PRISM: Demystifying Retention and Interaction in Mid-Training

• +15 to +40 points on math, +5 to +12 on code, and +6 to +13 on science benchmarks result from PRISM mid-training while general-purpose performance is preserved.These gains are observed across all tested models, with science gains reported for Granite and hybrid models.Source: §1 · p. 1
• From under 12 to 29–42, the full PRISM→RL pipeline raises macro-average performance across six reasoning benchmarks, whereas RL on base models leaves AIME near zero.This corresponds to a 3–4× improvement; the six benchmarks are AIME’24, AIME’25, MATH500, LiveCodeBench, Codeforces, and GPQA-Diamond.Source: §1 · p. 2
• +17 to +28 point GPQA-Diamond gains during RL are unlocked by including science data during mid-training, while changing the RL mix produces less than 2 point differences.Changing the mid-training mix from Math+Code to Math+Code+Science shifts AVG1 by +3 to +6 points.Source: §1 · p. 2
• PRISM benefits both dense Transformers and attention-Mamba hybrids from 3B to 24B parameters, and RL progressively solves initially unsolvable Granite-3.3 prompts with non-saturating curves.The cross-architecture and cross-scale scope is evaluated across seven base models from the Granite, LLaMA, Mistral, and Nemotron-H families.Source: §1 · pp. 1–2
• Mid-training densely restructures over 90% of parameters, whereas RL sparsely refines approximately 5% through front-loaded changes concentrated in the first approximately 200–400 steps.RL applies identical weight footprints regardless of whether mid-training preceded it, indicating distinct parameter-update patterns.Source: §1 · p. 2
• RL preserves mid-training’s representational geometry above 0.998 CKA across dense and hybrid architectures, while the full pipeline raises held-out MATH500 pass rates from 2.6–66.6% to 64.6–83.0%.Mid-training’s representational impact is model-specific, and its behavioral effect includes extended reasoning chains.Source: §1 · p. 2

Conceptual scope

• Prior work improves targeted coding and mathematical reasoning, but “mid-training” encompasses inconsistent strategies without a unified framework or standardized evaluation (Olmo et al., 2025; Wang et al., 2025).The literature includes long-context extension, data annealing, and domain-specific capability refinement.Source: §2 · p. 3

Evaluation limitations

• Narrow domain benchmarks can hide regressions in general capabilities, cross-domain robustness, and other reasoning dimensions (Wang et al., 2025; Abdin et al., 2024; OLMo et al., 2025).Long-context studies emphasize context-window scaling and retrieval, while domain-focused recipes emphasize math or code.Source: §2 · p. 3

RL interaction

• Prior studies rarely control how mid-training affects downstream RL across model families, domains, and benchmark suites (Wang et al., 2025; Zhang et al., 2025).Claims that mid-training facilitates RL are generally tested in narrow experimental settings.Source: §2 · p. 3

Concurrent work

• At 3B–24B scale, PRISM extends prior controlled work across four model families, two architecture types, and multi-stage pipelines including RL (Liu et al., 2025; Zhang et al., 2025).Concurrent studies provide distributional and mechanistic insights but do not address PRISM’s empirical coverage at this scale.Source: §2 · p. 3

Motivation

• PRISM addresses these gaps by evaluating mid-training choices across domains, benchmark axes, model families, and downstream RL behavior in a retention-aware framework.This scope is motivated by limitations in holistic evaluation and controlled studies of RL behavior.Source: §2 · p. 3

3 Data Mixtures for Mid-Training

• Tuned data mixtures balance general web and instruction data with domain-specific reasoning sources, yielding robust retention and consistent gains across experiments.The adopted mixtures are empirically validated for balancing broad pretraining knowledge with targeted domain improvements.Source: §3 · p. 4, §3.1 · p. 5
• Math and Code combine general web documents with domain-specific reasoning data, Science uses reasoning-focused datasets, and instruction data supports stable reinforcement learning across domains.The design includes DCLM-EDU general web data to retain broad pretraining knowledge while extending beyond math-focused reasoning.Source: §3 · p. 4

