機械学習例文

1. **The model’s performance is far from optimal.**  
2. **Who knows what data the AI will process next?**  
3. **This algorithm would be the last one to produce biased results.**  
4. **The AI system knows better than to overfit on a small dataset.**  
5. **Each neuron adjusted its weight so that the network could minimize the loss.**  
6. **The dataset was so large that it took hours to process.**  
7. **It was such a complex model that training required significant computation.**  
8. **Save model checkpoints in case of unexpected failures.**  
9. **He stored the training logs lest the model performance degrade.**  
10. **On completing pretraining, the model was fine-tuned on a new dataset.**  
11. **As soon as the loss converged, the optimizer stopped updating parameters.**  
12. **The algorithm had hardly started when the GPU utilization spiked.**  
13. **No sooner had we increased the batch size than training stabilized.**  
14. **We had not waited long before the model showed promising results.**  
15. **It was last week that we deployed the AI system.**  
16. **What we need is high-quality labeled data, not just more samples.**  
17. **All you have to do is fine-tune the pretrained model.**  
18. **You can build whatever architecture you want for your deep learning model.**  
19. **Little did I expect the model to generalize so well.**  
20. **So complex was the dataset that additional preprocessing was required.**  
21. **It was not until more epochs were trained that accuracy improved.**  
22. **"I use deep learning models." --- "So do I."**  
23. **"I don’t use decision trees." --- "Neither do I."**  
24. **It is true that AI requires large datasets, but explainability is also important.**  
25. **Even if the model fails to generalize, we will still analyze its outputs.**  
26. **Whether you use CNNs or transformers, model architecture matters.**  
27. **To reduce bias is difficult, if not impossible.**  
28. **I'm going to optimize the model today no matter what happens.**  
29. **Whoever trains the AI, wherever they train it, the results are crucial.**  
30. **Noisy as the dataset was, the model extracted useful features.**  
31. **This dataset remains biased, while the new one is well-balanced.**  
32. **I tested two AI architectures. One used LSTMs, and the other used transformers.**  
33. **Some researchers prefer SVMs, while others favor deep learning.**  
34. **Suppose that the dataset is imbalanced, how will you address it?**  
35. **You can use this model as long as its accuracy remains high.**  
36. **As far as we know, this is the most efficient neural network.**  
37. **As far as I am concerned, reinforcement learning is more promising.**  
38. **This AI won’t perform well unless trained with diverse datasets.**  
39. **The fact is that explainability is crucial in AI development.**  
40. **Chances are the model will require fine-tuning before deployment.**  
41. **Let's retrain the model. After all, the error rate is still high.**  
42. **Now that the AI model is trained, we can evaluate its performance.**  
43. **That misclassification cost the company significant revenue.**  
44. **A moment’s analysis will reveal the bias in the dataset.**  
45. **This model will guide you through the prediction process.**  
46. **Data corruption prevented the AI from producing reliable outputs.**  
47. **Hyperparameter tuning keeps the training process optimized.**  
48. **This loss function will make the model converge faster.**  
49. **The researcher believes that AI should be explainable and interpretable.**  
50. **Gradient boosting is effective when applied to structured data.**
1. **Would you be so kind as to check the system logs for any anomalies in the AI model’s performance?**  
2. **The server's response time was too slow for real-time inference processing.**  
3. **The lead engineer said that it is possible for every motivated data scientist to optimize a deep learning model.**  
4. **The AI system is usually very efficient, but this time it was quite unexpected of it to misclassify the data.**  
5. **All you have to do is fine-tune the model parameters to achieve better accuracy.**  
6. **Don’t worry. You only have to retrain the model with more diverse data.**  
7. **Although the dataset was imbalanced, it was large enough for the model to generalize well.**  
8. **I didn’t know what parameters to tweak because there were no optimization guidelines.**  
9. **Excuse me. Do you happen to know how to access the AI inference API?**  
10. **Do you know where to find the latest dataset for the machine learning project?**  
11. **The research team decided not to deploy the biased model into production.**  
12. **The development team is to meet with cloud engineers to discuss AI deployment this weekend.**  
13. **Our AI mentor made us analyze multiple datasets every day, and it gradually improved our data processing skills.**  
14. **The system administrator had the engineers debug the AI server overnight.**  
15. **I saw the neural network recognize complex patterns with amazing accuracy.**  
16. **The anomaly detection model seems to have identified an unusual data pattern.**  
17. **It was very difficult for the new AI researcher to get the neural network to converge.**  
