, achieving a bound of roughly mathfrak S^{2/p} for 1leq p<2 and mathfrak S^{2-2/p} for 2<p<infty. For 1leq p<2, we show that this bound is tight, in the sense that there exist matrices for which mathfrak S^{2/p} samples is necessary. Furthermore, our techniques yield further new results in the study of sampling algorithms, showing that the root leverage score sampling algorithm achieves a bound of roughly d for 1leq p<2, and that a combination of leverage score and sensitivity sampling achieves an improved bound of roughly d^{2/p}mathfrak S^{2-4/p} for 2<p<infty. Our sensitivity sampling results yield the best known sample complexity for a wide class of structured matrices that have small ell_p sensitivity.

Existing Programming-By-Example (PBE) systems often rely on simplified benchmarks that fail to capture the high structural complexity of real-world regexes, such as deeper nesting and frequent use of union operations. To overcome the resulting performance drop, we propose ReSyn, a synthesizer-agnostic divide-and-conquer framework that decomposes complex synthesis problem into manageable sub-problems. We also introduce Set2Regex, a parameter-efficient synthesizer capturing the permutation invariance of examples. Experimental results demonstrate that ReSyn significantly boosts accuracy across various synthesizers, and its combination with Set2Regex establishes a new state-of-the-art on challenging real-world benchmark. The complete source code, datasets, and pre-trained model checkpoints are publicly available at https://github.com/mrseongminkim/ReSyn.

Large language models (LLMs) are increasingly characterised in recent evaluation work as having stable, model-level preference and value systems. However, accompanying robustness checks are limited to incidental prompt perturbations such as syntax variation and option reordering. This leaves open whether the measured properties survive when the surrounding task context changes, as it does in most real deployments. We test this directly across two established pairwise paradigms: ranking country preferences and eliciting utility judgements. In both, we make the deployment context -- the high-level task the model is performing while making concrete value-dependent choices -- our controlled variable, varied across framings such as writing a Reddit post or a news article. Across five LLMs and over 1.2M pairwise decisions, deployment context produces variation far larger than prompt paraphrasing and temperature controls. In country preference rankings over 15 countries, context induces widespread, statistically significant rank shifts; the aggregate Global North favouritism reported in prior work is itself context-dependent, with each model's bias shifting systematically across contexts. In utility elicitation over 50 outcomes, broad cross-category ordering is preserved, but fine-grained rankings within domains vary substantially, and cardinal exchange rates between outcomes (e.g. how many lives in one region equal one in another) shift by a factor of 2.47 at the median. Reported model-level preferences and utilities are therefore better understood as context-conditioned measurements than fixed model-level properties: safety guarantees obtained under one framing provide limited assurance in another.

We consider objective evaluation measures of saliency explanations for complex black-box machine learning models. We propose simple robust variants of two notions that have been considered in recent literature: (in)fidelity, and sensitivity. We analyze optimal explanations with respect to both these measures, and while the optimal explanation for sensitivity is a vacuous constant explanation, the optimal explanation for infidelity is a novel combination of two popular explanation methods. By varying the perturbation distribution that defines infidelity, we obtain novel explanations by optimizing infidelity, which we show to out-perform existing explanations in both quantitative and qualitative measurements. Another salient question given these measures is how to modify any given explanation to have better values with respect to these measures. We propose a simple modification based on lowering sensitivity, and moreover show that when done appropriately, we could simultaneously improve both sensitivity as well as fidelity.

Large language models hallucinate most about entities they have never seen. We ask whether a model's activations betray entity familiarity before a single answer token is generated, and whether that signal predicts the factual reliability of the answers. On four Polish Bielik models (1.5B-11B parameters), we probe four entity domains (athletes, cities, writers, musicians), each with 42 well-known, 42 obscure-but-real, and 42 fabricated entities addressed by a one-sentence question (504 prompts per model). Two unsupervised, single-forward-pass dispersion measures over post-SwiGLU MLP activations, inverse participation ratio and spectral entropy, separate known from fabricated entities at AUROC 0.95-1.00 across all domains and scales; a supervised linear probe reaches 0.99-1.00. Both clear selection-aware permutation floors of about 0.70-0.74 (empirical p<=1e-3), survive held-out layer selection (0.93-0.99), and persist on real names (known vs. obscure-but-real: 0.96-1.00). The signal transfers across entity types (mean off-diagonal AUROC 0.92-0.99); a matched-template counterfactual shows the only large drops are template-caused, not entity-type effects, and the signal is diffuse across heads. This representational signal is already at ceiling at 1.5B, whereas behavioral factual reliability scales sharply: 0, 2, 10, and 19 of 42 known athletes are answered fully correctly by the 1.5B, 4.5B, 7B, and 11B models under a strict judge. Within known entities, separating correct from hallucinated answers is much harder (probe 0.93; dispersion no better than a first-token-entropy baseline). A five-sample semantic-entropy baseline reaches only 0.71-0.83 at 5x the inference cost. Despite this internal awareness, the models almost never abstain: an audit of 2,520 answers finds 2 refusals and 1 hedge. Entity familiarity and factual reliability are distinct phenomena on different scaling curves.

Modern recommender systems may output considerably different recommendations due to small perturbations in the training data. Changes in the data from a single user will alter the recommendations as well as the recommendations of other users. In applications like healthcare, housing, and finance, this sensitivity can have adverse effects on user experience. We propose a method to stabilize a given recommender system against such perturbations. This is a challenging task due to (1) the lack of a ``reference'' rank list that can be used to anchor the outputs; and (2) the computational challenges in ensuring the stability of rank lists with respect to all possible perturbations of training data. Our method, FINEST, overcomes these challenges by obtaining reference rank lists from a given recommendation model and then fine-tuning the model under simulated perturbation scenarios with rank-preserving regularization on sampled items. Our experiments on real-world datasets demonstrate that FINEST can ensure that recommender models output stable recommendations under a wide range of different perturbations without compromising next-item prediction accuracy.

Neural network training is inherently sensitive to initialization and the randomness induced by stochastic gradient descent. However, it is unclear to what extent such effects lead to meaningfully different networks, either in terms of the models' weights or the underlying functions that were learned. In this work, we show that during the initial "chaotic" phase of training, even extremely small perturbations reliably causes otherwise identical training trajectories to diverge-an effect that diminishes rapidly over training time. We quantify this divergence through (i) L^2 distance between parameters, (ii) the loss barrier when interpolating between networks, (iii) L^2 and barrier between parameters after permutation alignment, and (iv) representational similarity between intermediate activations; revealing how perturbations across different hyperparameter or fine-tuning settings drive training trajectories toward distinct loss minima. Our findings provide insights into neural network training stability, with practical implications for fine-tuning, model merging, and diversity of model ensembles.

Existing cross-encoder models can be categorized as pointwise, pairwise, or listwise. Pairwise and listwise models allow passage interactions, which typically makes them more effective than pointwise models but less efficient and less robust to input passage order permutations. To enable efficient permutation-invariant passage interactions during re-ranking, we propose a new cross-encoder architecture with inter-passage attention: the Set-Encoder. In experiments on TREC Deep Learning and TIREx, the Set-Encoder is as effective as state-of-the-art listwise models while being more efficient and invariant to input passage order permutations. Compared to pointwise models, the Set-Encoder is particularly more effective when considering inter-passage information, such as novelty, and retains its advantageous properties compared to other listwise models. Our code is publicly available at https://github.com/webis-de/ECIR-25.

