Ladder

Every supervised fine-tuning run forces the same chain of decisions, such as learning rate, batch size, LoRA or full fine-tuning, how many epochs, which optimiser, and what data to feed the model. Each of these is typically rediscovered from scratch for every new model and dataset. Here we measure them under one instrument: a sweep that varies one lever at a time, and spans dense and mixture-of-experts models in two families (Qwen3 and Llama), on four real-world customer SFT datasets, for both LoRA and full fine-tuning. These datasets give a controlled testbed: each task carries an evaluation built with the customer, and its training data is produced by iterative supervised fine-tuning that refines model outputs until they pass that evaluation, so the supervised target is internally consistent and the task judge we report against is the criterion the data was built to satisfy. We ask how the optimal learning rate and batch size move with model scale, family, and data, and whether one selection rule transfers across them; what LoRA trades against full fine-tuning, and how its rank and alpha set what the adapter can learn; whether validation loss (or other metrics, such as loss landscape flatness) faithfully ranks downstream quality; whether post-training gains scale with model size and data volume, on a model ladder extended through mixtures-of-experts to 235B parameters; how many epochs to train before general instruction-following erodes; and whether a geometry-aware optimiser improves on AdamW. Each recommendation is paired with a measure of its uncertainty.

Maintaining price consistency and executing an Every Day Low Price strategy is critical for global retailers. However, with catalogs spanning millions of active items, manual governance of price relationships is infeasible. Inconsistent pricing across item variants distorts customer value perception and cannibalizes sales. To address this, we present a scalable, context-aware Multi-Agent Framework designed to automate the construction of "Lines and Ladders" pricing taxonomies. Our framework employs specialized LLM agents to construct these coherent pricing structures by identifying key attributes, extracting multi-modal values, and applying hierarchical grouping logic. Evaluated on real-world enterprise data and deployed in production, our 3-Agent system achieves an F1-score of 0.83 for Lines, outperforming single-agent baselines by mitigating cognitive overload. The system achieves >90% precision and >75% recall in Food & Consumables, and 80.2% assignment accuracy in the unstructured General Merchandise catalog.

Extraction produces candidate entities and relationships; writing them into a graph is where identity is decided, and identity decisions are destructive in a way extraction errors are not. A wrong type can be corrected later, but two records merged under one identity cannot be separated once their properties have been combined, and the merge leaves no error behind. This paper describes the ingestion and ontology-tagging layer that turns a validated extraction stream into a knowledge graph of 537,157 entities and 2,198,567 relationships drawn from 98,795 government documents. We describe a record-identity ladder that decides sameness from identifier columns, name columns, display names and type-scoped position rather than from name similarity. The ladder governs de-duplication within parsed tables, while the graph write applies a coarser canonical-name key, so records sharing a canonical name merge automatically on exact equality. We argue rather than demonstrate that this is where the automation line belongs: no identity benchmark is reported, and the over-merges the key permits are undetectable by construction. That policy, under which entity resolution only ever flags candidates, followed an incident in which two surface forms of one name were merged, corrupting a correct record and deleting eight entities from an unrelated document. We then describe multi-class ontology tagging and an evidence asymmetry we did not anticipate: an entity name is an instance label rather than a type assertion, so matching name fragments against a class index invents classifications. Requiring anchored evidence cut role assignments on an enriched sample from 36 to 4, all confirmed correct. We quantify the graph's conformance debt, show secondary classifications compensating for a mis-parented primary class, and describe a curation queue grown to 48,403 pending proposals against 775 human decisions.

Artificial intelligence is changing the task composition of computing work faster than curricula and training typically adapt. This is a curriculum-framework paper, grounded in a structured narrative review of labor-market and software-engineering evidence and illustrated through an exploratory pilot course: the review supports the framework, and the pilot illustrates it rather than serving as primary evidence. The central claim is that near-term change is task reallocation rather than full replacement: routine implementation is increasingly automated while verification, systems thinking, security, and the ability to supervise and orchestrate AI (keeping a human in the loop) gain value. We organize the response as a capability-assurance framework anchored by a Capability Ladder: a five-level progression (trigger, automation, workflow, AI agent, agent team) that classifies the operational autonomy of AI-augmented work and the human supervision it requires. We map the ladder to course-level updates, workload-aware assessment, and stackable workforce credentials, and illustrate it through a two-semester pilot of a team-based, no-code course enrolling computing and business students. We argue for targeted modernization around durable capabilities rather than wholesale curriculum replacement, and we are explicit about evidence limits: labor signals are confounded by non-AI forces, industry reports are directional, and the pilot is exploratory.

