In cryptography, an initialization vector (IV) or starting variable is an input to a cryptographic primitive being used to provide the initial state. The IV is typically required to be random or pseudorandom, but sometimes an IV only needs to be unpredictable or unique. Randomization is crucial for some encryption schemes to achieve semantic security, a property whereby repeated usage of the scheme under the same key does not allow an attacker to infer relationships between (potentially similar) segments of the encrypted message. For block ciphers, the use of an IV is described by the modes of operation. Some cryptographic primitives require the IV only to be non-repeating, and the required randomness is derived internally. In this case, the IV is commonly called a nonce (a number used only once), and the primitives (e.g. CBC) are considered stateful rather than randomized. This is because an IV need not be explicitly forwarded to a recipient but may be derived from a common state updated at both sender and receiver side. (In practice, a short nonce is still transmitted along with the message to consider message loss.) An example of stateful encryption schemes is the counter mode of operation, which has a sequence number for a nonce. The IV size depends on the cryptographic primitive used; for block ciphers it is generally the cipher's block-size. In encryption schemes, the unpredictable part of the IV has at best the same size as the key to compensate for time/memory/data tradeoff attacks. When the IV is chosen at random, the probability of collisions due to the birthday problem must be taken into account. Traditional stream ciphers such as RC4 do not support an explicit IV as input, and a custom solution for incorporating an IV into the cipher's key or internal state is needed. Some designs realized in practice are known to be insecure; the WEP protocol is a notable example, and is prone to related-IV attacks. == Motivation == A block cipher is one of the most basic primitives in cryptography, and frequently used for data encryption. However, by itself, it can only be used to encode a data block of a predefined size, called the block size. For example, a single invocation of the AES algorithm transforms a 128-bit plaintext block into a ciphertext block of 128 bits in size. The key, which is given as one input to the cipher, defines the mapping between plaintext and ciphertext. If data of arbitrary length is to be encrypted, a simple strategy is to split the data into blocks each matching the cipher's block size, and encrypt each block separately using the same key. This method is not secure as equal plaintext blocks get transformed into equal ciphertexts, and a third party observing the encrypted data may easily determine its content even when not knowing the encryption key. To hide patterns in encrypted data while avoiding the re-issuing of a new key after each block cipher invocation, a method is needed to randomize the input data. In 1980, the NIST published a national standard document designated Federal Information Processing Standard (FIPS) PUB 81, which specified four so-called block cipher modes of operation, each describing a different solution for encrypting a set of input blocks. The first mode implements the simple strategy described above, and was specified as the electronic codebook (ECB) mode. In contrast, each of the other modes describe a process where ciphertext from one block encryption step gets intermixed with the data from the next encryption step. To initiate this process, an additional input value is required to be mixed with the first block, and which is referred to as an initialization vector. For example, the cipher-block chaining (CBC) mode requires an unpredictable value, of size equal to the cipher's block size, as additional input. This unpredictable value is added to the first plaintext block before subsequent encryption. In turn, the ciphertext produced in the first encryption step is added to the second plaintext block, and so on. The ultimate goal for encryption schemes is to provide semantic security: by this property, it is practically impossible for an attacker to draw any knowledge from observed ciphertext. It can be shown that each of the three additional modes specified by the NIST are semantically secure under so-called chosen-plaintext attacks. == Properties == Properties of an IV depend on the cryptographic scheme used. A basic requirement is uniqueness, which means that no IV may be reused under the same key. For block ciphers, repeated IV values devolve the encryption scheme into electronic codebook mode: equal IV and equal plaintext result in equal ciphertext. In stream cipher encryption uniqueness is crucially important as plaintext may be trivially recovered otherwise. Example: Stream ciphers encrypt plaintext P to ciphertext C by deriving a key stream K from a given key and IV and computing C as C = P xor K. Assume that an attacker has observed two messages C1 and C2 both encrypted with the same key and IV. Then knowledge of either P1 or P2 reveals the other plaintext since C1 xor C2 = (P1 xor K) xor (P2 xor K) = P1 xor P2. Many schemes require the IV to be unpredictable by an adversary. This