A key to knowledge graph embedding (KGE) is to choose a proper representation space, e.g., point-wise Euclidean space and complex vector space. In this paper, we propose a unified perspective of embedding and introduce uncertainty into KGE from the view of group theory. Our model can incorporate existing models (i.e., generality), ensure the computation is tractable (i.e., efficiency) and enjoy the expressive power of complex random variables (i.e., expressiveness). The core idea is that we embed entities/relations as elements of a symmetric group, i.e., permutations of a set. Permutations of different sets can reflect different properties of embedding. And the group operation of symmetric groups is easy to compute. In specific, we show that the embedding of many existing models, point vectors, can be seen as elements of a symmetric group. To reflect uncertainty, we first embed entities/relations as permutations of a set of random variables. A permutation can transform a simple random variable into a complex random variable for greater expressiveness, called a normalizing flow. We then define scoring functions by measuring the similarity of two normalizing flows, namely NFE. We construct several instantiating models and prove that they are able to learn logical rules. Experimental results demonstrate the effectiveness of introducing uncertainty and our model. The code is available at https://github.com/changyi7231/NFE.

This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty quantification guarantees for machine learning systems. Much of the current interest in conformal prediction is due to its ability to integrate into complex machine learning workflows, solving the problem of forming prediction sets without any assumptions on the form of the data generating distribution. Since contemporary machine learning algorithms have generally proven difficult to analyze directly, conformal prediction's main appeal is its ability to provide formal, finite-sample guarantees when paired with such methods. The goal of this book is to teach the reader about the fundamental technical arguments that arise when researching conformal prediction and related questions in distribution-free inference. Many of these proof strategies, especially the more recent ones, are scattered among research papers, making it difficult for researchers to understand where to look, which results are important, and how exactly the proofs work. We hope to bridge this gap by curating what we believe to be some of the most important results in the literature and presenting their proofs in a unified language, with illustrations, and with an eye towards pedagogy.

Serving large-scale machine learning (ML) models efficiently and with low latency has become challenging owing to increasing model size and complexity. Quantizing models can simultaneously reduce memory and compute requirements, facilitating their widespread access. However, for large models not all layers are equally amenable to the same numerical precision and aggressive quantization can lead to unacceptable loss in model accuracy. One approach to prevent this accuracy degradation is mixed-precision quantization, which allows different tensors to be quantized to varying levels of numerical precision, leveraging the capabilities of modern hardware. Such mixed-precision quantiztaion can more effectively allocate numerical precision to different tensors `as needed' to preserve model accuracy while reducing footprint and compute latency. In this paper, we propose a method to efficiently determine quantization configurations of different tensors in ML models using post-training mixed precision quantization. We analyze three sensitivity metrics and evaluate them for guiding configuration search of two algorithms. We evaluate our method for computer vision and natural language processing and demonstrate latency reductions of up to 27.59% and 34.31% compared to the baseline 16-bit floating point model while guaranteeing no more than 1% accuracy degradation.

While reinforcement learning algorithms can learn effective policies for complex tasks, these policies are often brittle to even minor task variations, especially when variations are not explicitly provided during training. One natural approach to this problem is to train agents with manually specified variation in the training task or environment. However, this may be infeasible in practical situations, either because making perturbations is not possible, or because it is unclear how to choose suitable perturbation strategies without sacrificing performance. The key insight of this work is that learning diverse behaviors for accomplishing a task can directly lead to behavior that generalizes to varying environments, without needing to perform explicit perturbations during training. By identifying multiple solutions for the task in a single environment during training, our approach can generalize to new situations by abandoning solutions that are no longer effective and adopting those that are. We theoretically characterize a robustness set of environments that arises from our algorithm and empirically find that our diversity-driven approach can extrapolate to various changes in the environment and task.

Instruction-tuning plays a vital role in enhancing the task-solving abilities of large language models (LLMs), improving their usability in generating helpful responses on various tasks. However, previous work has demonstrated that they are sensitive to minor variations in instruction phrasing. In this paper, we explore whether introducing perturbations in instruction-tuning data can enhance LLMs' resistance against noisy instructions. We focus on how instruction-tuning with perturbations, such as removing stop words or shuffling words, affects LLMs' performance on the original and perturbed versions of widely-used benchmarks (MMLU, BBH, GSM8K). We further assess learning dynamics and potential shifts in model behavior. Surprisingly, our results suggest that instruction-tuning on perturbed instructions can, in some cases, improve downstream performance. These findings highlight the importance of including perturbed instructions in instruction-tuning, which can make LLMs more resilient to noisy user inputs.

In "Embers of Autoregression" (McCoy et al., 2023), we showed that several large language models (LLMs) have some important limitations that are attributable to their origins in next-word prediction. Here we investigate whether these issues persist with o1, a new system from OpenAI that differs from previous LLMs in that it is optimized for reasoning. We find that o1 substantially outperforms previous LLMs in many cases, with particularly large improvements on rare variants of common tasks (e.g., forming acronyms from the second letter of each word in a list, rather than the first letter). Despite these quantitative improvements, however, o1 still displays the same qualitative trends that we observed in previous systems. Specifically, o1 - like previous LLMs - is sensitive to the probability of examples and tasks, performing better and requiring fewer "thinking tokens" in high-probability settings than in low-probability ones. These results show that optimizing a language model for reasoning can mitigate but might not fully overcome the language model's probability sensitivity.

Deep learning models are intrinsically sensitive to distribution shifts in the input data. In particular, small, barely perceivable perturbations to the input data can force models to make wrong predictions with high confidence. An common defense mechanism is regularization through adversarial training which injects worst-case perturbations back into training to strengthen the decision boundaries, and to reduce overfitting. In this context, we perform an investigation of 3x3 convolution filters that form in adversarially-trained models. Filters are extracted from 71 public models of the linf-RobustBench CIFAR-10/100 and ImageNet1k leaderboard and compared to filters extracted from models built on the same architectures but trained without robust regularization. We observe that adversarially-robust models appear to form more diverse, less sparse, and more orthogonal convolution filters than their normal counterparts. The largest differences between robust and normal models are found in the deepest layers, and the very first convolution layer, which consistently and predominantly forms filters that can partially eliminate perturbations, irrespective of the architecture. Data & Project website: https://github.com/paulgavrikov/cvpr22w_RobustnessThroughTheLens

Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a probabilistic foundation. This paper begins by providing a theoretical justification for the role of perturbations in UQ for LLMs. We then introduce a dual random walk perspective, modeling input-output pairs as two Markov chains with transition probabilities defined by semantic similarity. Building on this, we propose a fully probabilistic framework based on an inverse model, which quantifies uncertainty by evaluating the diversity of the input space conditioned on a given output through systematic perturbations. Within this framework, we define a new uncertainty measure, Inv-Entropy. A key strength of our framework is its flexibility: it supports various definitions of uncertainty measures, embeddings, perturbation strategies, and similarity metrics. We also propose GAAP, a perturbation algorithm based on genetic algorithms, which enhances the diversity of sampled inputs. In addition, we introduce a new evaluation metric, Temperature Sensitivity of Uncertainty (TSU), which directly assesses uncertainty without relying on correctness as a proxy. Extensive experiments demonstrate that Inv-Entropy outperforms existing semantic UQ methods. The code to reproduce the results can be found at https://github.com/UMDataScienceLab/Uncertainty-Quantification-for-LLMs.