18. **Everybody was impressed by the AI’s ability to generate realistic images, to say nothing of its speed.**  
19. **To tell you the truth, I’m fascinated by the potential of AI-driven automation.**  
20. **The system was about to finish training when an unexpected hardware failure occurred.**  
21. **The developer first came to understand deep reinforcement learning during a robotics project.**  
22. **The AI had no choice but to relearn from scratch after a catastrophic failure.**  
23. **The sudden increase in server requests has something to do with the AI model going viral.**  
24. **The lead engineer helped the interns set up the cloud environment for AI deployment.**  
25. **The data scientist attends extra courses after work in order to improve his AI skills.**  
26. **The researcher's innovative approach never fails to push AI boundaries.**  
27. **I’m honored to be invited to this AI conference and introduced to these brilliant researchers.**  
28. **Would you mind running the model on a different dataset and verifying the accuracy?**  1. **This neural network model is worth optimizing because it is very efficient.**  
2. **The AI model was so accurate that it detected anomalies instantly.**  
3. **There is no telling whether the next dataset will improve the model’s performance.**  
4. **I'm looking forward to deploying the trained model in production.**  
5. **Reading machine learning papers aloud can help deepen your understanding of AI concepts.**  
6. **It is no use training the model with low-quality data.**  
7. **He never fine-tunes a model without evaluating its baseline performance.**  
8. **The data scientist insisted on improving feature engineering techniques.**  
9. **Adding more training data should make the model generalize better.**  
10. **After running multiple experiments, the researcher finally achieved state-of-the-art accuracy.**  
11. **The AI system learned to classify images with high accuracy by using convolutional neural networks.**  
12. **If it were not for big data, deep learning models would not perform as well.**  
13. **With transfer learning, we were able to train the model with a smaller dataset.**  
14. **Feature selection plays an essential role in optimizing machine learning models.**  
15. **A good AI system should be interpretable, to say nothing of being accurate.**  
16. **I didn't feel like retraining the model that night because it took too long.**  
17. **The researcher suggested that we use a pre-trained model to reduce training time.**  
18. **The AI engineer was about to deploy the new model when a critical bug was found.**  
19. **Deep reinforcement learning is what makes modern robotics more intelligent.**  
20. **No sooner had the training started than the GPU usage spiked.**  
21. **The AI system was trained with adversarial examples, which made it more robust.**  
22. **Whatever model architecture you choose, hyperparameter tuning is crucial.**  
23. **Whoever keeps refining their model will eventually achieve high performance.**  
24. **The optimizer adjusted the learning rate dynamically as training progressed.**  
25. **The deep learning framework, as is evident from its popularity, is widely used in industry.**  
26. **If you don't preprocess the data properly, the model will fail to learn meaningful patterns.**  
27. **Had I known about batch normalization earlier, I would have trained the model more efficiently.**  
28. **Even if the training loss is low, the model might still overfit.**  
29. **The more epochs you run, the better the model generalizes—up to a certain point.**  
30. **Nothing improves model accuracy more than high-quality data.**  
31. **It was not until I visualized the loss curve that I realized the model was overfitting.**  
32. **So complex was the model that it required a high-end GPU to train.**  
33. **Few researchers fully understand the implications of explainable AI.**  
34. **Only by reducing bias in training data can we ensure fair AI predictions.**  
35. **Seldom do traditional algorithms outperform deep learning models on large datasets.**  
36. **The AI model, which was fine-tuned with domain-specific data, performed exceptionally well.**  
37. **Had it not been for data augmentation, the model’s accuracy would have suffered.**  
38. **The research team suggested that we try a different activation function.**  
39. **It is essential that all AI models be evaluated for fairness.**  
40. **Should the model fail in production, we will roll back to a previous version.**  
41. **The larger the dataset, the more computational power is required.**  
42. **I would rather optimize the model than collect more data.**  
43. **The framework allows researchers to experiment with different neural architectures.**  
44. **I have never seen a model converge so quickly.**  
45. **This paper discusses techniques by which AI models can be made interpretable.**  
46. **If you never stop learning, you can be whatever kind of AI expert you want to be.**  
47. **Whoever fine-tunes their model carefully will achieve better performance.**  
48. **As long as the training data is diverse, the model should generalize well.**  
49. **Now that we have enough labeled data, we can train the supervised model.**  
50. **With a better optimizer, we would be able to achieve faster convergence.**





