In November 2023, the Financial Accounting Standards Board, or FASB, issued a new accounting standard requiring disclosures of significant expenses in operating segments. We adopted this standard in our fiscal year 2025 annual report. Refer to Note 16 of the Notes to the Consolidated Financial Statements in Part IV, Item 15 of this Annual Report on Form 10-K for further information.
Recent Accounting Pronouncements Not Yet Adopted
In December 2023, the FASB issued a new accounting standard which includes new and updated income tax disclosures, including disaggregation of information in the rate reconciliation and income taxes paid. We expect to adopt this standard in our fiscal year 2026 annual report. We do not expect the adoption of this standard to have a material impact on our Consolidated Financial Statements other than additional disclosures.
In November 2024, the FASB issued a new accounting standard requiring disclosures of certain additional expense information on an annual and interim basis, including, among other items, the amounts of purchases of inventory, employee compensation, depreciation and intangible asset amortization included within each income statement expense caption, as applicable. We expect to adopt this standard in our fiscal year 2028 annual report. We do not expect the adoption of this standard to have a material impact on our Consolidated Financial Statements other than additional disclosures.
Note 2 - Business Combination
Termination of the Arm Share Purchase Agreement
In February 2022, NVIDIA and SoftBank Group Corp, or SoftBank, announced the termination of the Share Purchase Agreement whereby NVIDIA would have acquired Arm from SoftBank. The parties agreed to terminate it due to significant regulatory challenges preventing the completion of the transaction. We recorded an acquisition termination cost of $1.4 billion in fiscal year 2023 reflecting the write-off of the prepayment provided at signing.
Note 3 - Stock-Based Compensation
Stock-based compensation expense is associated with RSUS, PSUs, market-based PSUs, and our ESPP.
Consolidated Statements of Income include stock-based compensation expense, net of amounts capitalized into inventory and subsequently recognized to cost of revenue, as follows:
Table 1 Composition of the pretraining data for OLMo 2. The OLMo 2 1124 Mix is composed of StarCoder (Li et al., 2023b; Kocetkov et al., 2022), peS2o (Soldaini and Lo, 2023), web text from DCLM (Li et al., 2024) and Wiki come from Dolma 1.7 (Soldaini et al., 2024). arXiv comes from Red-Pajama (Together AI, 2023), while OpenWebMath (Paster et al., 2023) and Algebraic Stack come from ProofPile II (Azerbayev et al., 2023).
## 2.1.1 Pretraining data: OLMo 2 Mix 1124
The mix used for this stage is shown in Table 1. It consists of approximately 3.9 trillion tokens, with over 95% derived from web data. We refer to this set as OLMo 2 Mix 1124. This is the same pretraining data used in OLMoE (Muennighoff et al., 2024).
We combine data from DCLM (Li et al., 2024) and Dolma 1.7 (Soldaini et al., 2024). From DCLM, we use the “baseline 1.0" mix. From Dolma, we use the arXiv (Together AI, 2023), OpenWebMath (Paster et al., 2023), Algebraic Stack, peS2o (Soldaini and Lo, 2023), and Wikipedia subsets. arXiv, OpenWebMath, and Algebraic Stack were originally part of ProofPile II (Azerbayev et al., 2023).
Finally, we include code from StarCoder (Li et al., 2023b), which is derived from permissively-licensed repositories from GitHub (Kocetkov et al., 2022). In an attempt to include higher quality code, we remove any document from a repository with fewer than 2 stars on GitHub. Further, through manual inspection of this source, we found it to contain documents encoded in binary format or containing mostly numerical content; to remove them, we discarded documents whose most frequent word constitutes over 30% of the document, or whose top-2 most frequent words constitute over 50% of the document. To mitigate possible training loss spikes, we remove documents with repeated sequences of 32 or more n-grams. We report details and show effectiveness of this intervention in Section §3.1.
