Developmental robotics (DevRob), sometimes called epigenetic robotics, is a scientific field which aims at studying the developmental mechanisms, architectures and constraints that allow lifelong and open-ended learning of new skills and new knowledge in embodied machines. As in human children, learning is expected to be cumulative and of progressively increasing complexity, and to result from self-exploration of the world in combination with social interaction. The typical methodological approach consists in starting from theories of human and animal development elaborated in fields such as developmental psychology, neuroscience, developmental and evolutionary biology, and linguistics, then to formalize and implement them in robots, sometimes exploring extensions or variants of them. The experimentation of those models in robots allows researchers to confront them with reality, and as a consequence, developmental robotics also provides feedback and novel hypotheses on theories of human and animal development. Developmental robotics is related to but differs from evolutionary robotics (ER). ER uses populations of robots that evolve over time, whereas DevRob is interested in how the organization of a single robot's control system develops through experience, over time. DevRob is also related to work done in the domains of robotics and artificial life. == Background == Can a robot learn like a child? Can it learn a variety of new skills and new knowledge unspecified at design time and in a partially unknown and changing environment? How can it discover its body and its relationships with the physical and social environment? How can its cognitive capacities continuously develop without the intervention of an engineer once it is "out of the factory"? What can it learn through natural social interactions with humans? These are the questions at the center of developmental robotics. Alan Turing, as well as a number of other pioneers of cybernetics, already formulated those questions and the general approach in 1950, but it is only since the end of the 20th century that they began to be investigated systematically. Because the concept of adaptive intelligent machines is central to developmental robotics, it has relationships with fields such as artificial intelligence, machine learning, cognitive robotics or computational neuroscience. Yet, while it may reuse some of the techniques elaborated in these fields, it differs from them from many perspectives. It differs from classical artificial intelligence because it does not assume the capability of advanced symbolic reasoning and focuses on embodied and situated sensorimotor and social skills rather than on abstract symbolic problems. It differs from cognitive robotics because it focuses on the processes that allow the formation of cognitive capabilities rather than these capabilities themselves. It differs from computational neuroscience because it focuses on functional modeling of integrated architectures of development and learning. More generally, developmental robotics is uniquely characterized by the following three features: It targets task-independent architectures and learning mechanisms, i.e. the machine/robot has to be able to learn new tasks that are unknown by the engineer; It emphasizes open-ended development and lifelong learning, i.e. the capacity of an organism to acquire continuously novel skills. This should not be understood as a capacity for learning "anything" or even “everything”, but just that the set of skills that is acquired can be infinitely extended at least in some (not all) directions; The complexity of acquired knowledge and skills shall increase (and the increase be controlled) progressively. Developmental robotics emerged at the crossroads of several research communities including embodied artificial intelligence, enactive and dynamical systems cognitive science, connectionism. Starting from the essential idea that learning and development happen as the self-organized result of the dynamical interactions among brains, bodies and their physical and social environment, and trying to understand how this self-organization can be harnessed to provide task-independent lifelong learning of skills of increasing complexity, developmental robotics strongly interacts with fields such as developmental psychology, developmental and cognitive neuroscience, developmental biology (embryology), evolutionary biology, and cognitive linguistics. As many of the theories coming from these sciences are verbal and/or descriptive, this implies a crucial formalization and computational modeling activity in developmental robotics. These computational models are then not only used as ways to explore how to build more versatile and adaptive machines but also as a way to evaluate their coherence and possibly explore alternative explanations for understanding biological development. == Research directions == === Skill domains === Due to the general