arxiv: 2604.18177 · v2 · submitted 2026-04-20 · 💻 cs.CL · cs.AI

Recognition: unknown

STaD: Scaffolded Task Design for Identifying Compositional Skill Gaps in LLMs

Sungeun An , Swanand Ravindra Kadhe , Shailja Thakur , Chad DeLuca , Hima Patel

Authors on Pith no claims yet

Pith reviewed 2026-05-10 04:35 UTC · model grok-4.3

classification 💻 cs.CL cs.AI

keywords LLM evaluationcompositional reasoningscaffolded tasksreasoning benchmarksskill gapsblack-box probing

0 comments

The pith

Scaffolded Task Design creates controlled variations of benchmarks to pinpoint the exact reasoning skill combinations missing in large language models.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces the STaD framework to generate incremental, structured variations of standard reasoning benchmarks using the idea of scaffolding. This method treats models as black boxes and systematically reveals the specific compositions of skills that cause failures, which overall accuracy numbers obscure. Experiments across six models of different sizes on three benchmarks demonstrate that each model has its own distinct pattern of gaps. A reader would care because this diagnostic approach turns opaque performance scores into actionable maps of what each model can and cannot compose.

Core claim

Applying STaD to three reasoning benchmarks produces controlled task variations that isolate multiple failure points in LLMs, exposing that each of the six tested models lacks a unique combination of reasoning skills rather than sharing uniform weaknesses.

What carries the argument

The STaD framework, which generates controlled variations of benchmark tasks by introducing structured incremental support in a step-by-step manner to probe model behavior for missing skill compositions.

Load-bearing premise

That the controlled variations based on scaffolding accurately isolate specific compositional skill gaps without introducing confounding effects from the task modifications themselves.

What would settle it

A model that maintains identical error patterns and performance levels on both original and scaffolded task versions, showing no new failures traceable to the added incremental supports.

Figures

Figures reproduced from arXiv: 2604.18177 by Chad DeLuca, Hima Patel, Shailja Thakur, Sungeun An, Swanand Ravindra Kadhe.

**Figure 2.** Figure 2: Original vs. scaffolded performance across benchmarks. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: Frequency of compositional-skill bottlenecks in (a) ToT Arithmetic, (b) GSM8K, and (c) Math-Hard. For [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Skill Distribution Across (m, n) Settings. X-axis skill ID each distinct skill and y axis represent the ratio [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗

**Figure 6.** Figure 6: ToT Skill Granularity m=40 and where n=5, 10, 20, 40. [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗

**Figure 7.** Figure 7: GSM8K Skill Granularity m=40 and where n=5, 10, 20, 40. [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗

**Figure 8.** Figure 8: Math-Hard Skill Granularity m=80 and where n=5, 10, 20, 40. [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗

read the original abstract

Benchmarks are often used as a standard to understand LLM capabilities in different domains. However, aggregate benchmark scores provide limited insight into compositional skill gaps of LLMs and how to improve them. To make these weaknesses visible, we propose Scaffolded Task Design (STaD) framework. STaD generates controlled variations of benchmark tasks based on the concept of scaffolding, which introduces structured, incremental support in a step-by-step manner. Rather than inspecting failures individually, this approach enables systematic and scalable probing of model behavior by identifying the specific reasoning skill compositions they lack. Treating the LLM as a black box, our experiments on six models of varying sizes reveal multiple failure points in three reasoning benchmarks and highlight each model's unique and distinct skill gaps.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

STaD applies scaffolding to create task variants for diagnosing LLM skill gaps, but the variations likely change too many surface features at once to cleanly attribute failures.