Multiple choice questions (MCQs) are commonly used to evaluate the capabilities of large language models (LLMs). One common way to evaluate the model response is to rank the candidate answers based on the log probability of the first token prediction. An alternative way is to examine the text output. Prior work has shown that first token probabilities lack robustness to changes in MCQ phrasing, and that first token probabilities do not match text answers for instruction-tuned models. Therefore, in this paper, we investigate the robustness of text answers. We show that the text answers are more robust to question perturbations than the first token probabilities, when the first token answers mismatch the text answers. The difference in robustness increases as the mismatch rate becomes greater. As the mismatch reaches over 50\%, the text answer is more robust to option order changes than the debiased first token probabilities using state-of-the-art debiasing methods such as PriDe. Our findings provide further evidence for the benefits of text answer evaluation over first token probability evaluation.

We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order. This class of functions includes monotone submodular functions as a sub-family. To understand the importance of this structure in optimization problems we consider the problem of maximizing function value under various types of constraints. To demonstrate the modeling power of submodular order functions we show applications in two different settings. First, we apply our results to the extensively studied problem of assortment optimization. While the objectives in assortment optimization are known to be non-submodular (and non-monotone) even for simple choice models, we show that they are compatible with the notion of submodular order. Consequently, we obtain new and in some cases the first constant factor guarantee for constrained assortment optimization in fundamental choice models. As a second application of submodular order functions, we show an intriguing connection to the maximization of monotone submodular functions in the streaming model. We recover some best known guarantees for this problem as a corollary of our results.

We compress KV cache entries by quantizing angles in the Fast Walsh-Hadamard domain, where a random diagonal rotation makes consecutive element pairs approximately uniformly distributed on the unit circle. We extend this angular quantizer with per-layer early-boost, which independently configures K and V codebook sizes at each layer, allocating higher precision to a model-specific subset of critical layers. Across seven models (1B to 7B parameters), per-layer early-boost achieves lossless compression on four models and near-lossless quality on six of seven, at 3.28 to 3.67 angle bits per element. Asymmetric norm quantization (8-bit for keys, 4-bit log-space for values) yields 6.56 total bits per element on Mistral-7B with perplexity degradation of +0.0014 and no calibration data. A layer-group sensitivity analysis reveals model-specific bottleneck patterns, including K-dominated versus V-dominated layers and negative-transfer layers where increased precision degrades quality.

Robustness to adversarial attack is typically evaluated with adversarial accuracy. This metric quantifies the number of points for which, given a threat model, successful adversarial perturbations cannot be found. While essential, this metric does not capture all aspects of robustness and in particular leaves out the question of how many perturbations can be found for each point. In this work we introduce an alternative approach, adversarial sparsity, which quantifies how difficult it is to find a successful perturbation given both an input point and a constraint on the direction of the perturbation. This constraint may be angular (L2 perturbations), or based on the number of pixels (Linf perturbations). We show that sparsity provides valuable insight on neural networks in multiple ways. analyzing the sparsity of existing robust models illustrates important differences between them that accuracy analysis does not, and suggests approaches for improving their robustness. When applying broken defenses effective against weak attacks but not strong ones, sparsity can discriminate between the totally ineffective and the partially effective defenses. Finally, with sparsity we can measure increases in robustness that do not affect accuracy: we show for example that data augmentation can by itself increase adversarial robustness, without using adversarial training.

Benchmarks like GSM8K are popular measures of mathematical reasoning, but leaderboard gains can overstate true capability due to memorization of fixed test sets. Most robustness variants apply surface-level perturbations (paraphrases, renamings, number swaps, distractors) that largely preserve the underlying facts, and static releases can themselves become memorization targets over time. We introduce GSM-SEM, a reusable and stochastic framework for generating semantically diverse benchmark variants with substantially higher semantic variance than prior approaches. GSM-SEM perturbs problem statements by modifying entities, attributes, and/or relationships, frequently altering underlying facts and requiring models to recompute solutions under new conditions, while constraining generation to preserve the original calculations/answer and approximate problem difficulty. GSM-SEM generates fresh variants on each run without requiring re-annotation, reducing reliance on static public benchmarks for evaluation and thereby lowering the bias of memorization. We apply GSM-SEM on GSM8K and two existing variation suites (GSM-Symbolic and GSM-Plus), producing GSM8K-SEM, GSM-Symbolic-SEM, and GSM-Plus-SEM. Evaluating 14 SOTA LLMs, we observe consistent performance drops with larger decline when semantic perturbations are coupled with symbolic/plus variations (average drop rate 28% in maximum strictness configuration of GSM-SEM). We publicly release the three SEM variants as fully human-validated datasets. Finally, to demonstrate applicability beyond GSM-style math problems, we apply GSM-SEM to additional benchmarks including BigBenchHard, LogicBench, and NLR-BIRD.

Large Language Models are routinely compressed via post-training quantization to reduce inference costs and memory footprint for cloud and edge deployment, yet the impact of this compression on model quality remains poorly understood. Existing studies typically compare only two conditions (full-precision vs. a single quantized variant), rely on aggregate bias metrics, and evaluate a single model family, making it impossible to distinguish gradual degradation from threshold-dependent safety failures. We conduct a controlled empirical study of three instruction-tuned models (Qwen2.5-7B, Mistral-7B, Phi-3.5-mini) at five precision levels (BF16 through 3-bit) on 12,148 BBQ bias benchmark items across 5 random seeds, totaling 911,100 inference records. Our results reveal that 3-bit quantization causes 6-21% of previously unbiased items to develop new stereotypical behaviors, following a clear dose-response pattern confirmed via logistic regression, while models' willingness to select "unknown" answers declines by 17.4%. Crucially, these item-level changes are invisible to standard quality metrics: perplexity increases by less than 0.5% at 8-bit and under 3% at 4-bit across all three models, yet 2.5-5.6% of items already develop new biases at 4-bit. These findings demonstrate that aggregate evaluation metrics systematically miss fairness-critical degradation, underscoring the need for quality-aware compression protocols that explicitly test for bias emergence before deployment.

Understanding when learning is statistically possible yet computationally hard is a central challenge in high-dimensional statistics. In this work, we investigate this question in the context of single- and multi-index models, classes of functions widely studied as benchmarks to probe the ability of machine learning methods to discover features in high-dimensional data. Our main contribution is to show that a Noise Sensitivity Exponent (NSE) - a simple quantity determined by the activation function - governs the existence and magnitude of statistical-to-computational gaps within a broad regime of these models. We first establish that, in single-index models with large additive noise, the onset of a computational bottleneck is fully characterized by the NSE. We then demonstrate that the same exponent controls a statistical-computational gap in the specialization transition of large separable multi-index models, where individual components become learnable. Finally, in hierarchical multi-index models, we show that the NSE governs the optimal computational rate in which different directions are sequentially learned. Taken together, our results identify the NSE as a unifying property linking noise robustness, computational hardness, and feature specialization in high-dimensional learning.

