Listwise reranking with large language models (LLMs) enhances top-ranked results in retrieval-based applications. Due to the limit in context size and high inference cost of long context, reranking is typically performed over a fixed size of small subsets, with the final ranking aggregated from these partial results. This fixed computation disregards query difficulty and document distribution, leading to inefficiencies. We propose AcuRank, an adaptive reranking framework that dynamically adjusts both the amount and target of computation based on uncertainty estimates over document relevance. Using a Bayesian TrueSkill model, we iteratively refine relevance estimates until reaching sufficient confidence levels, and our explicit modeling of ranking uncertainty enables principled control over reranking behavior and avoids unnecessary updates to confident predictions. Results on the TREC-DL and BEIR benchmarks show that our method consistently achieves a superior accuracy-efficiency trade-off and scales better with compute than fixed-computation baselines. These results highlight the effectiveness and generalizability of our method across diverse retrieval tasks and LLM-based reranking models.

We present causal head gating (CHG), a scalable method for interpreting the functional roles of attention heads in transformer models. CHG learns soft gates over heads and assigns them a causal taxonomy - facilitating, interfering, or irrelevant - based on their impact on task performance. Unlike prior approaches in mechanistic interpretability, which are hypothesis-driven and require prompt templates or target labels, CHG applies directly to any dataset using standard next-token prediction. We evaluate CHG across multiple large language models (LLMs) in the Llama 3 model family and diverse tasks, including syntax, commonsense, and mathematical reasoning, and show that CHG scores yield causal, not merely correlational, insight validated via ablation and causal mediation analyses. We also introduce contrastive CHG, a variant that isolates sub-circuits for specific task components. Our findings reveal that LLMs contain multiple sparse task-sufficient sub-circuits, that individual head roles depend on interactions with others (low modularity), and that instruction following and in-context learning rely on separable mechanisms.

This paper establishes the theoretical limits of graph clustering under the Popularity-Adjusted Block Model (PABM), addressing limitations of existing models. In contrast to the Stochastic Block Model (SBM), which assumes uniform vertex degrees, and to the Degree-Corrected Block Model (DCBM), which applies uniform degree corrections across clusters, PABM introduces separate popularity parameters for intra- and inter-cluster connections. Our main contribution is the characterization of the optimal error rate for clustering under PABM, which provides novel insights on clustering hardness: we demonstrate that unlike SBM and DCBM, cluster recovery remains possible in PABM even when traditional edge-density signals vanish, provided intra- and inter-cluster popularity coefficients differ. This highlights a dimension of degree heterogeneity captured by PABM but overlooked by DCBM: local differences in connectivity patterns can enhance cluster separability independently of global edge densities. Finally, because PABM exhibits a richer structure, its expected adjacency matrix has rank between $k$ and $k^2$, where $k$ is the number of clusters. As a result, spectral embeddings based on the top $k$ eigenvectors may fail to capture important structural information. Our numerical experiments on both synthetic and real datasets confirm that spectral clustering algorithms incorporating $k^2$ eigenvectors outperform traditional spectral approaches.

Knowledge distillation is a promising approach to transfer capabilities from complex teacher models to smaller, resource-efficient student models that can be deployed easily, particularly in task-aware scenarios. However, existing methods of task-aware distillation typically require substantial quantities of data which may be unavailable or expensive to obtain in many practical scenarios. In this paper, we address this challenge by introducing a novel strategy called Counterfactual-explanation-infused Distillation CoD for few-shot task-aware knowledge distillation by systematically infusing counterfactual explanations. Counterfactual explanations (CFEs) refer to inputs that can flip the output prediction of the teacher model with minimum perturbation. Our strategy CoD leverages these CFEs to precisely map the teacher's decision boundary with significantly fewer samples. We provide theoretical guarantees for motivating the role of CFEs in distillation, from both statistical and geometric perspectives. We mathematically show that CFEs can improve parameter estimation by providing more informative examples near the teacher's decision boundary. We also derive geometric insights on how CFEs effectively act as knowledge probes, helping the students mimic the teacher's decision boundaries more effectively than standard data. We perform experiments across various datasets and LLMs to show that CoD outperforms standard distillation approaches in few-shot regimes (as low as 8-512 samples). Notably, CoD only uses half of the original samples used by the baselines, paired with their corresponding CFEs and still improves performance.