3.1 Dataset Preprocessing

• Preprocessing applies deterministic quality filtering, evaluator-based selection, deduplication, and conversation normalization across web, reasoning, chat, and instruction datasets.DCLM-EDU keeps documents scoring at least 3; OpenCodeReasoning-2 contributes 60k Python and 60k C++ examples after filtering; WildChat-1M retains GPT-4-generated conversations.Source: §3.1 · p. 4
• Three progressively richer configurations—Math-only, Math+Code, and Math+Code+Science—use tuned per-source sampling weights selected to balance retention and targeted improvements.These configurations and sampling percentages are summarized in Figure 2 and adopted as the default policy for all experiments.Source: §3.1 · pp. 4–5, Figure 2 · p. 5

• PRISM combines general leaderboards with long-context, code, math, and science evaluations so gains in one domain cannot conceal capability loss elsewhere.Table 2 summarizes the benchmark categories and their roles.Source: §4 · p. 5
• Effective benchmark selection mixes breadth and depth by pairing general-purpose leaderboards, LB-V1 and LB-V2, with targeted domain benchmarks.LB-V1 is attributed to Beeching et al. (2023), and LB-V2 to Fourrier et al. (2024).Source: §4 · p. 6
• Long-context reasoning should be measured explicitly because short-context-dominated mid-training can degrade long-context capabilities.RULER is given as an example, and a lightweight fine-tuning stage may be needed for recovery.Source: §4 · p. 6

• Phase 4 modestly improves Leaderboard V2 from 19.44 to 20.85 over Phase 3, but both earlier phases underperform the final base model on math and science.Earlier phases still produce meaningful improvements, while code performance remains similar between Phase 3 and Phase 4.Source: §5 · p. 6
• 23.59 AIME24, 77.44 MATH500, 10.39 LiveCodeBench, and 25.93 GPQA-Diamond are achieved when mid-training follows long-context extension.This timing produces the best overall performance and exceeds both earlier phases on the reported benchmarks.Source: §5 · p. 6, Table 3 · p. 6
• General-purpose leaderboards remain relatively stable across timing choices, indicating that later mid-training does not cause large regressions in broad capabilities.The strongest cross-domain gains therefore occur without materially reducing general performance.Source: §5 · p. 6
• The timing result is preliminary because it uses one 3B model, and post-long-context models may be stronger starting points, confounding timing with base-model quality.Post-long-context mid-training is consequently a reasonable practical default rather than a proven universal ordering across scales or architectures.Source: §5 · p. 6

6 Domain-wise Effects of Mid-Training Data

• +27.48 points raises Math average from 8.95 to 36.43 with Math-only data, while Math+Code+Science raises GPQA-Diamond from 19.02 to 29.12 (+10.10) without sacrificing math or code gains.Balanced mixtures deliver the best overall trade-off: broader coverage improves domain reasoning while preserving general capabilities, though individual regressions such as approximately 5 points on HellaSwag remain.Source: §6 · p. 7, Table 5 · p. 7, Appendix Table 19 · p. 7

7 PRISM Effects Across Model Families

• Across dense and hybrid model families, PRISM mid-training improves mathematical, coding, and scientific reasoning, while general-purpose leaderboard changes are smaller and more model dependent.Examples include Mistral-7B MATH500 improving from 1.68 to 70.71 and Codeforces from 0.15 to 9.42, and Nemotron-H MATH500 from 49.46 to 76.63.Source: §7 · pp. 8–9

8.1 Restoring Long-Context Ability After Mid-Training

• 42.16 RULER@128k is recovered after a 15% base plus 85% mid-trained merge followed by long-context extension, while Code Avg reaches 25.54 and Math Avg 44.48.Direct 1k-step extension raises RULER@128k from 6.46 to 38.41 with full-parameter training, but the base-model merge gives the strongest recovery; attention-only training remains a practical efficiency/performance trade-off.Source: §8.1 · pp. 9–10, Figure 3 · p. 10