Vulnerabilities related to option combinations pose a significant challenge in software security testing due to their vast search space. Previous research primarily addressed this challenge through mutation or filtering techniques, which inefficiently treated all option combinations as having equal potential for vulnerabilities, thus wasting considerable time on non-vulnerable targets and resulting in low testing efficiency. In this paper, we utilize carefully designed prompt engineering to drive the large language model (LLM) to predict high-risk option combinations (i.e., more likely to contain vulnerabilities) and perform fuzz testing automatically without human intervention. We developed a tool called ProphetFuzz and evaluated it on a dataset comprising 52 programs collected from three related studies. The entire experiment consumed 10.44 CPU years. ProphetFuzz successfully predicted 1748 high-risk option combinations at an average cost of only \$8.69 per program. Results show that after 72 hours of fuzzing, ProphetFuzz discovered 364 unique vulnerabilities associated with 12.30\% of the predicted high-risk option combinations, which was 32.85\% higher than that found by state-of-the-art in the same timeframe. Additionally, using ProphetFuzz, we conducted persistent fuzzing on the latest versions of these programs, uncovering 140 vulnerabilities, with 93 confirmed by developers and 21 awarded CVE numbers.

As the probability (and thus perplexity) of a text is calculated based on the product of the probabilities of individual tokens, it may happen that one unlikely token significantly reduces the probability (i.e., increase the perplexity) of some otherwise highly probable input, while potentially representing a simple typographical error. Also, given that perplexity is a scalar value that refers to the entire input, information about the probability distribution within it is lost in the calculation (a relatively good text that has one unlikely token and another text in which each token is equally likely they can have the same perplexity value), especially for longer texts. As an alternative to scalar perplexity this research proposes a simple algorithm used to calculate vector values based on n-gram perplexities within the input. Such representations consider the previously mentioned aspects, and instead of a unique value, the relative perplexity of each text token is calculated, and these values are combined into a single vector representing the input.

Population-based search has recently emerged as a possible alternative to Reinforcement Learning (RL) for black-box neural architecture search (NAS). It performs well in practice even though it is not theoretically well understood. In particular, whereas traditional population-based search methods such as evolutionary algorithms (EAs) draw much power from crossover operations, it is difficult to take advantage of them in NAS. The main obstacle is believed to be the permutation problem: The mapping between genotype and phenotype in traditional graph representations is many-to-one, leading to a disruptive effect of standard crossover. This paper presents the first theoretical analysis of the behaviors of mutation, crossover and RL in black-box NAS, and proposes a new crossover operator based on the shortest edit path (SEP) in graph space. The SEP crossover is shown theoretically to overcome the permutation problem, and as a result, have a better expected improvement compared to mutation, standard crossover and RL. Further, it empirically outperform these other methods on state-of-the-art NAS benchmarks. The SEP crossover therefore allows taking full advantage of population-based search in NAS, and the underlying theory can serve as a foundation for deeper understanding of black-box NAS methods in general.

Large pre-trained language models have recently gained significant traction due to their improved performance on various down-stream tasks like text classification and question answering, requiring only few epochs of fine-tuning. However, their large model sizes often prohibit their applications on resource-constrained edge devices. Existing solutions of yielding parameter-efficient BERT models largely rely on compute-exhaustive training and fine-tuning. Moreover, they often rely on additional compute heavy models to mitigate the performance gap. In this paper, we present Sensi-BERT, a sensitivity driven efficient fine-tuning of BERT models that can take an off-the-shelf pre-trained BERT model and yield highly parameter-efficient models for downstream tasks. In particular, we perform sensitivity analysis to rank each individual parameter tensor, that then is used to trim them accordingly during fine-tuning for a given parameter or FLOPs budget. Our experiments show the efficacy of Sensi-BERT across different downstream tasks including MNLI, QQP, QNLI, SST-2 and SQuAD, showing better performance at similar or smaller parameter budget compared to various alternatives.

Transformers achieve state-of-the-art accuracy and robustness across many tasks, but an understanding of the inductive biases that they have and how those biases are different from other neural network architectures remains elusive. Various neural network architectures such as fully connected networks have been found to have a simplicity bias towards simple functions of the data; one version of this simplicity bias is a spectral bias to learn simple functions in the Fourier space. In this work, we identify the notion of sensitivity of the model to random changes in the input as a notion of simplicity bias which provides a unified metric to explain the simplicity and spectral bias of transformers across different data modalities. We show that transformers have lower sensitivity than alternative architectures, such as LSTMs, MLPs and CNNs, across both vision and language tasks. We also show that low-sensitivity bias correlates with improved robustness; furthermore, it can also be used as an efficient intervention to further improve the robustness of transformers.

Large Vision-Language Models (VLMs) enable strong multimodal reasoning but incur heavy inference costs from redundant visual tokens. Token pruning alleviates this issue, yet existing approaches face limitations. Attention-based methods rely on raw attention scores, which are often unstable across layers and heads and can lead to redundant selections. Diversity-based methods improve robustness by selecting tokens far apart in feature space but risk dropping regions needed for accurate prediction. We propose \ours, a training-free framework built on a simple intuition: tokens with higher sensitivity are more likely to influence the model's output, and they should also capture complementary visual cues rather than overlapping information. To achieve this, we estimate token sensitivity using zeroth-order perturbations at the projection layer, a shallow and computationally light component of the model. This approach measures how small random perturbations affect the projection outputs, allowing us to approximate each token's influence through lightweight forward passes without backpropagation. Extensive experiments across multiple VLMs and benchmarks show that \ours consistently outperforms prior methods, pruning up to 94.4\% of tokens while maintaining accuracy and significantly improving efficiency, achieving up to 2.30x faster end-to-end inference over the baseline.

The ability of language models in RAG systems to selectively refuse to answer based on flawed context is critical for safety, yet remains a significant failure point. Our large-scale study reveals that even frontier models struggle in this setting, with refusal accuracy dropping below 50% on multi-document tasks, while exhibiting either dangerous overconfidence or overcaution. Static benchmarks fail to reliably evaluate this capability, as models exploit dataset-specific artifacts and memorize test instances. We introduce RefusalBench, a generative methodology that programmatically creates diagnostic test cases through controlled linguistic perturbation. Our framework employs 176 distinct perturbation strategies across six categories of informational uncertainty and three intensity levels. Evaluation of over 30 models uncovers systematic failure patterns: refusal comprises separable detection and categorization skills, and neither scale nor extended reasoning improves performance. We find that selective refusal is a trainable, alignment-sensitive capability, offering a clear path for improvement. We release two benchmarks -- RefusalBench-NQ (single document) and RefusalBench-GaRAGe (multi-document) -- and our complete generation framework to enable continued, dynamic evaluation of this critical capability.

