Reliable temporal representation learning is important for end-to-end autonomous driving, particularly when visual observations are degraded by occlusion, motion blur, illumination variation, and sensor noise. Existing Bird's-Eye-View (BEV) approaches provide a unified representation for perception and planning; however, temporal features are commonly aggregated across frames without explicitly accounting for the reliability of individual observations. Consequently, low-quality or inconsistent features may propagate through temporal representations and degrade downstream perception, prediction, and planning. To address this problem, we propose RCT-AD, a Reliability-Aware Context and Temporal BEV Reasoning framework for end-to-end autonomous driving that explicitly models feature reliability and temporal consistency within a shared BEV representation. RCT-AD introduces a Reliable Context Awareness (RCA) module that estimates frame-level reliability using spatial, semantic, temporal, and visual-quality cues, and selectively preserves trustworthy information through a reliability-guided temporal memory mechanism. When the current observation is unreliable, historical high-reliability features are aligned and integrated to construct a more stable temporal BEV representation. A Temporal Trajectory Planner models long-term temporal dependencies and multi-agent interactions, while semantic segmentation and motion-guided detection provide complementary supervision for refining the shared BEV representation. Experiments on the nuScenes benchmark demonstrate consistent improvements across perception, motion prediction, and trajectory planning. RCT-AD achieves 61.5 NDS, 52.9 mAP, and 52.3 mIoU while maintaining competitive computational efficiency. These results demonstrate the effectiveness of reliability-aware temporal BEV reasoning for unified perception, prediction, and planning.
Large language models (LLMs) are increasingly deployed as critical decision-making components in high-stakes real-world AI systems, rendering LLM reliability a foremost practical concern. In this paper, we focus on enhancing LLM reliability through selective prediction (SP), a strategy that allows an LLM to only predict for inputs where it is likely to be correct (i.e., coverage) and hence reduce the error rate (i.e., risk) on that portion of inputs---flagging the remaining inputs for future human discretion. In other words, SP improves LLM reliability by balancing the risk-coverage trade-off and enabling seamless human-AI collaboration. To integrate SP into LLMs, we focus on the LLM post-training alignment stage and propose to align LLMs with SP performance metrics, in contrast with existing LLM alignment methods that focus primarily on correctness or calibration metrics. Specifically, we propose a novel alignment framework, Reinforcement Learning for Selection Reward (RLSR), which targets the area under the risk-coverage curve (AURC)---a popular SP performance metric---as its alignment objective. RLSR achieves substantially better risk-coverage trade-off compared to multiple alignment baselines on both in-domain and out-of-domain tasks.
Many everyday programming tasks resist clean rule-based implementation, such as alerting on important log lines, repairing malformed JSON, or ranking search results by intent, and are increasingly outsourced to large language model APIs at the cost of locality, reproducibility, and price. We propose fuzzy-function programming: compiling such a function from a natural-language specification into a compact, locally executable neural artifact. We instantiate this paradigm with Program-as-Weights (PAW), in which a 4B compiler trained on FuzzyBench, a 10M-example dataset we release, emits parameter-efficient adapters for a frozen, lightweight interpreter. A 0.6B Qwen3 interpreter executing PAW programs matches the performance of direct prompting of Qwen3-32B, while using roughly one fiftieth of the inference memory and running at 30 tokens/s on a MacBook M3. PAW reframes the foundation model from a per-input problem solver into a tool builder: invoked once per function definition, it produces a small reusable artifact whose subsequent calls per function application are cheap and offline.
Chain-of-thought (CoT) reasoning enables large language models (LLMs) to solve complex problems by generating intermediate reasoning steps. While much attention has been paid to the length and content of these reasoning chains, far less is known about their internal geometry. We study the geometry of CoT trajectories in the hidden state space of transformer models, formalizing each reasoning chain as a discrete curve in $\mathbb{R}^d$ and characterizing it through spectral, positional, and kinematic geometric functionals. We introduce the effective dimension $d_\rho$ as a measure of trajectory complexity and empirically show that harder tasks exhibit greater effective dimension. Lastly, we explore how kinematic features of the trajectory, mean position, positional dispersion, initial and final 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 86 mathematical reasoning problems from the MATH500 dataset and three Qwen2.5 model scales (0.5B, 1.5B, and 7B), $d_\rho$ achieves difficulty-prediction AUROC of $0.90$, $0.94$, and $0.96$, respectively. Seven kinematic and positional features predict correctness from only the first $20\%$ of generated tokens, with AUROC between $0.77$ and $0.88$ across scales. These correctness signatures transfer across held-out questions, establishing that the shape of a model's internal reasoning trajectory is a principled window into both task hardness and solution quality.