8.2 Effect of Mid-Training Context Length

• Increasing context from 8k to 16k improves MATH500 from 79.40 to 82.47 (+3.07), AIME24 from 27.19 to 31.82 (+4.63), Codeforces from 6.25 to 8.90 (+2.65), and GPQA-Diamond from 34.34 to 38.89 (+4.55), with gains largely saturating beyond 16k.Extending to 32k yields a small LiveCodeBench improvement from 12.19 to 14.93, while 16k provides the most favorable balance between reasoning gains and training efficiency.Source: §8.2 · pp. 10–11

8.3 Effect of Mid-Training Token Budget

• At 10.49B tokens, Math Avg rises from 26.28 to 40.21 (+13.93) and Code Avg reaches 9.59; most benefits are realized within approximately 15B to 27B tokens.Beyond 26.21B tokens, Math Avg remains nearly constant while Code Avg declines from 8.69 to 7.62 at 31.46B, with leaderboard scores stable.Source: §8.3 · p. 11, Table 9 · p. 11

9 Effects of Reinforcement Learning on Mid-Trained Models

• The PRISM→RL pipeline raises the six-benchmark macro-average from under 12 to 29–42, whereas RL on base models leaves most AIME scores near zero and finishes approximately 37 math, 14 code, and 5 science points lower for Granite-3.3.Including science during mid-training unlocks +17 to +28 GPQA-Diamond points during RL; base-model RL can also regress GPQA-Diamond for LLaMA-3.1 and Mistral-7B.Source: §9 · p. 11, §9.3 · pp. 13–14

9.1 RL Setup: Data, Filtering, and Mixes

• The RL setup uses balanced and unbalanced math-code-science mixes, with the unbalanced mix filtering Granite-3.3 prompts to 19k hard math, 7k code, and 17k science examples.Despite domain imbalance, the unbalanced mix produces strong improvements across reasoning benchmarks, while the balanced mix equalizes domains to 19k prompts and adds randomized science instruction templates.Source: §9.1 · pp. 11–12, Table 10 · p. 11

9.2 RL on PRISM: Consistent Gains Across Models

• +27.95 GPQA-Diamond points is the largest reported RL gain, while RL on PRISM checkpoints also improves coding by up to +10.30 and math benchmarks by 3–10.74 points across models.The PRISM→RL curves often continue improving late in training rather than cleanly saturating, and gains transfer to the held-out AIME 2026 benchmark.Source: §9.2.1 · p. 12, Figure 5 · p. 13, §9.2.2 · p. 13

9.3 PRISM vs Base Models: Mid-Training is Essential for RL

• RL on base models yields limited, unstable gains, whereas RL on PRISM checkpoints produces large, stable, monotonic improvements, including for Nemotron-H despite its stronger base initialization.Nemotron-H shows some base-model progress, but its gap from PRISM→RL remains substantial.Source: §9.3 · p. 14

9.4 Balanced vs Unbalanced RL Mix

• Balanced RL produces comparable math and code gains to the unbalanced mix, with Granite-4 Micro gains reaching +4.63 AIME24, +3.07 AIME25, and +6.06 GPQA-Diamond.Science effects are model-dependent: Granite-4 variants benefit more from balanced RL, while Mistral-Small 24B achieves higher GPQA-Diamond with unbalanced RL (+27.95 versus +25.93).Source: §9.4 · p. 15

9.5 RL Expands the Solvability Frontier

• RL expands the solvability frontier: initially unsolved code prompts and hardest math prompts show steadily increasing pass rates during training.This indicates that RL learns new problem-solving strategies beyond mid-training rather than merely polishing already-solvable problems.Source: §9.5 · p. 16, Figure 10 · p. 16

9.6 The Full Pipeline: Broader RL Analysis

• +13.84 to +18.29 AVG points from mid-training and +8.36 to +12.28 from RL yield a combined improvement from under 12 to 29–42, or 3–4×.Across LLaMA, Granite-3.3, and Mistral, mid-training produces the largest single-stage jump, while RL consistently adds a second-stage boost.Source: §9.6.1 · p. 17

9.6.2 Science data at mid-training unlocks large RL gains on GPQA.

• MCS mid-training enables GPQA-Diamond scores of 52.86 for Granite-3.3, 36.03 for LLaMA, and 41.75 for Mistral, substantially above corresponding MC configurations.The gains persist even when RL is not science-heavy, indicating that science data during mid-training supplies representations that RL can leverage.Source: §9.6.2 · p. 17

