Science & Mathematics

Retrieval Augmented Generation (RAG) grounds large language models in external knowledge. Modern pipelines combine embedding, chunking, retrieval, reranking, query augmentation, context compression, and agentic verification, yet these techniques are typically evaluated one at a time. It remains unclear whether their isolated gains survive composition, whether retrieval quality and answer faithfulness favor the same design choices, and whether conclusions from small corpora hold at large scale. We pre-declare three hypotheses and introduce LASAGNA, an open-source framework for controlled RAG evaluation. We test 450 configurations across eight benchmarks and corpora ranging from 5K to 200K documents. Three findings emerge. First, individually strong techniques from different phases of a RAG pipeline do not necessarily compose: three retrieval techniques predict a +47% combined improvement but deliver only +17% when used together. Second, component gains stack differently for retrieval and faithfulness, and optimizing one can hurt the other. Third, the best composition changes as the corpus grows: the combination that wins on a small corpus may not remain best at large scale. These findings show that gains measured in isolation are not reliable predictors of realistic performance, and that new RAG techniques should be tested with the full surrounding stack. We call on researchers to do so and supply LASAGNA to simplify these experiments.

Understanding failures of autonomous systems is challenging, particularly when their behavior depends on black-box components such as neural networks. In this work, we make a distinction between two objectives of failure analysis: reproduction, which seeks to identify conditions sufficient to reproduce an observed failure, and avoidance, which seeks to identify the changes required to prevent it. Previous work on causal explanations of system failures is based on the concept of sufficient explanations and naturally supports reproduction. Nevertheless, we observe that it does not address the problem of avoiding the failure. In this paper, we introduce and formalize the concept of necessary explanations for system analysis as the correct formalism for failure avoidance. We place necessary explanations in the framework of actual causality and show that, together with sufficient explanations, they provide a unified causal framework for addressing both objectives of failure analysis. We present an efficient approximation algorithm for generating necessary explanations based on the notion of causal responsibility. We evaluate the efficiency of our approach across multiple environments. We demonstrate the practical utility of necessary explanations for failure avoidance through counterfactual generation and show that it outperforms existing methods.

Motivated by the recent experimental interest in honeycomb molybdates A$_2$Mo$_3$O$_8$, we return and develop the minimal models to capture the essential physics for Fe$_2$Mo$_3$O$_8$. It is pointed out that, the magnetism in these materials arises from the mutual induction between the spin-orbit coupling of the tetrahedral sublattice with active orbitals and the superexchange with the spins from the octahedral sublattice. Essentially, the superexchange between the tetrahedral and octahedral sublattices directly drives the ferrimagnetism, and the residual spin-orbit coupling on the tetrahedral sublattice induces the complex orbital order. The hybrid magnon-phonon excitations are further explored together with their resulting Berry curvatures and thermal Hall effect. We discuss the experimental relevance with Fe$_2$Mo$_3$O$_8$, and the framework can be extended to FeNiMo$_3$O$_8$, Ni$_2$Mo$_3$O$_8$ and other isostructural magnets.

Vision-language-action (VLA) policies need to recognize gaps in their training knowledge to request useful demonstrations or assistance in new situations, especially when failures are costly. Disagreement within an ensemble of independently trained policies can guide these decisions, but requires training and running multiple policies. We propose post-hoc kernel-variance heads that estimate epistemic uncertainty from the embeddings of a single policy. Each head computes the conditional variance of a Gaussian process conditioned on embeddings from the training demonstrations. Fitting requires no regression targets or gradient updates and leaves the policy unchanged. In experiments with SmolVLA on LIBERO-10, the kernel variance heads perform competitively with two-policy ensemble scores in task-level correlation with task success, in demonstration acquisition during active learning, and in referral to a stronger supervisor policy as a proxy for human assistance. For SmolVLA, the head on the vision-language backbone reduces uncertainty-scoring time by up to approximately a factor of 50 compared with ensemble scores, while also substantially reducing setup costs. We also show that the established evaluation protocol on LIBERO-10 primarily rewards recognition of coverage differences between tasks, while execution variability weakens assessment of within-task rankings. Thus, controlled perturbations provide a complementary evaluation: modality-specific heads identify unfamiliar camera, instruction, or state inputs, while fused heads can detect unfamiliar combinations of individually familiar inputs. With a supervisor proxy trained on the evaluated perturbation families, the decoder head improves within-task referral over ensemble disagreement. These findings show that useful uncertainty estimates for adaptive robot learning can be obtained from a single policy.