Spatiotemporal point processes (STPPs) model event data in continuous time and space, with applications in mobility, epidemiology, and public safety. Recent neural STPPs span expressive intensities, density models, continuous-time latent dynamics, normalizing-flow spatial decoders, and score-based generative mechanisms. Yet comparison remains fragile because implementations differ in preprocessing, coordinate normalization, splits, likelihood conventions, and evaluation protocols. We present Seahorse, a unified framework for reproducible training and evaluation of STPPs. Seahorse provides an encode-evolve-decode interface and an executable benchmarking contract that standardizes dataset handling, tuning, raw-coordinate likelihood reporting, and run artifacts across classical baselines, neural likelihood models, continuous-time Neural STPP variants, and sample-based generative models. On 13 real datasets and 19 presets, no model dominates: likelihood, calibration, and next-event prediction favor different models, and the strongest models take from minutes to hours to train. Using HawkesNest as a controlled synthetic stress-test suite, we show how diagnostic benchmarking can probe neural STPP behavior under increasing spatiotemporal entanglement. Seahorse provides reusable infrastructure for comparing, diagnosing, and extending STPP models beyond implementation-specific leaderboards. The implementation, including preset configurations and reproduction scripts, is available at https://github.com/YahyaAalaila/seahorse.
When does training language models (LMs) to generate explanations of their predictions yield faithful introspection, rather than superficial imitation? We study LMs trained to explain which features of their inputs influenced their behavior, using models' counterfactual behavior on modified inputs as supervision. Surprisingly, we find that LMs trained on fixed counterfactual explanations derived from their earlier checkpoints, or even from behaviorally similar models in different families, frequently produce explanations more faithful to their own current behaviors than to those of their training targets. This "introspective" coupling between LM explanations and behaviors occurs when training explanations remain sufficiently correlated with current behaviors over the course of training, even as behaviors themselves shift. We also show that introspective coupling tracks behavior shifts: when explanation training is provided concurrently with other post-training objectives, explanations change to match without requiring updated supervision. This phenomenon appears in multiple tasks, including sycophancy and refusal, and is robust to label noise. Overall, our results show that even fixed datasets of counterfactual explanations can provide scalable and generalizable post-training signal for introspection.
Modern LLM workflows move coordinate-indexed objects across checkpoints: steering vectors, sparse autoencoders, top-$k$ neuron sets, attribution lists, LoRA updates, optimizer states, and merge alignments. This requires fixing the model's residual-stream gauge. We show that the native coordinate-preserving orthogonal gauge is architecture-dependent: LayerNorm residual charts have permutation gauge $S_d$ up to a global sign flip, while RMSNorm charts with generic gains have signed-permutation gauge $B_d = S_d \ltimes \{\pm 1\}^d$. Permutation-only alignment is thus symmetry-incomplete for RMSNorm models. We introduce sign-marginalized Hungarian matching and prove that with decorrelated coordinates, signed-correlation matching has a permutation-accuracy ceiling equal to the true gauge's positive-sign fraction up to $O(d 2^{-d})$, which sign-marginalized matching removes. Omitting signs induces expected squared error $2\|\Delta W\|_F^2$ on weight updates and loses orientation on vectors and AdamW first moments, while RMSNorm gains and AdamW second moments permute without signs. Controlled tests confirm these laws: a Qwen2.5-1.5B SST-2 LoRA adapter retains 0.944 accuracy (from 0.945) under $B_d$ transport vs. 0.523 under $S_d$, and steering preserves effects to $<10^{-4}$ at zero raw top-10 overlap. Across natural checkpoints, inherited slots suffice for same-base descendants (96.2%-100% retention), whereas cross-generation pairs support sparse prompt-stable subsets with causally decisive negative signs ($+0.185$ vs. $-0.010$ at $8\sigma$ on Qwen2/2.5-0.5B; $+0.189$ vs. $-0.021$ on 1.5B). Along fine-tuning trajectories, composing local $B_d$ gauges recovers 91.1% of cross-run Qwen2.5-1.5B coordinates at 1,500 steps vs. 60.3% for endpoint matching. Merge and interpretability audits confirm that coordinate names are reproducible only relative to an explicit $B_d$ gauge.