## 2.1.2 Mid-training data: Dolmino Mix 1124
After the initial pretraining stage on mostly web data, we further train with a mixture of web data that has been more restrictively filtered for quality and a collection of domain-specific high quality data, much of which is synthetic. The purpose of this mixture is to imbue the model with math-centric skills and provide focused exposure to STEM references and high quality text. We generate several variants of this mixture, with varying sizes, but generally refer to this mixture as Dolmino Mix 1124. The base sources from which Dolmino Mix 1124 is subsampled are described in Table 2. We refer the reader to Section §4 for a deep dive detailing our processes for experimenting and curating data for this mix.
Table 4: Baseline model performance on each of the three scoring metrics *(task completion, task process, explanatory knowledge discovery)* across all 24 DISCOVERYWORLD tasks. Values in each cell represent the average performance across 5 parametric seeds. *Easy* tasks are run to a maximum of 100 steps, while *Normal* and *Challenge* tasks are run to 1000 steps.
Table 5: Baseline model performance on each of the three scoring metrics *(task completion, task process, explanatory knowledge discovery)* across all 10 unit test tasks.Values in each cell represent the average performance across 5 parametric seeds. Unit tests tasks are run to a maximum of 100 steps.
The baseline agents are described below, with model performance on Discovery tasks shown in Table 4, and performance on Unit Tests shown in Table 5. We use the GPT-4O model for all our agents due to its higher performance and lower cost compared to other models. For space we provide
In November 2023, the Financial Accounting Standards Board, or FASB, issued a new accounting standard requiring disclosures of significant expenses in operating segments. We adopted this standard in our fiscal year 2025 annual report. Refer to Note 16 of the Notes to the Consolidated Financial Statements in Part IV, Item 15 of this Annual Report on Form 10-K for further information.
#### **Recent Accounting Pronouncements Not Yet Adopted**
In December 2023, the FASB issued a new accounting standard which includes new and updated income tax disclosures, including disaggregation of information in the rate reconciliation and income taxes paid. We expect to adopt this standard in our fiscal year 2026 annual report. We do not expect the adoption of this standard to have a material impact on our Consolidated Financial Statements other than additional disclosures.
In November 2024, the FASB issued a new accounting standard requiring disclosures of certain additional expense information on an annual and interim basis, including, among other items, the amounts of purchases of inventory, employee compensation, depreciation and intangible asset amortization included within each income statement expense caption, as applicable. We expect to adopt this standard in our fiscal year 2028 annual report. We do not expect the adoption of this standard to have a material impact on our Consolidated Financial Statements other than additional disclosures.
# **Note 2 - Business Combination**
#### **Termination of the Arm Share Purchase Agreement**
In February 2022, NVIDIA and SoftBank Group Corp, or SoftBank, announced the termination of the Share Purchase Agreement whereby NVIDIA would have acquired Arm from SoftBank. The parties agreed to terminate it due to significant regulatory challenges preventing the completion of the transaction. We recorded an acquisition termination cost of \$1.4 billion in fiscal year 2023 reflecting the write-off of the prepayment provided at signing.
# **Note 3 - Stock-Based Compensation**
Stock-based compensation expense is associated with RSUs, PSUs, market-based PSUs, and our ESPP.