is effected by selecting the IV at random or pseudo-randomly. In such schemes, the chance of a duplicate IV is negligible, but the effect of the birthday problem must be considered. As for the uniqueness requirement, a predictable IV may allow recovery of (partial) plaintext. Example: Consider a scenario where a legitimate party called Alice encrypts messages using the cipher-block chaining mode. Consider further that there is an adversary called Eve that can observe these encryptions and is able to forward plaintext messages to Alice for encryption (in other words, Eve is capable of a chosen-plaintext attack). Now assume that Alice has sent a message consisting of an initialization vector IV1 and starting with a ciphertext block CAlice. Let further PAlice denote the first plaintext block of Alice's message, let E denote encryption, and let PEve be Eve's guess for the first plaintext block. Now, if Eve can determine the initialization vector IV2 of the next message she will be able to test her guess by forwarding a plaintext message to Alice starting with (IV2 xor IV1 xor PEve); if her guess was correct this plaintext block will get encrypted to CAlice by Alice. This is because of the following simple observation: CAlice = E(IV1 xor PAlice) = E(IV2 xor (IV2 xor IV1 xor PAlice)). Depending on whether the IV for a cryptographic scheme must be random or only unique the scheme is either called randomized or stateful. While randomized schemes always require the IV chosen by a sender to be forwarded to receivers, stateful schemes allow sender and receiver to share a common IV state, which is updated in a predefined way at both sides. == Block ciphers == Block cipher processing of data is usually described as a mode of operation. Modes are primarily defined for encryption as well as authentication, though newer designs exist that combine both security solutions in so-called authenticated encryption modes. While encryption and authenticated encryption modes usually take an IV matching the cipher's block size, authentication modes are commonly realized as deterministic algorithms, and the IV is set to zero or some other fixed value. == Stream ciphers == In stream ciphers, IVs are loaded into the keyed internal secret state of the cipher, after which a number of cipher rounds are executed prior to releasing the first bit of output. For performance reasons, designers of stream ciphers try to keep that number of rounds as small as possible, but because determining the minimal secure number of rounds for stream ciphers is not a trivial task, and considering other issues such as entropy loss, unique to each cipher construction, related-IVs and other IV-related attacks are a known security issue for stream ciphers, which makes IV loading in stream ciphers a serious concern and a subject of ongoing research. == WEP IV == The 802.11 encryption algorithm called WEP (short for Wired Equivalent Privacy) used a short, 24-bit IV, leading to reused IVs with the same key, which led to it being easily cracked. Packet injection allowed for WEP to be cracked in times as short as several seconds. This ultimately led to the deprecation of WEP. == SSL 2.0 IV == In cipher-block chaining mode (CBC mode), the IV need not be secret, but must be unpredictable (In particular, for any given plaintext, it must not be possible to predict the IV that will be associated to the plaintext in advance of the generation of the IV.) at encryption time. Additionally for the output feedback mode (OFB mode), the IV must be unique. In particular, the (previously) common practice of re-using the last ciphertext block of a message as the IV for the next message is insecure (for example, this method was used by SSL 2.0). If an attacker knows
Neural scaling law
In machine learning, a neural scaling law is an empirical scaling law that describes how neural network performance changes as key factors are scaled up or down. These factors typically include the number of parameters, training dataset size, and training cost. Some models also exhibit performance gains by scaling inference through increased test-time compute (TTC), extending neural scaling laws beyond training to the deployment phase. == Introduction == In general, a deep learning model can be characterized by four parameters: model size, training dataset size, training cost, and the post-training error rate (e.g., the test set error rate). Each of these variables can be defined as a real number, usually written as N , D , C , L {\displaystyle N,D,C,L} (respectively: parameter count, dataset size, computing cost, and loss). A neural scaling law is a theoretical or empirical statistical law between these parameters. There are also other parameters with other scaling laws. === Size of the model === In most cases, the model's size is simply the number of parameters. However, one complication arises with the use of sparse models, such as mixture-of-expert models. With sparse models, during inference, only a fraction of their parameters are used. In comparison, most other kinds of neural networks, such as transformer models, always use all their parameters during inference. === Size of the training dataset === The size of the training