1. **It is important for engineers to optimize machine learning models.**  
2. **It is kind of you to share your dataset for research.**  
3. **It is crucial that AI systems be fair and unbiased.**  
4. **It is surprising that deep learning can generate realistic images.**  
5. **It is said that reinforcement learning improves robotic control.**  
6. **Deep learning is said to outperform traditional methods in image recognition.**  
7. **It seems that the model is overfitting to the training data.**  
8. **It appears that transfer learning speeds up convergence.**  
9. **It happens that we discovered a new optimization technique.**  
10. **It takes weeks to train a large-scale neural network.**  
11. **It costs millions to build high-performance AI models.**  
12. **It is the GPU that accelerates deep learning computations.**  
13. **What is it that determines a model’s accuracy?**  
14. **The report says that AI will revolutionize industries.**  
15. **The dataset tells us that data augmentation is necessary.**  
16. **The performance chart reminds researchers of model decay.**  
17. **I always remember the importance of data preprocessing when training models.**  
18. **Data augmentation enables models to generalize better.**  
19. **Cloud computing allows companies to train AI efficiently.**  
20. **Hardware limitations prevent larger models from being deployed.**  
21. **Insufficient data keeps AI from learning effectively.**  
22. **The fact is that bias in AI models can cause ethical issues.**  
23. **It may well take years to perfect quantum AI.**  
24. **You may as well use PyTorch if you prefer dynamic computation graphs.**  
25. **The problem is that AI models require vast amounts of data.**  
26. **Neural networks are easy to use but hard to interpret.**  
27. **The trouble is that explainability is still a challenge in AI.**  
28. **The point is that interpretability matters in critical applications.**  
29. **In order to fine-tune models, hyperparameter optimization is needed.**  
30. **The truth is that data quality matters more than model complexity.**  
31. **We added dropout so as to reduce overfitting.**  
32. **The point is whether the AI model can handle real-world data.**  
33. **The challenge is whether reinforcement learning can scale up.**  
34. **I wonder how AI will evolve in the next decade.**  
35. **The model was to have been deployed, but the accuracy was insufficient.**  
36. **Researchers ask whether AI can reach human-level intelligence.**  
37. **The experiment seems to have confirmed the hypothesis.**  
38. **We want our model to generalize well to unseen data.**  
39. **The professor asked students to implement a CNN from scratch.**  
40. **The results seem to have improved after feature engineering.**  
41. **The mentor told us to try different activation functions.**  
42. **To tell the truth, I prefer Python for AI development.**  
43. **To be frank, model interpretability is still lacking.**  
44. **We got the model to achieve higher accuracy with tuning.**  
45. **The research team kept optimizing the hyperparameters.**  
46. **To be honest, AI still struggles with generalization.**  
47. **To begin with, data preprocessing is essential.**  
48. **The team kept the dataset balanced to avoid bias.**  
49. **To make matters worse, the model started overfitting.**  
50. **Transfer learning lets AI models adapt to new tasks.**  
51. **AI models are made to learn from large datasets.**  
52. **To say nothing of speed, AI also improves accuracy.**  
53. **We saw the AI model improving with more data.**  
54. **Not to mention deep learning, reinforcement learning is also powerful.**  
55. **We saw the neural network detecting anomalies.**  
56. **Strange to say, the simple model outperformed the complex one.**  
57. **Needless to say, quality data is crucial for AI.**  
58. **I remember testing an early version of the model.**  
59. **We had the model retrained on a larger dataset.**  
60. **We got the AI system optimized for real-time processing.**  
61. **I remembered to validate the test set.**  
62. **In deploying AI, scalability must be considered.**  
63. **Those who use AI responsibly will succeed.**  
64. **On training completion, the model was evaluated.**  
65. **The model’s performance was similar to that of humans.**  
66. **I cannot help experimenting with new AI architectures.**  
67. **Those of us who work with AI know its potential.**  
68. **We cannot but acknowledge the power of AI.**  
69. **One model uses CNNs, the other uses transformers.**  
70. **Would you mind running another experiment?**  
71. **Do you mind if we use reinforcement learning?**  
72. **AI used to be rule-based, but now it learns from data.**  
73. **Neural networks would often struggle with small datasets.**  
74. **We're looking forward to testing the AI model.**  
75. **AI researchers are used to debugging complex models.**  
76. **It would be better for businesses to adopt AI gradually.**  
77. **In case AI fails, we need a backup system.**  
78. **There is no solving AI ethics easily.**  
79. **It is no use deploying an untested model.**  
80. **For fear that AI might make errors, human oversight is needed.**  
81. **Judging from the logs, the model needs more training.**  
82. **We optimize hyperparameters so that AI can perform better.**  
83. **The AI model was updated, so it improved its predictions.**  
84. **Considering computational cost, simpler models may be better.**  
85. **It is suggested that AI regulations be implemented.**  
86. **Generally speaking, AI models require large amounts of data.**  
87. **Speaking of AI, explainability is a major challenge.**  
88. **If AI should fail, it must have fallback mechanisms.**  
89. **With AI evolving, new applications emerge daily.**  
90. **If AI were to become sentient, it would change everything.**  
91. **With new algorithms, training time was reduced.**  
92. **If it were not for GPUs, AI training would be slow.**  
93. **But for cloud computing, large AI models wouldn’t be feasible.**  
94. **What AI is now is vastly different from what it was.**  
95. **If only AI could perfectly interpret human emotions!**  
96. **It’s about time we regulated AI applications.**  
97. **What AI is like varies depending on the algorithm used.**  
98. **It’s time for AI to be integrated into education.**  
99. **What it is like to train large AI models is difficult to describe.**  
100. **If AI learns as efficiently as humans, it will be revolutionary.**




