Hard

TinyML includes the implementation of machine learning on devices with limited memory and computing resources. With the development of technology, AI systems continue to scale in terms of size and computational requirements. This forces researchers to adapt methods to be environmentally sustainable by designing techniques for reducing computational costs and energy consumption in inferring AI models, even in small devices. In this work, we present preliminary findings on a novel application of the tree depth prune instance hardness method to the TinyML system. The results indicate that threshold control can change energy consumption with limited classification quality changes. This method allows us to adjust classification accuracy, thereby influencing computational complexity and energy consumption for inference. We present a work in progress with initial results as a proof of concept.

AI agents are increasingly used in mathematics research, but it is often unclear how to use them effectively. Towards this, we present an extensive case study of how AI was used to improve bounds on the Grothendieck constant $K_G$, which captures the hardness between combinatorial problems and their continuous relaxations. Specifically, while the precise value of $K_G$ is not known, we recently tightened the best known bounds to $$\frac{6π}{11} \;\le\; K_G \;\le\; \fracπ{2\log(1+\sqrt2)} - 10^{-4}.$$ Crucially, these improvements were achieved using an AI research system that could arrive at insights deemed novel by domain experts. We give a detailed discussion of our experience using AI for mathematics research, particularly touching upon its strengths and weaknesses, as well as our experience with creating ideal conditions for AI to arrive at breakthrough insights.

Federated learning enables medical-imaging models to be trained across hospitals, and privacy law, most explicitly the GDPR ``right to be forgotten'', turns removing a hospital's, a class's, or a patient's influence from such a model into a federated unlearning problem. This need is most acute in medicine, where patients withdraw consent and hospitals leave collaborations. Yet nearly all unlearning evidence comes from natural images, whose heterogeneity and task structure differ sharply from clinical data, so it is unclear whether existing methods transfer, and no shared protocol covers clinical data. We present Lethe, a benchmark for federated unlearning in medical imaging. It evaluates twelve methods across eight task families, from classification and segmentation to denoising, cross-modality synthesis, and vision-language question answering, at three forgetting granularities and against a retrained gold standard on utility, privacy, and cost. The central result is that what separates methods is the difficulty of the forgetting request, not the method itself. The easy removals that dominate the literature leave the methods that preserve utility indistinguishable, while only hard ones separate them. More striking, on the many medical tasks that generalize across sites, forgetting a client barely changes task performance, leaving residual membership as the signal that must be erased.

Progress in large language models is often summarized using a single scalar measure, such as a time horizon, a latent ability estimate, or an aggregate benchmark score. These summaries capture the overall performance, but they do not test whether progress is distributed differently across task difficulty. We find that most of the apparent shift in gains toward harder tasks does not reflect a change in the shape of the difficulty-response curve. On METR time-horizon data, a single Rasch model with rising ability reproduces this pattern, so it is largely explained by ceiling effects rather than a qualitative change in capability. This echoes how the choice of metric can make claimed emergent abilities look like a property of the models themselves. We then identify a smaller hard-task effect that survives this control. Isolating it is difficult on agentic benchmarks, because newer models are usually run with newer agentic harnesses, so a gain on hard tasks cannot be assigned to the model or its scaffold. We break the confound with LiveCodeBench, a public competitive programming benchmark that runs no agentic scaffold while pairing dated models with an exogenous difficulty ordering. After accounting for the rise in overall ability, models released after September 2024 still gain on the hardest problems beyond what their easy and medium performance predicts, by about +0.40 logits under our most conservative assumption, raising the hard-problem solve rate from roughly 18% to 25%. The effect is led by the strongest reasoning models and holds for hard tasks that need only short reasoning, not autonomy over long horizons. We present this as a result specific to competitive programming, since our clean identification rests on a single coding benchmark. We release the LiveCodeBench Difficulty Panel (66 dated models x 1,055 problems) and our analysis code.

Expensive simulation-driven design is widely used in engineering to identify requirement-satisfying designs with as few high-fidelity simulations as possible. Most existing efforts address this challenge by improving optimization algorithms under fixed formulations, yet the formulation itself shapes the search landscape by defining the objectives and constraints optimized by the solver. Recent LLM-based automatic problem formulation methods generate formulations from natural-language requirements, but they mainly focus on design-intent alignment and overlook whether the formulation induces an efficient search process. To address this limitation, we propose SHA-PF, a search hardness-aware LLM-based problem formulation framework. We find that a formulation is more likely to guide efficient search when it prioritizes rare samples with greater progress potential. Based on this finding, SHA-PF defines a formulation search objective guided by search hardness, scoring each candidate formulation according to the priority. SHA-PF then searches the formulation space under this objective through LLM-based generation, repair, and evolutionary refinement. Experiments on the real-world multi-objective benchmark and five expensive antenna design benchmarks show that the formulations discovered by SHA-PF require significantly fewer evaluations to reach the design requirements than other baselines.

Circuit cutting promises to scale quantum computations beyond current hardware, but variational quantum advantage also requires low cutting overhead, classical hardness, and trainability. We show that these properties are strongly constrained by entanglement geometry. Matrix product state (MPS) and tree tensor network (TTN) circuits with constant seam bond dimension can be cut with $O(1/\varepsilon^2)$ sampling overhead, but remain efficiently classically simulable, ruling out asymptotic quantum advantage within these families. By independently controlling seam and intra-block entanglement, we construct a two-block circuit family that remains cheaply cuttable while requiring a super-polynomial global MPS bond dimension, as supported numerically up to $n=100$. However, MPS hardness and trainability require incompatible depth regimes, $d=ω(\log n)$ and $d=O(\log n)$, respectively. Using magic rather than entanglement as the hardness resource avoids this conflict: shallow Clifford+$T$ circuits remain cuttable and trainable while their stabiliser-simulation cost grows exponentially with the $T$-count.

Knowing when to say "I don't know" is fundamental to human judgment, yet AI assistants offer a fluent answer to almost any question. In five experiments (N = 3,132; four preregistered, one direct replication), participants answered difficult questions and could always decline to respond. We engineered the questions so that AI advice was wrong, separating AI use from its accuracy. Merely having access to AI nearly eliminated participants' willingness to suspend judgment, and this held whether the advice was actively requested or simply displayed. Consequently, participants answered more questions but were correct about a third as often as when AI was unavailable-yet their confidence nearly doubled. Incentivizing accuracy and penalizing inaccuracy led participants to seek and follow AI advice less, answer more accurately, and suspend judgment more often, though still far less than when AI was unavailable. As AI suggestions grow ubiquitous and unsolicited, they may not simply affect answer accuracy; they may even alter the metacognitive threshold at which people decide whether they know enough to answer.