9.6.3 RL data mix matters less than mid-training mix.

• Switching RL from MC to MCS changes AVG by typically less than 2 points, whereas switching mid-training from MC to MCS shifts AVG by +3 to +6 points.For Granite-3.3, RL-mix switching changes AVG by −0.21, while mid-training-mix switching increases it by +5.60, showing that RL primarily amplifies established capabilities.Source: §9.6.3 · p. 18

10.1 Weight-Level Analysis: Dense Restructuring vs. Sparse Refinement

• Mid-training changes over 90% of parameters with 370–580× larger weight divergence, while RL changes approximately 5% and leaves over 93% of weights within 1% of mid-trained values.The dense-versus-sparse pattern holds across dense and attention-Mamba architectures and across component types.Source: §10 · p. 19, §10.1 · pp. 19–20, Figure 11 · p. 20

10.2 Representation Similarity Across Pipeline Stages

• MT-versus-RL CKA exceeds 0.998 across three models and three input types, showing that RL preserves mid-training’s representational geometry while improving performance within it.RL makes nearly identical weight changes from base and mid-trained starting points, yet succeeds primarily after mid-training, indicating that the starting configuration matters.Source: §10 · p. 19, §10.1 · pp. 21–22, §10.2 · p. 23
• >0.998 minimum CKA shows that RL consistently preserves mid-training’s representational geometry across three models, three input types, and dense and hybrid architectures.Mid-training’s divergence is model- and input-specific: for example, Granite-3.3 reaches CKA ≈0.63 on GSM8K, Nemotron-H ≈0.41 at a later GSM8K layer, and LLaMA ≈0.71 on C4.Source: §10.2 · pp. 23–24, Table 14 · p. 24

10.3 Prediction Confidence and Correctness Across Pipeline Stages

• 16.9%→79.5%, 2.6%→64.6%, and 66.6%→83.0% are the Granite-3.3, LLaMA, and Nemotron-H MATH500 pass-rate improvements from base to the full pipeline.Mid-training expands responses into multi-step reasoning chains, while RL improves over mid-training alone and can recover Nemotron-H’s mid-training regression.Source: §10.3 · pp. 24–25

10.4 RL Weight Trajectory: Front-Loaded Optimization

• ∼200–400 steps contain most RL weight divergence, while the changed-parameter fraction grows from ∼1.5% at step 20 to ∼5–6% by step 960.MT→RL and Base→RL have nearly identical trajectories, with final divergence differing by less than 20% and sparsity converging within 1 percentage point.Source: §10.4 · pp. 26–27, Figure 16 · p. 26

11 Conclusion and Future Work

• +15 to +40 math points, +5 to +12 code points, and +6 to +13 science points result from ∼27B-token mid-training, while the full pipeline raises six-benchmark macro-average from under 12 to 29–42.Science data during mid-training unlocks +17 to +28 GPQA-Diamond points during RL, whereas changing the RL mix produces <2-point differences; mid-training restructures >90% of parameters and RL refines ∼5%.Source: §11 · pp. 27–28

Appendix

• The appendix covers model specifications, benchmarks, extended results, GRPO training details, learning curves, mechanistic analyses, AIME 2026 evaluation, and qualitative generations.It includes long-context restoration hyperparameters and supplementary analyses across four models and three input distributions.Source: Appendix · p. 35, Table 17 · p. 35

A.1 Model Specifications

• The study evaluates 3B–24B dense Transformer and attention-Mamba hybrid models, including LLaMA-3.1, Mistral, Granite, Mistral-Small, and Nemotron-H variants.The model set is intended to evaluate PRISM’s cross-architecture robustness.Source: §A.1 · p. 35

A.2 PRISM Training Details

• PRISM mid-training uses shared training hyperparameters across models unless otherwise specified.Table 16 summarizes these settings.Source: §A.2 · p. 35