Methods for forecasting time series adhering to linear constraints have seen notable development in recent years, especially with the advent of forecast reconciliation. This paper extends forecast reconciliation to the open question of non-linearly constrained time series. Non-linear constraints can emerge with variables that are formed as ratios such as mortality rates and unemployment rates. On the methodological side, Non-linearly Constrained Reconciliation (NLCR) is proposed. This algorithm adjusts forecasts that fail to meet non-linear constraints, in a way that ensures the new forecasts meet the constraints. The NLCR method is a projection onto a non-linear surface, formulated as a constrained optimisation problem. On the theoretical side, optimisation methods are again used, this time to derive sufficient conditions for when the NLCR methodology is guaranteed to improve forecast accuracy. Finally on the empirical side, NLCR is applied to two datasets from demography and economics and shown to significantly improve forecast accuracy relative to relevant benchmarks.

Bayesian Optimization (BO) is a powerful tool for optimizing expensive black-box objective functions. While extensive research has been conducted on the single-objective optimization problem, the multi-objective optimization problem remains challenging. In this paper, we propose MOBO-OSD, a multi-objective Bayesian Optimization algorithm designed to generate a diverse set of Pareto optimal solutions by solving multiple constrained optimization problems, referred to as MOBO-OSD subproblems, along orthogonal search directions (OSDs) defined with respect to an approximated convex hull of individual objective minima. By employing a well-distributed set of OSDs, MOBO-OSD ensures broad coverage of the objective space, enhancing both solution diversity and hypervolume performance. To further improve the density of the set of Pareto optimal candidate solutions without requiring an excessive number of subproblems, we leverage a Pareto Front Estimation technique to generate additional solutions in the neighborhood of existing solutions. Additionally, MOBO-OSD supports batch optimization, enabling parallel function evaluations to accelerate the optimization process when resources are available. Through extensive experiments and analysis on a variety of synthetic and real-world benchmark functions with two to six objectives, we demonstrate that MOBO-OSD consistently outperforms the state-of-the-art algorithms. Our code implementation can be found at https://github.com/LamNgo1/mobo-osd.

Selective classifiers improve model reliability by abstaining on inputs the model deems uncertain. However, few practical approaches achieve the gold-standard performance of a perfect-ordering oracle that accepts examples exactly in order of correctness. Our work formalizes this shortfall as the selective-classification gap and present the first finite-sample decomposition of this gap to five distinct sources of looseness: Bayes noise, approximation error, ranking error, statistical noise, and implementation- or shift-induced slack. Crucially, our analysis reveals that monotone post-hoc calibration -- often believed to strengthen selective classifiers -- has limited impact on closing this gap, since it rarely alters the model's underlying score ranking. Bridging the gap therefore requires scoring mechanisms that can effectively reorder predictions rather than merely rescale them. We validate our decomposition on synthetic two-moons data and on real-world vision and language benchmarks, isolating each error component through controlled experiments. Our results confirm that (i) Bayes noise and limited model capacity can account for substantial gaps, (ii) only richer, feature-aware calibrators meaningfully improve score ordering, and (iii) data shift introduces a separate slack that demands distributionally robust training. Together, our decomposition yields a quantitative error budget as well as actionable design guidelines that practitioners can use to build selective classifiers which approximate ideal oracle behavior more closely.

Edge intelligence enables low-latency inference via compact on-device models, but assuring reliability remains challenging. We study edge-cloud cascades that must preserve conditional coverage: whenever the edge returns a prediction set, it should contain the true label with a user-specified probability, as if produced by the cloud model. We formalize conditional coverage with respect to the cloud predictive distribution, and introduce a conformal alignment-based (CAb) cascading mechanism that certifies this property with user control over the risk level. Our method casts escalation from edge to cloud models as a multiple-hypothesis testing (MHT) problem, tailoring conformal alignment (CA) to select which inputs can be safely handled at the edge. The proposed CAb model cascading method yields statistical guarantees on the average fraction of edge decisions that satisfy cloud-level conditional coverage. The procedure applies to arbitrary edge prediction sets, including variants of conformal prediction (CP), and exposes a tunable trade-off among coverage, deferral rate, and set size. Experiments on CIFAR-100 image classification and the TeleQnA question-answering (QA) benchmark show that the proposed CAb cascade maintains the target conditional coverage for edge predictions while substantially reducing offloading to the cloud and incurring modest increases in prediction-set size.