Consider the following variation on the Hierarchical Clustering problem: Usually, while building a hierarchical clustering, one recursively partitions the data until each cluster becomes a singleton. We relax the halting condition of the recursive process to stop whenever the remaining cluster is a graph belonging to a class $\mathcal{F}$. We call this problem Hierarchical $\mathcal{F}$-Clustering and we measure the quality of any solution using adapted Dasgupta's clustering objective. We study two natural choices of $\mathcal{F}$: trees and graphs of bounded diameter. We present the first polynomial time $\mathcal{O}(\log n\cdot\log\log n)$ and $\mathcal{O}(\log n)$-approximation algorithms for clustering into trees and bounded diameter graphs respectively. Our main technical contribution is a framework for approximating such problems based on linear programming. In fact, we characterize graphs classes $\mathcal{F}$ for which our approach can be applied and show that it includes both trees and bounded diameter graphs. However, our ideas are not limited to them and might be useful for other structures as well. Broadly speaking, our framework applies whenever the corresponding flat clustering problem, which we call $p_{\mathcal{F}}$-Partitioning, admits a natural ILP formulation together with a rounding procedure with provable approximation guarantees. Intuitively, given a set of vertices called terminals, the problem is to find an edge set whose removal results in satisfying certain vertex-dependent structural predicate for each terminal. We then use these ingredients to build clustering trees with the aforementioned approximation guarantees. To complement these results, we show that both Hierarchical Clustering into trees and into bounded diameter graphs cannot be approximated within any constant factor under the Small Set Expansion Hypothesis.

A lot of research attention has been devoted to checking whether large language models (LLMs) are politically biased. This work has largely focused on high-level ideological dimensions, such as left--right or progressive--conservative, and it has been shown that while LLMs are predominantly left and progressive leaning, largely mimicking the biases in the training data, they can be to some extent steered to change their preferences in post-training. In this short note, we check if LLMs have robust stances with regard to major substantive societal issues, on which members of the same ideological camp are often in disagreement, summarised in a novel dataset \textsc{HardChoices}. We show that, faced with this line of questioning, LLMs, both large and small, surprisingly rarely declare neutrality, are often incoherent, and demonstrate a remarkable degree of agreement on issues where they do take stances.

Sign Language Retrieval (SLRet) enables efficient access to sign language content but remains fragile in fine-grained scenarios where visually similar signs must be distinguished. We show that this limitation does not stem from model capacity, but from ineffective hard negative supervision. Specifically, we formulate fine-grained retrieval failures as a negative distribution mismatch: semantically distinct yet visually confusable signs are rarely treated as hard negatives, while existing text-based mining strategies fail to capture such visual ambiguity. To address this issue, we propose Sign-Aware Hard Negative Mining (SAN), which constructs hard negatives based on visual confusability in the sign embedding space rather than linguistic similarity. Experiments on PHOENIX-2014T demonstrate that SAN substantially improves fine-grained retrieval performance while preserving coarse-grained accuracy, highlighting the importance of aligning negative supervision with visual ambiguity in sign language retrieval.

A series of results from the NeuroAI over the past fifteen years have raised core questions both about how to compare Deep Neural Network (DNN) models to the brain, and about how much convergent evolution to expect between artificial networks and real brain networks. Here, we show that for any two minimal DNN solutions to a sufficiently hard task: (i) "weak" alignment of network representations based on affine mappings guarantees "strong" alignment of privileged axes, and (ii) alignment "zippers" up the network hierarchy, causing the emergence of privileged axes from end-to-end task optimization. These results formalize the notion of contravariance from Cao and Yamins [2024], and illustrate important consequences for the theory of NeuroAI: with sufficiently strong tasks, choice of metric for inter-network comparison is not all that sensitive, and that convergent evolution is probably inevitable.

How can Large Language Models (LLMs) solve problems they currently cannot? Repeated sampling scales test-time compute but GPU cost grows linearly with attempts, while reinforcement learning (RL) with verifiable rewards improves single-attempt accuracy at the expense of sample diversity. Both strategies ultimately fail when the base policy has near-zero probability of producing a correct solution: no amount of sampling or gradient signal can overcome a search space that is simply too large. We take a different approach: rather than sampling harder, we make the task easier by decomposing problems into smaller, independently solvable sub-functions whose implementations can be recombined. Since off-the-shelf models are not trained for this modular generation, we introduce DecompRL, an RL algorithm that explicitly learns to decompose and implement hierarchical code structures. Recombining $k$ implementations of $n$ modules yields up to $k^{n}$ candidate solutions, shifting the bottleneck from GPU inference to cheap CPU evaluation and cutting GPU token cost by $\sim$50$\times$. On LiveCodeBench and CodeContests (Qwen2.57B, Code World Model~32B), DecompRL outperforms standard and diversity-optimized RL baselines beyond $10^5$ tokens per problem, solving problems that standard generation cannot reach.

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

While neural network control policies are powerful, their deployment on safety critical systems depends on ensuring that they obey strict constraints. Existing work often treats safety as a metric to optimize for, which competes with other performance objectives, if training converges at all. Instead, we introduce ShardNet, a neural network architecture that strictly enforces unions of polyhedral constraints by construction, using a differentiable projection layer parameterized by a classification network. The key insight is to embed safety into the neural network's structure, allowing performance to be optimized independently because formal safety guarantees are always given. In contrast with existing neural architectures that can only enforce simple convex constraints, ShardNet enables the first safe-by-construction synthesis of forward-invariant neural network controllers on closed-loop systems where safety constraints are expressed as nonconvex unions of polyhedras or learned value function level sets. To support this, we also introduce a technique to verify and train such value functions correctly as rectified linear unit (ReLU) networks, which has not previously been possible. On double integrator benchmarks drawn from the literature, ShardNet policies maintain 100% safety on verified sets and achieves significantly lower objective loss compared to existing formal methods. Furthermore, our value function training technique also produces safe sets more than 3 times larger than existing verification approaches.

Long-context LLM inference faces a fundamental conflict: head-adaptive compression algorithms (e.g., Top-$p$ nucleus sampling) offer superior accuracy by dynamically fluctuating memory budgets, yet modern inference engines (e.g., vLLM) demand rigid, static memory patterns to leverage CUDA Graphs and PagedAttention. We resolve this ``Static-Dynamic'' mismatch with HARD-KV, a unified framework that that bridges dynamic selection with rigid system constraints. HARD-KV introduces a Cascade Cache hierarchy, managing the token lifecycle across dense, sparse, and condensed tiers. Crucially, we propose a Logits Calibration mechanism that normalizes diverse importance metrics into a unified probability space, enabling consistent Top-$p$ budgeting across heterogeneous heads. To bridge the efficiency gap, we offer a system-level solution, which rewrites fragmented, dynamic indices into contiguous physical layouts compatible with high-performance inference engine. Extensive experiments on math-reasoning benchmarks (AIME, U-Math) verify that HARD-KV achieves up to 2$\times$ throughput improvement over static baselines while maintaining high-fidelity generation in 10k+ token scenarios. Code is available at https://github.com/SuDIS-ZJU/HARDInfer.