半導体



## ⚙️【1. Fundamental Concepts（基礎概念）】

1. **Semiconductor** – A material with conductivity between that of a conductor and an insulator.  
2. **Intrinsic Semiconductor** – Pure semiconductor without any doping.  
3. **Extrinsic Semiconductor** – Semiconductor with added impurities (doping).  
4. **Doping** – The process of adding impurities to change conductivity.  
5. **n-type** – Doping with elements that add electrons.  
6. **p-type** – Doping with elements that create holes (positive carriers).  
7. **Electron** – Negatively charged carrier in semiconductors.  
8. **Hole** – Positively charged carrier representing the absence of an electron.  
9. **Band Gap** – Energy difference between the valence and conduction bands.  
10. **Conduction Band** – Energy level where electrons can move freely.  
11. **Valence Band** – Highest energy band filled with electrons in a semiconductor.  
12. **Fermi Level** – The energy level at which the probability of occupancy is 50%.  
13. **Carrier Mobility** – Speed at which carriers move under electric field.  
14. **Resistivity** – The resistance of a material to electric current.  
15. **Dielectric Constant** – The ability of a material to store electrical energy.  

---

## 🏗️【2. Semiconductor Devices（デバイス）】

16. **Diode** – A component that allows current in one direction.  
17. **Zener Diode** – A diode designed to operate in reverse breakdown.  
18. **Photodiode** – Converts light into electrical current.  
19. **LED (Light Emitting Diode)** – Emits light when current flows through.  
20. **Laser Diode** – Produces coherent light used in communication.  
21. **Transistor** – A device used to amplify or switch electronic signals.  
22. **BJT (Bipolar Junction Transistor)** – Current-controlled transistor.  
23. **MOSFET** – Voltage-controlled transistor used in digital circuits.  
24. **JFET** – Voltage-controlled resistor using junction gate.  
25. **IGBT** – Combines features of BJT and MOSFET for power switching.  
26. **SCR (Silicon Controlled Rectifier)** – A four-layer semiconductor used in power control.  
27. **Triac** – A bidirectional thyristor used for AC control.  
28. **Phototransistor** – A transistor that responds to light.  
29. **Tunnel Diode** – A diode with negative resistance due to quantum tunneling.  
30. **CMOS** – Complementary MOSFET technology for logic circuits.  

---

## 🛠️【3. Fabrication & Materials（製造と材料）】

31. **Wafer** – A thin slice of semiconductor material.  
32. **Crystal Growth** – The process of growing single crystal silicon (e.g., Czochralski).  
33. **Epitaxy** – Deposition of a crystal layer on a crystal substrate.  
34. **Oxidation** – Creating an oxide layer on silicon for insulation.  
35. **Photolithography** – Patterning using light exposure through a mask.  
36. **Etching** – Removing material using wet or dry processes.  
37. **Ion Implantation** – Introducing dopants using ion beams.  
38. **Annealing** – Heating to activate dopants and repair damage.  
39. **Chemical Vapor Deposition (CVD)** – Depositing thin films from gas-phase chemicals.  
40. **Physical Vapor Deposition (PVD)** – Depositing materials using sputtering or evaporation.  
41. **Chemical Mechanical Polishing (CMP)** – Surface planarization process.  
42. **Mask** – A pattern used to define structures in lithography.  
43. **Photoresist** – Light-sensitive material used in lithography.  
44. **Cleanroom** – A controlled environment for chip manufacturing.  
45. **Yield** – The ratio of functional chips to total produced.  

---

## 🔌【4. Electrical Characteristics（電気特性）】

46. **Threshold Voltage (Vth)** – The minimum gate voltage to turn on a MOSFET.  
47. **Breakdown Voltage** – The voltage at which a device conducts uncontrollably.  
48. **On-Resistance (Rds(on))** – Resistance when the device is on.  
49. **Leakage Current** – Unwanted current when a device is off.  
50. **Capacitance** – Ability to store charge.  
51. **Inductance** – Property opposing current changes.  
52. **Gate Oxide** – Insulating layer in a MOSFET gate.  
53. **Subthreshold Region** – Region where MOSFET conducts weakly below Vth.  
54. **Drain Current (Id)** – Current through the drain of a MOSFET.  
55. **Saturation Region** – Where the MOSFET behaves like a current source.  

---

## 🔋【5. Analog & Digital Circuits】

56. **Amplifier** – Increases signal amplitude.  
57. **Inverter** – Outputs the logical NOT of the input.  
58. **Flip-Flop** – A bistable memory element.  
59. **Latch** – A simpler memory storage element.  
60. **Counter** – A sequential circuit that counts pulses.  
61. **Shift Register** – Moves bits through a series of flip-flops.  
62. **Multiplexer** – Selects one input from many.  
63. **Demultiplexer** – Sends input to one of many outputs.  
64. **Comparator** – Compares two analog voltages.  
65. **Analog-to-Digital Converter (ADC)** – Converts analog signals to digital.  
66. **Digital-to-Analog Converter (DAC)** – Converts digital signals to analog.  
67. **Schmitt Trigger** – A comparator with hysteresis.  
68. **PLL (Phase Locked Loop)** – Synchronizes signal phase and frequency.  
69. **Clock Generator** – Produces timing signals.  
70. **Voltage Reference** – Provides a stable voltage regardless of conditions.  

---

## 🧪【6. Testing & Measurement（評価・測定）】

71. **Oscilloscope** – Visualizes voltage over time.  
72. **Multimeter** – Measures voltage, current, and resistance.  
73. **LCR Meter** – Measures inductance, capacitance, and resistance.  
74. **Curve Tracer** – Plots I-V characteristics of semiconductor devices.  
75. **Probe Station** – Tests ICs at the wafer level.  
76. **Parametric Test** – Measures device electrical parameters.  
77. **Function Generator** – Produces waveform signals.  
78. **Spectrum Analyzer** – Measures signal frequency components.  
79. **TDR (Time Domain Reflectometry)** – Detects faults in interconnects.  
80. **Noise Figure** – Measures the added noise of a device.  