dataset is usually quantified by the number of data points within it. Larger training datasets are typically preferred, as they provide a richer and more diverse source of information from which the model can learn. This can lead to improved generalization performance when the model is applied to new, unseen data. However, increasing the size of the training dataset also increases the computational resources and time required for model training. With the "pretrain, then finetune" method used for most large language models, there are two kinds of training dataset: the pretraining dataset and the finetuning dataset. Their sizes have different effects on model performance. Generally, the finetuning dataset is less than 1% the size of pretraining dataset. In some cases, a small amount of high quality data suffices for finetuning, and more data does not necessarily improve performance. Many scaling laws, due to their inherent diminishing returns nature, value data based on a submodular set function which was shown in a paper on this topic. === Cost of training === Training cost is typically measured in terms of time (how long it takes to train the model) and computational resources (how much processing power and memory are required). It is important to note that the cost of training can be significantly reduced with efficient training algorithms, optimized software libraries, and parallel computing on specialized hardware such as GPUs or TPUs. The cost of training a neural network model is a function of several factors, including model size, training dataset size, the training algorithm complexity, and the computational resources available. In particular, doubling the training dataset size does not necessarily double the cost of training, because one may train the model for several times over the same dataset (each being an "epoch"). === Performance === The performance of a neural network model is evaluated based on its ability to accurately predict the output given some input data. Common metrics for evaluating model performance include: Negative log-likelihood per token (logarithm of perplexity) for language modeling; Accuracy, precision, recall, and F1 score for classification tasks; Mean squared error (MSE) or mean absolute error (MAE) for regression tasks; Elo rating in a competition against other models, such as gameplay or preference by a human judge. Performance can be improved by using more data, larger models, different training algorithms, regularizing the model to prevent overfitting, and early stopping using a validation set. When the performance is a number bounded within the range of [ 0 , 1 ] {\displaystyle [0,1]} , such as accuracy, precision, etc., it often scales as a sigmoid function of cost, as seen in the figures. == Examples == === (Hestness, Narang, et al, 2017) === The 2017 paper is a common reference point for neural scaling laws fitted by statistical analysis on experimental data. Previous works before the 2000s, as cited in the paper, were either theoretical or orders of magnitude smaller in scale. Whereas previous works generally found the scaling exponent to scale like L ∝ D − α {\displaystyle L\propto D^{-\alpha }} , with α ∈ { 0.5 , 1 , 2 } {\displaystyle \alpha \in \{0.5,1,2\}} , the paper found that α ∈ [ 0.07 , 0.35 ] {\displaystyle \alpha \in [0.07,0.35]} . Of the factors they varied, only task can change the exponent α {\displaystyle \alpha } . Changing the architecture optimizers, regularizers, and loss functions, would only change the proportionality factor, not the exponent. For example, for the same task, one architecture might have L = 1000 D − 0.3 {\displaystyle L=1000D^{-0.3}} while another might have L = 500 D − 0.3 {\displaystyle L=500D^{-0.3}} . They also found that for a given architecture, the number of parameters necessary to reach lowest levels of loss, given a fixed dataset size, grows like N ∝ D β {\displaystyle N\propto D^{\beta }} for another exponent β {\displaystyle \beta } . They studied machine translation with LSTM ( α ∼ 0.13 {\displaystyle \alpha \sim 0.13} ), generative language modelling with LSTM ( α ∈ [ 0.06 , 0.09 ] , β ≈ 0.7 {\displaystyle \alpha \in [0.06,0.09],\beta \approx 0.7} ), ImageNet classification with ResNet ( α ∈ [ 0.3 , 0.5 ] , β ≈ 0.6 {\displaystyle \alpha \in [0.3,0.5],\beta \approx 0.6} ), and speech recognition with two hybrid (LSTMs complemented by either CNNs or an attention decoder) architectures ( α ≈ 0.3 {\displaystyle \alpha \approx 0.3} ). === (Henighan, Kaplan, et al, 2020) === A 2020 analysis studied statistical relations between C , N , D , L {\displaystyle C,N,D,L} over a wide range of values and found similar scaling laws, over the range of N ∈ [ 10 3 , 10 9 ] {\displaystyle N\in [10^{3},10^{9}]} , C ∈ [ 10 12 , 10 21 ] {\displaystyle C\in [10^{12},10^{21}]} , and over multiple modalities (text, video, image, text to image, etc.). In particular, the scaling laws it found are (Table 1 of ): For each modality, they fixed one of the two C , N {\displaystyle C,N} , and varying the other one ( D {\displaystyle D} is varied along using D = C / 6 N {\displaystyle D=C/6N} ), the achievable test loss satisfies L = L 0 + ( x 0 x ) α {\displaystyle