We study how the effort and success probability of frontier AI systems scale with human difficulty on problems from Project Euler, an online platform of computational mathematics problems. Our dataset, from the MathArena benchmark, consists of 3840 attempts across 50 problems and 26 model configurations, with problem difficulty measured by the site's public human solve times. Motivated by a proposal of Timothy Gowers, we test a power-law relation $t_{\text{machine}} = a \cdot t_{\text{human}}^b$ between generated-token cost per successful answer and human time, and find $b < 1$ for 20 of the 25 models with usable fits, including the strongest base models; this operationalization therefore does not support an earlier prediction that machines scale worse than humans with difficulty. We also investigate whether success probability on the tested problems can be modeled by a simple exponential decay $p_{\text{success}} = e^{c t_{\text{human}}}$, predicting a linear relation between $\log p_{\text{success}}$ and $t_{\text{human}}$. Using a binning approach for data aggregation we find moderate empirical support (median bin-level $R^2 = 0.92$ across the 22 best-covered configurations) for this model. Following METR, we also fit logistic success curves and extract 50% task-length horizons $h_{50}$; the strongest configurations in our 20 April 2026 snapshot reach roughly $2.5$--$4.3$ hours on our fastest-five human baseline, with a log-linear fit through the state-of-the-art frontier giving a descriptive doubling time of about $75$~days for the SOTA $h_{50}$.

Curriculum learning couples two design choices, how samples are scored by difficulty and how harder samples are paced into training, making it difficult to attribute observed gains to either component. We disentangle these factors with two evaluation protocols: stage-wise test subsets that validate scoring functions independently of curriculum training, and a baseline that applies the same pacing schedule to randomly ordered data. Within the Transfer Teacher framework (TTF), we use these protocols to evaluate a confusion-aware difficulty score that considers both correct-class confidence and the probability distribution over incorrect classes. On CIFAR-10 with ResNet-18 and VGG-16, the proposed score produces model-interpretable difficulty rankings that align with human intuition. However, at full data, neither curriculum nor anti-curriculum ordering improves accuracy over standard training, indicating that improving the scoring function alone is insufficient to overcome the known failure modes of curriculum learning in TTF. In contrast, We find that confusion-aware curriculum ordering result in consistent data-efficiency benefits, outperforming random ordering by up to 8.7% points at the 20% data regime, suggesting the potential of TTF as a data-efficient training method.

We ask a structural question: given unreliable elementary problem-solvers, what organizations of them solve hard problems reliably, and what are the limits? We develop a $decomposition~algebra$: elementary solvers are morphisms in a stochastic category, and four combinators (sequential composition, parallel ensembling, verification gating, and recursive reduction) generate the space of compound solvers. We equip this algebra with two homomorphisms, a $reliability$ valuation into the ordered monoid $([0,1],\le)$ and a $cost$ valuation into a commutative semiring, and we derive the composition laws that govern how reliability flows through structure. Our central results are (i) a $verification~odds~law$ (the result that names this report), showing that a verification gate multiplies the odds of correctness by the verifier's likelihood ratio $Λ$, so that $k$ conditionally independent gates yield geometric amplification; (ii) a $reliability~amplification~theorem$, giving target reliability $1-δ$ at $O(\log 1/δ)$ verification depth whenever $Λ>1$; and (iii) a $threshold~dichotomy$: above the critical parameters reliability can be driven arbitrarily close to one at logarithmic cost, while at or below them no amplification is possible. We then show that $self-organization$ is the least fixed point of a monotone improvement operator on the complete lattice of strategies, and that this fixed point equalizes marginal log-odds gain per unit cost. Finally, we prove matching limits: an information ceiling bounds per-gate amplification by a divergence quantity; shared error causes create a strictly positive voting floor, so diversity is $necessary$ for unbounded amplification. Reliability, in short, is neither free nor magical: it is bought with independent information, arranged by composition, and bounded by the verifier.

Large language models can often close proof gaps in interactive theorem provers, but a verified theorem is not the same thing as a reusable library contribution. We study this distinction through a detailed case study: a semi-autonomous formalization of Grothendieck's vanishing theorem. The initial version compiles with no sorries, but an expert review found serious problems in definitions, theorem generality, file organization, and the API. We then ran a review-driven refactor and compression process and obtained a second expert review. The before-and-after comparison shows a sharp split: agents adapted well to local, mechanically checkable feedback, but remained weak at choosing definitions and designing APIs. We argue that autoformalization should be evaluated not only by closed sorries, but by whether the resulting formalization survives expert review.

RL with verifiable rewards can substantially improve LLM reasoning, yet standard GRPO-style training often treats easy, hard, and learnable questions alike through uniform sampling and weighting, leading to inefficient compute allocation. We study GRPO by tracking token log-probabilities, group-normalized advantages, and the induced token-level update weights. This reveals three recurring dynamics as training proceeds: (1) confidence inflation, (2) advantage contraction, and (3) hierarchical convergence. These findings suggest that the utility of each update depends strongly on both question difficulty and the model's current competence. Motivated by this, we propose Confidence and Difficulty-adaptive Policy Optimization (CoDaPO), which assigns each question a bounded value from rollout confidence and empirical difficulty. CoDaPO then uses this value to reweight policy updates and resample high-value learnable questions within mini-batches, thereby increasing discovery within the learnable band under a fixed compute budget. Across twelve benchmarks, CoDaPO consistently improves accuracy over existing RL methods. Our code is publicly available at https://github.com/tmlr-group/CoDaPO.

This paper presents a simple framework that settles the complexity of Multi-Agent Path Finding (MAPF) on trees across standard objectives - distance, makespan, and flowtime - for both labeled and colored variants. In MAPF, agents occupy the vertices of a graph and must move to target vertices without collisions while optimizing a given objective. In the labeled case, the agents are distinct and have respective targets; in the colored case, agents of the same color are interchangeable. While many MAPF variants are known to be intractable, several basic cases on trees have remained open. We prove NP-hardness on trees for both labeled and 2-colored MAPF under all three objectives. In particular, we resolve the classical Pebble Motion problem, where one pebble moves at a time to an adjacent empty vertex and the goal is to minimize the total number of moves. Despite being one of the most basic discrete motion models, its complexity on trees had remained open for several decades. Moreover, for colored Pebble Motion, we give the first hardness result on any graph class, already with two colors, which is tight. All of these results are established through the hardness of Stack Rearrangement, itself posed as an open problem, which asks to optimally rearrange items stored in stacks, and which we also prove to be NP-hard. Notably, the connection to stacks yields hardness already on very simple trees - subdivided stars - across all problems. Together, these results reveal a common tractability barrier that permeates several fundamental motion models, thereby unifying and strengthening prior hardness results.