The nucleon is the multiplicative counterpart of the nucleolus: it lexicographically maximizes the fraction of its stand-alone value that each coalition receives. We study exact nucleon computation in matching games and in two extensions: $b$-matching games, in which players may have several partners, and partitioned matching games, in which one player may own several vertices. We resolve three open problems from a recent survey. For ordinary matching games with nonnegative rational weights, we give a polynomial-time combinatorial algorithm using maximum-weight matching, shortest paths, and minimum-cost flow, ; it returns both a nucleon allocation and a compact description of the full nucleon. In contrast, computing any nucleon allocation is NP-hard for unit-weight $b$-matching games with capacities at most three and for unit-weight partitioned matching games of width at most three. Finally, for the unresolved capacity-two case, we show that exact nucleon computation is polynomial-time Turing reducible to SHORTEST NON-ZERO CYCLE.

Compact chest X-ray (CXR) models that localize findings suit deployment, but box annotations are limited and report-aware multimodal models are expensive at inference. We introduce APED-CXR, which distills report-informed spatial evidence from a frozen multimodal teacher into a student with 11.1M parameters that predicts diseases and boxes from shared evidence maps and requires the image alone at test time. During training, the teacher uses the radiograph, report, and queried class to evaluate regions proposed from the student's current evidence maps, and its support scores serve as training targets for the student's pooled evidence scores within these regions. Trained on PadChest and evaluated on held-out PadChest-GR, refreshing the student's proposals for teacher evaluation improves box-level localization F1 from 0.302 with fixed warm-up proposals to 0.338 (IoU >= 0.5; gain 0.036, 95% CI [0.022, 0.049]), while maintaining diagnostic AUC. This gain depends on the teacher checking current proposals: with equally many random boxes, a fixed dense box set, teacher-generated boxes, or report rules instead of the teacher, F1 stays near the fixed-proposal level, and proposals two refreshes old recover only part of the gain. On NIH ChestX-ray14, a secondary test set, box recall also rises from 0.423 to 0.447.

How teams engineer requirements for systems built around Generative AI (GenAI) Agents remains empirically uncharted. Existing Requirements Engineering (RE) research mainly addresses AI and ML-based systems broadly but provides no process account for agentic systems, whose non-deterministic behavior cannot be anticipated at design time. To understand how teams actually proceed, we applied Socio-Technical Grounded Theory across 36 semi-structured interviews with practitioners, interleaving data collection and analysis so that emerging findings drove our theoretical sampling and shaped successive rounds of coding. The result is Behavioral Agent Requirement Discovery (BARD), the process theory of RE for GenAI Agents. BARD holds that requirements are not fixed up front but discovered through a recurring cycle of four activities: teams scope the need, build the agent, observe its behavior, and revise what they ask for. Through this four-phase loop, the requirement evolves from a fixed specification towards behavioral and evaluation criteria. Four tensions drive transitions between phases, and two conditions frame the loop. BARD provides researchers with a framework for iteratively refining RE workflows, while giving practitioners a structured basis to embed into their development processes.