approach and methodology, developmental robotics projects typically focus on having robots develop the same types of skills as human infants. A first category that is important being investigated is the acquisition of sensorimotor skills. These include the discovery of one's own body, including its structure and dynamics such as hand-eye coordination, locomotion, and interaction with objects as well as tool use, with a particular focus on the discovery and learning of affordances. A second category of skills targeted by developmental robots are social and linguistic skills: the acquisition of simple social behavioural games such as turn-taking, coordinated interaction, lexicons, syntax and grammar, and the grounding of these linguistic skills into sensorimotor skills (sometimes referred as symbol grounding). In parallel, the acquisition of associated cognitive skills are being investigated such as the emergence of the self/non-self distinction, the development of attentional capabilities, of categorization systems and higher-level representations of affordances or social constructs, of the emergence of values, empathy, or theories of mind. === Mechanisms and constraints === The sensorimotor and social spaces in which humans and robot live are so large and complex that only a small part of potentially learnable skills can actually be explored and learnt within a life-time. Thus, mechanisms and constraints are necessary to guide developmental organisms in their development and control of the growth of complexity. There are several important families of these guiding mechanisms and constraints which are studied in developmental robotics, all inspired by human development: Motivational systems, generating internal reward signals that drive exploration and learning, which can be of two main types: extrinsic motivations push robots/organisms to maintain basic specific internal properties such as food and water level, physical integrity, or light (e.g. in phototropic systems); intrinsic motivations push robot to search for novelty, challenge, compression or learning progress per se, thus generating what is sometimes called curiosity-driven learning and exploration, or alternatively active learning and exploration; Social guidance: as humans learn a lot by interacting with their peers, developmental robotics investigates mechanisms that can allow robots to participate to human-like social interaction. By perceiving and interpreting social cues, this may allow robots both to learn from humans (through diverse means such as imitation, emulation, stimulus enhancement, demonstration, etc. ...) and to trigger natural human pedagogy. Thus, social acceptance of developmental robots is also investigated; Statistical inference biases and cumulative knowledge/skill reuse: biases characterizing both representations/encodings and inference mechanisms can typically allow considerable improvement of the efficiency of learning and are thus studied. Related to this, mechanisms allowing to infer new knowledge and acquire new skills by reusing previously learnt structures is also an essential field of study; The properties of embodiment, including geometry, materials, or innate motor primitives/synergies often encoded as dynamical systems, can considerably simplify the acquisition of sensorimotor or social skills, and is sometimes referred as morphological computation. The interaction of these constraints with other constraints is an important axis of investigation; Maturational constraints: In human infants, both the body and the neural system grow progressively, rather than being full-fledged already at birth. This implies, for example, that new degrees of freedom, as well as increases of the volume and resolution of available sensorimotor signals, may appear as learning and development unfold. Transposing these mechanisms in developmental robots, and understanding how it may hinder or on the contrary ease the acquisition of novel complex skills is a central questi
Necrobotics
Necrobotics is the practice of using biotic materials (or dead organisms) as robotic components. Necrobotics can serve as an alternative to mechanical components that are difficult to manufacture by using biological components designed by natural selection in order to exploit the highly developed selective design implemented in biological lifeforms via the process of evolution. In July 2022, researchers in the Preston Innovation Lab at Rice University in Houston, Texas published a paper in Advanced Science introducing the concept and demonstrating its capability by repurposing dead spiders as robotic grippers and applying pressurized air to activate their gripping arms. In April 2025 researchers at Shinshu University created a “bio-hybrid drone” using silk-worm moth antennae to detect the source of a smell. In November 2025 researchers at McGill University demonstrated the use of a mosquito proboscis as a fine nozzle in experimental 3D printing. Necrobotics