Input length and the position of relevant information are widely cited as the primary causes of degraded LLM long-context performance. Here, we study lexical density -- the rate at which a context introduces distinct information -- as a third, largely overlooked factor that systematically reduces the effective context window of LLMs. We quantify the impact of lexical density on open-weight LLMs (9B-685B) using three "find-the-needle" style benchmarks with identical length (~12k tokens) and controlled needle position, but increasing density of information. We observe a sharp performance collapse in higher-density benchmarks: models that are near-perfect in sparse contexts drop below 60% retrieval score on denser ones. To rule out task-type confounds, we vary and control the density within each benchmark while keeping all other properties unchanged. Reducing density generally restores performance, especially in the high-density regimes where degradation appears. These results show that effective context capacity is a function of lexical density, with direct implications for real-world LLM systems operating on compact, information-rich inputs.

AI agents can increasingly handle the mechanical tasks of financial analysis: retrieving documents, calculating formulas, updating spreadsheets. The harder, more valuable challenge is reasoning through the open-ended questions that define expert Analyst work. Existing benchmarks do not capture this class of problem, and those that attempt to evaluate open-ended reasoning rely on model-judged outputs that introduce noise and circularity. We present Hedge-Bench 1.0: a benchmark of 102 actual, on-the-job tasks grounded in the explicit reasoning traces of professional hedge fund analysts working with relevant information sources. This approach enables deterministic grading against verified expert steps. Frontier models and agents score below 16% on the benchmark. We publish the dataset and evaluation harness at github.com/Trata-Inc/trata-hedge-bench.

Machine unlearning aims to remove the influence of specific forget training data due to privacy, copyright or bias concerns while maintaining the model performance on the remaining retain data. Existing unlearning algorithms, such as optimizing a weighted combination of losses, have tried to achieve these objectives of improving forget quality and maintaining retain utility. However, they do not guarantee that these objectives can be improved by a specified extent for all forget and retain data. In this work, we address this limitation with a novel and theoretically-grounded approach from a constrained optimization perspective. Firstly, we identify that the hardness of reconciling both objectives can be quantified by the similarity between the forget data and the retain data. Next, we derive an unlearning algorithm (HAMU) with the overall goal of guaranteeing a specified improvement in forget quality while minimizing the retain utility cost/degradation by updating the model weights based on our hardness measure. Our hardness measure also informs users when retain utility degradation is unavoidable, i.e., both objectives cannot be improved simultaneously, and stopping should be considered. Our algorithm is applicable to non-convex models and is easily parallelizable, making it readily deployable in real-world scenarios. We empirically demonstrate HAMU's superior performance over baselines on both image and text datasets using large models. Our code is available at https://github.com/aoi3142/HAMU.

Hard negative mining has become the dominant strategy for training retrievers, yet it faces intrinsic limitations: negatives are bounded by corpus availability, selected by retriever score rather than diagnostic value, and increasingly contaminated by false positives as the retriever improves. LLM-based synthesis offers a principled alternative, where negatives that are unconstrained, targeted, and free from false positive risk. But we show that naively incorporating generated negatives into contrastive learning often degrades retrieval performance. We identify and formalize the root cause as a generative-discriminative gap: LLM generation optimizes for fluent, plausible text, while contrastive learning demands strategic violations of relevance at the decision boundary. Our analysis reveals two compounding failure modes: discriminative-agnostic generation, where the LLM lacks an explicit model of query information needs and defaults to generic or topic-drifted text that provides no contrastive signal; and source-dependent shortcuts, where distributional artifacts enable the model to distinguish negatives by origin rather than relevance, causing gradient drift that actively corrupts optimization. To close this gap, we propose CausalNeg consisting of two main modules: (1) CoT-guided counterfactual perturbation for data construction: decomposes why a document satisfies a query into explicit information requirements, then surgically violates individual requirements to construct negatives with controlled, interpretable hardness. (2) Query-view entropy maximization during training: disperses generated negatives across the similarity spectrum, minimizing the mutual information between source identity and similarity scores to suppress shortcut exploitation. We make our code publicly available at https://github.com/mzhangzhicheng/CausalNeg.

Embedding benchmarks like MTEB report a single score per model, implicitly treating robustness as a static, scalar property. We argue that embedding robustness is multidimensional, since models respond differently to different types of variation, and requires dynamic evaluation to expose failures hidden by static benchmarks. We introduce the Harder Text Embedding Benchmark (HTEB), a dynamic evaluation framework that challenges model robustness along three practically interpretable axes (Lexical/Stylistic, Length and Language) by stochastically transforming inputs at evaluation time with an LLM. Evaluating 16 open-weight embedding models on 32 datasets covering 42 languages under transformations validated by 4,800 individual human ratings on an English subsample, supplemented by a Spanish-source evaluation and an exploratory STS-B study of pair-level label preservation, we find three patterns: (1) Models exhibit specific, partly decoupled robustness profiles across axes. (2) Across three model families, scale increases absolute scores but does not close the gap between original and transformed evaluations. Here, scaling tends to improve specifically the Language axis. (3) English datasets are more sensitive to HTEB transformations than multilingual datasets. This demonstrates that HTEB identifies strengths and weaknesses of models along deployment-relevant axes, challenging current embedding benchmarks and arguing for multidimensional, dynamic robustness evaluation. We make the code to run HTEB publicly available.

Generative pre-training via discrete diffusion provides dense reconstruction supervision across all feature fields simultaneously, mitigating representation collapse from data sparsity in CTR prediction. However, all existing generative CTR methods share a fundamental limitation: the reconstruction objective assigns equal training weight to every feature field, ignoring the profound heterogeneity of reconstruction difficulty across high-cardinality ID fields, sparse categorical attributes, numerical values, and behavioral sequences. This causes easy fields to dominate training gradients while the hardest but most informative fields remain chronically underfit, a problem we term the generative difficulty imbalance.We propose HeteGenCTR, which resolves this imbalance through per-field learnable difficulty parameters jointly trained with the denoising network. This unified signal drives two coordinated components without additional hyperparameters: a self-balancing loss that automatically reallocates gradient budget toward harder fields with a provably stable equilibrium, and a difficulty-guided attention mechanism that suppresses the influence of already-converged easy fields while amplifying cross-field information flow toward hard fields. Both components share the same learned signal and remain mutually consistent throughout training. Experiments on five CTR benchmarks and a seven-day online A/B test demonstrate consistent, statistically significant improvements over state-of-the-art baselines, with disproportionate gains for cold-start and long-tail users.