Mined code corpora are abundant but uncontrolled: a snippet's semantics, surface "messiness," and difficulty are whatever the wild contained; there is no known-optimal reference to grade against; and any public sample may already sit in a model's training set. We present Spaghetti Architect, a tool that mints code datasets with the control such corpora lack. An anti-optimization transpiler maps a clean, language-agnostic JSON intermediate representation to deliberately redundant, fully-flattened programs in five languages (Python, JavaScript, Go, Java, C++); every program is compiled, run, and checked against a reference oracle, so each instance is correct by construction. The clean IR is a known-optimal reference, messiness is dialed by strictly-nested anti-pattern profiles, each instance is labelled along two orthogonal difficulty axes, intrinsic (problem size) and incidental (presentation at fixed semantics), and contamination is resisted by minting fresh variants from a private held-out seed. We give construct-validity evidence that the quality order moves established complexity and readability metrics, and report baselines on a four-model open ladder: exact match rises with scale, and the intrinsic knob collapses arithmetic-aggregation accuracy of even the strongest model to zero. Further, development-set scores equal freshly re-minted held-out counterparts within $|Δ|\le 0.012$ (comprehension) and $\le 0.011$ (refactoring); on identical programs, refactoring equivalence ($0.73 \rightarrow 0.99$) is scale-invariant while output prediction collapses; and ablating the generator's self-annotations shows they inflate the weakest model an order of magnitude more than the strongest ($-0.173$ vs $-0.017$): the annotated ladder resolves one of three adjacent pairs where the unannotated resolves all three. Open source (MIT), dependency-free, archived under a persistent DOI.

A Ladder Logic Bomb (LLB) is malicious control logic in a Programmable Logic Controller (PLC) program that lies dormant until a trigger activates a payload to manipulate actuators, forge sensor readings, or deny operator control. We observe that real malicious logic hides inside function-block bodies, which existing ladder-diagram verifiers drop from their intermediate representation (IR), making bombs invisible to provers. We present ESBMC-LLB, which uses ESBMC-PLC+ as its verification engine and adds a modeling layer that exposes function-block logic and recasts bomb detection as a formal verification problem: a scan-watchdog exposes non-termination payloads, and output wiring exposes actuator-forgery payloads as safety violations. k-induction gives an unbounded proof of bomb-absence across all scans, and the bounded model checker returns a counterexample that is the trigger - guarantees that signature, anomaly, and CFG-triage detectors lack. On the public Iacobelli 2024 dataset, ESBMC-LLB detects all 30 bombs and recovers every trigger; it also detects adaptive triggers (computed, opaque-arithmetic, multi-scan) that evade CFG-triage. We also report the first semantic model-checker evaluation on PLC-Defuser's SWaT corpus: our analog extension makes the full corpus parseable; on v1.0.0, it detects 149/150 bombs (99%) with zero false positives, recovering each trigger; on a later version with nonlinear non-termination bombs, detection drops to 49% as the SMT solver times out. We conclude that semantic model checking and CFG-triage are complementary - the former gives unbounded proofs, adaptive-trigger robustness, and handles Boolean/integer and linear analog logic; the latter leads to nonlinear analog non-termination, and we delineate where each wins.

We present a new method for structural sequence analysis grounded in Algorithmic Information Theory (AIT). At its core is the Ladderpath approach, which extracts nested and hierarchical relationships among repeated substructures in linguistic sequences -- an instantiation of AIT's principle of describing data through minimal generative programs. These structures are then used to define three distance measures: a normalized compression distance (NCD), and two alternative distances derived directly from the Ladderpath representation. Integrated with a $k$-nearest neighbor classifier, these distances achieve strong and consistent performance across in-distribution, out-of-distribution (OOD), and few-shot text classification tasks. In particular, all three methods outperform both gzip-based NCD and BERT under OOD and low-resource settings. These results demonstrate that the structured representations captured by Ladderpath preserve intrinsic properties of sequences and provide a lightweight, interpretable, and training-free alternative for text modeling. This work highlights the potential of AIT-based approaches for structural and domain-agnostic sequence understanding.