read the letter

The paper's main contribution is a framework called STaD that takes existing reasoning benchmarks and generates controlled variants by adding incremental support in steps, drawing from educational scaffolding. This lets them run the same core task with different levels of help and observe where each model breaks. They test this on six models across three benchmarks and report that the failure patterns differ by model size and architecture, which is the kind of granular output that aggregate scores usually hide. That part is useful and directly addresses the problem of opaque benchmark results. The experiments are presented as black-box probes, which keeps the method simple to apply. What stands out is the systematic variation rather than post-hoc error analysis on single failures. The soft spot is exactly the one the stress test flags. Any scaffolding step changes prompt length, explicitness of intermediates, and overall structure at the same time. Without matched controls or ablations that isolate the skill composition from those surface changes, the performance deltas could come from easier prompting mechanics instead of the targeted reasoning gap. The abstract gives no details on how the variants were generated or validated, and the high-level results do not include error breakdowns that would let a reader check the attribution. This makes the central claim about unique, distinct skill gaps harder to accept at face value. The paper is aimed at people who build or evaluate LLMs and want diagnostic tools beyond overall accuracy. Readers working on model improvement or benchmark design would get practical ideas from the framework even if they end up modifying the controls. I would send it for peer review because the idea is concrete, the experiments cover multiple models, and the limitation is fixable with additional checks rather than a load-bearing flaw in the setup itself.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes the Scaffolded Task Design (STaD) framework, which generates controlled variations of existing benchmark tasks by introducing incremental scaffolding support. Treating LLMs as black boxes, the authors apply STaD to three reasoning benchmarks and evaluate six models of varying sizes, claiming to identify multiple failure points and each model's unique compositional skill gaps.

Significance. If the central claim holds, STaD would offer a scalable, systematic alternative to aggregate benchmark scores for diagnosing LLM reasoning limitations. The multi-model evaluation across varying sizes provides a useful comparative dimension, and the black-box framing aligns with practical deployment constraints. The approach draws on educational scaffolding concepts in a novel way for LLM probing.

major comments (2)

[§3 (STaD Framework)] The core assumption that STaD variations isolate specific compositional skill gaps (e.g., by adding incremental support) is load-bearing for the claim of mapping failures to unique model skill gaps, yet the manuscript provides no ablations, matched controls, or validation that performance deltas arise from the targeted composition rather than changes in prompt length, explicitness, or overall structure. This directly engages the weakest assumption identified in the stress-test.
[§4 (Experiments)] The experimental section reports failure points and distinct skill gaps across six models but supplies insufficient detail on task variation generation procedures, the exact three reasoning benchmarks used, quantitative metrics for gap identification, or error analysis. Without these, the strongest claim (unique skill gaps revealed by controlled variations) cannot be verified or reproduced.

minor comments (2)

[Abstract] The abstract is overly high-level and omits key methodological and quantitative details; expanding it to include brief descriptions of the benchmarks, metrics, and example variations would improve accessibility.
[§2 (Background)] Notation for skill compositions and scaffolding levels should be defined more explicitly early in the paper to aid readers in following the mapping from variations to claimed gaps.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the detailed review of our manuscript on the STaD framework. We value the feedback on the need for stronger validation and experimental details. We will undertake a major revision to incorporate ablations, controls, and expanded descriptions as outlined below.

read point-by-point responses

Referee: [§3 (STaD Framework)] The core assumption that STaD variations isolate specific compositional skill gaps (e.g., by adding incremental support) is load-bearing for the claim of mapping failures to unique model skill gaps, yet the manuscript provides no ablations, matched controls, or validation that performance deltas arise from the targeted composition rather than changes in prompt length, explicitness, or overall structure. This directly engages the weakest assumption identified in the stress-test.

Authors: We agree that demonstrating the isolation of compositional skill gaps is crucial for the framework's validity. The current version presents the STaD approach and its application but does not include explicit ablations. In the revised manuscript, we will add a dedicated ablation study with matched controls that vary prompt length, explicitness, and structure independently while keeping the core task constant. We will also include quantitative analysis and error categorization to show that observed performance deltas correspond to the specific scaffolding levels targeting compositional skills. revision: yes
Referee: [§4 (Experiments)] The experimental section reports failure points and distinct skill gaps across six models but supplies insufficient detail on task variation generation procedures, the exact three reasoning benchmarks used, quantitative metrics for gap identification, or error analysis. Without these, the strongest claim (unique skill gaps revealed by controlled variations) cannot be verified or reproduced.