A.3 Long-Context Extension Phase

• The long-context extension phase applies after mid-training and uses dedicated hyperparameters and datasets.Tables 17 and 18 summarize the phase settings and its datasets, respectively.Source: §A.3 · p. 36
• Best-Fit Decreasing packing sorts chunks by length and greedily fills the feasible buffer with minimal remaining capacity.Overlong documents may be split into overlapping chunks, while the strategy reduces truncation and wasted capacity and preserves document coherence.Source: §A.3 · p. 36

B Evaluation Details

• Evaluation covers general ability with LB-V1 and LB-V2, long-context reasoning with RULER, contamination-free code with LiveCodeBench and Codeforces, mathematics with AIME and MATH500, and science with GPQA-Diamond.These benchmark suites target generalization regressions, massive-context reasoning, algorithmic coding, mathematical proficiency, and PhD-level science questions.Source: B Evaluation Details · p. 36
• Math evaluations use 32k maximum generation tokens, temperature 0.6, top-p 0.95, and 64 samples per prompt.MATH500 and AIME24/25 are evaluated with Qwen-eval (Yang et al., 2024).Source: B Evaluation Details · p. 36
• Code evaluations use 32k maximum generation tokens, temperature 0.7, and 3 samples per prompt, while RULER uses HELMET (Yen et al., 2025).Codeforces and LiveCodeBench are evaluated with Evalchemy.Source: B Evaluation Details · p. 36

Domain ablation

• Table 19 reports per-benchmark results for the Granite-3.3-8B domain ablation across Math only, Math+Code, and Math+Code+Science.The table complements the summary presented in Section 5.Source: C Extended Results Tables · p. 36

Token-budget scaling

• Table 20 reports how Granite-4 Micro (3B) performance evolves as the mid-training budget increases from 10.5B to 31.5B tokens.Source: C Extended Results Tables · p. 36

• The section consolidates detailed results underlying the paper’s main-text comparisons.Source: C Extended Results Tables · p. 36

• GRPO (Shao et al., 2024) is used as the RL algorithm for all models.The paper specifies the objective and advantage computation for this algorithm.Source: D RL Training Details · p. 36
• The training configuration uses on-policy updates, soft reference-policy updates, and Truncated Importance Sampling.Train and inference batch sizes are equal, while soft updates support convergence and importance sampling controls training–inference mismatch.Source: D RL Training Details · p. 37
• A response receives correctness reward only when formatted as <think> thoughts </think> response; stop-token and repetition penalties are also applied.Responses violating the required thinking format receive reward 0.0.Source: D RL Training Details · p. 37
• All experiments use the open-instruct codebase.Source: D RL Training Details · p. 37

E RL Training Curves for Granite-4 Micro Dense

• ∼0.48→∼0.72 overall correctness over 2k steps demonstrates stable RL training for 3B Granite-4 Micro Dense after PRISM mid-training.Math rises ∼0.52→∼0.70, science ∼0.45→∼0.78, and code ∼0.35→∼0.65.Source: E RL Training Curves for Granite-4… · pp. 37–38, Figure 17 · p. 38
• The 3B model’s domain curves improve monotonically across math, science, and code, confirming PRISM as a stable RL foundation at small scale.The reported trajectories remain steadily improving rather than indicating instability or saturation.Source: E RL Training Curves for Granite-4… · pp. 37–38

F Additional RL Learning Curves

• Additional appendix curves cover PRISM RL, base-model RL, and balanced-mix RL experiments for models omitted from the main text.These learning-curve groups are presented in Figures 18–25.Source: F Additional RL Learning Curves · p. 38

F.1 PRISM RL: Additional Models

• Mistral-7B, LLaMA-3.1-8B, and Granite-4 Micro Dense show monotonically increasing correctness across math, code, and science benchmarks.Figures 18–20 provide PRISM RL curves for these additional models.Source: §F.1 · p. 38
• Non-saturating trajectories across the additional models indicate that PRISM→RL benefits generalize across model families and scales.This extends the pattern observed for Granite-3.3-8B in the main paper.Source: §F.1 · pp. 38–39
• Figure 18 reports consistent code and math improvements for Mistral-7B using the unbalanced MCS mix.The displayed benchmarks include LiveCodeBench, Codeforces, AIME24, AIME25, and MATH500.Source: Figure 18 · p. 39

F.2 RL on Base Models (No Mid-Training)