We introduce the ladderpath index as a measure of language complexity grounded in algorithmic information theory. It counts the minimum steps needed to reconstruct a sequence through hierarchical reuse of repeated substructures, capturing an exactly computable but constrained form of algorithmic compressibility related to, but distinct from, Kolmogorov complexity. We apply the ladderpath approach to 21 parallel corpora from the Parallel Universal Dependencies dataset. The ladderpath index is approximately invariant across the languages, and varies much less than the corpus length. This is more pronounced when all corpora are mapped to a unified binary representation, providing evidence for the equi-complexity hypothesis from a representation-independent perspective. We also observe trade-offs between character inventory size and corpus length, and between vocabulary-level and corpus-level reconstruction complexity, supporting the trade-off hypothesis that total complexity is conserved and redistributed across linguistic levels. The reusable substructures identified by the ladderpath approach, without any linguistic input, overlap with words and morphological components attested in the natural vocabulary. The hierarchical reuse captured by the ladderpath approach parallels the chunking mechanisms proposed in cognitive science, where the human cognitive system compresses linguistic input into nested, reusable units under shared memory and processing constraints. This connection between cognitive chunking and the ladderpath approach provides a new interpretation for the equi-complexity and trade-off hypotheses, grounding both in the shared cognitive architecture that underlies language processing across human languages.

Humanoid robots hold great promise for operating in human-centered environments, yet ladder climbing remains one of the most challenging tasks due to sparse footholds and handholds, complex whole-body coordination, and sensitivity to perception and control errors. We present \textbf{LadderMan}, a unified system that enables humanoid robots to robustly climb diverse ladders and perform manipulation under such constrained conditions. Our climbing policy is built on a scalable two-stage learning pipeline, where we use hybrid motion tracking to learn multiple climbing experts from a single reference motion, and distill these experts into a unified depth-based visuomotor climbing policy via hybrid imitation and reinforcement learning. To enable real-world deployment, we leverage vision foundation models to bridge the sim-to-real gap in depth perception. Building on the learned climbing policy, we further train a separate manipulation policy using a dual-agent formulation, allowing stable on-ladder manipulation via teleoperation. Experiments demonstrate that LadderMan achieves robust ladder climbing across a wide range of geometries, successfully transfers to real-world hardware in a zero-shot manner, and supports various manipulation tasks under challenging ladder constraints. Video results are available at https://ladderman-robot.github.io .

Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and risk-analysis applications. We break this circularity with a pipeline in which implied volatility emerges as an output of a structural model of equity returns. A Jump Hidden Markov Model produces multi-asset price paths with realistic stylized facts and cross-asset tail dependence; a modified Heston variance process, whose mean-reversion target depends on regime state, days to expiration, moneyness, and a market-mood indicator, converts those paths into implied-volatility paths; and a recombining binomial lattice prices American options from the resulting surface. Initializing variance at its mean-reversion target for each strike-expiration pair lets smile, skew, and term structure emerge without external calibration. We calibrate the shape function through a hierarchy spanning a parametric baseline, a globally shared neural surrogate, and a sector-specific neural surrogate fit to a multi-ticker, multi-sector option ladder. A temporal holdout on a multi-day capture isolated scheduled corporate events as the dominant source of test-time generalization error, and calendar-derived earnings-distance and same-sector peer-coupling features recovered the anticipatory portion of that signal. We then apply the framework as a synthetic-data generator on real near-the-money put and call contracts, forward-simulating price paths, and recovering path-conditional implied volatility, finite-difference American Greeks, and terminal short-premium profit and loss from one coherent simulation, and confirm cross-ticker robustness by re-running on a second underlying from a different sector and volatility regime. The framework is released as an open-source Julia package.

Production agentic systems make many model calls per user request, and most of those calls are short, structured, and routine. This raises a practical routing question that existing evaluations do not directly answer: which parts of an agent workflow truly require large frontier intelligence, and which can be handled by smaller models? We introduce AgentFloor, a deterministic 30-task benchmark organized as a six-tier capability ladder, spanning instruction following, tool use, multi-step coordination, and long-horizon planning under persistent constraints. We evaluate 16 open-weight models, from 0.27B to 32B parameters, alongside GPT-5 across 16,542 scored runs. Our results reveal a clear boundary of model necessity. Small and mid-sized open-weight models are already sufficient for much of the short-horizon, structured tool use work that dominates real agent pipelines, and in aggregate, the strongest open-weight model matches GPT-5 on our benchmark while being substantially cheaper and faster to run. The gap appears most clearly on long-horizon planning tasks that require sustained coordination and reliable constraint tracking over many steps, where frontier models still hold an advantage, though neither side reaches strong reliability. We also find that this boundary is not explained by scale alone: some failures respond to targeted interventions, but the effects are model-specific rather than universal. These findings suggest a practical design principle for agentic systems: use smaller open-weight models for the broad base of routine actions, and reserve large frontier models for the narrower class of tasks that truly demand deeper planning and control. We release the benchmark, harness, sweep configurations, and full run corpus.