Entitled son, 21, of top lawyer mows down police with his Mercedes G-Wagen...as he smiles in his mugshot Trump'humiliates' speaker Mike Johnson in private conversation as government shutdown rumbles on Tupac's humiliating intimate disfigurement revealed... and how his lies to cover it up led to his murder'I'm Madeline - and this is what I have to say to Lily Allen': Read world exclusive reveal of mother who had affair with star's husband David Harbour, how it started and how she feels about THOSE texts being exposed Loved up Katy Perry holds hands with Justin Trudeau as they officially confirm romance while celebrating the singer's birthday in Paris Furrow-browed boyfriend'strangled girlfriend and set her house on fire while newborn baby was inside' I've uncovered my husband's filthy Viagra habit: But, warns DEAR JANE, one thing YOU are doing is making it so much worse I've started having heart palpitations. Jackie Kennedy's revenge romance with American political icon: Revealed for first time in titillating love letters, the man who helped her cope with JFK's cheating The night that haunted a Wisconsin town forever... and the little girl whose trick-or-treat next door ended in horror Why going gray may save you from CANCER... as scientists make bombshell breakthrough Brazen demands for flying private REVEALED by the woman paid to fulfill them: 'Answer is always yes' They sneered at Trump's'eagle graveyards' - but now Biden's hated windmills crippling an American legend are haunting the US military Kim Kardashian's just been caught in a despicable lie. She can cry all she wants... there's no hiding the truth now: CAROLINE BULLOCK Tua Tagovailoa's swollen eye sparks concern after Dolphins QB woke up with mystery illness on day of Falcons game JD Vance's wife is given secret role in Trump's deal-making inner circle: 'I'll have Usha look at it' The Biden blunder that allowed an alleged October 7 'monster' to become a restaurant worker in Louisiana How I reversed my hair loss and lost 8 stone aged 45 - without weight-loss jabs. Urgent warning over cannabis as UK's top psychiatrist warns it isn't safe for young brains still developing It may seem like a relatively harmless right of passage. But cannabis isn't safe for young brains still developing, the UK's top psychiatrist has warned.

Entitled son, 21, of top lawyer mows down police with his Mercedes G-Wagen...as he smiles in his mugshot Tupac's humiliating intimate disfigurement revealed... and how his lies to cover it up led to his murder Trump'humiliates' speaker Mike Johnson in private conversation as government shutdown rumbles on'I'm Madeline - and this is what I have to say to Lily Allen': Read world exclusive reveal of mother who had affair with star's husband David Harbour, how it started and how she feels about THOSE texts being exposed Loved up Katy Perry holds hands with Justin Trudeau as they officially confirm romance while celebrating the singer's birthday in Paris Furrow-browed boyfriend'strangled girlfriend and set her house on fire while newborn baby was inside' I've uncovered my husband's filthy Viagra habit: But, warns DEAR JANE, one thing YOU are doing is making it so much worse I've started having heart palpitations. Jackie Kennedy's revenge romance with American political icon: Revealed for first time in titillating love letters, the man who helped her cope with JFK's cheating The night that haunted a Wisconsin town forever... and the little girl whose trick-or-treat next door ended in horror Why going gray may save you from CANCER... as scientists make bombshell breakthrough Brazen demands for flying private REVEALED by the woman paid to fulfill them: 'Answer is always yes' They sneered at Trump's'eagle graveyards' - but now Biden's hated windmills crippling an American legend are haunting the US military Kim Kardashian's just been caught in a despicable lie. She can cry all she wants... there's no hiding the truth now: CAROLINE BULLOCK Tua Tagovailoa's swollen eye sparks concern after Dolphins QB woke up with mystery illness on day of Falcons game JD Vance's wife is given secret role in Trump's deal-making inner circle: 'I'll have Usha look at it' The Biden blunder that allowed an alleged October 7 'monster' to become a restaurant worker in Louisiana How I reversed my hair loss and lost 8 stone aged 45 - without weight-loss jabs. A growing network of at least 5,000 data centers across the US is becoming a hidden public health threat, scientists have warned. That is because the energy-hungry backbone of artificial intelligence pumps out dangerous pollutants that can cause asthma, cancer and even death.