Recent work has shown that well-optimized individual decision trees can match complex black box models in some settings, primarily in noisy domains. For the remaining settings, however, complex ensembled compositions of trees often achieve higher accuracy at the cost of interpretability, leaving practitioners with difficult modeling decisions along an accuracy-interpretability tradeoff. Ideally, we would like to classify as much of the data as possible with one or a small number of trees, achieving interpretability for most samples while maintaining state-of-the-art accuracy. We introduce Multistage Defer Trees: a sequence of sparse decision trees that each make predictions for most samples, while deferring a small proportion to the next tree in the sequence or, ultimately, to a black box. We demonstrate that we can train this model class to match the performance of complex tree-based ensembles while routing most samples through only one or a small number of sparse decision trees. We discuss a range of techniques for training these models while maintaining simplicity. Our method expands the accuracy--interpretability frontier in settings where single-tree methods remain insufficient, demonstrating that even when complex models are necessary, they need not be fully opaque.
Prototype-based medical image classifiers present three clinical limitations: they treat findings as independent, silently amplify unsafe physician feedback, and require full retraining whenever a new finding is needed. We present GRAPE (Graph-Augmented Prototype Explanations), a unified architecture that targets all three challenges. First, a Graph Attention Task Head boosts macro-F1 by +13.8,pp over the prototype baseline on TBX11K but not on NIH ChestX-ray14, with no graph-specific benefit established. Second, a Concept-Mismatch Safety Check, to our knowledge the first such mechanism in prototype-based medical classifiers, warns when the model's dominant finding inside a doctor-drawn region conflicts with the claimed label, catching 85% of simulated erroneous annotations with no extra inference cost at a favorable operating point, though sensitivity falls substantially at clinically realistic false-positive budgets. Third, Open-Vocabulary Prototype Anchoring aligns visual prototypes to clinical text, allowing a new finding to be added from a single labeled image without modifying any other component, evaluated for localization only. On NIH ChestX-ray14, one Effusion example matched that concept's low fully-supervised Pointing Game ceiling in one run but not in a second. On TBX11K, prototype maps achieve 2.1x better lesion localization than end-to-end concept-based baselines. The graph head adds only +1~ms latency at interactive batch size. The project page is available at https://kurbanintelligencelab.github.io/GRAPE.
Matrix factorization (i.e., problems of the form $\min_{\mathbf{P},\mathbf{Q}} \|\mathbf{M}^\star - \mathbf{P}^\top\mathbf{Q}\|_\mathrm{F}^2$) is a minimal learning problem that exhibits both nonlinear parameter dynamics and representation learning. In this setting, we study how parameter trajectories under the Muon optimizer differ from those of gradient descent. We identify three main dynamical differences: (1) Muon avoids the slow saddle-to-saddle dynamics of GD from small initialization. Muon instead learns all the top singular vectors of $\mathbf{M}^\star$ at the same rate, and they saturate in order of increasing (rather than decreasing) singular value. (2) Muon does not diverge even when the learning rate exceeds the critical threshold set by the local loss sharpness. This frees the learning rate from the condition number of the problem, enabling rapid convergence via exponential learning rate annealing. (3) Once the weights are aligned with each other and the target, Muon flow conserves the matrix quantity $\sqrt{\mathbf{P}^\top \mathbf{P}}-\sqrt{\mathbf{Q}^\top \mathbf{Q}}$, while gradient flow is known to conserve the matrix $\mathbf{P}^\top\mathbf{P} - \mathbf{Q}^\top\mathbf{Q}$. Despite having distinct conserved quantities, both optimizers find the so-called balanced solution from vanishing initialization. When training from small random initialization, the weights spontaneously align early in training. We derive the alignment rates in simple settings and show that they predict the empirical alignment rates in general. Finally, we exploit structural properties of Muon to construct a learning rate schedule that achieves near-perfect alignment in only two optimization steps.