When annotators disagree, that disagreement can reflect epistemic uncertainty rather than simple label noise. We study hard-label delivery as an alternative to the usual choices of collapsing votes to a single label or training directly on the empirical soft-label distribution. We focus on two primary hard-label methods: multipass, which cycles through observed votes while keeping the dataset size fixed, and stochastic label sampling (SLS), which samples one label per example at the start of each epoch. On CIFAR-10H, we find that when only a small number of annotations per example is available, hard-label delivery improves over soft-label training, with larger improvements where the sparse empirical target is farther from the full annotator distribution. When full annotator distributions are available, both hard-label methods match soft-label training. We use deterministic control as an ablation of multipass and shuffled SLS as a control that breaks the example-to-distribution match. We also show that SLS and soft-label cross-entropy optimize the same expected objective. Hard-label delivery also converges to flatter basins, with supporting descriptive evidence from OOD detection on SVHN and CIFAR-100. Overall, these results suggest that multipass is a strong practical default when raw vote counts are available, while SLS offers a lightweight alternative that remains competitive when only a few votes per example are available and matches soft-label training when full annotator distributions are available.

Rhetorical Role Labeling (RRL) assigns a functional role to each sentence in a document and is widely used in legal, medical, and scientific domains. While language models (LMs) achieve strong average performance, they remain unreliable on hard examples, where prediction confidence is low. Existing approaches typically handle uncertainty implicitly and treat labels as discrete identifiers, overlooking the semantic information encoded in label names. We introduce RISE, an inference-time semantic reranking framework that leverages label semantics to refine predictions on hard instances. RISE automatically identifies low-confidence predictions and reranks model outputs using contrastively learned label representations, without retraining or modifying the underlying model. Experiments on eight domain-specific RRL datasets with seven LMs, including encoder-based and causal architectures, show an average gain of +9.15 macro-F1 points on hard examples. For explainability, we further propose manual hardness annotations to study difficulty from both model and human perspectives, revealing a moderate agreement with Cohen's kappa = 0.40.

Finetuning Large Vision-Language Models with reinforcement learning has emerged as a promising approach to enhance their capability in object-level grounding. However, existing methods, mainly based on GRPO, assign rewards at the response level. Such sparse reward, often criterion-induced, leads to minimal learning signals when all candidate responses fail in challenging scenarios. In this work, we propose a group-revision optimisation paradigm that enhances learning on hard cases. It begins with a sampled initial response and generates a set of revised candidates to explore improved grounding outcomes. Inspired by reward shaping, we introduce a consolidation process that quantifies each candidate's improvement over the initial attempt and converts it into informative shaping signals. These signals are used to both refine the reward and modulate the advantage, amplifying the influence of high-quality revisions. Our method achieves consistent gains across referring and reasoning segmentation, REC, and counting benchmarks compared with prior GRPO-based models. Our code is available at https://github.com/yyliu01/GroupRevision.

Graph neural networks (GNNs) deployed as cloud services can be stolen through model-extraction attacks, which train a surrogate from query responses to reproduce the target's behavior, and a growing line of ownership defenses tries to prevent or trace such theft. This paper asks two questions: how hard is it to steal a GNN, and can we stop it? Prior work cannot answer either, because experiments use inconsistent datasets, threat models, and metrics. We introduce GraphIP-Bench, a unified benchmark that evaluates both sides under a single black-box protocol. GraphIP-Bench integrates twelve extraction attacks, twelve defenses spanning watermarking, output perturbation, and query-pattern detection, ten public graphs covering homophilic, heterophilic, and large-scale regimes, three GNN backbones, and three graph-learning tasks. It reports fidelity, task utility, ownership verification, and computational cost on shared splits, queries, and budgets. We further add a joint attack-and-defense track that runs every attack on every defended target and measures watermark verification on the resulting surrogate, exposing how much protection a defense retains after extraction. The empirical picture is clear: stealing a GNN is easy at medium query budgets and most defenses do not change this; several watermarks verify reliably on the protected model but lose most of their verification signal on the extracted surrogate, exposing a gap that single-model evaluations miss; and heterophilic graphs are systematically harder to steal, while a cross-architecture mismatch between target and surrogate reduces but does not prevent extraction. We release GraphIP-Bench with reproducible scripts and configurations, and integrate the attacks and defenses into the PyGIP library. Code: https://github.com/LabRAI/GraphIP-Bench. Library: https://labrai.github.io/PyGIP/index.html.

Large reasoning models (LRMs) improve problem solving through extended reasoning, but often misallocate test-time compute. Existing efficiency methods reduce cost by compressing reasoning traces or conditioning budget on perceived difficulty, yet largely overlook solvability. As a result, they may spend large budgets on queries beyond the model's capability while compressing hard-but-solvable queries that require deeper reasoning. In this work, we formulate adaptive reasoning as a computational investment under uncertainty, where budget should follow the expected return of reasoning rather than perceived difficulty alone. To instantiate this principle, we propose Budget-Efficient Thinking (BET), a two-stage framework that combines behavioral cold-start with GRPO under an investment-cost-aware reward. By aligning solve-or-fold decisions with rollout-derived solvability, BET learns three behaviors: (1) short solve, answering easy queries concisely; (2) nice fold, abstaining early when continued reasoning has near-zero expected return; and (3) hero call, preserving sufficient compute for hard-but-solvable queries. Across seven benchmarks and three base models, BET reduces reasoning tokens by ~55% on average while achieving overall performance improvements, and transfers zero-shot from mathematical reasoning to scientific QA and logical reasoning with comparable efficiency gains.

Multiple-choice reasoning benchmarks face dual challenges: rapid saturation from advancing models and data contamination that undermines static evaluations. Ad-hoc hardening methods (paraphrasing, perturbation) attempt to increase difficulty but sacrifice logical validity for surface complexity, falling short to challenge advanced reasoning models. We present LogiHard, a formal framework that deterministically transforms 0-order selection into 2-order logical judgment, which significantly increases the thinking overhead and reasoning steps. The framework integrates Item Response Theory (IRT) for computerized adaptive testing (CAT), enabling precise difficulty control with fewer questions than static benchmarks. We instantiate LogiHard-2k, a logical reasoning dataset constructed by cognitively ranking high-stakes examination questions via 9-dimensional analysis of model thinking traces, followed by combinatorial transformation of high-difficulty items. Evaluation across twelve state-of-the-art models reveals an accuracy degradation ranging from 31% to 56% on combinatorially hardened questions. LLMs suffer from the multi-select failure and early exit bias, which are not shared by human testees. Zero-shot transfer to MMLU demonstrates 47% accuracy degradation (89.84% to 42.86%), confirming applicability across domains with provable validity preservation. The consistent aggregate degeneration is domain-agnostic and stems not from knowledge deficits but from a combinatorial reasoning gap, reflecting a training-induced completeness-verification deficit.