• AIME24 and AIME25 remain near zero under direct RL on LLaMA-3.1-8B and Mistral-7B, while GPQA-Diamond stagnates or regresses.This contrasts with the large, sustained gains observed when RL follows PRISM mid-training.Source: §F.2 · p. 39, Figure 21 · p. 41
• The failure of direct RL on base models reinforces that mid-training provides the reasoning substrate required for RL to become effective.This interpretation follows the contrast between near-zero or regressing base-model results and gains after PRISM mid-training.Source: §F.2 · p. 39

F.3 Balanced Mix RL: Additional Models

• +8.09 on Codeforces and +11.95 on GPQA-Diamond are achieved by Granite-4-H Micro under balanced-mix RL.Across most additional models, balanced RL produces comparable overall gains to the unbalanced mix, with modest domain-specific differences.Source: §F.3 · p. 39
• Balanced-mix RL yields the largest small-model improvements for Granite-4-H Micro, suggesting hybrid architectures respond well to domain-balanced training.The reported gains are +8.09 on Codeforces and +11.95 on GPQA-Diamond.Source: §F.3 · p. 39

G Sparsity Threshold Sensitivity

• Even at the 0.1% threshold, 82.3% of RL parameters remain unchanged, whereas mid-training remains broadly distributed across parameters.These findings support the robustness of the sparsity conclusions to threshold choice.Source: G Sparsity Threshold Sensitivity · pp. 39, 41
• At the 1% threshold, RL leaves 95.0% of Granite-3.3 parameters unchanged, while mid-training changes the vast majority.Table 22 shows this dense/sparse asymmetry across thresholds from 0.1% to 10%.Source: G Sparsity Threshold Sensitivity · pp. 39, 41, Table 22 · p. 41

• RL’s sub-component targeting is nearly identical with or without mid-training, with condition differences of at most 1.8 percentage points and most below 1 point.The analysis covers attention Q, K, V, and O projections; MLP gate, up, and down projections; and Mamba in_proj, out_proj, conv1d, A, and dt parameters.Source: H RL Sub-component Weight Analysis · p. 41
• Value and output projections are most affected during RL: Granite-3.3 shows 5.7% and 5.6% changed, while Nemotron-H shows 8.5% and 7.2%.These changes suggest RL preferentially adjusts how models read from and write to the residual stream.Source: H RL Sub-component Weight Analysis · p. 42
• Mamba A and dt parameters remain effectively frozen at <0.1% changed, while in_proj and out_proj change at rates comparable to attention projections.This pattern indicates that RL respects the architectural priors encoded in SSM state dynamics while modifying learned projection matrices.Source: H RL Sub-component Weight Analysis · p. 42

I Extended CKA Representation Analysis

• The analysis compares Base vs. MT, Base vs. RL, and MT vs. RL using mean-pooled hidden representations from 200 prompts per input type across Wikipedia, C4, and GSM8K.It covers Granite-3.3, LLaMA-3.1, and Nemotron-H, with CKA=1.0 denoting identical representational geometry.Source: I Extended CKA Representation Analysis · p. 42
• CKA between mid-trained and RL models remains above 0.998 at every layer across all three input distributions and both dense Transformer and attention-Mamba architectures.Base-versus-RL and Base-versus-mid-training similarities are nearly identical, indicating that RL adds no additional representational shift.Source: I Extended CKA Representation Analysis · p. 42
• Mid-training’s representational divergence from the base model is model-specific: Granite-3.3 dips most at the GSM8K output layer, LLaMA-3.1 on C4, and Nemotron-H across later middle layers.These patterns depend on what each base model learned during pretraining rather than following a universal profile.Source: I Extended CKA Representation Analysis · p. 42

J AIME 2026 Evaluation

• AIME 2026 accuracy rose from ∼33% to ∼37% for Granite-3.3 (8B) and from ∼30% to ∼38% for Mistral-Small (24B) during RL training.AIME 2026 was published after all training runs, so the gains transfer to a held-out math benchmark unseen during training.Source: J AIME 2026 Evaluation · p. 43