Authors: We acknowledge the need for greater reproducibility and detail in the experimental section. The revised manuscript will expand §4 to fully describe the task variation generation procedures, explicitly identify the three reasoning benchmarks employed, specify the quantitative metrics used to identify gaps (such as performance thresholds across scaffolding levels), and provide a detailed error analysis breaking down model failures by skill composition. These additions will enable verification of the unique skill gaps observed across the six models. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical framework application with independent experimental observations

full rationale

The paper introduces the STaD framework by adapting the established educational concept of scaffolding to create controlled task variations, then reports direct experimental results from applying these variations to three standard reasoning benchmarks across six LLMs. No equations, fitted parameters, or derivations are present; claims about skill gaps follow from observed performance differences rather than reducing to any self-defined inputs or self-citation chains. The central argument is self-contained as an observational probing method without load-bearing premises that loop back to the paper's own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract describes a conceptual framework and high-level experiments without mathematical derivations, fitted parameters, or new postulated entities. It relies on the established educational concept of scaffolding but provides no explicit axioms or assumptions.

pith-pipeline@v0.9.0 · 5436 in / 1083 out tokens · 40936 ms · 2026-05-10T04:35:50.093894+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

91 extracted references · 2 canonical work pages · 1 internal anchor

[1]

Training Verifiers to Solve Math Word Problems

Training verifiers to solve math word prob- lems.arXiv preprint arXiv:2110.14168. Dheeru Dua, Shivanshu Gupta, Sameer Singh, and Matt Gardner. 2022. Successive prompting for decomposing complex questions.arXiv preprint arXiv:2212.04092. Bahare Fatemi, Mehran Kazemi, Anton Tsitsulin, Karishma Malkan, Jinyeong Yim, John Palowitch, Sungyong Seo, Jonathan Hal...

work page internal anchor Pith review Pith/arXiv arXiv 2022
[2]

arXiv preprint arXiv:2210.02406 , year=

Mistral - a journey towards reproducible lan- guage model training. Tushar Khot, Harsh Trivedi, Matthew Finlayson, Yao Fu, Kyle Richardson, Peter Clark, and Ashish Sab- harwal. 2022. Decomposed prompting: A modular approach for solving complex tasks.arXiv preprint arXiv:2210.02406. Douwe Kiela, Max Bartolo, Yixin Nie, Divyansh Kaushik, Atticus Geiger, Zhe...

work page arXiv 2022
[3]

Natural-language date/time parsing: Extract dates, times, and durations from varied textual expressions and formats
[4]

Unit conversion for time spans: Translate hours, minutes, seconds, days, weeks, months, and years into a common unit (e.g., total seconds) and back
[5]

Arithmetic on durations: Add, subtract, multiply, or divide time intervals, including scaling rates to larger quantities
[6]

Calendar arithmetic: Compute new dates by adding or removing days, weeks, months, or years, respecting month lengths and leap years
[7]

Leap-year and month-length handling: Determine the correct number of days in February and other months when performing date calculations
[8]

Time-zone conversion: Apply UTC offsets to convert times between zones and adjust the resulting day if needed
[9]

Day-of-week determination: Find the weekday for a given date or after a specified offset using modular arithmetic on a 7-day cycle
[10]

X days before/after Y

Relative-date reasoning: Interpret statements like “X days before/after Y” or “X weeks earlier” to locate the target date
[11]

Normalization of incomplete timestamps: Fill missing components (e.g., assume 00:00:00 for absent time) to create comparable datetime values
[12]

Chronological ordering of events: Sort a set of dates/times ascending or descending to identify earliest or latest occurrences
[13]

Extremum identification: Locate the maximum or minimum date/time among a collection (e.g., latest exam, earliest activity)
[14]

Overlap and intersection of time intervals: Determine common free periods among multiple schedules and compute their length
[15]

Discrete slot counting under constraints: Enumerate possible meeting or event slots that satisfy granularity rules (e.g., start on the hour or half-hour)
[16]

Midnight and date-boundary wrap-around: Correctly handle intervals that cross midnight or span month/year boundaries
[17]

16.Era linearization: Convert BC and AD years to a single numeric timeline for comparison