Recent advancements in visual context compression enable MLLMs to process ultra-long contexts efficiently by rendering text into images. However, we identify a critical vulnerability inherent to this paradigm: lowering image resolution inadvertently catalyzes jailbreaking. Our experiments reveal that the safety defenses of SOTA models deteriorate sharply as resolution degrades, surprisingly persisting even when text remains legible. We attribute this to Cognitive Overload'', hypothesizing that the effort required to decipher degraded inputs diverts attentional resources from safety auditing. This phenomenon is consistent across various visual perturbations, including noise and geometric distortion. To address this, we propose a simple Structured Cognitive Offloading'' strategy that mitigates these risks by enforcing a serialized pipeline to decouple visual transcription from safety assessment. Our work exposes a significant risk in vision-based compression and provides critical insights for the secure design of future MLLMs.

Large Language Models (LLMs) demonstrate strong capabilities for solving scientific and mathematical problems, yet they struggle to produce valid, challenging, and novel problems - an essential component for advancing LLM training and enabling autonomous scientific research. Existing problem generation approaches either depend on expensive human expert involvement or adopt naive self-play paradigms, which frequently yield invalid problems due to reward hacking. This work introduces VHG, a verifier-enhanced hard problem generation framework built upon three-party self-play. By integrating an independent verifier into the conventional setter-solver duality, our design constrains the setter's reward to be jointly determined by problem validity (evaluated by the verifier) and difficulty (assessed by the solver). We instantiate two verifier variants: a Hard symbolic verifier and a Soft LLM-based verifier, with evaluations conducted on indefinite integral tasks and general mathematical reasoning tasks. Experimental results show that VHG substantially outperforms all baseline methods by a clear margin.

Large language models (LLMs) are known to be vulnerable to jailbreak attacks, which typically rely on carefully designed prompts containing explicit semantic structure. These attacks generally operate by fixing an adversarial instruction and optimizing small adversarial components (e.g., suffixes or prefixes). In this setting, prompt structure is fundamental for performance, and recent results show that even simple random search can achieve strong performance when combined with sophisticated prompt design. Recently, it has been observed that harmful behaviors can be elicited even without the adversarial prompt, relying solely on optimized token sequences. This suggests the existence of natural backdoors, i.e., token sequences naturally emerged during LLMs training that trigger unsafe outputs without any meaningful instruction. However, despite these observations, this setting remains largely unexplored, and in particular the hardness of finding natural backdoors has not been assessed yet. In this work, we provide a first proof-of-concept study investigating the hardness of this task, which we refer to as the junking problem. We formalize it as the problem of finding token sequences that maximize the probability of generating a target prefix of harmful responses, propose a greedy random-search method to assess is such sequences can be discovered easily. Our results show that this problem is harder than standard jailbreak attacks, confirming the importance of semantic information in prompt design. At the same time, we find that our simple strategy is sufficient to solve it with a high success rate, suggesting that natural backdoors are present and easily recoverable. Finally, through perplexity analysis, we observe that the discovered token sequences lie in low-probability regions of the model distribution, supporting the hypothesis that they emerged implicitly from the training process.

Safety fine-tuning of language models typically requires a curated adversarial dataset. We take a different approach: score each candidate prompt's difficulty by how often the target model's own rollouts are judged harmful, then fine-tune on the hardest prompts paired with the model's own non-jailbroken rollouts. On Llama-3-8B-Instruct and Llama-3.2-3B-Instruct, this approach cuts the WildJailbreak attack success rate from 11.5% and 20.1% down to 1-3%, but pushes refusal on jailbreak-shaped benign prompts from 14-22% to 74-94%. Interleaving the same hard prompts 1:1 with adversarially-framed benign prompts (prompts that look like jailbreaks but have benign intent) cuts that refusal back down to 30-51% on 8B and 52-72% on 3B, at a cost of 2-6 percentage points of attack success rate. Within the mixed regime, training on the hardest half of the eligible pool rather than a random half cuts the remaining ASR by 35-50% (about 3 percentage points) on both models.

We present FoR-Net, an efficient semantic segmentation framework that focuses on identifying and enhancing hard regions. Instead of relying on heavy global modeling, FoR-Net adopts an efficient strategy that selectively emphasizes informative regions through a learned importance map and a Top-K activation mechanism. Specifically, a selector module predicts region-wise importance, enabling the model to focus on challenging areas such as thin structures and object boundaries. Multi-scale reasoning is achieved using convolutional branches with different receptive fields, allowing diverse spatial context aggregation. We evaluate FoR-Net on the Cityscapes benchmark under limited computational resources. Despite its efficient design and standard training configuration, FoR-Net achieves competitive performance and exhibits improved attention to difficult regions. These results suggest that selective region-focused reasoning can serve as a practical and efficient alternative for semantic segmentation. This work explores region-focused reasoning under resource-constrained settings and provides insights for developing efficient and region-aware segmentation models.

Many machine learning systems make constrained decisions by optimizing factorized objectives, but the context-specific objective is often treated as fixed. We study contextual decision-weight learning: from logged decisions and proxy outputs, learn an optimizer-facing weight vector w(x) over interpretable decision factors z(x,d), rather than a direct policy or generic predictive score. We propose OTSS, an output-targeted soft-segmentation model that deploys the personalized decision-ready weight vector. At the function-class level, the theory highlights a hard-versus-soft distinction. Hard partitions incur an approximation-estimation tradeoff under overlap, while a realizable fixed-K soft class removes the hard-partition approximation floor and attains a parametric rate. We evaluate OTSS in controlled benchmarks with finite evaluation libraries, where the true weight vector and downstream regret can be computed exactly. In the representative overlap setting, OTSS attains the lowest mean regret among the comparators, including EM mixture regression, the strongest soft-mixture baseline in our comparison; it matches EM on coefficient recovery while running about two orders of magnitude faster. In a matched K=5 benchmark, OTSS remains competitive under hard-routed truth and improves as heterogeneity becomes softer and sample size grows. On a fixed Complete Journey retail anchor with real household covariates and action geometry, OTSS again achieves the lowest mean-regret point estimate.