Spreadsheets are widely used for business analysis, financial modeling, reporting, and decision-making. However, most existing spreadsheet benchmarks evaluate isolated operations such as single-formula generation or local cell edits, and therefore fail to capture end-to-end workflows in realistic business settings. We introduce \textsc{SpreadsheetBench 2}, a workflow-level benchmark for spreadsheet agents that covers three task categories: generation, debugging, and visualization. The benchmark is constructed from authentic business data, including financial reports and corporate filings, and is annotated and validated by domain experts. The benchmark contains 321 tasks; each instance averages 11.8 worksheets and requires 593.5 cell modifications, reflecting large multi-sheet workbooks with cross-sheet dependencies. We evaluate eight frontier large language models under a unified multi-turn agent scaffold, and additionally include several LLM-based spreadsheet products as complementary baselines. Results show that current systems remain far from reliable on real-world workflows: the best model achieves 34.89\% overall task accuracy, and debugging accuracy is as low as 12.00\%. Trajectory analysis and a failure taxonomy further indicate that insufficient spreadsheet inspection and incorrect target-cell selection are the dominant bottlenecks. Together, these findings position \textsc{SpreadsheetBench 2} as a challenging testbed for advancing reliable spreadsheet automation. Project page: https://spreadsheetbench.github.io/
Language model loss follows remarkably regular scaling laws over model and data size, yet it remains unclear why the aggregate loss should exhibit a power-law form. Existing explanations often attribute this regularity to a heavy-tailed spectrum of pattern difficulty in natural language, but this view has not been directly validated at token-level granularity in large-scale real-data training. We present a token-level framework that decomposes scaling laws into localized learning events of individual contextualized tokens. By fitting token loss trajectories with sigmoids, we show that token learning is concentrated in localized transitions, giving rise to a learning-time spectrum that dominates the scaling-law shape. Across more than one hundred pre-training runs on large and diverse real-language corpora with modern LLM architectures, scaling up to 6B parameters and 300B training tokens, the measured learning-time spectrum quantitatively reconstructs the validation loss derivative along the training-step $T$, data-scale $D$, and model-scale $M$ axes. We further show that the same signal is actionable: by reshaping the training distribution according to when tokens become learnable, we alter the optimization trajectory and achieve 11\% faster validation-loss reduction. These results provide direct empirical evidence that scaling laws are governed primarily by the distribution of token-level learning times, and that this distribution can be used not only to explain scaling behavior but also to improve training performance.
Rare events govern the safety profile of modern AI systems, yet their probabilities are extremely difficult to estimate: direct Monte Carlo requires prohibitive sample budgets. Subset Simulation (SS) addresses this by decomposing a rare-event probability into moderate conditional probabilities over nested intermediate events. However, classical SS requires a handcrafted scalar performance function whose sublevel sets define those events, demanding detailed knowledge of the failure geometry and limiting transfer to new domains. We propose SCARCE (Scalable Cascade Analysis for Rare-event Characterisation via Embeddings), which replaces the performance function with learned latent representations and geometric rulers that score proximity to failure regions. Adaptive thresholding constructs nested intermediate events directly from data. We formalise SCARCE through a non-negative supermartingale, yielding a high-probability upper envelope that remains valid under early stopping. On MNIST misclassification, where dense Monte Carlo provides ground truth, SCARCE achieves approximately 400--500 times lower mean absolute error than grid-searched traditional SS while eliminating systematic over-counting. We then study PAIR-style LLM jailbreaks under a fleet-level threat model with adversarial fraction $\eta$. On Llama-Guard-3-8B hidden states, a PCA-based ruler attains 2.6% mean relative error for $\eta \geq 10^{-3}$ against finite-sample references whose average bootstrap relative half-width is 27.9%, and transfers to a GCG-style corpus with 2.93% relative error after recalibration. A directional criterion $\mathrm{KL}(p_{\mathrm{good}}\,\|\,p_{\mathrm{bad}})$ ranks rulers consistently with estimation error (Spearman $\rho=0.83$).