utilizes the spider's organic hydraulic system and their compact legs to create an efficient and simple gripper system. The necrobotic spider gripper is capable of lifting small and light objects, thereby serving as an alternative to complex and costly small mechanical grippers. == Background == The main appeal of the spider's body in necrobotics is its compact leg mechanism and use of hydraulic pressure. The spider's anatomy utilizes a simple hydraulic (fluid) pressure system. Spider legs have flexor muscles that naturally constrict their legs when relaxed. A force is required to straighten and extend their legs, which spiders accomplish by pumping hemolymph fluid (blood) through their joints as a means of hydraulic pressure. It takes no external power to curl their legs due to their flexor muscles' natural curled state. In July 2022, researchers in the Preston Innovation Lab at Rice University published a paper detailing their experiments with the gripper. Although dead spiders no longer produce hemolymph, Te Faye Yap (lead author and mechanical engineering graduate) found that pumping air through a needle into the spider's cephalothorax (main body) accomplishes the same results as hemolymph. The original hydraulic (fluid) system is essentially converted into a pneumatic (air) system. == Fabrication == Obtain a spider Euthanize the spider using a cold temperature of around -4°C for 5-7 days Insert a 25 gauge hypodermic needle into the spider's cephalothorax (main body) Apply glue around the needle to form a seal and allow it to dry Connect a syringe or pump to the needle Extend the spider's legs by pumping air in == Testing and Data == === Internal Force Versus Gripping Force === The typical pressure in a resting spider's legs ranges from 4 kPa to 6.1 kPa. Researchers extended the legs by increasing the spider's internal pressure to 5.5 kPa. Pumping air into the body increases the internal pressure, causing the legs to expand. Pumping air out of the body decreases internal pressure, causing the legs to contract due to their flexor leg muscles. When the internal pressure decreases to 0 kPa, the gripper would be fully closed, allowing for the gripper to grasp objects. This action demonstrates that as internal pressure decreases, the gripping force increases. Inversely, when internal pressure increases, the gripping force decreases. By gripping individual weighted acetate beads, it is found that the necrobotic gripper achieves a maximum gripping force of 0.35 milinewtons. === Spider Weight Versus Gripping Force === To estimate the gripping forces of smaller and larger spiders, researchers created a plot to predict the gripping force relative to the size of the spider. The wolf spider's body weight is relatively equal to the gripping force of its legs. The mass of the gripper is 33.5 mg and can lift 1.3 times its body weight (43.6 mg or 0.35 mN). However, with larger spiders, the gripping force relative to body weight decreases. For example, a 200-gram goliath birdeater is predicted to lift 10% of its weight (20 grams or 196 mN). Though there is an inverse relationship between spider mass and gripping force, larger spiders exert greater gripping forces than smaller spiders. === Gripper Lifespan === The necrobotic gripper's functionality is entirely reliant on the structural integrity of the spider. If the spider were to break down easily and frequently, the gripper would not be practical. Using cyclic testing, a series of repeated actions, it is found that the necrobotic gripper can actuate 700 to 1000 times. After 1000 cycles, cracks begin forming on the membrane of the leg joints due to dehydration. Weakened and decomposing joints lead to frequent breakage and replacement, thereby serving as an obstacle in applying necrobotics to real-world scenarios. One theorized fix to this issue is applying beeswax or a lubricant to the joints. Researchers found that over 10 days, the mass of an uncoated spider decreased 17 times more than the mass of a spider coated with beeswax. Lubricating joints combats dehydration and slows the loss of organic material. == Constraints == With the usage of organic material, there is a higher chance of the component decomposing and breaking down as opposed to traditional mechanical systems. There may be additional work and management required to replace these grippers if they fail. Additionally, organic inconsistencies with the spiders will yield inaccurate results. Not all wolf spiders develop the same, so gripping force and leg contraction can vary between grippers. There are moral implications behind euthanizing spiders for robotics. The ethical boundaries that necrobotics push in the pursuit of biohybrid systems raise concerns, as opponents say it may lead to the hybridization of mammals and is intrusive to nature. Proponents respond that repurposing dead animals has been human practice for millennia and that necrobotics should be pursued to advance science.