PGD adversarial training, the standard robustness method, can reduce Jacobian Frobenius norm yet worsen clean-input geometry (e.g., TDI 1.336 vs. ERM 1.093). We show this is not an implementation artifact but a theorem-level consequence of supervised learning. We prove that any encoder minimizing supervised loss must retain non-zero sensitivity along directions correlated with training labels, including directions that are nuisance at test time. This holds across proper scoring rules, architectures, and dataset sizes. We call this the geometric blind spot of supervised learning. This theorem unifies four empirical phenomena often treated separately: non-robust features, texture bias, corruption fragility, and the robustness-accuracy tradeoff. It also explains why suppressing sensitivity in one adversarial direction can redistribute sensitivity elsewhere. We introduce Trajectory Deviation Index (TDI), a diagnostic of geometric isotropy. Unlike CKA, intrinsic dimension, or Jacobian Frobenius norm alone, TDI captures the failure mode above. In our experiments, PGD attains low Frobenius norm but high TDI, while PMH attains the lowest TDI with one additional training term and no architectural changes. Across seven tasks, BERT/SST-2, and ImageNet ViT-B/16 (backbone family underlying CLIP/DINO/SAM), the blind spot is measurable and repairable. It appears at foundation-model scale, worsens with model scale and task-specific fine-tuning, and is substantially reduced by PMH. PMH also leads on non-Gaussian corruption types (blur/brightness/contrast) without corruption-specific training.

Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose various structural conditions on the clustering schemes, under the general heading of functoriality. Functoriality refers to the idea that one should be able to compare the results of clustering algorithms as one varies the data set, for example by adding points or by applying functions to it. We show that within this framework, one can prove a theorems analogous to one of J. Kleinberg, in which for example one obtains an existence and uniqueness theorem instead of a non-existence result. We obtain a full classification of all clustering schemes satisfying a condition we refer to as excisiveness. The classification can be changed by varying the notion of maps of finite metric spaces. The conditions occur naturally when one considers clustering as the statistical version of the geometric notion of connected components. By varying the degree of functoriality that one requires from the schemes it is possible to construct richer families of clustering schemes that exhibit sensitivity to density.

Kernelized Stein discrepancy (KSD) is a score-based discrepancy widely used in goodness-of-fit tests. It can be applied even when the target distribution has an unknown normalising factor, such as in Bayesian analysis. We show theoretically and empirically that the KSD test can suffer from low power when the target and the alternative distributions have the same well-separated modes but differ in mixing proportions. We propose to perturb the observed sample via Markov transition kernels, with respect to which the target distribution is invariant. This allows us to then employ the KSD test on the perturbed sample. We provide numerical evidence that with suitably chosen transition kernels the proposed approach can lead to substantially higher power than the KSD test.

We have recently witnessed a number of impressive results on hard mathematical reasoning problems with language models. At the same time, the robustness of these models has also been called into question; recent works have shown that models can rely on shallow patterns in the problem description when generating a solution. Building on the idea of behavioral testing, we propose a novel framework, which pins down the causal effect of various factors in the input, e.g., the surface form of the problem text, the operands, and math operators on the output solution. By grounding the behavioral analysis in a causal graph describing an intuitive reasoning process, we study the behavior of language models in terms of robustness and sensitivity to direct interventions in the input space. We apply our framework on a test bed of math word problems. Our analysis shows that robustness does not appear to continuously improve as a function of size, but the GPT-3 Davinci models (175B) achieve a dramatic improvement in both robustness and sensitivity compared to all other GPT variants.

Quantization addresses the high resource demand for large language models (LLMs) by alleviating memory pressure and bandwidth congestion and providing significantly scaled compute power with a tolerable impact on accuracy. Four-bit floating point (FP4), the lowest-precision format that preserves essential numerical properties such as exponent and sign, has begun to be adopted in cutting-edge architectures, including Blackwell and AMD CDNA, to support LLM quantization and reduce deployment costs. Although aggressive quantization can yield efficiency gains, the quantization sensitivity of within-transformer layers and whether these sensitivities generalize across existing FP4 formats and model scales remain underexplored. To elucidate quantization sensitivity, this study conducts a systematic analysis of two FP4 formats, MXFP4 and NVFP4, across three Qwen2.5 model scales (0.5B, 7B, and 14B), using controlled component-wise and block-wise isolation methodologies. We observe that MLP up- and down-projection layers consistently dominate in terms of sensitivity, while gate and attention projections are moderately and substantially less sensitive to FP4 quantization, respectively. We further find that sensitivity does not universally localize to the final blocks, but early blocks can be highly sensitive, particularly under MXFP4. Our results provide a diagnostic characterization of the inference behavior of FP4 across components, depths, and FP4 formats.

We document empirical capability ceilings in decoder-only autoregressive language models across knowledge-intensive tasks. Systematic evaluation of OPT and Pythia model families (70M-30B parameters, spanning 240 times scaling) reveals that knowledge retrieval tasks show negligible accuracy improvement despite smooth loss reduction. On MMLU mathematics benchmarks, accuracy remains flat at 19-20% (below 25% random chance) across all scales while cross-entropy loss decreases by 31%. In contrast, procedural tasks like arithmetic show conventional scaling where both metrics improve together. Attention intervention experiments reveal high sensitivity to perturbation: swapping attention patterns between models causes catastrophic performance collapse (complete accuracy loss) rather than graceful degradation. These measurements have immediate engineering implications: for knowledge-intensive applications using OPT and Pythia architectures, parameter scaling beyond 1-2B offers minimal accuracy gains despite continued loss improvement. Our findings quantify capability-specific scaling failures in these model families to inform resource allocation decisions. Whether these patterns reflect fundamental constraints of decoder-only architectures or implementation-specific limitations remains an open question requiring investigation across diverse architectural approaches.

The study of hardest and easiest fitness landscapes is an active area of research. Recently, Kaufmann, Larcher, Lengler and Zou conjectured that for the self-adjusting (1,lambda)-EA, Adversarial Dynamic BinVal (ADBV) is the hardest dynamic monotone function to optimize. We introduce the function Switching Dynamic BinVal (SDBV) which coincides with ADBV whenever the number of remaining zeros in the search point is strictly less than n/2, where n denotes the dimension of the search space. We show, using a combinatorial argument, that for the (1+1)-EA with any mutation rate p in [0,1], SDBV is drift-minimizing among the class of dynamic monotone functions. Our construction provides the first explicit example of an instance of the partially-ordered evolutionary algorithm (PO-EA) model with parameterized pessimism introduced by Colin, Doerr and F\'erey, building on work of Jansen. We further show that the (1+1)-EA optimizes SDBV in Theta(n^{3/2}) generations. Our simulations demonstrate matching runtimes for both static and self-adjusting (1,lambda) and (1+lambda)-EA. We further show, using an example of fixed dimension, that drift-minimization does not equal maximal runtime.

Safety alignment mechanisms in large language models prevent responses to harmful queries through learned refusal behavior, yet these same mechanisms impede legitimate research applications including cognitive modeling, adversarial testing, and security analysis. While abliteration techniques enable surgical removal of refusal representations through directional orthogonalization, the relative effectiveness of available implementations remains uncharacterized. This study evaluates four abliteration tools (Heretic, DECCP, ErisForge, FailSpy) across sixteen instruction-tuned models (7B-14B parameters), reporting tool compatibility on all 16 models and quantitative metrics on subsets dictated by tool support. Single-pass methods demonstrated superior capability preservation on the benchmarked subset (avg GSM8K change across three models: ErisForge -0.28 pp; DECCP -0.13 pp), while Bayesian-optimized abliteration produced variable distribution shift (KL divergence: 0.043-1.646) with model-dependent capability impact. These findings provide researchers with evidence-based selection criteria for abliteration tool deployment across diverse model architectures. The principal finding indicates that mathematical reasoning capabilities exhibit the highest sensitivity to abliteration interventions, with GSM8K change ranging from +1.51 pp to -18.81 pp (-26.5% relative) depending on tool selection and model architecture.