Multi-format date conversion: Translate between representations such as mm/dd/yyyy, yyyy-mm- dd, dd-Mon-yyyy, etc. 16.Era linearization: Convert BC and AD years to a single numeric timeline for comparison
[18]

Parsing and applying weekly cycles: Use recurring periods (e.g., every 19 days) to compute next occurrence from a reference date
[19]

Rate-based scaling: Derive per-unit time from a given total and apply it to a different quantity (e.g., time per box)
[20]

Structured JSON output generation: Assemble explanations and computed values into the required JSON schema with correct field names
[21]

before noon

Ambiguity resolution in temporal language: Disambiguate phrases like “before noon”, “same day”, or “earliest possible time” to select the appropriate interpretation. G.2 40 Skills in GSM8K
[22]

Extracting quantitative data from narrative text: Identify all numbers, entities, and relationships described in a word problem
[23]

Converting percentages to fractions or decimals: Translate percentage statements into usable numeric forms for calculation
[24]

4.Calculating a percentage of a quantity: Apply a percent to find part-of-a-whole values

Performing operations with fractions: Add, subtract, multiply, and divide fractional quantities accurately. 4.Calculating a percentage of a quantity: Apply a percent to find part-of-a-whole values
[25]

twice as many

Proportional reasoning: Set up multiplicative relationships based on comparative language (e.g., “twice as many”, “half as much”)
[26]

Formulating and solving simple linear equations: Turn a verbal condition into an equation and isolate the variable
[27]

at least

Formulating and solving basic inequalities: Use “at least”, “no more than”, etc., to create and solve inequality constraints
[28]

Using unit rates to compute totals: Multiply a per-unit value (price, speed, etc.) by a quantity to obtain a total amount
[29]

Multi-digit multiplication and division: Carry out accurate arithmetic with two- or three-digit numbers
[30]

Sequential quantity tracking: Update a running total through successive additions and subtractions
[31]

Converting between time units: Change minutes to hours or vice versa for combined-time calcula- tions
[32]

Area calculation for rectangles and aggregation: Compute length times width and sum multiple areas to find a total
[33]

Total cost from per-item price and quantity: Multiply unit price by number of items and sum across categories
[34]

Finding change or remaining amount after purchases: Subtract total expense from given money to obtain leftover funds
[35]

Rounding up when dividing into packs: Determine the smallest whole number of packs needed to cover a quantity
[36]

17.Profit calculation: Subtract total expenses from total sales to obtain net gain

Applying average rates to determine total output or time: Use a rate over a period to compute overall amount. 17.Profit calculation: Subtract total expenses from total sales to obtain net gain
[37]

Applying discount percentages to original prices: Reduce a price by a given percent and compute the discounted amount
[38]

Computing savings from price differences over time: Multiply per-unit savings by quantity and by number of periods
[39]

Inventory tracking over multiple days: Account for daily usage, additions, and removals to find initial or final stock
[40]

more than

Interpreting “more than” or “less than” relationships: Translate comparative statements into addition or subtraction equations
[41]

per” statements into multiplication: Convert expressions like “$X per hour

Translating “per” statements into multiplication: Convert expressions like “$X per hour” into a product of rate and time
[42]

Mixed-operation word problems with order of operations: Apply PEMDAS when several operations appear together
[43]

Substitution to solve for unknowns: Replace a variable with its known value to evaluate an expression
[44]

Consistent handling of mixed measurement units: Keep units (gallons, inches, miles, etc.) uniform throughout calculations
[45]

Calculating totals from grouped items: Multiply group size by members per group and sum across groups
[46]

Determining remaining quantity after consumption and distribution: Subtract used and given- away amounts from an initial total
[47]

Equal sharing of a total among participants: Divide a quantity evenly to find each person’s share
[48]

at least

Using “at least” conditions to find minimum required values: Set up an inequality and solve for the smallest feasible number
[49]

Converting dozens to individual units: Multiply a dozen count by 12 to obtain the exact number of items
[50]

Summing contributions from multiple sources: Add separate amounts (e.g., earnings, donations) to obtain a combined figure
[51]

