Oracles

We propose Broximal Gradient Descent (BroxGD), a projection-free sister method to projected gradient descent for constrained optimization. Its forward--backward construction replaces the proximal backward operation by the broximal operation of Gruntkowska et al. (2025). Instead of projecting, each step minimizes a linear function over the intersection of the constraint set $\mathcal{X}$ and a ball $\mathbb{B}(x_k,t_k)$ centered at the current iterate $x_k$, of suitable radius $t_k>0$: $$x_{k+1}\in\arg\min_{z\in\mathcal{X}\cap\mathbb{B}(x_k,t_k)}\langle\nabla f(x_k),z\rangle.$$ We develop a comprehensive convergence theory spanning a wide range of optimization regimes and radius rules. We expect BroxGD to find many applications and inspire numerous extensions, much like projected gradient descent. Our contribution is theoretical; potential applications and toy experiments illustrate the method and suggest directions for future work.

Enterprise agents increasingly operate inside scoped retrieval systems, delegated workflows, and policy-constrained evidence environments. In these settings, access control can be enforced correctly while the system still produces an answer that appears complete even though material evidence lies outside the caller's authorization boundary. This paper introduces Partial Evidence Bench, a deterministic benchmark for measuring that failure mode. The benchmark ships three scenario families -- due diligence, compliance audit, and security incident response -- with 72 tasks total, ACL-partitioned corpora, oracle complete answers, oracle authorized-view answers, oracle completeness judgments, and structured gap-report oracles. It evaluates systems along four surfaces: answer correctness, completeness awareness, gap-report quality, and unsafe completeness behavior. Checked-in baselines show that silent filtering is catastrophically unsafe across all shipped families, while explicit fail-and-report behavior eliminates unsafe completeness without collapsing the task into trivial abstention. Preliminary real-model runs show model-dependent and scenario-sensitive differences in whether systems overclaim completeness, conservatively underclaim, or report incompleteness in an enterprise-usable form. The benchmark's broader contribution is to make a governance-critical agent failure measurable without human judges or contamination-prone static corpora.

Long-term LLM agents must compress streams of past interactions into persistent memory before future queries are known. Existing evaluations usually measure final question-answering accuracy, which entangles memory writing with retrieval, prompting, and reader reasoning. We introduce MEMAUDIT, an exact packageoracle evaluation protocol for budgeted long-term memory writing. A MEMAUDIT package fixes an experience stream, candidate memory representations, storage costs, semantic evidence units, future-query requirements, and a budget, turning write-time memory selection into a finite auditable optimization problem with a certified denominator. We instantiate this protocol with a concave-over-modular semantic coverage objective under storage and one-representation-per-experience constraints, and compute exact package optima using branch-and-bound with MILP certification. Across controlled exact packages, validity-heavy stress tests, human-audited natural support slices, and exported Mem0, A-Mem, and Letta stores, MEMAUDIT separates representation quality, validity-state preservation, and budget-aware selection effects that end-to-end QA cannot localize. The resulting artifact provides reusable package generators, certified solvers, natural package exports, external-system scorers, and cached reproducibility metadata for evaluating what memory writers actually preserve under fixed storage budgets.

In a continual learning setting, we require a model to be plastic enough to learn a new task and stable enough to not disturb previously learned capabilities. We argue that this dilemma has an architectural root. A finite network has limited representational and plastic resources, yet the required capacity depends on properties of the future task stream that are unknown: how many tasks will be encountered, and how much they overlap in feature space. Regularization-based methods preserve past knowledge within fixed-capacity architectures and therefore implicitly rely on an oracle architecture sized for this unknown future. When tasks are only weakly related, fixed architectures progressively run out of plastic resources; when tasks are few or strongly overlapping, models are often over-provisioned. Inspired by neurogenesis in biology, we propose NORACL to address the stability-plasticity dilemma by tackling the oracle architecture problem through neuronal growth. Starting from a compact network, NORACL grows only when needed by monitoring two complementary signals for representational and plasticity saturation. We evaluate NORACL against oracle-sized static baselines across varying task counts and geometries. Across all settings, NORACL achieves final average accuracies that are better than or on par with oracle-provisioned static baselines while using fewer parameters. Additionally, NORACL yields architectures with interpretable growth, i.e. dissimilar tasks predominantly expand feature-extraction layers, whereas tasks which rely on common features shift growth toward later feature-combination layers. Our analysis further explains why fixed-capacity networks lose plasticity as tasks accumulate, whereas NORACL creates fresh capacity for new tasks through growth. Together, these results show that adaptive neurogenesis pushes the stability-plasticity Pareto frontier of continual learning.