Note on v2 (Nov 2026): errors found in the evaluation code mean the empirical results reported in v1 are not supported; the theoretical corollary is unaffected. Details are in the notice on page 1 and in KNOWN_ISSUES.md in the linked repository. We compare five inference-time safety paradigms (no defense, static steering, CAST, AlphaSteer, probe-gated steering) across seven instruction-tuned models (7-31B) and five attack types (GCG, AutoDAN, DeepInception, prefilling, intent laundering). We derive a corollary: any defense that gates intervention on a single layer's activation alignment with a benign reference (cone, subspace, or null-space) is blind to attacks that craft activations to lie inside that reference, whether checked at prompt time or per token. For prefilling attacks we propose response-time probing, a linear probe on the hidden state at the first generated tokens combined with a halt, and compose this halt with AlphaSteer's null-space steering. We also examine whether MMLU captures steering's utility cost and how the diversity of negative training sets affects probe false-positive rates. Code, attacks, and per-sample results are released.
LLM agents handle user requests on behalf of organizations through tool calls and must follow the company policies stated in their system prompts. Prior work approaches this as a safeguarding problem -- external checks that block non-compliant agent actions. We argue that policy adherence is broader: real workflows unfold across many turns, require explicit user confirmation and prerequisite reads, and hinge on dialogue rather than on any single argument value. We introduce PolicyGuard, a sub-agent verifier that shares the agent's view of the dialogue, reasons over the policy in context, and returns actionable remediation. On $\tau^2$-bench airline across GPT 5.4, Claude Sonnet 4.6, and Gemini 2.5 Pro, PolicyGuard improves $\mathrm{Pass}^4$, the fraction of tasks successful in all four trials, by +12.0 / +6.0 / +12.0 pp; pooled paired tests support an overall cross-vendor effect. We further evaluate PolicyGuard on the full retail and telecom base splits, covering all three $\tau^2$-bench customer-service domains. Further analyses show that PolicyGuard improves reliability beyond agent self-checking, catches more policy violations with fewer blocks than argument-level guards, and preserves its refusal accuracy under three adversarial probes.
Latent reasoning models perform multi-step inference in embedding space, reducing the token overhead of chain-of-thought reasoning. Recent training-free refinement methods steer latent trajectories using contrastive signals from stronger and weaker reference checkpoints. We identify three sources of fragility in these methods: hyperparameter sensitivity, reference-pair dependence, and input sensitivity. We propose Trajectory-Invariant Latent Refinement (TILR), a training-free framework that constrains corrections to a stable refinement subspace and adaptively controls their magnitude. First, we extract a spectrally concentrated subspace from strong-weak reference differences across a calibration set and project contrastive updates onto it to filter unstable variation. Second, an adaptive gate scales each update according to its alignment with the learned subspace, suppressing unreliable corrections and recovering the unmodified backbone when alignment is low. Across six reasoning benchmarks, TILR improves robustness to input perturbations and reference selection while maintaining competitive accuracy. On the Coconut backbone, TILR improves answer agreement under semantically equivalent paraphrasing by 11.4% and reduces latent trajectory variance by approximately 30% relative to existing refinement baselines. These results support invariant subspaces as a practical basis for reliable latent refinement without retraining or backpropagation.
Tool-connected agents need execution-time invariants that hold even when a model follows an adversarial instruction. We formulate eight execution-layer invariants (I1-I8) covering structured authority, canonical resource resolution, principal and delegation binding, handle lifecycle, explicit source-to-target transfer, request-correlated denial evidence, and single-use approval state. To test whether these protections require a centralized runtime or follow from the invariants themselves, we compare HCP, an in-memory runtime with managed handles and tasks, against an independent gateway/server ACL (B3) enforcing the same I1-I8 contract over identical grants and labels. Both block 18 modeled violations and complete 25 workflows, while 16 source-code ablations pinpoint the checks responsible. Outside our scripted corpus, we test three boundaries. First, on 24 held-out AgentDojo tasks with live models, DeepSeek reaches attacker goals in 4 direct sessions while both controllers deny every attacker call; however, strict reference-derived grants also deny 40 non-attacker calls, and first-divergence replay under an approve-all control reaches 4 new attacker goals. Second, across 132 conditions on unmodified ChainCaps and Playwright MCP servers, per-call grants block ungranted writes but cannot stop a secret passed as an ordinary argument to an authorized sink; session source budgets block that copy but refuse unrelated actions; and explicit handle pipes or sealed reads block handle-mediated exfiltration while preserving unrelated workflows. Third, on a matched MCP backend, HCP adds 0.13 ms per workflow outside MCP calls while retaining 7.7 MB of state over one thousand workflows versus 0.7 MB for B3. Identical decisions across HCP and B3 show that enforcing explicit I1-I8 invariants at controlled entrances secures tool execution across centralized and gateway designs.