Set function learning has emerged as a crucial area in machine learning, addressing the challenge of modeling functions that take sets as inputs. Unlike traditional machine learning that involves fixed-size input vectors where the order of features matters, set function learning demands methods that are invariant to permutations of the input set, presenting a unique and complex problem. This survey provides a comprehensive overview of the current development in set function learning, covering foundational theories, key methodologies, and diverse applications. We categorize and discuss existing approaches, focusing on deep learning approaches, such as DeepSets and Set Transformer based methods, as well as other notable alternative methods beyond deep learning, offering a complete view of current models. We also introduce various applications and relevant datasets, such as point cloud processing and multi-label classification, highlighting the significant progress achieved by set function learning methods in these domains. Finally, we conclude by summarizing the current state of set function learning approaches and identifying promising future research directions, aiming to guide and inspire further advancements in this promising field.

Despite the remarkable success of deep neural networks in a myriad of settings, several works have demonstrated their overwhelming sensitivity to near-imperceptible perturbations, known as adversarial attacks. On the other hand, prior works have also observed that deep networks can be under-sensitive, wherein large-magnitude perturbations in input space do not induce appreciable changes to network activations. In this work, we study in detail the phenomenon of under-sensitivity in vision models such as CNNs and Transformers, and present techniques to study the geometry and extent of "equi-confidence" level sets of such networks. We propose a Level Set Traversal algorithm that iteratively explores regions of high confidence with respect to the input space using orthogonal components of the local gradients. Given a source image, we use this algorithm to identify inputs that lie in the same equi-confidence level set as the source image despite being perceptually similar to arbitrary images from other classes. We further observe that the source image is linearly connected by a high-confidence path to these inputs, uncovering a star-like structure for level sets of deep networks. Furthermore, we attempt to identify and estimate the extent of these connected higher-dimensional regions over which the model maintains a high degree of confidence. The code for this project is publicly available at https://github.com/SriramB-98/blindspots-neurips-sub

Large language models (LLMs) are widely used as zero-shot and few-shot classifiers, where task behaviour is largely controlled through prompting. A growing number of works have observed that LLMs are sensitive to prompt variations, with small changes leading to large changes in performance. However, in many cases, the investigation of sensitivity is performed using underspecified prompts that provide minimal task instructions and weakly constrain the model's output space. In this work, we argue that a significant portion of the observed prompt sensitivity can be attributed to prompt underspecification. We systematically study and compare the sensitivity of underspecified prompts and prompts that provide specific instructions. Utilising performance analysis, logit analysis, and linear probing, we find that underspecified prompts exhibit higher performance variance and lower logit values for relevant tokens, while instruction-prompts suffer less from such problems. However, linear probing analysis suggests that the effects of prompt underspecification have only a marginal impact on the internal LLM representations, instead emerging in the final layers. Overall, our findings highlight the need for more rigour when investigating and mitigating prompt sensitivity.

A challenging problem in many modern machine learning tasks is to process weight-space features, i.e., to transform or extract information from the weights and gradients of a neural network. Recent works have developed promising weight-space models that are equivariant to the permutation symmetries of simple feedforward networks. However, they are not applicable to general architectures, since the permutation symmetries of a weight space can be complicated by recurrence or residual connections. This work proposes an algorithm that automatically constructs permutation equivariant models, which we refer to as universal neural functionals (UNFs), for any weight space. Among other applications, we demonstrate how UNFs can be substituted into existing learned optimizer designs, and find promising improvements over prior methods when optimizing small image classifiers and language models. Our results suggest that learned optimizers can benefit from considering the (symmetry) structure of the weight space they optimize. We open-source our library for constructing UNFs at https://github.com/AllanYangZhou/universal_neural_functional.

Neural field is an emerging paradigm in data representation that trains a neural network to approximate the given signal. A key obstacle that prevents its widespread adoption is the encoding speed-generating neural fields requires an overfitting of a neural network, which can take a significant number of SGD steps to reach the desired fidelity level. In this paper, we delve into the impacts of data transformations on the speed of neural field training, specifically focusing on how permuting pixel locations affect the convergence speed of SGD. Counterintuitively, we find that randomly permuting the pixel locations can considerably accelerate the training. To explain this phenomenon, we examine the neural field training through the lens of PSNR curves, loss landscapes, and error patterns. Our analyses suggest that the random pixel permutations remove the easy-to-fit patterns, which facilitate easy optimization in the early stage but hinder capturing fine details of the signal.

This study investigates the reasoning robustness of large language models (LLMs) on mathematical problem-solving tasks under systematically introduced input perturbations. Using the GSM8K dataset as a controlled testbed, we evaluate how well state-of-the-art models maintain logical consistency and correctness when confronted with four categories of prompt perturbations: irrelevant context, pathological instructions, factually relevant but non-essential context, and a combination of the latter two. Our experiments, conducted on thirteen open-source and closed-source LLMs, reveal that introducing irrelevant context within the model's context window significantly degrades performance, suggesting that distinguishing essential from extraneous details remains a pressing challenge. Surprisingly, performance regressions are relatively insensitive to the complexity of the reasoning task, as measured by the number of steps required, and are not strictly correlated with model size. Moreover, we observe that certain perturbations inadvertently trigger chain-of-thought-like reasoning behaviors, even without explicit prompting. Our findings highlight critical vulnerabilities in current LLMs and underscore the need for improved robustness against noisy, misleading, and contextually dense inputs, paving the way for more resilient and reliable reasoning in real-world applications.

Excluding irrelevant features in a pattern recognition task plays an important role in maintaining a simpler machine learning model and optimizing the computational efficiency. Nowadays with the rise of large scale datasets, feature selection is in great demand as it becomes a central issue when facing high-dimensional datasets. The present study provides a new measure of saliency for features by employing a Sensitivity Analysis (SA) technique called the extended Fourier amplitude sensitivity test, and a well-trained Feedforward Neural Network (FNN) model, which ultimately leads to the selection of a promising optimal feature subset. Ideas of the paper are mainly demonstrated based on adopting FNN model for feature selection in classification problems. But in the end, a generalization framework is discussed in order to give insights into the usage in regression problems as well as expressing how other function approximate models can be deployed. Effectiveness of the proposed method is verified by result analysis and data visualization for a series of experiments over several well-known datasets drawn from UCI machine learning repository.

Sorting is a fundamental operation of all computer systems, having been a long-standing significant research topic. Beyond the problem formulation of traditional sorting algorithms, we consider sorting problems for more abstract yet expressive inputs, e.g., multi-digit images and image fragments, through a neural sorting network. To learn a mapping from a high-dimensional input to an ordinal variable, the differentiability of sorting networks needs to be guaranteed. In this paper we define a softening error by a differentiable swap function, and develop an error-free swap function that holds a non-decreasing condition and differentiability. Furthermore, a permutation-equivariant Transformer network with multi-head attention is adopted to capture dependency between given inputs and also leverage its model capacity with self-attention. Experiments on diverse sorting benchmarks show that our methods perform better than or comparable to baseline methods.