We show that pre-training a Transformer on music before language significantly accelerates language acquisition. Using piano performances (MAESTRO dataset), a developmental pipeline -- music $\to$ poetry $\to$ prose -- yields a $17.5\%$ perplexity improvement over random initialization ($p < 0.001$, 5 seeds), with music and poetry improving orthogonal model components (internal computation and embeddings, respectively). Convergence tests confirm that this is not a transient head start: at $d\!=\!64$, multi-seed validation (5 seeds) shows a persistent 5.5% gap at plateau ($p = 0.017$), with the pipeline converging faster and to a lower loss in every run. Real music matches the transfer ceiling of synthetic patterns with one-third the data, and scaling experiments reveal that optimal pre-training data volume shifts with model capacity ($-3\% \to +3\% \to +6\%$ advantage of larger datasets from $d\!=\!16$ to $d\!=\!64$). Across the scales we study ($d\!\in\!\{16,32,64\}$, up to ${\sim}400$K parameters), these results suggest a capacity-dependent data curation principle and indicate that structured human creative outputs can provide an efficient pre-training substrate for small language models; stronger conclusions at modern pre-training scale will require substantially larger experiments.

Automotive anomaly detectors are often selected from accuracy only benchmarks on workstation class hardware, whereas in-vehicle monitoring requires predictable scoring latency under limited CPU parallelism. This mismatch can make methods that appear competitive offline infeasible for deployment. We present ECoLAD (Efficiency Compute Ladder for Anomaly Detection), a deployment-oriented evaluation protocol for automotive time-series anomaly detection (TSAD). ECoLAD defines a monotone compute reduction ladder with explicit CPU thread caps, mechanical integer only hyperparameter scaling, inference/full run timing separation, and auditable run logs. Applied to proprietary in-vehicle telemetry and two public benchmarks, it shows that accuracy stability and deployment feasibility can diverge: some deep detectors retain AUC-PR while losing feasible throughput, whereas lightweight classical detectors sustain high scoring rates with positive lift above the random baseline, providing a practical screening procedure for detector selection under deployment relevant constraints.

Continual learning systems face a fundamental geometric obstacle: as experience accumulates on a fixed-capacity manifold, covering numbers grow linearly with time, eventually forcing representational overlap and catastrophic interference. Prevailing approaches attack this problem by \emph{expansion} - projecting into higher-dimensional spaces via kernels, overparameterization, or replay. We argue the solution is the opposite: \emph{contraction}. We formalize abstraction as the \textbf{Urysohn Ladder}, a hierarchy of quotient maps that recursively collapse validated metric neighborhoods into compact tokens, converting unbounded ambient-space search into bounded navigation on a low-dimensional intrinsic scaffold. Geometrically, each collapsed token acts as a shortcut - a region of extreme metric contraction that bridges distant experiences, much like a wormhole in the representational manifold. We establish four results that collectively guarantee \emph{separability} (metric contraction renders nonlinearly entangled structure linearly separable at each quotient level, and this separability propagates faithfully through the entire hierarchy), \emph{bounded capacity} (covering numbers remain $O(1)$ per quotient level, independent of stream length), \emph{stability} (parity-partitioned flow/scaffold subspaces enable unbounded plasticity without catastrophic interference), and \emph{scalability} (inference cost scales with quotient distance, not ambient distance). We validate each claim empirically with pretrained models and real-world datasets. Moreover, we demonstrate the potential of Urysohn Ladder for scalable continual learning via scaffold amortization.

As large language model (LLM) based systems take on high-stakes roles in real-world decision-making, they must reconcile competing instructions from multiple sources within a single prompt context. Enforcing an instruction hierarchy, where higher-level directives override lower-priority requests, is critical to the reliability and control of LLMs. In this work, we reframe instruction hierarchy resolution as a reasoning task. The model must first "think" about the relationship between a given user prompt and higher-priority instructions before generating a response. To enable this capability, we construct VerIH, a training dataset of constraint-following tasks with verifiable answers, comprising aligned and conflicting system-user instructions. We show that lightweight reinforcement learning with VerIH effectively transfers general reasoning capabilities of models to instruction prioritization. Our method leads to consistent improvements across multiple model families on both instruction following and instruction hierarchy benchmarks, achieving ~20% absolute improvement in conflict setups. Our method also leads to improved alignment to safety-critical scenarios beyond the training distribution, exhibiting increased robustness against jailbreak and prompt injection, reducing absolute attack success rates by up to 20%. Our results establish reasoning over instruction hierarchies as a practical mechanism for improving AI reliability, where targeted updates to system prompts produce predictable, controllable, and robust changes in model behavior.