While recent vision-language models (VLMs) have achieved significant improvements on static visual-to-code tasks such as generating code for webpages, charts, or SVGs, it remains unclear whether they can recover temporal dynamics when motion is present. To this end, we introduce Animation2Code, a benchmark for evaluating temporal visual reasoning via reconstructing executable web animation code from videos. Animation2Code consists of 1,069 web animation videos with diverse visual appearances and motion patterns, paired with corresponding HTML/CSS/JavaScript implementations. We propose two human-aligned metrics, appearance similarity and temporal similarity, which allow us to disentangle visual fidelity from temporal alignment when comparing rendered animations against ground-truth samples. Benchmarking state-of-the-art VLMs on this dataset shows that current VLMs struggle to maintain temporal consistency in reconstruction, even when achieving high appearance similarity, including under finetuning and iterative refinement settings. Code and data are available at https://anya-ji.github.io/animation2code-website .
Pixel-space continuous-token autoregressive (AR) generation directly models images as sequences of raw pixel patches, avoiding discrete tokenization or a separately pretrained tokenizer. However, it faces coupled challenges: high-dimensional patch generation causes large single-step errors, and teacher-forced training creates a train--inference gap that makes these errors accumulate across AR steps. Existing fixes such as $x$-prediction and input noise injection only partially mitigate these issues. Exact rollout training better matches inference-time conditions, but is impractical due to prohibitively slow sequential sampling. We propose Parallel Rollout Approximation (PRA), a scalable framework that addresses both challenges jointly. PRA generates low-dimensional intermediate states and maps them to pixel patches through a one-step denoising pixel decoder, preserving a pixel-in, pixel-out AR interface. The same decoder also constructs inference-like training inputs from perturbed intermediate states through the same intermediate-state-to-pixel path used at inference, while retaining parallel training over positions. On class-conditional ImageNet-1K generation at $256\times256$ resolution, PRA-S with 135M parameters achieves an FID of 2.58, surpassing the previous billion-scale pixel-space AR result of 3.60. Scaling to PRA-L with 511M parameters further improves FID to 1.94, establishing a new SOTA among pixel-space AR models. Beyond generation, PRA achieves higher ImageNet classification probing accuracy than other AR and diffusion baselines, suggesting its potential for unified pixel-space image generation and understanding.
Differentiable partial differential equation (PDE) solvers underpin solver-in-the-loop MLtraining, gradient-based optimal control, and inverse problems, yet the practical cost of obtaining correct, usable gradients from a given solver on a given problem is largely undocumented. Integration effort, computational cost, memory, gradient accuracy, and numerical stability vary widely across solvers and are discoverable only by trial and error. We introduce Mosaic, an extensible benchmarking framework for differentiable PDE solvers that standardizes access to solver gradients. Each solver is packaged as a containerized component (Tesseract) exposing a uniform gradient API regardless of language or automatic differentiation (AD) strategy, enabling researchers to evaluate, compare, and build on non-trivial physical solvers. Our evaluation of 14 solvers across fluid dynamics, structural mechanics, and heat transfer demonstrates that the benchmark surfaces practically relevant differences: order-of-magnitude variation in computational cost and memory, alongside setup incompatibilities and instabilities that rule out solvers for specific tasks. Despite this variation, all solvers that produce gradients converge to similar optima on our tasks, indicating that the practical barriers are memory limits, numerical stability, and setup compatibility rather than gradient accuracy alone. Mosaic is open-source and available at github.com/pasteurlabs/mosaic.