K Model Generations

• Across math, code, and science prompts, mid-training introduces structured reasoning and RL further refines chains into more accurate, complete solutions.The examples compare base, mid-trained, and RL outputs from Granite-3.3-8B.Source: K Model Generations · p. 43

K.1 Math Prompt

• The math prompt asks for the dealership’s total cars given 60% hybrids, 40% one-headlight hybrids, and 216 hybrids with full headlights.The requested output format is boxed notation.Source: §K.1 · p. 44

K.2 Granite 3.3 8b base math generation

• The base model gives an incorrect answer after rushing to the conclusion in 192 tokens, without reasoning through the intermediate steps.The supplied passage identifies the correct answer as 600.Source: §K.2 · p. 44

K.3 Granite 3.3 8b midtrain math generation

• Mid-training produces the correct math answer through explicit step-by-step reasoning, using 933 tokens before reaching the final result.The generated reasoning decomposes the percentages and checks the resulting value.Source: §K.3 · pp. 46–48

K.4 Granite 3.3 8b PRISM−> RL math generation

• RL also gives the correct math answer, using 917 tokens and presenting a step-by-step derivation that verifies the result.The final generated answer is 600.Source: §K.4 · pp. 49–50

K.5 Code Prompt

• The coding prompt requires finding a point inside a convex polygon such that every line through it divides the polygon into equal areas.Inputs are integer polygon vertices, and outputs must meet 0.0001 coordinate accuracy or return NA if no point exists.Source: §K.5 · pp. 50–51

K.6 Granite 3.3 8b base code generation

• On the coding task, the base model jumps to a final answer without reasoning and uses 246 tokens.The supplied code excerpts show an attempted coordinate-averaging approach.Source: §K.6 · p. 52

K.7 Granite 3.3 8b midtrain code generation

• The mid-trained model remains unable to solve the coding problem, exhausting its 8k context limit after entering a repeating loop.Its response incorrectly identifies the centroid and proposes averaging vertex coordinates.Source: §K.7 · pp. 52–53
• The mid-trained code-generation output initially claims an oversimplified centroid property, then acknowledges the limitation and supplies corrected convex-polygon code.The correction states that the centroid is always inside for convex polygons but not necessarily for concave polygons.Source: §K.7 · p. 53

K.8 Granite 3.3 8b PRISM−> RL code generation

• The RL-trained code-generation model produces a correct solution using 7864 tokens, and its sorted partner check works on the tested polygon cases.The reasoning tests an odd-vertex case, a rectangle producing (1,1), and a regular hexagon producing (1.5, 1.5).Source: §K.8 · pp. 54–56

K.9 Science Prompt

• The science prompt asks which environmental process primarily depletes oxygen in water bodies, creates dead zones, and involves excessive algae growth from nutrient pollution.The listed choices include C: Eutrophication.Source: §K.9 · p. 57

K.10 Granite 3.3 8b base science generation

• 1185 tokens: The base model enters a repeating loop on the science prompt instead of providing a concise answer.The prompt asks which process causes oxygen depletion and dead zones through excessive algae growth.Source: §K.10 · p. 57, §K.9 · p. 57

K.11 Granite 3.3 8b midtrain science generation

• Max 16384 tokens: The mid-trained model enters an infinite loop, although it repeatedly outputs C: Eutrophication for the science question.Its repeated answer identifies the option describing nutrient pollution, algae growth, and oxygen depletion.Source: §K.11 · pp. 59–61

K.12 Granite 3.3 8b PRISM−> RL science generation

• 811 tokens: The RL-trained model gives the correct science answer, far fewer than the base and mid-trained models use.The answer is C: Eutrophication, which describes nutrient-driven algae growth and oxygen depletion leading to dead zones.Source: §K.12 · pp. 61–62
• Eutrophication is identified as the environmental process responsible for oxygen depletion in water bodies and resulting dead zones.The generation selects answer C.Source: §K.12 · p. 62
• Excess nitrogen or phosphorus causes algal blooms whose decomposition consumes oxygen, creating hypoxic dead zones where aquatic life cannot survive.Source: §K.12 · p. 62
• Photochemical smog, biomagnification, and methane oxidation do not directly cause oxygen depletion in this context.Source: §K.12 · p. 62