Consolidated Statements of Income include stock-based compensation expense, net of amounts capitalized into inventory and subsequently recognized to cost of revenue, as follows:
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$\text{Proof. Let } \mathcal{S} \text{ be the generating set associated with } D \text{ as described in Proposition 2.5. By} $ $\text{the circulant diagonalization theorem, the spectrum of } G\_\mathbb{R}(D) = \Gamma(\mathbb{R}, \mathbb{S}) \text{ is the multiset} $ $\{\lambda\_{\mathcal{S}}\}\_{\mathcal{S}\in\mathcal{R}}\text{ where} $
$\text{We remark that by Corollary 2.7, if } \mathbf{s} \in \mathbb{R} \text{ such that } \mathbf{R}\mathbf{s} = \mathbb{Z}\_{\mathbf{i}} = \mathbf{R}\mathbf{x}\_{\mathbf{i}} \text{ then } \mathbf{s} \text{ has a unique} $ $\text{representation of the form } s = \mathfrak{l}x\_{\mathbb{I}} \text{ where } u \in (\mathbb{R}/\text{Ann}\_{\mathbb{R}}(x\_{\mathbb{I}}))^{\times} \text{ and } \mathfrak{l} \text{ is a fixed lift of } u $ $\text{to } \mathbb{R}^\times. \text{ With this presentation, we can write} $
$\text{Here we recall that } \psi\_{\mathbf{x}\_i} \text{ is the induced linear functional on } \mathbb{R}/\text{Ann}\_{\mathbb{R}}(\mathbf{x}\_i). \text{ We conclude} $ $\text{that } \lambda\_{\mathcal{S}} = \sum\_{i=1}^{k} $ *c*(*g*, *R*/Ann*R*(*xi*)). □
The following corollary is simple yet important for our future work on perfect state transfers on gcd-graphs.
$\textbf{Corollary 4.17.}\text{ Suppose that }\mathsf{g'} = \mathsf{ug}\text{ for some }\mathsf{u}\in\mathsf{R}^\times.\text{ Then }\lambda\_{\mathcal{S}} = \lambda\_{\mathcal{g'}}. $
## ACKNOWLEDGEMENTS
We thank the Department of Mathematics and Computer Science at Lake Forest College for their generous financial support through an Overleaf subscription. We also thank Jan Min ´ a´c for his constant encouragement and support. ˇ
## REFERENCES
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- 3. Maria Chudnovsky, Michal Cizek, Logan Crew, Jan Min ´ a´c, Tung T. Nguyen, Sophie Spirkl, and ˇ Nguyen Duy T ˆ an, ˆ *On prime Cayley graphs*, arXiv:2401.06062, to appear in Journal of Combinatorics (2024).
- 4. Thomas Honold, *Characterization of finite frobenius rings*, Archiv der Mathematik **76** (2001), no. 6, 406– 415.
- 5. Irving Kaplansky, *Elementary divisors and modules*, Transactions of the American Mathematical Society **66** (1949), no. 2, 464–491.
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- 9. , *On the gcd graphs over polynomial rings*, arXiv preprint arXiv:2409.01929 (2024).
## **The 20 Most Important Mathematical Equations**
A journey through the most elegant and influential formulas in mathematics
**1. Euler's Identity** $\text{Contextsts } \text{five } \text{fundamental} \text{ constraints (e, i, n, 1, 0), } \text{revezling the} $ profound relationship between exponential functions and trigonometry. **3. The Fundamental Theorem of Calculus** Establishes that differentiation and integration are inverse operations. If F is an antiderivative of f, the definite integral $\text{еquals } \mathsf{F}(\mathsf{b}) \text{ - } \mathsf{F}(\mathsf{a}). \text{ Веvolutionized паўнепайсаl то problem-so/wing.} $ **2. Pythagorean Theorem 4. Maxwell's Equations***e* + *iπ* 1 = 0 ∫ *f*(*x*) *dx* = *a b F*(*b*) − *F*(*a*) $a^2 + b^2 = c^2 $ <sup>2</sup><sup>∇</sup><sup>⋅</sup>**<sup>E</sup>**<sup>=</sup>*ρ*
In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture.
Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones.
## **The 20 Most Important Mathematical Equations**
A journey through the most elegant and influential formulas in mathematics
**1. Euler's Identity** $\text{Contextsts five fundamental constraints (e., i., 7, 0), reveziling} $ the profound relationship between exponential functions and trigonometry. **2. Pythagorean Theorem** In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture. *e* + *iπ* 1 = 0 *a* + $c^2 + b^2 = c^2 $
Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones.