---

## 🔍【7. Analysis & Simulation】

81. **SPICE** – Circuit simulation tool.  
82. **Monte Carlo Simulation** – Probabilistic simulation for process variation.  
83. **HSPICE** – High-performance SPICE simulator.  
84. **S-parameters** – Describe RF performance of devices.  
85. **Bode Plot** – Frequency response plot (gain & phase).  
86. **Nyquist Plot** – Used in stability analysis.  
87. **Verilog** – Hardware description language.  
88. **VHDL** – Another hardware description language.  
89. **RTL (Register Transfer Level)** – Hardware design abstraction.  
90. **DRC (Design Rule Check)** – Ensures layout compliance.  
91. **LVS (Layout vs Schematic)** – Ensures layout matches circuit.  
92. **Parasitic Extraction** – Finds unwanted capacitance and resistance.  
93. **Thermal Simulation** – Estimates heat distribution.  
94. **IR Drop Analysis** – Checks voltage drops due to resistance.  
95. **Electromigration** – Material movement due to high current density.  

---

## 🌍【8. Advanced Topics & Applications】

96. **SoC (System on Chip)** – Integrates all components on one chip.  
97. **ASIC (Application-Specific IC)** – Custom-designed chip for specific task.  
98. **FPGA** – Reconfigurable logic device.  
99. **MEMS** – Miniature mechanical systems on a chip.  
100. **Image Sensor** – Converts light into electrical signal.  
101. **CMOS Sensor** – A popular type of image sensor.  
102. **Quantum Dot** – Nanoscale semiconductors with unique optical properties.  
103. **Power IC** – Designed for high-voltage or high-current applications.  
104. **GaN (Gallium Nitride)** – High-efficiency wide bandgap semiconductor.  
105. **SiC (Silicon Carbide)** – Used in high-temperature power electronics.  
106. **Photonics** – Using light for computation or communication.  
107. **Neuromorphic Chip** – Mimics brain neural networks.  
108. **Edge Computing** – Processing near data source using local chips.  
109. **IoT Chip** – Low-power, networked semiconductor for IoT devices.  
110. **5G Modem** – Supports next-gen wireless communication.  

---

## 🧱【9. Packaging & Interconnects】

111. **Package** – Encases and protects semiconductor chips.  
112. **Die** – A single unit of a semiconductor chip.  
113. **Wire Bonding** – Connects die to package leads.  
114. **Flip Chip** – Chip mounted upside down for direct connection.  
115. **Ball Grid Array (BGA)** – Type of surface-mount packaging.  
116. **Through-Silicon Via (TSV)** – Vertical interconnect in 3D ICs.  
117. **Fan-Out Packaging** – Advanced packaging for better performance.  
118. **Interposer** – Intermediate layer in multi-die packages.  
119. **Lead Frame** – Metal structure for packaging.  
120. **Solder Bump** – Used for flip-chip connections.  

---





### Ⅰ. Numbers, Expressions, and Sets (1–40)

1. **Natural number**  
In classification, each category is often labeled with a natural number starting from 0 or 1.

2. **Integer**  
Integer values are used to index data points or represent discrete classes in models.

3. **Even number**  
An even number of neurons is sometimes preferred for symmetry in neural network layers.

4. **Odd number**  
Odd batch sizes might cause slight inefficiencies in GPU-based model training.

5. **Prime number**  
Hash functions in ML often use prime numbers to minimize collisions.

6. **Divisor**  
We use divisors to align data shapes for matrix operations during training.

7. **Multiple**  
Image dimensions are often resized to a multiple of 8 for faster GPU computation.

8. **Greatest common divisor**  
Calculating the greatest common divisor helps simplify feature ratios in preprocessing.

9. **Least common multiple**  
To synchronize data streams, the least common multiple of their periods is calculated.

10. **Rational number**  
Normalized features are usually represented as rational numbers between 0 and 1.

11. **Irrational number**  
Euclidean distances between vectors often yield irrational numbers like √2.

12. **Real number**  
Most ML parameters are optimized over the domain of real numbers.

13. **Imaginary number**  
Imaginary numbers may appear in models involving complex-valued signal processing.

14. **Complex number**  
Fourier transforms used in image processing involve complex numbers.

15. **Pure imaginary number**  
In certain simulations, pure imaginary numbers represent phase shifts.

16. **Algebraic expression**  
The loss function is simplified using algebraic expressions during derivation.

17. **Like terms**  
Symbolic differentiation requires combining like terms for simplification.

18. **Expansion**  
Polynomial expansion is used in kernel methods like polynomial SVM.

19. **Factorization**  
Factorizing expressions helps in deriving closed-form solutions in linear models.

20. **Common factor**  
Common factors are extracted when simplifying symbolic models or loss functions.

21. **Monomial**  
Each feature in linear regression corresponds to a monomial term.

22. **Polynomial**  
Polynomial regression models complex trends in non-linear data.

23. **Degree (of polynomial)**  
The degree of a polynomial model determines its flexibility and risk of overfitting.

24. **Coefficient**  
Coefficients in regression represent the contribution of each feature to the prediction.

25. **Algebraic expression (polynomial)**  
Algebraic expressions define the form of hypothesis functions in ML.

26. **Long division (of polynomials)**  
Polynomial division helps in simplifying rational function models.

27. **Division formula**  
We use division formulas in symbolic computation engines to manipulate expressions.

28. **Remainder**  
The remainder from polynomial division is used in the Remainder Theorem for root finding.