In high-mobility channels, the widely adopted orthogonal frequency division multiplexing (OFDM) modulation waveform suffers from significant performance degradation due to channel variation and severe inter-carrier interference. Although delay-Doppler (DD) domain multicarrier (DDMC) modulation enjoys a higher channel estimation (CE) accuracy via exploiting the inherent DD-domain channel stability, sparsity, and separability, its high detection complexity limits its practical deployment, making OFDM still a promising waveform candidate for the sixth-generation (6G) cellular networks. To simultaneously harness the complementary strengths of DDMC and OFDM and mitigate their respective limitations, this paper proposes a DD-domain aided OFDM (DD-a-OFDM) framework, including a pulsone pilot (PP) design and a cross-domain iterative receiver design, to enhance the CE and detection performance of OFDM in high-mobility channels. Specifically, a pulsone pilot sequence is periodically inserted before the cyclic prefix (CP) for each OFDM symbol in the time-domain, which is equivalent to a single DD-domain pilot impulse and enables accurate DD-domain CE. Then, we propose a cross-domain iterative receiver in which the time-frequency (TF) domain detection results are transformed into the DD-domain for interference cancellation and CE; in turn, the DD-domain estimated channel is transformed into the TF-domain for channel reconstruction and symbol detection. The proposed cross-domain iterative receiver achieves a higher CE accuracy and detection performance with a much lower pilot overhead, compared to the conventional OFDM system. Simulation results validate the fast convergence and superior performance of the proposed DD-a-OFDM scheme and demonstrate that it maintains a robust CE and detection performance even in high-mobility channels.

Let $\mathcal{C}$ be an almost maximum distance separable (AMDS) code over the finite fields with parameters $[n,k,n-k]$ whose minimum-weight codewords support an $(n-k-1)$-$(n,n-k,λ)$ design. We first determine the parameters of the dual code $\mathcal{C}^{\bot}$. We also characterize the design and its complementary design supported by the minimum weight codewords of $\mathcal{C}^{\bot}$. In particular, we present explicit formulas for the weight enumerators of all subset codes of $\mathcal{C}^{\bot}$ with length at least $k+1$. These formulas are completely determined by the cardinality of the subset, the dimension, together with the parameter $λ$, and are independent of the specific choice of subsets. As an application, we answer an open problem posed by Wang, Tang and Ding in 2023 by proving that the $3$-design supported by the minimum-weight codewords in their proposed cyclic dual code is isomorphic to the complementary design of the Witt spherical geometry design.

Whole slide image (WSI) analysis enables computational diagnosis and prognosis, but gigapixel images and limited annotations make slide-level learning challenging. Multiple instance learning addresses this task by aggregating patch representations from frozen pretrained encoders. Recently, Mamba has enabled efficient modeling of long patch sequences. However, task supervision alone does not explicitly constrain information recovery during feature adaptation, while Mamba couples local processing with long-range propagation rather than retaining separate representations for fusion. Motivated by these challenges, we introduce LEAF-Mamba, a framework that jointly addresses latent evidence adaptation and fusion for frozen-feature WSI analysis. A reconstruction-regularized adapter learns compact, task-specific representations while reconstructing the input features. Parallel Mamba and convolutional streams then capture long-range dependencies and sequence-local interactions, with an input-dependent gate modulating their joint representation before slide-level pooling. Experiments across feature extractors demonstrate improved average performance over strong MIL baselines in both diagnostic classification and survival prediction. Component analyses further support the contributions of adaptation and fusion. These findings highlight the value of jointly designing feature transformation and contextual aggregation to translate pretrained representations into effective slide-level predictions.

Large language models (LLMs) are entering digital forensics as examination assistants and autonomous agents. Digital forensics inverts the usual setting for indirect prompt injection: the evidence under analysis is attacker-controlled by definition, and the examiner is obliged to read it closely. This makes the reasoning layer a new anti-forensic target, next to the classical ones of data and tools. Classical anti-forensic taxonomies do not cover it, and prompt injection defences do not anticipate it. We extend the anti-forensic model to reflect the manipulation of reasoning, and present a taxonomy of attacks carried through adversarial evidence: an attacker selects an objective, a technique, a payload location, and a concealment method. We observe a perception gap, i.e., the fact that deterministic tools, the human examiner, and the model perceive the same evidence differently, which is what lets an injection reach the model unseen by the examiner. We demonstrate three attacks against an LLM-assisted analysis pipeline, changing a reported conclusion, writing attacker-chosen content to the analyst's workstation, and causing outbound network traffic, each driven only by text planted on the seized device. Mitigations to these attacks are also proposed.