L=L_{0}+\left({\frac {x_{0}}{x}}\right)^{\alpha }} where x {\displaystyle x} is the varied variable, and L 0 , x 0 , α {\displaystyle L_{0},x_{0},\alpha } are parameters to be found by statistical fitting. The parameter α {\displaystyle \alpha } is the most important one. When N {\displaystyle N} is the varied variable, α {\displaystyle \alpha } ranges from 0.037 {\displaystyle 0.037} to 0.24 {\displaystyle 0.24} depending on the model modality. This corresponds to the α = 0.34 {\displaystyle \alpha =0.34} from the Chinchilla scaling paper. When C {\displaystyle C} is the varied variable, α {\displaystyle \alpha } ranges from 0.048 {\displaystyle 0.048} to 0.19 {\displaystyle 0.19} depending on the model modality. This corresponds to the β = 0.28 {\displaystyle \beta =0.28} from the Chinchilla scaling paper. Given fixed computing budget, optimal model parameter count is consistently around N o p t ( C ) = ( C 5 × 10 − 12 petaFLOP-day ) 0.7 = 9.0 × 10 − 7 C 0.7 {\displaystyle N_{opt}(C)=\left({\frac {C}{5\times 10^{-12}{\text{petaFLOP-day}}}}\right)^{0.7}=9.0\times 10^{-7}C^{0.7}} The parameter 9.0 × 10 − 7 {\displaystyle 9.0\times 10^{-7}} varies by a factor of up to 10 for different modalities. The exponent parameter 0.7 {\displaystyle 0.7} varies from 0.64 {\displaystyle 0.64} to 0.75 {\displaystyle 0.75} for different modalities. This exponent corresponds to the ≈ 0.5 {\displaystyle \approx 0.5} from the Chinchilla scaling paper. It's "strongly suggested" (but not statistically checked) that D o p t ( C ) ∝ N o p t ( C ) 0.4 ∝ C 0.28 {\displaystyle D_{opt}(C)\propto N_{opt}(C)^{0.4}\propto C^{0.28}} . This exponent corresponds to the ≈ 0.5 {\displaystyle \approx 0.5} from the Chinchilla scaling paper. The scaling law of L = L 0 + ( C 0 / C ) 0.048 {\displaystyle L=L_{0}+(C_{0}/C)^{0.048}} was confirmed during the training of GPT-3 (Figure 3.1 ). === Chinchilla scaling (Hoffmann, et al, 2022) === One particular scaling law ("Chinchilla scaling") states that, for a large language model (LLM) autoregressively trained for one epoch, with a cosine learning rate schedule, we have: { C = C 0 N D L = A N α + B D β + L 0 {\displaystyle {\begin{cases}C=C_{0}ND\\L={\frac {A}{N^{\alpha }}}+{\frac {B}{D^{\beta }}}+L_{0}\end{cases}}} where the variables are C {\displaystyle C} is the cost o
Grokking (machine learning)
In machine learning, grokking, or delayed generalization, is a phenomenon observed in some settings where a model abruptly transitions from overfitting (performing well only on training data) to generalizing (performing well on both training and test data), after many training iterations with little or no improvement on the held-out data. This contrasts with what is typically observed in machine learning, where generalization occurs gradually alongside improved performance on training data. == Origin == Grokking was introduced by OpenAI researcher Alethea Power and colleagues in the January 2022 paper "Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets". It is derived from the word grok coined by Robert Heinlein in his novel Stranger in a Strange Land. In ML research, "grokking" is not used as a synonym for "generalization"; rather, it names a sometimes-observed delayed‑generalization training phenomenon in which training and held‑out performance do not improve in tandem, and in which held‑out performance rises abruptly later. Authors also analyze the "grokking time", the epoch or step at which this transition occurs in those scenarios. == Interpretations == Grokking can be understood as a phase transition during the training process. In particular, recent work has shown that grokking may be due to a complexity phase transition in the model during training. While grokking has been thought of as largely a phenomenon of relatively shallow models, grokking has been observed in deep neural networks and non-neural models and is the subject of active research. One potential explanation is that the weight decay (a component of the loss function that penalizes higher values of the neural network parameters, also called regularization) slightly favors the general solution that involves lower weight values, but that is also harder to find. According to Neel Nanda, the process of learning the general solution may be gradual, even though the transition to the general solution occurs more suddenly later. Recent theories have hypothesized that grokking occurs when neural networks transition from a "lazy training" regime where the weights do not deviate far from initialization, to a "rich" regime where weights abruptly begin to move in task-relevant directions. Follow-up empirical and theoretical work has accumulated evidence in support of this perspective, and it offers a unifying view of earlier work as the transition from lazy to rich training dynamics is known to arise from properties of adaptive optimizers, weight decay, initial parameter weight norm, and more. This perspective is complementary to a unifying "pattern learning speeds" framework that links grokking and double descent; within this view, delayed generalization can arise across training time ("epoch‑wise") or across model size ("model‑wise"), and the authors report "model‑wise grokking".
Robot learning
Robot learning is a research field at the intersection of machine learning and robotics. It studies techniques allowing a robot to acquire novel skills or adapt to its environment through learning algorithms. The embodiment of the robot, situated in a physical embedding, provides at the same time specific difficulties (e.g. high-dimensionality, real time constraints for collecting data and learning) and opportunities for guiding the learning process (e.g. sensorimotor synergies, motor primitives). Example of skills that are targeted by learning algorithms include sensorimotor skills such as locomotion, grasping, active object categorization, as well as interactive skills such as joint manipulation of an object with a human peer, and linguistic skills such as the grounded and situated meaning of human language. Learning can happen either through autonomous self-exploration or through guidance from a human teacher, like for example in robot learning by imitation. Robot learning can be closely related to adaptive control, reinforcement learning as well as developmental robotics which considers the problem of autonomous lifelong acquisition of repertoires of skills. While machine learning is frequently used by computer vision algorithms employed in the context of robotics, these applications are usually not referred to as "robot learning". == Imitation learning == Many research groups are developing techniques where robots learn by imitating. This includes various techniques for learning from demonstration (sometimes also referred to as "programming by demonstration") and observational learning. == Sharing learned skills and knowledge == In Tellex's "Million Object Challenge", the goal is robots that learn how to spot and handle simple items and upload their data to the cloud to allow other robots to analyze and use the information. RoboBrain is a knowledge engine for robots which can be freely accessed by any device wishing to carry out a task. The database gathers new information about tasks as robots perform them, by searching the Internet, interpreting natural language text, images, and videos, object recognition as well as interaction. The project is led by Ashutosh Saxena at Stanford University. RoboEarth is a project that has been described as a "World Wide Web for robots" − it is a network and database repository where robots can share information and learn from each other and a cloud for outsourcing heavy computation tasks. The project brings together researchers from five major universities in Germany, the Netherlands and Spain and is backed by the European Union. Google Research, DeepMind, and Google X have decided to allow their robots share their experiences. == Vision-language-action model == Research groups and companies are developing vision-language-action models, foundation models that allow robotic control through the combination of vision and language. Google DeepMind, Figure AI and Hugging Face are actively working on that.
Feature (machine learning)
In machine learning and pattern recognition, a feature is an individual measurable property or characteristic of a data set. Choosing informative, discriminating, and independent features is crucial to producing effective algorithms for pattern recognition, classification, and regression tasks. Features are usually numeric, but other types such as strings and graphs are used in syntactic pattern recognition, after some pre-processing step such as one-hot encoding. The concept of "features" is related to that of explanatory variables used in statistical techniques such as linear regression. == Feature types == In feature engineering, two types of features are commonly used: numerical and categorical. Numerical features are continuous values that can be measured on a scale. Examples of numerical features include age, height, weight, and income. Numerical features can be used in machine learning algorithms directly. Categorical features are discrete values that can be grouped into categories. Examples of categorical features include gender, color, and zip code. Categorical features typically need to be converted to numerical features before they can be used in machine learning algorithms. This can be done using a variety of techniques, such as one-hot encoding, label encoding, and ordinal encoding. The type of feature that is used in feature engineering depends on the specific machine learning algorithm that is being used. Some machine learning algorithms, such as decision trees, can handle both numerical and categorical features. Other machine learning algorithms, such as linear regression, can only handle numerical features. == Classification == A numeric feature can be conveniently described by a feature vector. One way to achieve binary classification is using a linear predictor function (related to the perceptron) with a feature vector as input. The method consists of calculating the scalar product between the feature vector and a vector of weights, qualifying those observations whose result exceeds a threshold. Algorithms for classification from a feature vector include nearest neighbor classification, neural networks, and statistical techniques such as Bayesian approaches. == Examples == In character recognition, features may include histograms counting the number of black pixels along horizontal and vertical directions, number of internal holes, stroke detection and many others. In speech recognition, features for recognizing phonemes can include noise ratios, length of sounds, relative power, filter matches, logarithmic Mel-scale spectral vectors and Mel-frequency cepstral