29. **Rationalization**  
We rationalize denominators in expressions to improve numerical stability in models.

30. **Multiplication formula**  
Multiplication formulas expand expressions in symbolic algebra packages.

31. **Equation**  
An ML model solves an equation to minimize the loss function.

32. **Identity**  
Identities are used to simplify expressions when proving model behavior.

33. **Inequality**  
Inequality constraints define feasible regions in optimization problems.

34. **Absolute value**  
The absolute value function is commonly used in robust loss functions like MAE.

35. **Approximate value**  
Approximate values are used during iterative training procedures like gradient descent.

36. **Error**  
Prediction error is minimized during the learning process.

37. **Significant figure**  
Reporting model accuracy to significant figures ensures clarity and consistency.

38. **Set**  
Feature selection involves identifying a relevant set of input variables.

39. **Element (member)**  
Each element in the training set represents one sample for the model.

40. **Venn diagram**  
Venn diagrams help visualize overlaps in class distributions or feature sets.

---

### Ⅱ. Equations and Functions (41–80)

41. **Linear equation**  
Linear regression fits a linear equation to predict continuous outcomes.

42. **Quadratic equation**  
Quadratic equations can arise in optimization problems involving squared terms.

43. **Cubic equation**  
Solving cubic equations helps in polynomial regression with higher-order terms.

44. **Discriminant**  
The discriminant determines the number of real roots, which is useful in analyzing model behavior.

45. **Repeated root**  
A repeated root in the loss function’s derivative indicates a flat region during training.

46. **Imaginary solution**  
In complex-valued models, parameters may have imaginary solutions.

47. **Quadratic formula**  
The quadratic formula can solve for parameters in second-degree optimization problems.

48. **Factor theorem**  
The factor theorem helps determine polynomial roots in symbolic ML models.

49. **Substitution method**  
The substitution method is used to solve systems of equations in constraint optimization.

50. **Elimination method**  
The elimination method is applied in solving systems for Lagrange multipliers.

51. **Simultaneous equations**  
Simultaneous equations appear when optimizing models with multiple variables.

52. **Linear function**  
A linear function models the relationship between features and target in simple regression.

53. **Quadratic function**  
Quadratic functions describe U-shaped loss curves like in ridge regression.

54. **Cubic function**  
Cubic functions allow more flexibility when modeling complex data patterns.

55. **Domain**  
Defining the domain of a function is essential to avoid undefined model outputs.

56. **Range**  
The range of an activation function affects the output space of neural networks.

57. **Graph of a function**  
Visualizing the graph of a loss function helps in understanding convergence behavior.

58. **Horizontal/Vertical shift of graph**  
Data normalization results in a horizontal or vertical shift in feature graphs.

59. **Axis of symmetry**  
Some loss functions like MSE are symmetric around a minimum point.

60. **Vertex (of a parabola)**  
The vertex of a quadratic loss curve indicates the optimal solution.

61. **Symmetry**  
Symmetry in data distributions can lead to simplified model assumptions.

62. **Maximum value**  
We often seek the maximum value of a reward function in reinforcement learning.

63. **Minimum value**  
Training minimizes the loss function to find the model’s optimal parameters.

64. **Monotonicity table**  
A monotonicity table is used to analyze the increase or decrease of functions in optimization.

65. **Completing the square**  
Completing the square is a method to rewrite loss functions for analysis.

66. **Irrational function**  
Irrational functions may appear in models involving square roots of feature terms.

67. **Fractional function**  
Fractional functions describe inverse relationships in models like inverse distance weighting.

68. **Exponential function**  
Exponential functions are used in models like exponential smoothing or decay in learning rates.

69. **Logarithmic function**  
Logarithmic functions appear in log-loss or when applying log-transformations to skewed data.

70. **Composite function**  
A neural network can be seen as a composition of many activation and linear functions.

71. **Inverse function**  
Inverse functions are used to reverse scale transformations in data preprocessing.

72. **Monotonic increasing**  
A monotonic increasing activation function ensures gradients do not vanish.

73. **Monotonic decreasing**  
Monotonic decreasing behavior in a metric may indicate overfitting.

74. **Monotonicity**  
Monotonicity constraints are imposed in certain models like monotonic gradient boosting.

75. **Range of values (value domain)**  
Setting the range of values helps restrict model outputs to valid domains.

76. **Point of intersection (of graphs)**  
The point where hypothesis and data graphs intersect represents a solution.

77. **Inverse proportion**  
Inverse proportion is modeled in systems where increase in one feature leads to decrease in another.

78. **Linear inequality**  
Linear inequalities define feasible regions in linear programming for ML.

79. **Quadratic inequality**  
Quadratic inequalities are used in constraint-based optimization for support vector machines.

80. **Inequality with absolute value**  
Absolute value inequalities define robust margin conditions in classification models.

---




Point
Each point in a scatter plot represents one sample in the dataset.

Line
Linear regression draws a line that best fits the relationship between input and output.

Line segment
In k-NN graphs, line segments connect neighboring data points based on distance.

Straight line
A straight line in 2D feature space separates classes in linear classifiers like SVM.

Angle
The angle between weight vectors can indicate feature similarity in high-dimensional space.