Multiplicative scaling for unknown quantities: Represent “n times” relationships as multiplication in equations
[52]

34.Total weight determination: Sum the weights of all objects carried or listed

Distance calculation from speed and time segments: Multiply speed by each time interval and sum the distances. 34.Total weight determination: Sum the weights of all objects carried or listed
[53]

total minus known equals unknown

Using difference statements to isolate unknown quantities: Rearrange “total minus known equals unknown” relationships to solve
[54]

total of

Interpreting “total of” statements to set up equations: Translate “the total is X” into an equation linking component parts
[55]

per pack

Applying “per pack” pricing to compute overall cost: Multiply number of packs by price per pack, accounting for partial packs if needed
[56]

Calculating weekly or monthly earnings from hourly wages: Multiply hourly rate by total hours worked in the period
[57]

Solving mixture problems with weighted averages: Use weighted-average formulas to find unknown component values
[58]

G.3 20 Skills in Math-Hard

Budget allocation across multiple items under constraints: Distribute a fixed amount among purchases while respecting given limits. G.3 20 Skills in Math-Hard
[59]

Translating word problems into algebraic statements: Extract quantities, relationships, and constraints from prose and express them as equations or inequalities
[60]

Multi-step arithmetic with integers and fractions: Perform sequences of additions, subtractions, multiplications, and divisions accurately, including reduction of fractions
[61]

Combinatorial counting: Use binomial coefficients and factorial reasoning to enumerate selections, arrangements, and distributions
[62]

Inclusion-exclusion reasoning: Account for overlapping cases by adding and subtracting intersecting counts to obtain correct totals
[63]

Probability via counting: Compute probabilities by determining the number of favorable outcomes divided by total equally likely outcomes
[64]

Solving linear equations and systems: Isolate variables, substitute, and use elimination or matrix methods to find unknown values
[65]

Quadratic equation techniques: Factor, complete the square, or apply the quadratic formula to find real or complex roots
[66]

Converting repeating decimals to fractions: Set up algebraic equations for repeating blocks, solve for the unknown, and simplify to lowest terms
[67]

Arithmetic and geometric series analysis: Identify first term and common difference/ratio, use sum formulas, and test convergence for infinite series
[68]

Modular arithmetic and congruence solving: Work with residues, solve linear congruences, and apply the Chinese Remainder Theorem when needed
[69]

GCD and LCM via prime factorization: Decompose integers into primes to compute greatest common divisor and least common multiple efficiently
[70]

Absolute-value inequality manipulation: Split into casewise linear inequalities, solve each case, and intersect solution sets
[71]

Domain and range of functions: Impose non-negativity, non-zero denominator, and piecewise analysis to describe permissible inputs and outputs
[72]

Completing the square for optimization: Rewrite quadratic expressions as a perfect square plus constant to locate minima or maxima
[73]

Calculus-based optimization: Differentiate area, volume, or other expressions, set derivatives to zero, and verify extremal values
[74]

Vector orthogonality via dot and cross products: Compute cross products, take dot products, and set results to zero to enforce perpendicularity
[75]

Rayleigh quotient and eigenvalue maximization: Recognize quadratic forms, relate them to eigenvalues, and use the largest eigenvalue to obtain maximal ratios
[76]

Solving higher-degree polynomials: Apply substitutions, depressed-cubic forms, and Cardano’s formula to obtain exact roots
[77]

Lattice-point counting under distance constraints: Use integer solutions of circle equations (x2 +y 2 =r 2) to enumerate points satisfying a given distance
[78]

add and divide

Symmetry counting with Burnside’s Lemma: Identify group actions (rotations, reflections), count fixed configurations under each, and average to obtain distinct arrangements. H Prompts Sub-Task Decomposition You will be given a question that requires multiple reasoning or computational steps. Your task is to break down the instruction into explicit, step-b...
[79]

Ignore formatting differences (e.g., 2, "2", 2.0, answer: 2 should all be treated as the same)
[80]

Treat numbers written as words (e.g., two, forty-five) as equivalent to their numeric forms

Showing first 80 references.