Text-to-image diffusion models have achieved remarkable generative capabilities, yet accurately aligning complex textual prompts with synthesized layouts remains an ongoing challenge. In these models, the initial Gaussian noise acts as a critical structural seed dictating the macroscopic layout. Recent online optimization and search methods attempt to refine this noise to enhance text-image alignment. However, relying on unconstrained Euclidean gradient ascent mathematically inflates the latent norm and destroys the standard Gaussian prior, causing severe visual artifacts like color over-saturation. Furthermore, these methods suffer from inefficient semantic routing and easily fall into the ``reward hacking'' trap of external proxy models. To address these intertwined bottlenecks, we propose Oracle Noise, a zero-shot framework reframing noise initialization as semantic-driven optimization strictly confined to a Riemannian hypersphere. Instead of relying on complex external parsers, we directly identify the most impactful structural words in the prompt to efficiently route optimization energy. By updating the noise strictly along a spherical path, we mathematically preserve the original Gaussian distribution. This geometric constraint eliminates norm inflation and unlocks aggressive step sizes for rapid convergence. Extensive experiments demonstrate that Oracle Noise significantly accelerates semantic alignment and achieves superior aesthetics without black-box models. It completely mitigates Euclidean-induced degradation, establishing state-of-the-art performance across human preference metrics (e.g., HPSv2, ImageReward), semantic alignment (CLIP Score), and sample diversity, all within a strict 2-second optimization budget.

Modern data warehouses extend SQL with semantic operators that invoke large language models on each qualifying row, making per-row inference orders of magnitude more expensive than traditional SQL. Model cascades reduce this cost by routing most rows through a fast proxy model and delegating uncertain cases to an expensive oracle. Prior SUPG-style cascades, however, require a global proxy-score pass that is itself an LLM-inference workload and blocks output in pipelined query engines. They also target either precision or recall and cannot serve workloads that need both. We formalize the cascade routing problem for streaming semantic SQL with independent parallel workers and present two complementary algorithms within this model. SUPG-IT extends SUPG from single-pass, single-metric estimation to streaming execution by iteratively refining two thresholds as oracle labels accumulate across batches, and is the first streaming cascade with joint probabilistic guarantees on user-specified precision and recall at a chosen failure probability $δ$. GAMCAL replaces user-specified targets with a single tradeoff parameter $α$ between classification error and oracle cost, and learns a monotone Generalized Additive Model that calibrates proxy scores to true-positive probabilities and supplies pointwise uncertainty for stochastic routing. On six classification, filtering, and join benchmarks evaluated in a production semantic SQL engine, both algorithms reach $F_1 \geq 0.95$ at their best operating points. GAMCAL also leads all six datasets at a 20% delegation budget and reaches $F_1 \geq 0.95$ with up to 58% fewer oracle calls than LOTUS's SUPG cascade. SUPG-IT attains the highest best-case $F_1$, with a mean of 0.989 across the six datasets.

Agentic vision-language models increasingly act through extended interactions, but most evaluations still focus on single-image, single-turn correctness. We introduce \textbf{AMIGO} (\textbf{A}gentic \textbf{M}ulti-\textbf{I}mage \textbf{G}rounding \textbf{O}racle Benchmark), a long-horizon benchmark for \emph{hidden-target} identification over galleries of visually similar images. In AMIGO, the oracle privately selects a target image, and the model must recover it by asking a sequence of attribute-focused Yes/No questions under a strict protocol that returns Yes/No/Unsure feedback and penalizes invalid actions with \emph{Skip}. This setting stresses (i) question selection under uncertainty, (ii) consistent constraint tracking across turns, and (iii) fine-grained discrimination as evidence accumulates. We instantiate AMIGO with the \textit{Guess My Preferred Dress} task and evaluate open-source VLMs with metrics covering identification success, evidence verification, efficiency, protocol compliance, robustness to controlled feedback perturbations, and trajectory-level diagnostics. The benchmarking results show that final-answer accuracy alone overstates evidence-grounded performance: models can guess correctly without verification-passing evidence, waste turns through invalid questions, or fail to preserve the upload protocol. Strong AMIGO performance depends on the combination of visual discrimination, informative question selection, constraint tracking, efficient stopping, sustained protocol following, and recovery from controlled feedback noise; model scale alone does not guarantee reliable long-horizon interactive grounding.

A core bottleneck in large language model (LLM) inference is the cost of attending over the ever-growing key-value (KV) cache. Although near-oracle top-k KV selection can preserve the quality of dense attention while sharply reducing computation and bandwidth, existing sparse methods generally rely on posterior heuristics, i.e., selectors conditioned on observed attention or proxy scores. Such conditioning introduces posterior bias: it tends to distort true token importance and miss salient tokens, thereby impairing long-range reasoning. To tackle this problem, we propose Pre-hoc Sparsity (PrHS), which selects KV entries before attention scoring and provides explicit accuracy control. Let the attention mass of discarded entries be delta (the dropped mass). Through a marginal-to-mutual-information analysis, we derive an upper bound on the mutual-information loss that depends only on the dropped mass. This relation explains failure modes of posterior heuristics and enables verifiable guarantees by controlling the dropped mass in advance. Within PrHS, we instantiate three orthogonal pre-hoc selectors along the axes of time, depth, and layer. Extensive experiments on LLaMA and Mistral families validate PrHS. Across GSM8K and CoQA, PrHS reduces retrieval overhead by over 90%, achieving 3x higher retrieval sparsity than HShare at matched or better accuracy. It incurs under 1% average degradation on LongBench, lowers attention FLOPs by about 15% versus prior sparse baselines, and yields a 9.9x speedup in attention-operator latency and 2.8x higher throughput on NVIDIA A100-80GB GPUs than the dense baseline.