Acute angle
A small acute angle between vectors suggests strong positive correlation.

Obtuse angle
An obtuse angle between feature vectors may imply weak or negative correlation.

Right angle
Orthogonal vectors form a right angle and are treated as uncorrelated in ML.

Triangle
Triangular relationships appear in hierarchical clustering of data points.

Equilateral triangle
In visualization, equilateral triangle structures can reveal balanced clustering.

Right triangle
Right triangles are used in calculating Euclidean distances via the Pythagorean theorem.

Isosceles triangle
Isosceles triangles in feature space can indicate symmetry in the dataset.

Quadrilateral
Quadrilaterals may appear in mesh visualizations of high-dimensional feature interactions.

Parallelogram
A parallelogram can represent the span of two vectors in feature space.

Trapezoid
Trapezoids can help approximate the area under a curve for numerical integration.

Rectangle
Confusion matrices are often displayed as rectangular heatmaps.

Square
Feature matrices are often square in autoencoder latent space visualizations.

Circle
Circular clusters may emerge in data with radial symmetry.

Radius
The radius of a cluster helps define neighborhood boundaries in clustering algorithms.

Diameter
The diameter of a graph reflects the maximum distance between any two nodes in a network.

Chord
Chords can appear when connecting non-adjacent points in similarity graphs.

Arc
Arcs are used in polar plots to show relationships between angles and magnitudes.

Radian
Angles in radians are used when applying trigonometric functions in signal analysis.

Radians (unit)
Neural networks using circular activation functions often rely on radian input.

Central angle
The central angle in a radar chart shows the spread of different feature values.

Sector
Sectors in pie charts help visualize class distribution in classification problems.

Perpendicular
Feature vectors that are perpendicular are statistically independent.

Parallel
Parallel vectors can indicate redundancy or multicollinearity in feature sets.

Congruent
Congruent triangles in diagrams can represent repeated patterns in data.

Similar (figures)
Similar shapes in cluster visualizations may indicate shared structure.

Perpendicular line
Decision boundaries are often drawn perpendicular to the gradient direction.

Perpendicular bisector
A perpendicular bisector is used in Voronoi diagrams to divide feature space.

Trigonometric ratio
Trigonometric ratios are used in time series models analyzing cyclic patterns.

Sine
Sine functions model seasonality in time series forecasting.

Cosine
Cosine similarity is widely used in NLP to compare word vector directions.

Tangent
The tangent function helps in modeling nonlinear transitions in sensor data.

Trigonometric identities
Trigonometric identities simplify equations in signal and audio feature analysis.

Trigonometric table
Lookup tables for sine and cosine speed up embedded ML models.

Sine rule
The sine rule can be used in triangulating GPS data for geospatial ML models.

Cosine rule
The cosine rule helps compute distances between points when angles are known.

Great! Here's the next batch of **English-only machine learning example sentences** using high school math terms from:

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### Ⅳ. Vectors and 3D Geometry (121–160)

121. **Vector**  
Feature vectors are the core representation of data in most machine learning models.

122. **Component form**  
In vectorized implementations, each input is represented in component form for computation.

123. **Plane vector**  
Plane vectors are used in 2D embeddings like PCA and t-SNE.

124. **Space vector**  
Space vectors are essential in 3D data visualization or physical simulations in ML.

125. **Zero vector**  
A zero vector can appear in models when features lack variance.

126. **Unit vector**  
Unit vectors are used to normalize direction without affecting magnitude.

127. **Vector addition**  
Vector addition combines multiple features or gradients in optimization.

128. **Vector subtraction**  
Subtracting vectors is common in calculating displacement or error vectors.

129. **Scalar multiplication**  
Scalar multiplication scales a feature vector to adjust its magnitude.

130. **Dot product (inner product)**  
The dot product measures similarity between two vectors in many ML algorithms.

131. **Cross product (vector product)**  
Cross products are used in 3D computer vision to calculate orientation or normals.

132. **Magnitude of vector**  
The magnitude of a gradient vector determines the learning step size.

133. **Perpendicular condition**  
Two vectors are perpendicular if their dot product is zero, useful in feature orthogonality.

134. **Parallel condition**  
Parallel vectors indicate strong correlation between features.

135. **Midpoint vector**  
The midpoint vector is used in clustering to define centroid locations.

136. **Internal division of a line segment**  
Weighted averaging of feature vectors is a form of internal division.

137. **External division of a line segment**  
Some geometric models use external division to extrapolate feature space boundaries.

138. **Centroid of triangle**  
In clustering, the centroid of triangle-shaped clusters minimizes within-group distance.

139. **Components of a vector**  
Breaking a vector into components helps in analyzing its influence per feature.

140. **Vector expression of a perpendicular**  
The projection of one vector onto another involves perpendicular vector components.

141. **Space (3D)**  
3D point clouds are processed in spatial machine learning models.

142. **Coordinates of a point**  
Each data sample has coordinates in a high-dimensional feature space.

143. **Line in space**  
Lines in 3D space represent trajectories or object paths in motion prediction.

144. **Plane in space**  
Decision boundaries in high-dimensional models may resemble planes in space.

145. **Perpendicular between line and plane**  
Determining perpendicularity is crucial in 3D object recognition.