Learning vector quantization
In computer science, learning vector quantization (LVQ) is a prototype-based supervised classification algorithm. LVQ is the supervised counterpart of vector quantization systems. LVQ can be understood as a special case of an artificial neural network, more precisely, it applies a winner-take-all Hebbian learning-based approach. It is a precursor to self-organizing maps (SOM) and related to neural gas and the k-nearest neighbor algorithm (k-NN). LVQ was invented by Teuvo Kohonen. == Definition == An LVQ system is represented by prototypes W = ( w ( i ) , . . . , w ( n ) ) {\displaystyle W=(w(i),...,w(n))} which are defined in the feature space of observed data. In winner-take-all training algorithms one determines, for each data point, the prototype which is closest to the input according to a given distance measure. The position of this so-called winner prototype is then adapted, i.e. the winner is moved closer if it correctly classifies the data point or moved away if it classifies the data point incorrectly. An advantage of LVQ is that it creates prototypes that are easy to interpret for experts in the respective application domain. LVQ systems can be applied to multi-class classification problems in a natural way. A key issue in LVQ is the choice of an appropriate measure of distance or similarity for training and classification. Recently, techniques have been developed which adapt a parameterized distance measure in the course of training the system, see e.g. (Schneider, Biehl, and Hammer, 2009) and references therein. LVQ can be a valuable aid in classifying text documents. == Algorithm == The algorithms are presented as in. Set up: Let the data be denoted by x i ∈ R D {\displaystyle x_{i}\in \mathbb {R} ^{D}} , and their corresponding labels by y i ∈ { 1 , 2 , … , C } {\displaystyle y_{i}\in \{1,2,\dots ,C\}} . The complete dataset is { ( x i , y i ) } i = 1 N {\displaystyle \{(x_{i},y_{i})\}_{i=1}^{N}} . The set of code vectors is w j ∈ R D {\displaystyle w_{j}\in \mathbb {R} ^{D}} . The learning rate at iteration step t {\displaystyle t} is denoted by α t {\displaystyle \alpha _{t}} . The hyperparameters w {\displaystyle w} and ϵ {\displaystyle \epsilon } are used by LVQ2 and LVQ3. The original paper suggests ϵ ∈ [ 0.1 , 0.5 ] {\displaystyle \epsilon \in [0.1,0.5]} and w ∈ [ 0.2 , 0.3 ] {\displaystyle w\in [0.2,0.3]} . === LVQ1 === Initialize several code vectors per label. Iterate until convergence criteria is reached. Sample a datum x i {\displaystyle x_{i}} , and find out the code vector w j {\displaystyle w_{j}} , such that x i {\displaystyle x_{i}} falls within the Voronoi cell of w j {\displaystyle w_{j}} . If its label y i {\displaystyle y_{i}} is the same as that of w j {\displaystyle w_{j}} , then w j ← w j + α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}+\alpha _{t}(x_{i}-w_{j})} , otherwise, w j ← w j − α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}-\alpha _{t}(x_{i}-w_{j})} . === LVQ2 === LVQ2 is the same as LVQ3, but with this sentence removed: "If w j {\displaystyle w_{j}} and w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have the same class, then w j ← w j − α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}-\alpha _{t}(x_{i}-w_{j})} and w k ← w k + α t ( x i − w k ) {\displaystyle w_{k}\leftarrow w_{k}+\alpha _{t}(x_{i}-w_{k})} .". If w j {\displaystyle w_{j}} and w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have the same class, then nothing happens. === LVQ3 === Initialize several code vectors per label. Iterate until convergence criteria is reached. Sample a datum x i {\displaystyle x_{i}} , and find out two code vectors w j , w k {\displaystyle w_{j},w_{k}} closest to it. Let d j := ‖ x i − w j ‖ , d k := ‖ x i − w k ‖ {\displaystyle d_{j}:=\|x_{i}-w_{j}\|,d_{k}:=\|x_{i}-w_{k}\|} . If min ( d j d k , d k d j ) > s {\displaystyle \min \left({\frac {d_{j}}{d_{k}}},{\frac {d_{k}}{d_{j}}}\right)>s} , where s = 1 − w 1 + w {\displaystyle s={\frac {1-w}{1+w}}} , then If w j {\displaystyle w_{j}} and x i {\displaystyle x_{i}} have the same class, and w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have different classes, then w j ← w j + α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}+\alpha _{t}(x_{i}-w_{j})} and w k ← w k − α t ( x i − w k ) {\displaystyle w_{k}\leftarrow w_{k}-\alpha _{t}(x_{i}-w_{k})} . If w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have the same class, and w j {\displaystyle w_{j}} and x i {\displaystyle x_{i}} have different classes, then w j ← w j − α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}-\alpha _{t}(x_{i}-w_{j})} and w k ← w k + α t ( x i − w k ) {\displaystyle w_{k}\leftarrow w_{k}+\alpha _{t}(x_{i}-w_{k})} . If w j {\displaystyle w_{j}} and w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have the same class, then w j ← w j − ϵ α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}-\epsilon \alpha _{t}(x_{i}-w_{j})} and w k ← w k + ϵ α t ( x i − w k ) {\displaystyle w_{k}\leftarrow w_{k}+\epsilon \alpha _{t}(x_{i}-w_{k})} . If w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have different classes, and w j {\displaystyle w_{j}} and x i {\displaystyle x_{i}} have different classes, then the original paper simply does not explain what happens in this case, but presumably nothing happens in this case. Otherwise, skip. Note that condition min ( d j d k , d k d j ) > s {\displaystyle \min \left({\frac {d_{j}}{d_{k}}},{\frac {d_{k}}{d_{j}}}\right)>s} , where s = 1 − w 1 + w {\displaystyle s={\frac {1-w}{1+w}}} , precisely means that the point x i {\displaystyle x_{i}} falls between two Apollonian spheres.