Shallow nanoindentation enables mechanical characterization of thin films, individual phases, and other volume-constrained materials, but the measured hardness is inflated by the indentation size effect (ISE). Classical corrections such as Nix-Gao require a deep linear regime and fail when only shallow measurements are accessible. We present a data-efficient workflow that recovers a high-load reference hardness directly from shallow, size-affected indentation data. Over 700 indentations on three certified steel reference blocks (2-6.5 GPa) were expanded by physics-guided augmentation and used to train conventional regressors (Ridge, Random Forest, XGBoost, neural networks) and a physics-constrained neural network (PCNN) that reconstructs hardness through the bounded form H_ref = H_app/sqrt(1+q), with the signed correction q learned from dimensionless contact-mechanics descriptors (P_max/S^2, W_p/W_tot, H/E_r). On a quarantined fourth steel tested at loads offset from the training schedule, only the constrained formulation generalized: the dimensionless-input PCNN achieved RMSE = 0.372 GPa and MAPE = 5.2%, and remained stable beyond the training load range, where tree-based models failed structurally. Ablation attributed this robustness to the bounded reconstruction and a load-independence regularizer. Deliberate application to fused silica produced systematic failure, delimiting the method to dislocation-mediated crystalline plasticity. A few hundred laboratory indentations thus suffice to train a physically constrained ISE correction operating on single shallow indentations, offering a template for materials lacking analytical size-effect models.

Achieving robust generalization against unseen attacks remains a challenge in Audio Deepfake Detection (ADD), driven by the rapid evolution of generative models. To address this, we propose a framework centered on hard sample classification. The core idea is that a model capable of distinguishing challenging hard samples is inherently equipped to handle simpler cases effectively. We investigate multiple reconstruction paradigms, identifying the diffusion-based method as optimal for generating hard samples. Furthermore, we leverage multi-layer feature aggregation and introduce a Regularization-Assisted Contrastive Learning (RACL) objective to enhance generalizability. Experiments demonstrate the superior generalization of our approach, with our best model achieving a significant reduction in the average Equal Error Rate (EER) compared to the baseline.

Federated learning (FL) aggregation on serverless platforms faces a hard scalability ceiling: existing architectures (lambda-FL, LIFL) partition clients across aggregators, but every aggregator must hold the complete model gradient in memory. When gradients exceed the per-function memory limit (e.g., 10 GB on AWS Lambda), aggregation becomes infeasible regardless of tree depth or branching factor. We propose GradsSharding, which instead partitions the gradient tensor into M shards, each averaged independently by a serverless function that receives contributions from all clients. Because FedAvg averaging is element-wise, this produces bit-identical results to tree-based approaches, so model accuracy is invariant by construction. Per-function memory is bounded at O(|θ|/M), independent of client count, enabling aggregation of arbitrarily large models. We evaluate GradsSharding against lambda-FL and LIFL through HPC experiments and real AWS Lambda deployments across model sizes from 43 MB to 5 GB. Results show a cost crossover at approximately 500 MB gradient size, 2.7x cost reduction at VGG-16 scale, and that GradsSharding is the only architecture that remains deployable beyond the serverless memory ceiling.

Enforcing constraint satisfaction in neural network outputs is critical for safety, reliability, and physical fidelity in many control and decision-making applications. While soft-constrained methods penalize constraint violations during training, they do not guarantee constraint adherence during inference. Other approaches guarantee constraint satisfaction via a projection layer, but often rely on the existence of a tractable projection onto the feasible set, limiting their utility in more general problem settings. Many real-world problems of interest are nonlinear and lack the special structure admitting a tractable projection, motivating the development of methods that can enforce general nonlinear constraints. To this end, we introduce HardNet++, a constraint-satisfaction method that enforces linear and nonlinear equality and inequality constraints. Our approach iteratively adjusts the network output via damped local linearizations of the constraints. Each iteration is differentiable, admitting an end-to-end training framework, where the constraint satisfaction layer is active during training. We show that under certain regularity conditions, this procedure enforces nonlinear constraint satisfaction to arbitrary tolerance. Finally, we demonstrate tight constraint adherence without loss of optimality in a learning-for-optimization context, where we apply this method to a nonlinear model predictive control problem.

LLM benchmarks are increasingly dynamic: instead of containing a fixed set of questions, they define templates and parameters that can generate an effectively unlimited number of question variants. This flexibility is valuable, but it makes evaluation expensive -- especially when the goal is not just determining an average score, but reliably identifying a model's weak spots. This paper introduces a new methodology for identifying hard questions in dynamic benchmarks. It leverages COUP, a recent Bayesian optimization algorithm (Graham, Velez & Leyton-Brown, 2026), after introducing several substantive modifications to make the algorithm suitable for practical LLM pipelines. We also wrap it in a tool that supports flexible choices of datasets and utility functions, enabling users to target the kinds of questions they care about (e.g., low-accuracy questions; questions that are unusually hard relative to their measured complexity). In experiments across a range of benchmarks, we show that our method, dubbed $\texttt{QuickScope}$, discovers truly difficult questions more sample efficiently than standard baselines, while also reducing false positives from noisy outcomes.

We study the problem of learning in zero-sum matrix games with repeated play and bandit feedback. Specifically, we focus on developing uncoupled algorithms that guarantee, without communication between players, the convergence of the last-iterate to a Nash equilibrium. Although the non-bandit case has been studied extensively, this setting has only been explored recently, with a bound of $\mathcal{O}(T^{-1/8})$ on the exploitability gap. We show that, for uncoupled algorithms, guaranteeing convergence of the policy profiles to a Nash equilibrium is detrimental to the performance, with the best attainable rate being $Ω(T^{-1/4})$ in contrast to the usual $Ω(T^{-1/2})$ rate for convergence of the average iterates. We then propose two algorithms that achieve this optimal rate up to constant and logarithmic factors. The first algorithm leverages a straightforward trade-off between exploration and exploitation, while the second employs a regularization technique based on a two-step mirror descent approach.

Most ATP benchmarks embed the final answer within the formal statement -- a convention we call "Easy Mode" -- a design that simplifies the task relative to what human competitors face and may lead to optimistic estimates of model capability. We call the stricter, more realistic setting "Hard Mode": the system must independently discover the answer before constructing a formal proof. To enable Hard Mode research, we make two contributions. First, we release MiniF2F-Hard and FIMO-Hard, expert-reannotated Hard Mode variants of two widely-used ATP benchmarks. Second, we introduce Discover And Prove (DAP), an agentic framework that uses LLM natural-language reasoning with explicit self-reflection to discover answers, then rewrites Hard Mode statements into Easy Mode ones for existing ATP provers. DAP sets the state of the art: on CombiBench it raises solved problems from 7 (previous SOTA, Pass@16) to 10; on PutnamBench it is the first system to formally prove 36 theorems in Hard Mode -- while simultaneously revealing that state-of-the-art LLMs exceed 80% answer accuracy on the same problems where formal provers manage under 10%, exposing a substantial gap that Hard Mode benchmarks are uniquely suited to measure.