With the advent of foundation models, robots are increasingly capable of understanding and executing explicitly specified human tasks. Extending these capabilities to open-ended tasks, however, requires robots to infer appropriate actions from the observed scene. Household organization exemplifies this challenge, as robots must often act without detailed instructions, predefined object vocabularies, or known object-receptacle associations. While robots may follow instructions or learn organization preferences from demonstrations, inferring the latent organization of an occasionally changing scene and placing a novel object consistently with it remains challenging. We propose an open-world multi-attribute reasoning pipeline that grounds unknown objects across views and constructs an instance-level 3D scene graph for placement reasoning. First, a vision-language model proposes labels together with attributes such as content and packaging type, which are grounded through segmentation, depth, and multi-view association. Then, an LLM reasons over this representation to infer the latent shelf organization and rank scene-consistent object placements without explicitly user-provided preferences. The resulting placement rankings guide subsequent geometric and kinematic feasibility checks for execution. Our experimental evaluation shows that our approach leads to improved instance mapping and placement coherence over single-view language-grounding and geometry-only baselines, enabling autonomous placement of previously unseen objects without predefined object-receptacle mappings or class-specific retraining.

Electronegativity remains conceptually ambiguous: is it a fixed atomic constant, or does it depend on the chemical environment? We resolve this debate by recasting electronegativity as a continuous response function rooted in the Atomic Mean Inner Potential (AMIP). Building on the established static scale \(χ_{\mathrm{AMIP},1/2}\), we expand the electronegativity in fractional positive charge \(δ\). The first-order term defines the Electrostatic Rigidity \(\mathcal{R}\), whose sign indicates whether an atom hardens or softens upon oxidation, and the second-order term defines the Electrostatic Anharmonic Modulus \(\mathcal{A}\). A logarithmic-derivative decomposition separates \(\mathcal{R}\) into an intrinsic, scale-independent response asymmetry \(\mathcal{D} \equiv \mathcal{R}_Ω/Ω_0 - \mathcal{R}_f/f_0\), which governs the competition between electronic screening loss (softening) and geometric volume collapse (hardening). Applying this to all 102 elements reveals a systematic dichotomy between softening main-group elements and hardening d-block elements, two scaling laws within the transition series, and two anomalies at half-filled d\(^5\) configurations and in Ce. The framework resolves the Cs--Fr controversy through relativistic analysis, reproduces classical electronegativity scales and Lewis acidity trends, and provides three falsifiable experimental predictions. It transforms electronegativity into a predictive, hierarchically structured quantum descriptor.

Memorization inflates the benchmark scores of large language models (LLMs), since a model can reproduce answers it saw in training. Researchers test for it with consistent identifier renaming (CIR), which gives every identifier in a task a new name, and treat a lower score on the renamed task as evidence of recall. We test this method on the Temporal Logic of Actions Plus (TLA+) language, whose model checker acts as an oracle by confirming whether a renamed task preserves the exact behaviors of the original. Across 111 TLA+-Bench tasks, renaming lowers the correctness of Claude Opus 4.8 from 28% to 18% and of GPT-5 from 9% to 7%. Most of this decrease comes from how the test grades, which requires exact names that most descriptions never state. Grading by behavior shrinks the decrease to about 3 percentage points for Opus 4.8 and to 0 for GPT-5. In two model families fine-tuned on disjoint halves of the tasks, renaming removes about half of the training gain in likelihood and costs 4.9 percentage points (Qwen) and 1.3 percentage points (Gemma) on unseen tasks. A lower score after renaming therefore mixes memorization, name-based grading, and the cost of new names.

Consider a standard multi-hop wireless radio network in which nodes relay messages for one another. While the contents of messages may be sensitive and thus encrypted, the very fact that two radios communicated can leak sensitive information about both the physical location of the origin and the physical location of the destination. We investigate the trade-off between protecting the privacy of a user's current location and the privacy of their location of interest, and how the user should choose dummy destinations to obfuscate their queries.