Illia Polosukhin
Illia Polosukhin is a Ukrainian-born computer scientist and entrepreneur known for his work on the transformer architecture in machine learning and for co-founding the NEAR blockchain. == Early life and education == Polosukhin studied at the Kharkiv Polytechnic Institute, later relocating to San Diego and then moving to Silicon Valley. == Career == === Google and transformer research === Polosukhin worked at Google and was part of the team associated with research on self-attention that culminated in the 2017 paper Attention Is All You Need, widely credited with introducing the transformer architecture used in modern large language models. === NEAR Protocol === After his work in machine learning, Polosukhin became a co-founder of NEAR Protocol and later associated with the NEAR Foundation ecosystem. In 2023, Polosukhin publicly argued that increasingly capable A.I. systems should be more transparent and user-controlled, and expressed skepticism that conventional regulation alone would solve problems created by closed, corporate models, warning about risks such as regulatory capture. He has promoted “user-owned AI” concepts that combine open approaches with decentralized infrastructure aligned with the blockchain technology. In 2024, Polosukhin downplayed scenarios of A.I. independently causing human extinction, arguing that conflicts are driven by people and that misuse of AI would reflect human intent and incentives. Later this year, Polosukhin said the NEAR Foundation would reduce its workforce by about 40%. == Publications == Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Lukasz Kaiser, Illia Polosukhin; et al. (2017). "Attention Is All You Need". arXiv.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Leela Zero
Leela Zero is a free and open-source computer Go program released on 25 October 2017. It is developed by Belgian programmer Gian-Carlo Pascutto, the author of chess engine Sjeng and Go engine Leela. Leela Zero's algorithm is based on DeepMind's 2017 paper about AlphaGo Zero. Unlike the original Leela, which has a lot of human knowledge and heuristics programmed into it, the program code in Leela Zero only knows the basic rules and nothing more. The knowledge that makes Leela Zero a strong player is contained in a neural network, which is trained based on the results of previous games that the program played. Leela Zero is trained by a distributed effort, which is coordinated at the Leela Zero website. Members of the community provide computing resources by running the client, which generates self-play games and submits them to the server. The self-play games are used to train newer networks. Generally, over 500 clients have connected to the server to contribute resources. The community has provided high quality code contributions as well. == Version history == Leela Zero finished third at the BerryGenomics Cup World AI Go Tournament in Fuzhou, Fujian, China on 28 April 2018. The New Yorker at the end of 2018 characterized Leela and Leela Zero as "the world’s most successful open-source Go engines". In early 2018, another team branched Leela Chess Zero from the same code base, also to verify the methods in the AlphaZero paper as applied to the game of chess. AlphaZero's use of Google TPUs was replaced by a crowd-sourcing infrastructure and the ability to use graphics card GPUs via the OpenCL library. Even so, it is expected to take a year of crowd-sourced training to make up for the dozen hours that AlphaZero was allowed to train for its chess match in the paper. The distributed training server was shut down on 2021-02-15, marking the end of Leela Zero project. The page now directs visitors to KataGo and SAI. The model sizes increased steadily over time. The first released model has hash name d645af97, size 1x8 (1 layer, 8 channels), and released at 2017-11-10 13:04. The last released model has hash name 0e9ea880, size 40x256, and was released at 2021-02-15 09:04. == Technology == Leela Zero is an (almost) exact replication of AlphaGo Zero in both training process and architecture. The training process is Monte-Carlo Tree Search with self-play, exactly the same as AlphaGo Zero. The architecture is the same as AlphaGo Zero (with one difference). Consider the last released model, 0e9ea880. It has 47 million parameters, and the following architecture: The stem of the network takes as input a 18x19x19 tensor representation of the Go board. 8 channels are the positions of the current player's stones from the last eight time steps. (1 if there is a stone, 0 otherwise. If the time step go before the beginning of the game, then 0 in all positions.) 8 channels are the positions of the other player's stones from the last eight time steps. 1 channel is all 1 if black is to move, and 0 otherwise. 1 channel is all 1 if white is to move, and 0 otherwise. (This channel is not present in the original AlphaGo Zero) The body is a ResNet with 40 residual blocks and 256 channels. There are two heads, a policy head and a value head. Policy head outputs a logit array of size 19 × 19 + 1 {\displaystyle 19\times 19+1} , representing the logit of making a move in one of the points, plus the logit of passing. Value head outputs a number in the range ( − 1 , + 1 ) {\displaystyle (-1,+1)} , representing the expected score for the current player. -1 represents current player losing, and +1 winning.