Supervised fine-tuning (SFT) is a critical step in aligning large language models (LLMs) with human instructions and values, yet many aspects of SFT remain poorly understood. We trained a wide range of base models on a variety of datasets including code generation, mathematical reasoning, and general-domain tasks, resulting in 1,000+ SFT models under controlled conditions. We then identified the dataset properties that matter most and examined the layer-wise modifications introduced by SFT. Our findings reveal that some training-task synergies persist across all models while others vary substantially, emphasizing the importance of model-specific strategies. Moreover, we demonstrate that perplexity consistently predicts SFT effectiveness--often surpassing superficial similarity between trained data and benchmark--and that mid-layer weight changes correlate most strongly with performance gains. We will release these 1,000+ SFT models and benchmark results to accelerate further research.

Code generation models have achieved impressive performance. However, they tend to be brittle as slight edits to a prompt could lead to very different generations; these robustness properties, critical for user experience when deployed in real-life applications, are not well understood. Most existing works on robustness in text or code tasks have focused on classification, while robustness in generation tasks is an uncharted area and to date there is no comprehensive benchmark for robustness in code generation. In this paper, we propose ReCode, a comprehensive robustness evaluation benchmark for code generation models. We customize over 30 transformations specifically for code on docstrings, function and variable names, code syntax, and code format. They are carefully designed to be natural in real-life coding practice, preserve the original semantic meaning, and thus provide multifaceted assessments of a model's robustness performance. With human annotators, we verified that over 90% of the perturbed prompts do not alter the semantic meaning of the original prompt. In addition, we define robustness metrics for code generation models considering the worst-case behavior under each type of perturbation, taking advantage of the fact that executing the generated code can serve as objective evaluation. We demonstrate ReCode on SOTA models using HumanEval, MBPP, as well as function completion tasks derived from them. Interesting observations include: better robustness for CodeGen over InCoder and GPT-J; models are most sensitive to syntax perturbations; more challenging robustness evaluation on MBPP over HumanEval.

In continual learning, catastrophic forgetting is affected by multiple aspects of the tasks. Previous works have analyzed separately how forgetting is affected by either task similarity or overparameterization. In contrast, our paper examines how task similarity and overparameterization jointly affect forgetting in an analyzable model. Specifically, we focus on two-task continual linear regression, where the second task is a random orthogonal transformation of an arbitrary first task (an abstraction of random permutation tasks). We derive an exact analytical expression for the expected forgetting - and uncover a nuanced pattern. In highly overparameterized models, intermediate task similarity causes the most forgetting. However, near the interpolation threshold, forgetting decreases monotonically with the expected task similarity. We validate our findings with linear regression on synthetic data, and with neural networks on established permutation task benchmarks.

Instruction finetuning is standard practice for improving LLM performance, yet it remains unclear whether it enhances reasoning or merely induces surface-level pattern matching. We investigate this by evaluating base and instruction-tuned models on standard math benchmarks, structurally perturbed variants, and domain-shifted tasks. Our analysis highlights two key (often overlooked) limitations of instruction tuning. First, the performance advantage is unstable and depends heavily on evaluation settings. In zero-shot CoT settings on GSM8K, base models consistently outperform instruction-tuned variants, with drops as high as 32.67\% (Llama3-70B). Instruction-tuned models only match or exceed this performance when provided with few-shot exemplars, suggesting a reliance on specific prompting patterns rather than intrinsic reasoning. Second, tuning gains are brittle under distribution shift. Our results show that base models surpass instruction-tuned variants on the domain-specific MedCalc benchmark. Additionally, instruction-tuned models show sharp declines on perturbed datasets, indicating sensitivity to prompt structure over robust reasoning.

Machine learning models are vulnerable to adversarial perturbations, and a thought-provoking paper by Bubeck and Sellke has analyzed this phenomenon through the lens of over-parameterization: interpolating smoothly the data requires significantly more parameters than simply memorizing it. However, this "universal" law provides only a necessary condition for robustness, and it is unable to discriminate between models. In this paper, we address these gaps by focusing on empirical risk minimization in two prototypical settings, namely, random features and the neural tangent kernel (NTK). We prove that, for random features, the model is not robust for any degree of over-parameterization, even when the necessary condition coming from the universal law of robustness is satisfied. In contrast, for even activations, the NTK model meets the universal lower bound, and it is robust as soon as the necessary condition on over-parameterization is fulfilled. This also addresses a conjecture in prior work by Bubeck, Li and Nagaraj. Our analysis decouples the effect of the kernel of the model from an "interaction matrix", which describes the interaction with the test data and captures the effect of the activation. Our theoretical results are corroborated by numerical evidence on both synthetic and standard datasets (MNIST, CIFAR-10).

Measuring diversity accurately is important for many scientific fields, including machine learning (ML), ecology, and chemistry. The Vendi Score was introduced as a generic similarity-based diversity metric that extends the Hill number of order q=1 by leveraging ideas from quantum statistical mechanics. Contrary to many diversity metrics in ecology, the Vendi Score accounts for similarity and does not require knowledge of the prevalence of the categories in the collection to be evaluated for diversity. However, the Vendi Score treats each item in a given collection with a level of sensitivity proportional to the item's prevalence. This is undesirable in settings where there is a significant imbalance in item prevalence. In this paper, we extend the other Hill numbers using similarity to provide flexibility in allocating sensitivity to rare or common items. This leads to a family of diversity metrics -- Vendi scores with different levels of sensitivity -- that can be used in a variety of applications. We study the properties of the scores in a synthetic controlled setting where the ground truth diversity is known. We then test their utility in improving molecular simulations via Vendi Sampling. Finally, we use the Vendi scores to better understand the behavior of image generative models in terms of memorization, duplication, diversity, and sample quality.

Code generation with large language models has shown significant promise, especially when employing retrieval-augmented generation (RAG) with few-shot examples. However, selecting effective examples that enhance generation quality remains a challenging task, particularly when the target programming language (PL) is underrepresented. In this study, we present two key findings: (1) retrieving examples whose presented algorithmic plans can be referenced for generating the desired behavior significantly improves generation accuracy, and (2) converting code into pseudocode effectively captures such algorithmic plans, enhancing retrieval quality even when the source and the target PLs are different. Based on these findings, we propose Plan-as-query Example Retrieval for few-shot prompting in Code generation (PERC), a novel framework that utilizes algorithmic plans to identify and retrieve effective examples. We validate the effectiveness of PERC through extensive experiments on the CodeContests, HumanEval and MultiPL-E benchmarks: PERC consistently outperforms the state-of-the-art RAG methods in code generation, both when the source and target programming languages match or differ, highlighting its adaptability and robustness in diverse coding environments.