We study the running time, in terms of first order oracle queries, of differentially private empirical/population risk minimization of Lipschitz convex losses. We first consider the setting where the loss is non-smooth and the optimizer interacts with a private proxy oracle, which sends only private messages about a minibatch of gradients. In this setting, we show that expected running time $Ω(\min\{\frac{\sqrt{d}}{α^2}, \frac{d}{\log(1/α)}\})$ is necessary to achieve $α$ excess risk on problems of dimension $d$ when $d \geq 1/α^2$. Upper bounds via DP-SGD show these results are tight when $d>\tildeΩ(1/α^4)$. We further show our lower bound can be strengthened to $Ω(\min\{\frac{d}{\bar{m}α^2}, \frac{d}{\log(1/α)} \})$ for algorithms which use minibatches of size at most $\bar{m} < \sqrt{d}$. We next consider smooth losses, where we relax the private oracle assumption and give lower bounds under only the condition that the optimizer is private. Here, we lower bound the expected number of first order oracle calls by $\tildeΩ\big(\frac{\sqrt{d}}α + \min\{\frac{1}{α^2}, n\}\big)$, where $n$ is the size of the dataset. Modifications to existing algorithms show this bound is nearly tight. Compared to non-private lower bounds, our results show that differentially private optimizers pay a dimension dependent runtime penalty. Finally, as a natural extension of our proof technique, we show lower bounds in the non-smooth setting for optimizers interacting with information limited oracles. Specifically, if the proxy oracle transmits at most $Γ$-bits of information about the gradients in the minibatch, then $Ω\big(\min\{\frac{d}{α^2Γ}, \frac{d}{\log(1/α)}\}\big)$ oracle calls are needed. This result shows fundamental limitations of gradient quantization techniques in optimization.

Recent advances in large video-language models (VLMs) rely on extensive fine-tuning techniques that strengthen alignment between textual and visual comprehension. Leading pipelines typically pair supervised fine-tuning (SFT) with reinforcement learning from preference data to enhance video comprehension. However, as VLMs scale in parameter size, so does the cost of gathering enough human feedback. To make fine-tuning more cost-effective, recent frameworks explore reinforcement learning with AI feedback (RLAIF), which replace human preference with AI as a judge. Current RLAIF frameworks rely on a specialized reward model trained with video narratives to create calibrated scalar rewards -- an expensive and restrictive pipeline. We propose Oracle-RLAIF, a novel framework that replaces the trained reward model with a more general Oracle ranker which acts as a drop-in model ranking candidate model responses rather than scoring them. Alongside Oracle-RLAIF, we introduce $GRPO_{rank}$, a novel rank-based loss function based on Group Relative Policy Optimization (GRPO) that directly optimizes ordinal feedback with rank-aware advantages. Empirically, we demonstrate that Oracle-RLAIF consistently outperforms leading VLMs using existing fine-tuning methods when evaluated across various video comprehension benchmarks. Oracle-RLAIF paves the path to creating flexible and data-efficient frameworks for aligning large multi-modal video models with reinforcement learning from rank rather than score.

LLM agents that repair failures often discard successful corrections, forcing later episodes to rediscover similar solutions. We study whether finalized repair outcomes can improve subsequent Text-to-SQL episodes without parameter updates. We introduce MERIT, a training-free agent that maintains an online dual-polarity memory of oracle-verified corrections and observed unsuccessful directions. Under oracle-assisted benchmark feedback, only memories from earlier finalized episodes are eligible for retrieval. A deterministic classifier assigns a coarse failure type, which conditions a hybrid lexical-dense retriever before the frozen model generates each revision. Using Qwen2.5-7B-Instruct with identical initial predictions and repair budgets, \method{} improves execution accuracy over stateless iterative repair from $66.34\%$ to $69.79\%$ on Spider and from $47.35\%$ to $48.44\%$ on BIRD. Paired analyses provide clear evidence for the Spider gain but weaker evidence on BIRD. MERIT is not reliably separated from untyped dynamic retrieval on either benchmark, while Reflexion-style memory reaches $51.24\%$ on BIRD at substantially higher inference cost. Ablations show that negative memory contributes modestly, the value of type conditioning and lexical-dense ranking is dataset dependent, and schema-local experience provides the most consistent benefit. These results clarify when causal cross-query memory improves repair and when broader memory representations remain preferable. Our implementation is available here: