In geometry and computer graphics, a supertoroid or supertorus is usually understood to be a family of doughnut-like surfaces (technically, a topological torus) whose shape is defined by mathematical formulas similar to those that define the superellipsoids. The plural of "supertorus" is either supertori or supertoruses. The family was described and named by Alan Barr in 1994. Barr's supertoroids have been fairly popular in computer graphics as a convenient model for many objects, such as smooth frames for rectangular things. One quarter of a supertoroid can provide a smooth and seamless 90-degree joint between two superquadric cylinders. However, they are not algebraic surfaces (except in special cases). == Formulas == Alan Barr's supertoroids are defined by parametric equations similar to the trigonometric equations of the torus, except that the sine and cosine terms are raised to arbitrary powers. Namely, the generic point P(u, v) of the surface is given by P ( u , v ) = ( X ( u , v ) Y ( u , v ) Z ( u , v ) ) = ( ( a + C u s ) C v t ( b + C u s ) S v t S u s ) {\displaystyle P(u,v)=\left({\begin{array}{c}X(u,v)\\Y(u,v)\\Z(u,v)\end{array}}\right)=\left({\begin{array}{c}(a+C_{u}^{s})C_{v}^{t}\\(b+C_{u}^{s})S_{v}^{t}\\S_{u}^{s}\end{array}}\right)} where C θ ε = sgn ( cos θ ) | cos θ | ε , S θ ε = sgn ( sin θ ) | sin θ | ε , {\displaystyle {\begin{aligned}C_{\theta }^{\varepsilon }&=\operatorname {sgn} (\cos \theta )\,\left|\,\cos \theta \,\right|^{\varepsilon },\\S_{\theta }^{\varepsilon }&=\operatorname {sgn} (\sin \theta )\ \left|\,\sin \theta \ \right|^{\varepsilon },\end{aligned}}} sgn is the sign function, and the parameters u, v range from 0 to 360 degrees (0 to 2π radians). In these formulas, the parameter s > 0 controls the "squareness" of the vertical sections, t > 0 controls the squareness of the horizontal sections, and a, b ≥ 1 are the major radii in the x and y directions. With s = t = 1 and a = b = R one obtains the ordinary torus with major radius R and minor radius 1, with the center at the origin and rotational symmetry about the z-axis. In general, the supertorus defined as above spans the intervals: − ( a + 1 ) ≤ x ≤ + ( a + 1 ) − ( b + 1 ) ≤ y ≤ + ( b + 1 ) − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}-(a+1)&\leq &x&\leq &+(a+1)\\[4pt]-(b+1)&\leq &y&\leq &+(b+1)\\[4pt]-1&\leq &z&\leq &+1\end{array}}} The whole shape is symmetric about the planes x = 0, y = 0, and z = 0. The hole runs in the z direction and spans the intervals − ( a − 1 ) ≤ x ≤ + ( a − 1 ) − ( b − 1 ) ≤ y ≤ + ( b − 1 ) − ∞ ≤ z ≤ + ∞ {\displaystyle {\begin{array}{rcccl}-(a-1)&\leq &x&\leq &+(a-1)\\[4pt]-(b-1)&\leq &y&\leq &+(b-1)\\[4pt]-\infty &\leq &z&\leq &+\infty \end{array}}} A curve of constant u on this surface is a horizontal Lamé curve with exponent 2 t , {\displaystyle {\tfrac {2}{t}},} scaled in x and y and displaced in z. A curve of constant v, projected on the plane x = 0 or y = 0, is a Lamé curve with exponent 2 s , {\displaystyle {\tfrac {2}{s}},} scaled and horizontally shifted. If v = 0, the curve is planar and spans the intervals: a − 1 ≤ x ≤ a + 1 − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}a-1&\leq &x&\leq &a+1\\[4pt]-1&\leq &z&\leq &+1\end{array}}} and similarly if v = 90°, 180°, 270°. The curve is also planar if a = b. In general, if a ≠ b and v is not a multiple of 90 degrees, the curve of constant v will not be planar; and, conversely, a vertical plane section of the supertorus will not be a Lamé curve. The basic supertoroid shape defined above is often modified by non-uniform scaling to yield supertoroids of specific width, length, and vertical thickness. == Plotting code == The following GNU Octave code generates plots of a supertorus:
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
Inductive programming
Inductive programming (IP) is a special area of automatic programming, covering research from artificial intelligence and programming, which addresses learning of typically declarative (logic or functional) and often recursive programs from incomplete specifications, such as input/output examples or constraints. Depending on the programming language used, there are several kinds of inductive programming. Inductive functional programming, which uses functional programming languages such as Lisp or Haskell, and most especially inductive logic programming, which uses logic programming languages such as Prolog and other logical representations such as description logics, have been more prominent, but other (programming) language paradigms have also been used, such as constraint programming or probabilistic programming. == Definition == Inductive programming incorporates all approaches which are concerned with learning programs or algorithms from incomplete (formal) specifications. Possible inputs in an IP system are a set of training inputs and corresponding outputs or an output evaluation function, describing the desired behavior of the intended program, traces or action sequences which describe the process of calculating specific outputs, constraints for the program to be induced concerning its time efficiency or its complexity, various kinds of background knowledge such as standard data types, predefined functions to be used, program schemes or templates describing the data flow of the intended program, heuristics for guiding the search for a solution or other biases. Output of an IP system is a program in some arbitrary programming language containing conditionals and loop or recursive control structures, or any other kind of Turing-complete representation language. In many applications the output program must be correct with respect to the examples and partial specification, and this leads to the consideration of inductive programming as a special area inside automatic programming or program synthesis, usually opposed to 'deductive' program synthesis, where the specification is usually complete. In other cases, inductive programming is seen as a more general area where any declarative programming or representation language can be used and we may even have some degree of error in the examples, as in general machine learning, the more specific area of structure mining or the area of symbolic artificial intelligence. A distinctive feature is the number of examples or partial specification needed. Typically, inductive programming techniques can learn from just a few examples. The diversity of inductive programming usually comes from the applications and the languages that are used: apart from logic programming and functional programming, other programming paradigms and representation languages have been used or suggested in inductive programming, such as functional logic programming, constraint programming, probabilistic programming, abductive logic programming, modal logic, action languages, agent languages and many types of imperative languages. == History == The early works of Plotkin, and his "relative least general generalization (rlgg)", had an enormous impact in inductive logic programming. There were some encouraging results on learning recursive Prolog programs such as quicksort from examples together with suitable background knowledge, for example with GOLEM. However, after initial success, the community got disappointed by limited progress about the induction of recursive programs with ILP less and less focusing on recursive programs and leaning more and more towards a machine learning setting with applications in relational data mining and knowledge discovery. In parallel to work in ILP, Koza proposed genetic programming in the early 1990s as a generate-and-test based approach to learning programs. The idea of genetic programming was further developed into the inductive programming system ADATE and the systematic-search-based system MagicHaskeller. Here again, functional programs are learned from sets of positive examples together with an output evaluation (fitness) function which specifies the desired input/output behavior of the program to be learned. The early work in grammar induction (also known as grammatical inference) is related to inductive programming, as rewriting systems or logic programs can be used to represent production rules. In fact, early works in inductive inference considered grammar induction and Lisp program inference as basically the same problem. The results in terms of learnability were related to classical concepts, such as identification-in-the-limit, as introduced in the seminal work of Gold. More recently, the language learning problem was addressed by the inductive programming community. In the recent years, the classical approaches have been resumed and advanced with great success. Therefore, the synthesis problem has been reformulated on the background of constructor-based term rewriting systems taking into account modern techniques of functional programming, as well as moderate use of search-based strategies and usage of background knowledge as well as automatic invention of subprograms. Many new and successful applications have recently appeared beyond program synthesis, most especially in the area of data manipulation, programming by example and cognitive modelling (see below). Other ideas have also been explored with the common characteristic of using declarative languages for the representation of hypotheses. For instance, the use of higher-order features, schemes or structured distances have been advocated for a better handling of recursive data types and structures; abstraction has also been explored as a more powerful approach to cumulative learning and function invention. One powerful paradigm that has been recently used for the representation of hypotheses in inductive programming (generally in the form of generative models) is probabilistic programming (and related paradigms, such as stochastic logic programs and Bayesian logic programming). == Application areas == The first workshop on Approaches and Applications of Inductive Programming (AAIP) Archived 2016-03-03 at the Wayback Machine held in conjunction with ICML 2005 identified all applications where "learning of programs or recursive rules are called for, [...] first in the domain of software engineering where structural learning, software assistants and software agents can help to relieve programmers from routine tasks, give programming support for end users, or support of novice programmers and programming tutor systems. Further areas of application are language learning, learning recursive control rules for AI-planning, learning recursive concepts in web-mining or for data-format transformations". Since then, these and many other areas have shown to be successful application niches for inductive programming, such as end-user programming, the related areas of programming by example and programming by demonstration, and intelligent tutoring systems. Other areas where inductive inference has been recently applied are knowledge acquisition, artificial general intelligence, reinforcement learning and theory evaluation, and cognitive science in general. There may also be prospective applications in intelligent agents, games, robotics, personalisation, ambient intelligence and human interfaces.
AIXI
AIXI is a theoretical mathematical formalism for artificial general intelligence. It combines Solomonoff induction with sequential decision theory. AIXI was first proposed by Marcus Hutter in 2000 and several results regarding AIXI are proved in Hutter's 2005 book Universal Artificial Intelligence. AIXI is a reinforcement learning (RL) agent. It maximizes the expected total rewards received from the environment. Intuitively, it simultaneously considers every computable hypothesis (or environment). In each time step, it looks at every possible program and evaluates how many rewards that program generates depending on the next action taken. The promised rewards are then weighted by the subjective belief that this program constitutes the true environment. This belief is computed from the length of the program: longer programs are considered less likely, in line with Occam's razor. AIXI then selects the action that has the highest expected total reward in the weighted sum of all these programs. == Etymology == According to Hutter, the word "AIXI" can have several interpretations. AIXI can stand for AI based on Solomonoff's distribution, denoted by ξ {\displaystyle \xi } (which is the Greek letter xi), or e.g. it can stand for AI "crossed" (X) with induction (I). There are other interpretations. == Definition == AIXI is a reinforcement learning agent that interacts with some stochastic and unknown but computable environment μ {\displaystyle \mu } . The interaction proceeds in time steps, from t = 1 {\displaystyle t=1} to t = m {\displaystyle t=m} , where m ∈ N {\displaystyle m\in \mathbb {N} } is the lifespan of the AIXI agent. At time step t, the agent chooses an action a t ∈ A {\displaystyle a_{t}\in {\mathcal {A}}} (e.g. a limb movement) and executes it in the environment, and the environment responds with a "percept" e t ∈ E = O × R {\displaystyle e_{t}\in {\mathcal {E}}={\mathcal {O}}\times \mathbb {R} } , which consists of an "observation" o t ∈ O {\displaystyle o_{t}\in {\mathcal {O}}} (e.g., a camera image) and a reward r t ∈ R {\displaystyle r_{t}\in \mathbb {R} } , distributed according to the conditional probability μ ( o t r t | a 1 o 1 r 1 . . . a t − 1 o t − 1 r t − 1 a t ) {\displaystyle \mu (o_{t}r_{t}|a_{1}o_{1}r_{1}...a_{t-1}o_{t-1}r_{t-1}a_{t})} , where a 1 o 1 r 1 . . . a t − 1 o t − 1 r t − 1 a t {\displaystyle a_{1}o_{1}r_{1}...a_{t-1}o_{t-1}r_{t-1}a_{t}} is the "history" of actions, observations and rewards. The environment μ {\displaystyle \mu } is thus mathematically represented as a probability distribution over "percepts" (observations and rewards) which depend on the full history, so there is no Markov assumption (as opposed to other RL algorithms). Note again that this probability distribution is unknown to the AIXI agent. Furthermore, note again that μ {\displaystyle \mu } is computable, that is, the observations and rewards received by the agent from the environment μ {\displaystyle \mu } can be computed by some program (which runs on a Turing machine), given the past actions of the AIXI agent. The only goal of the AIXI agent is to maximize ∑ t = 1 m r t {\displaystyle \sum _{t=1}^{m}r_{t}} , that is, the sum of rewards from time step 1 to m. The AIXI agent is associated with a stochastic policy π : ( A × E ) ∗ → A {\displaystyle \pi :({\mathcal {A}}\times {\mathcal {E}})^{}\rightarrow {\mathcal {A}}} , which is the function it uses to choose actions at every time step, where A {\displaystyle {\mathcal {A}}} is the space of all possible actions that AIXI can take and E {\displaystyle {\mathcal {E}}} is the space of all possible "percepts" that can be produced by the environment. The environment (or probability distribution) μ {\displaystyle \mu } can also be thought of as a stochastic policy (which is a function): μ : ( A × E ) ∗ × A → E {\displaystyle \mu :({\mathcal {A}}\times {\mathcal {E}})^{}\times {\mathcal {A}}\rightarrow {\mathcal {E}}} , where the ∗ {\displaystyle } is the Kleene star operation. In general, at time step t {\displaystyle t} (which ranges from 1 to m), AIXI, having previously executed actions a 1 … a t − 1 {\displaystyle a_{1}\dots a_{t-1}} (which is often abbreviated in the literature as a < t {\displaystyle a_{ Label noise refers to errors or inaccuracies in the class labels of data instances. This is a widespread issue in machine learning datasets, arising from human annotator mistakes, unclear labeling instructions, automated labeling methods, or adversarial attacks in supervised learning. Label noise can be roughly divided into random noise, where labels are flipped independently of input features, and systematic noise, where mislabeling is dependent on certain patterns or biases in the data. Label noise can be damaging to model performance, especially for complex models that may overfit to noisy labels rather than generalizable patterns. Many approaches have been proposed to deal with the effects of label noise, including robust loss functions, noise-tolerant algorithms, data cleaning methods, and semi-supervised learning approaches. To reduce the impact of wrong labels during training, techniques like label smoothing, sample reweighting and using trusted validation sets are used. The role of noise-robust training paradigms and curriculum learning strategies to improve resilience against mislabeled data is also explored in recent research. Dataset shift is a phenomenon in machine learning and statistics in which the joint distribution of input variables and target labels is different in the training phase and the deployment or test phase (i.e., P t r a i n ( X , Y ) ≠ P t e s t ( X , Y ) {\displaystyle P_{train}(X,Y)\neq P_{test}(X,Y)} ). This happens when the statistical properties of data used to train a model are no longer representative of the data encountered in real-world use, often resulting in degraded predictive performance and diminished generalization ability. Dataset shift is a generic term for a number of particular types of distributional change. Covariate shift is when the distribution of the input features changes, but the conditional relationship between inputs and outputs remains constant . Prior probability shift (or label shift) happens when the distribution of target labels changes, but the conditional distribution of inputs given labels stays the same. Concept shift (also known as concept drift) is the change of the conditional relationship between inputs and outputs that renders previously learned patterns invalid over time. A key challenge for deploying machine learning systems is dataset shift, in particular in dynamic environments where the data distributions change over time. Detecting and mitigating such shifts is an active area of research, e.g., drift detection, domain adaptation, continual learning. Reciprocal Human Machine Learning (RHML) is an interdisciplinary approach to designing human-AI interaction systems. RHML aims to enable continual learning between humans and machine learning models by having them learn from each other. This approach keeps the human expert "in the loop" to oversee and enhance machine learning performance and simultaneously support the human expert continue learning. == Background == RHML emerged in the context of the rise of big data analytics and artificial intelligence for intelligent tasks like sense-making and decision-making. As machine learning advanced to take on more roles, researchers realized fully autonomous systems had limitations and needed human guidance. RHML extends the concept of human-in-the-loop systems by promoting reciprocal learning. Humans learn from their interactions with machine learning models, staying up-to-date on evolving technology. The models also learn from human feedback and oversight. This amplification of learning on both sides is a key focus of RHML. The approach draws on theories of learning in dyads from education and psychology. It also builds on human-computer interaction and human-centered design principles. Implementing RHML requires developing specialized tools and interfaces tailored to the application == Applications == RHML has been explored across diverse domains including: Cybersecurity - Software to enable reciprocal learning between experts and AI models for social media threat detection. Organizational decision-making - RHML to structure collaboration between humans and AI systems. Workplace training - Using RHML for workers to learn from AI technologies on the job. Open science - Using human and AI collaboration to promote open science. Production and logistics - turning workers and intelligent machines into teammates. RHML maintains human oversight and control over AI systems, while enabling cutting-edge machine learning performance. This collaborative approach highlights the importance of keeping the human expert involved in the loop. An example of RHML in application is Free Spirit (AFSFCV), an open-source architecture first published in early 2025 as a whitepaper, proposing a visually structured approach to intent-based human–AI interaction.Label noise
Dataset shift
Reciprocal human machine learning