coefficients, which represent the frequency characteristics of audio signals. In spam detection algorithms, features may include the presence or absence of certain email headers, the email structure, the language, the frequency of specific terms, the grammatical correctness of the text. In computer vision, there are a large number of possible features, such as edges and objects. == Feature vectors == In pattern recognition and machine learning, a feature vector is an n-dimensional vector of numerical features that represent some object. Many algorithms in machine learning require a numerical representation of objects, since such representations facilitate processing and statistical analysis. When representing images, the feature values might correspond to the pixels of an image, while when representing texts the features might be the frequencies of occurrence of textual terms. Feature vectors are equivalent to the vectors of explanatory variables used in statistical procedures such as linear regression. Feature vectors are often combined with weights using a dot product in order to construct a linear predictor function that is used to determine a score for making a prediction. The vector space associated with these vectors is often called the feature space. In order to reduce the dimensionality of the feature space, a number of dimensionality reduction techniques can be employed. Higher-level features can be obtained from already available features and added to the feature vector; for example, for the study of diseases the feature 'Age' is useful and is defined as Age = 'Year of death' minus 'Year of birth' . This process is referred to as feature construction. Feature construction is the application of a set of constructive operators to a set of existing features resulting in construction of new features. Examples of such constructive operators include checking for the equality conditions {=, ≠}, the arithmetic operators {+,−,×, /}, the array operators {max(S), min(S), average(S)} as well as other more sophisticated operators, for example count(S, C) that counts the number of features in the feature vector S satisfying some condition C or, for example, distances to other recognition classes generalized by some accepting device. Feature construction has long been considered a powerful tool for increasing both accuracy and understanding of structure, particularly in high-dimensional problems. Applications include studies of disease and emotion recognition from speech. == Selection and extraction == The initial set of raw features can be redundant and large enough that estimation and optimization is made difficult or ineffective. Therefore, a preliminary step in many applications of machine learning and pattern recognition consists of selecting a subset of features, or constructing a new and reduced set of features to facilitate learning, and to improve generalization and interpretability. Extracting or selecting features is a combination of art and science; developing systems to do so is known as feature engineering. It requires the experimentation of multiple possibilities and the combination of automated techniques with the intuition and knowledge of the domain expert. Automating this process is feature learning, where a machine not only uses features for learning, but learns the features itself.
CLEVER score
The CLEVER (Cross Lipschitz Extreme Value for nEtwork Robustness) score is a way of measuring the robustness of an artificial neural network towards adversarial attacks. It was developed by a team at the MIT-IBM Watson AI Lab in IBM Research and first presented at the 2018 International Conference on Learning Representations. It was mentioned and reviewed by Ian Goodfellow as well. It was adopted into an educational game Fool The Bank by Narendra Nath Joshi, Abhishek Bhandwaldar and Casey Dugan
Comparison of machine learning software
The following tables are a comparison of machine learning software such as software frameworks, libraries, and computer programs used for machine learning. == Machine learning software == == Other comparisons == == Machine learning helper libraries and platforms == Apache OpenNLP — natural language processing toolkit CUDA — GPU computing platform used to accelerate machine learning and deep learning workloads Horovod — distributed training framework for deep learning Hugging Face Transformers — library of pretrained transformer models built on other machine learning frameworks Kubeflow — machine learning platform for Kubernetes Mallet — toolkit for natural language processing and text analysis NumPy — numerical computing library used in machine learning OpenCV — computer vision library with machine learning functions ONNX — open format for representing machine learning models pandas — data analysis and data preparation library used in machine learning PlaidML — tensor compiler and backend for machine learning frameworks Polars — Dataframe library used for machine learning data preparation and analysis PyArrow — columnar data library used in machine learning data processing ROOT (TMVA) — data analysis framework with machine learning tools SciPy — scientific computing and optimization library used in machine learning == Online development environments for machine learning == Google Colab — hosted Jupyter Notebook environment commonly used for machine learning and deep learning JupyterLab — notebook-based development environment for machine learning and data science Jupyter Notebook — interactive notebook environment used for machine learning and data science Kaggle — online data science and machine learning platform