146. **Vector equation of a line**  
In geometric ML, a line can be expressed using a vector equation with direction and a point.

147. **Inner product of space vectors**  
The inner product helps assess similarity in 3D embedding spaces.

148. **Area of a triangle**  
In graphics or simulation, the triangle area is used for object surface calculation.

149. **Volume of a tetrahedron**  
Tetrahedrons can represent volume elements in 3D mesh analysis.

150. **Volume of a parallelepiped**  
The volume of a parallelepiped is calculated using vector cross and dot products in physics-informed ML.

151. **Distance in space**  
Euclidean distance in 3D space is used for similarity and clustering.

152. **Distance between line and plane**  
This distance metric is applied in LIDAR-based 3D object detection.

153. **Cross section of a solid**  
Cross sections of 3D data can reveal structure in medical imaging models.

154. **Net (unfolded shape)**  
Unfolded 3D nets are used in training models to understand geometric transformations.

155. **Surface area**  
Surface area estimation is essential in image segmentation of 3D shapes.

156. **Volume of solid**  
Volume calculation helps quantify tumors or objects in ML-based medical diagnostics.

157. **Volume of a sphere**  
Sphere volumes are estimated from segmented data in object recognition tasks.

158. **Volume of a cylinder**  
ML algorithms may calculate cylinder volumes in industrial quality control systems.

159. **Volume of a cone**  
3D reconstruction from images may involve modeling cones or conic sections.

160. **Regular polyhedron**  
Regular polyhedra are used in mesh modeling and geometric learning.



---

### Ⅴ. Data Analysis, Probability, and Statistics (161–180)

161. **Data**  
Machine learning models are built to learn patterns from large datasets.

162. **Frequency**  
The frequency of each class is used to balance imbalanced classification tasks.

163. **Relative frequency**  
Relative frequency is important for estimating probabilities from data distributions.

164. **Frequency distribution table**  
A frequency distribution table helps summarize categorical data before feeding it into a model.

165. **Cumulative frequency**  
Cumulative frequency is used in calculating percentiles and quantiles for feature analysis.

166. **Histogram**  
Histograms visualize the distribution of features or prediction outputs.

167. **Class interval**  
Choosing appropriate class intervals in histograms affects the clarity of feature distributions.

168. **Class mark (midpoint)**  
The class mark is used when approximating averages from grouped data.

169. **Mean**  
The mean is a basic statistical feature often used in feature engineering.

170. **Median**  
The median is robust against outliers and is commonly used in skewed data distributions.

171. **Mode**  
The mode helps identify the most frequent category in classification problems.

172. **Range**  
The range of a feature gives insight into its variability and scale.

173. **Quartile**  
Quartiles help divide data into four parts for advanced statistical analysis.

174. **Box-and-whisker plot**  
Box plots are used to detect outliers and compare feature distributions.

175. **Variance**  
Variance measures how spread out feature values are in a dataset.

176. **Standard deviation**  
Standard deviation is used in normalization and z-score standardization.

177. **Scatter plot**  
Scatter plots visualize relationships between two continuous variables.

178. **Correlation coefficient**  
The correlation coefficient quantifies the linear relationship between features.

179. **Regression line**  
The regression line predicts the target value from the input features in linear regression.

180. **Explanatory and response variables**  
Explanatory variables are used to predict response variables in supervised learning.

---

### Ⅵ. Calculus and Sequences (181–200)

181. **Sequence**  
Time series data is modeled as a sequence of observations over time.

182. **Term (of a sequence)**  
Each term in a sequence represents a data point at a specific time step.

183. **General term**  
The general term defines the rule for generating future values in time series prediction.

184. **Arithmetic sequence**  
Arithmetic sequences are used to model steady growth in financial predictions.

185. **Geometric sequence**  
Geometric sequences model exponential growth in population or resource usage.

186. **Recurrence formula**  
Recurrent formulas are fundamental in designing RNNs for sequential data.

187. **Summation notation (Σ)**  
Summation notation is used in expressing total loss in training models.

188. **Sum of arithmetic sequence**  
The sum of an arithmetic sequence appears in cumulative reward calculations.

189. **Sum of geometric sequence**  
Geometric sums are used in discounted reward calculations in reinforcement learning.

190. **Infinite geometric series**  
An infinite geometric series models decay processes like learning rate scheduling.

191. **Convergence**  
Convergence refers to the process where a model reaches a stable solution.

192. **Divergence**  
Divergence indicates instability in learning, often caused by poor parameter settings.

193. **Limit**  
Limits are used in defining the derivative of a function in model optimization.

194. **Differentiation**  
Differentiation is essential for computing gradients in backpropagation.

195. **Derivative**  
Derivatives determine how the model output changes with respect to inputs or weights.

196. **Differential coefficient**  
The differential coefficient at a point gives the local slope of the loss function.

197. **Equation of tangent**  
The tangent line approximates the behavior of the loss function near a local point.

198. **Maximum and minimum (local extrema)**  
Finding maxima or minima is the goal of optimization in training models.

199. **Definite integral**  
Definite integrals are used in computing areas under curves such as ROC or precision-recall.

200. **Area under the curve**  
The area under the ROC curve (AUC) is a standard metric for evaluating classifier performance.

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