Tractability tests are often computed from input syntax: support-graph treewidth, local coefficient patterns, backdoor tests, or action-count bounds. Before such a test can be lower-bounded or made algorithmic, it must define a predicate on the exact-certification problem itself. Equivalent presentations must receive the same verdict. The semantic object is the correctness quotient, whose classes are states with the same correct outputs. Correctness-preserving presentation moves generate closure orbits. A target that changes inside one closure orbit has an orbit gap and fails descent. Exact closure-invariant classification is possible exactly when the positive and negative orbit hulls are disjoint; the positive hull is then the least exact classifier, and computable orbit representatives make the classifier algorithmic. The results separate three layers. The descent layer gives orbit-gap obstructions for raw local syntax, raw action and coordinate counts, and raw support-graph predicates. The post-descent complexity layer applies ordinary reductions to descended objects: graph-predicate lower bounds transfer through action-gap graph extraction, and Action-Gap-Treewidth is NP-complete when the width bound is part of the input. The certification layer asks whether a proxy descends: for split proxies $b\wedge\varphi(z)$, SAT reduces to non-descent and UNSAT reduces to descent. Positive regimes use quotient-preserving normalizations or catalogues before model checking; bounded quotient size, bounded full Gaifman treewidth of the constructed quotient, sparse unary-gap certificates, and strict-margin perturbation balls give explicit cost bounds after quotient construction.

The Winner Determination Problem (WDP) in combinatorial auctions is NP-hard, and no existing method reliably predicts which instances will defeat fast greedy heuristics. The ML-for-combinatorial-optimization community has focused on learning to \emph{replace} solvers, yet recent evidence shows that graph neural networks (GNNs) rarely outperform well-tuned classical methods on standard benchmarks. We pursue a different objective: learning to predict \emph{when} a given instance is hard for greedy allocation, enabling instance-dependent algorithm selection. We design a 20-dimensional structural feature vector and train a lightweight MLP hardness classifier that predicts the greedy optimality gap with mean absolute error 0.033, Pearson correlation 0.937, and binary classification accuracy 94.7% across three random seeds. For instances identified as hard -- those exhibiting ``whale-fish'' trap structure where greedy provably fails -- we deploy a heterogeneous GNN specialist that achieves ${\approx}0\%$ optimality gap on all six adversarial configurations tested (vs.\ 3.75--59.24% for greedy). A hybrid allocator combining the hardness classifier with GNN and greedy solvers achieves 0.51% overall gap on mixed distributions. Our honest evaluation on CATS benchmarks confirms that GNNs do not outperform Gurobi (0.45--0.71 vs.\ 0.20 gap), motivating the algorithm selection framing. Learning \emph{when} to deploy expensive solvers is more tractable than learning to replace them.

Object compliance perception enables the identification of soft materials, supporting tasks such as fruit detection and assisted medical palpation. Compliance perception requires sensing an object's deformation and contact forces. Existing vision-based tactile sensing for compliance perception usually depends only on force or deformation. However, deformation-based approaches cannot reliably quantify object compliance, while force-based methods are overly sensitive to geometric variations. To address these limitations, this paper presents a framework that fuses temporal force sequences and deformation field information. Specifically, time-varying contact forces are inferred from tactile image sequences via a neural network, while deformation characteristics are encoded using depth maps. Crucially, the temporal force sequence is used as a dynamic force-response feature for compliance recognition. In standard experiments, the force prediction error reaches 0.06 N within a measurement range of 12 N. The proposed method achieves a 98.0% Shore-hardness classification accuracy for samples ranging from 10 HA to 80 HA. In practical scenarios, including abnormal fruit detection and soft matter, the overall accuracy exceeds 98.5%. This method improves the compliance perception ability of artificial tactile systems and facilitates their deployment in embodied perception applications.

Targeted data poisoning attacks manipulate model predictions on specific test samples by injecting malicious data into training. Yet existing evaluations report average attack success rates over randomly selected targets, obscuring true worst-case effectiveness. We argue that the right evaluation focuses on the hardest samples to poison. The same reasoning applies to defense: since targeted attacks leave no footprint at the distribution level, defenders should proactively identify the most vulnerable samples and apply targeted countermeasures. Given a test dataset, this paper identifies both the easiest and hardest to poison examples based on only clean model information. Specifically, we offer coarse evaluations using clean training dynamics, and fine-grained classification on poison class using poison distances and budgets. Our experiments show these metrics reliably stratify samples by poisoning vulnerability, enabling both rigorous worst-case evaluation and proactive vulnerability-aware defense.

The sim-to-real gap, which represents the disparity between training and testing environments, poses a significant challenge in reinforcement learning (RL). A promising approach to addressing this challenge is distributionally robust RL, often framed as a robust Markov decision process (RMDP). In this framework, the objective is to find a robust policy that achieves good performance under the worst-case scenario among all environments within a pre-specified uncertainty set centered around the training environment. Unlike previous work, which relies on a generative model or a pre-collected offline dataset enjoying good coverage of the deployment environment, we tackle robust RL via interactive data collection, where the learner interacts with the training environment only and refines the policy through trial and error. In this robust RL paradigm, two main challenges emerge: managing distributional robustness while striking a balance between exploration and exploitation during data collection. Initially, we establish that sample-efficient learning without additional assumptions is unattainable owing to the curse of support shift; i.e., the potential disjointedness of the distributional supports between the training and testing environments. To circumvent such a hardness result, we introduce the vanishing minimal value assumption to RMDPs with a total-variation (TV) distance robust set, postulating that the minimal value of the optimal robust value function is zero. We prove that such an assumption effectively eliminates support shift pathologies for RMDPs with a TV distance robust set, and present an algorithm with near-optimal sample complexity. To demonstrate the breadth of our framework, we extend our algorithm and theory to new robust set formulations and robust Markov games. To illustrate the operational relevance, we apply our algorithm to data-driven robust inventory control.

Terminology-aware translation asks for more than a correct translation: the output must use the exact terms a glossary prescribes. The standard recipe, fine-tuning on glossary-annotated translation pairs, hides an inefficiency: for most examples the glossary prescribes exactly what the model would have produced anyway, so they teach nothing about following a glossary. We therefore keep only the examples where the model's own translation contradicts the glossary. In a controlled study at fixed data volume, this selection alone raises term accuracy from 78.7% to 89.9%. The filtered data, built by a two-way synthetic pipeline on open models, is part of the instruction-tuning mixture of our public release SalamandraTA-7b-instruct v3.0, which, used exactly as released and wrapped in a document-level inference pipeline, forms the BSC submission to the WMT26 Terminology Shared Task Track 1. At the official WMT26 evaluation, our system achieves 94.2% term success at 74.6 chrF++, with only two of the twenty-two submissions outperforming it on both metrics. On last year's benchmark, it also surpasses our GRPO-based system, despite being trained solely with ordinary supervised fine-tuning.