Large language models are highly sensitive to prompts, but this sensitivity is usually studied through task-relevant instructions, demonstrations, or reasoning cues. In this paper, we study a different form of prompt sensitivity: whether prompts that are semantically unrelated to the task can nevertheless steer model behavior. We call them spurious prompts and show their surprising efficacy. We also propose a simple black-box search procedure for discovering them. Across reasoning and question-answering benchmarks, using models ranging from 0.8B to 27B parameters and spanning three model families, we show that spurious prompts can improve performance, often matching or outperforming standard prompting baselines and task-aware prompt optimization. We further show that they can steer models toward unintended behaviors, such as repeatedly selecting the first answer option, producing incorrect answers, returning an even, prime or small number without explicitly instructing the model to do so. These findings reveal a new kind of prompt sensitivity: LLMs can be systematically steered by prompts that are unrelated to the task they are asked to solve. Our code is available at https://github.com/Batorskq/spurious

While Large Language Models (LLMs) are widely documented to be sensitive to minor prompt perturbations and prone to sycophantic alignment with user biases, their robustness in consequential, rule-bound decision-making remains under-explored. In this work, we uncover a striking "Paradox of Robustness": despite their known lexical brittleness, instruction-tuned LLMs exhibit a behavioral and near-total invariance to emotional framing effects. Using a novel controlled perturbation framework across three high-stakes domains (healthcare, law, and finance), we quantify a robustness gap where LLMs demonstrate 110-300 times greater resistance to narrative manipulation than human subjects. Specifically, we find a near-zero effect size for models (Cohen's h = 0.003) compared to the substantial biases observed in humans (Cohen's h in [0.3, 0.8]). This result is highly counterintuitive and suggests the mechanisms driving sycophancy and prompt sensitivity do not necessarily translate to a failure in logical constraint satisfaction. We show that this invariance persists across models with diverse training paradigms. Our findings show that while LLMs may be "brittle" to how a query is formatted, they are remarkably "stable" against why a decision should be biased. Our findings establish that instruction-tuned models can decouple logical rule-adherence from persuasive narratives, offering a source of decision stability that complements, and even potentially de-biases, human judgment in institutional contexts. We release the 162-scenario benchmark, code, and data to facilitate the rigorous evaluation of narrative-induced bias and robustness on GitHub.com.

Prior work has shown that fine-tuning models on a narrow domain with misaligned data can lead to broad misalignment - a phenomenon termed "emergent misalignment" (Betley et al. 2025). While all tested models were susceptible to emergent misalignment, some models showed more resistance than others. Specifically the Qwen-2.5 family proved to be relatively resistant, while GPT-4o exhibited the strongest misalignment. In this paper we evaluate if current-generation open-weights models exhibit similar resistance to the Qwen-2.5 family and measure misalignment robustness over a range of model architectures and scales. We replicate the effect across nine modern open-weights models (Gemma 3 and Qwen 3 families, 1B-32B parameters). Models fine-tuned on insecure code generation show a 0.68% misalignment rate (compared to 0.07% for base models), matching the lower end of prior open-model results but dramatically lower than GPT-4o's 20%. We identify a critical format-dependent vulnerability: requiring JSON output doubles misalignment rates compared to natural language prompts (0.96% vs 0.42%). This suggests that structural constraints may bypass safety training by reducing the model's 'degrees of freedom' to refuse. These findings confirm emergent misalignment as a reproducible phenomenon in modern open-weights models, with rates substantially lower than observed in proprietary systems.

In this paper, we introduce a systematic framework beyond conventional method to assess LLMs' mathematical-reasoning robustness by stress-testing them on advanced math problems that are mathematically equivalent but with linguistic and parametric variation. These transformations allow us to measure the sensitivity of LLMs to non-mathematical perturbations, thereby enabling a more accurate evaluation of their mathematical reasoning capabilities. Using this new evaluation methodology, we created PutnamGAP, a new benchmark dataset with multiple mathematically-equivalent variations of competition-level math problems. With the new dataset, we evaluate multiple families of representative LLMs and examine their robustness. Across 18 commercial and open-source models we observe sharp performance degradation on the variants. OpenAI's flagship reasoning model, O3, scores 51.5% on the originals but drops by 4.7 percentage points on surface-renaming variants, and by 12.9 percentage points on parametric variants, while smaller models fare far worse. Overall, the results show that the proposed new evaluation methodology is effective for deepening our understanding of the robustness of LLMs and generating new insights for further improving their mathematical reasoning capabilities.

Sensitivity to staining variation remains a major barrier to deploying computational pathology (CPath) models as hematoxylin and eosin (H&E) staining varies across laboratories, requiring systematic assessment of how this variability affects model prediction. In this work, we developed a three-step protocol for evaluating robustness to H&E staining variation in CPath models. Step 1: Select reference staining conditions, Step 2: Characterize test set staining properties, Step 3: Apply CPath model(s) under simulated reference staining conditions. Here, we first created a new reference staining library based on the PLISM dataset. As an exemplary use case, we applied the protocol to assess the robustness properties of 306 microsatellite instability (MSI) classification models on the unseen SurGen colorectal cancer dataset (n=738), including 300 attention-based multiple instance learning models trained on the TCGA-COAD/READ datasets across three feature extractors (UNI2-h, H-Optimus-1, Virchow2), alongside six public MSI classification models. Classification performance was measured as AUC, and robustness as the min-max AUC range across four simulated staining conditions (low/high H&E intensity, low/high H&E color similarity). Across models and staining conditions, classification performance ranged from AUC 0.769-0.911 (Δ = 0.142). Robustness ranged from 0.007-0.079 (Δ = 0.072), and showed a weak inverse correlation with classification performance (Pearson r=-0.22, 95% CI [-0.34, -0.11]). Thus, we show that the proposed evaluation protocol enables robustness-informed CPath model selection and provides insight into performance shifts across H&E staining conditions, supporting the identification of operational ranges for reliable model deployment. Code is available at https://github.com/CTPLab/staining-robustness-evaluation .

Post-training quantization (PTQ) has emerged as a promising technique for mitigating memory consumption and computational costs in large language models (LLMs). However, a systematic examination of various quantization schemes, model families, and quantization bit precision has been absent from the literature. In this paper, we conduct a comprehensive analysis of these factors by investigating the effects of PTQ on weight-only, activation-only, and weight-and-activation quantization using diverse methods such as round-to-nearest (RTN), GPTQ, ZeroQuant, and their variants. We apply these methods to two distinct model families with parameters ranging from 125M to 176B. Our contributions include: (1) a sensitivity analysis revealing that activation quantization is generally more susceptible to weight quantization, with smaller models often outperforming larger models in terms of activation quantization; (2) an evaluation and comparison of existing PTQ methods to optimize model size reduction while minimizing the impact on accuracy, revealing that none of the current methods can achieve the original model quality for quantization with either INT4-weight or INT4-weight-and-INT8-activation; (3) based on these insights, we propose an optimized method called Low-Rank Compensation (LoRC), which employs low-rank matrices to enhance model quality recovery with a minimal increase in model size.

Quantizing large language models (LLMs) presents significant challenges, primarily due to outlier activations that compromise the efficiency of low-bit representation. Traditional approaches mainly focus on solving Normal Outliers-activations with consistently high magnitudes across all tokens. However, these techniques falter when dealing with Massive Outliers, which are significantly higher in value and often cause substantial performance losses during low-bit quantization. In this study, we propose DuQuant, an innovative quantization strategy employing rotation and permutation transformations to more effectively eliminate both types of outliers. Initially, DuQuant constructs rotation matrices informed by specific outlier dimensions, redistributing these outliers across adjacent channels within different rotation blocks. Subsequently, a zigzag permutation is applied to ensure a balanced distribution of outliers among blocks, minimizing block-wise variance. An additional rotation further enhances the smoothness of the activation landscape, thereby improving model performance. DuQuant streamlines the quantization process and demonstrates superior outlier management, achieving top-tier results in multiple tasks with various LLM architectures even under 4-bit weight-activation quantization. Our code is available at https://github.com/Hsu1023/DuQuant.