Legendre moment
In mathematics, Legendre moments are a type of image moment and are achieved by using the Legendre polynomial. Legendre moments are used in areas of image processing including: pattern and object recognition, image indexing, line fitting, feature extraction, edge detection, and texture analysis. Legendre moments have been studied as a means to reduce image moment calculation complexity by limiting the amount of information redundancy through approximation. == Legendre moments == Source: With order of m + n, and object intensity function f(x,y): L m n = ( 2 m + 1 ) ( 2 n + 1 ) 4 ∫ − 1 1 ∫ − 1 1 P m ( x ) P n ( y ) f ( x , y ) d x d y {\displaystyle L_{mn}={\frac {(2m+1)(2n+1)}{4}}\int \limits _{-1}^{1}\int \limits _{-1}^{1}P_{m}(x)P_{n}(y)f(x,y)\,dx\,dy} where m,n = 1, 2, 3, ...∞ with the nth-order Legendre polynomials being: P n ( x ) = ∑ k = 0 n a k , n x k = ( − 1 ) n 2 n n ! ( d d x ) [ ( 1 − x 2 ) n ] {\displaystyle P_{n}(x)=\sum _{k=0}^{n}a_{k,n}x^{k}={\frac {(-1)^{n}}{2^{n}n!}}\left({\frac {d}{dx}}\right)[(1-x^{2})^{n}]} which can also be written: P n ( x ) = ∑ k = 0 D ( n ) ( − 1 ) k ( 2 n − 2 k ) ! 2 n k ! ( n − k ) ! ( n − 2 k ) ! x n − 2 k = ( 2 n ) ! 2 n ( n ! ) 2 x n − ( 2 n − 2 ) ! 2 n 1 ! ( n − 1 ) ! ( n − 2 ) ! x n − 2 + ⋯ {\displaystyle {\begin{aligned}P_{n}(x)&=\sum _{k=0}^{D(n)}(-1)^{k}{\frac {(2n-2k)!}{2^{n}k!(n-k)!(n-2k)!}}x^{n-2k}\\[5pt]&={\frac {(2n)!}{2^{n}(n!)^{2}}}x^{n}-{\frac {(2n-2)!}{2^{n}1!(n-1)!(n-2)!}}x^{n-2}+\cdots \end{aligned}}} where D(n) = floor(n/2). The set of Legendre polynomials {Pn(x)} form an orthogonal set on the interval [−1,1]: ∫ − 1 1 P n ( x ) P m ( x ) d x = 2 2 n + 1 δ n m {\displaystyle \int _{-1}^{1}P_{n}(x)P_{m}(x)\,dx={\frac {2}{2n+1}}\delta _{nm}} A recurrence relation can be used to compute the Legendre polynomial: ( n + 1 ) P n + 1 ( x ) − ( 2 n + 1 ) x P n ( x ) + n P n − 1 ( x ) = 0 {\displaystyle (n+1)P_{n+1}(x)-(2n+1)xP_{n}(x)+nP_{n-1}(x)=0} f(x,y) can be written as an infinite series expansion in terms of Legendre polynomials [−1 ≤ x,y ≤ 1.]: f ( x , y ) = ∑ m = 0 ∞ ∑ n = 0 ∞ λ m n P m ( x ) P n ( y ) {\displaystyle f(x,y)=\sum _{m=0}^{\infty }\sum _{n=0}^{\infty }\lambda _{mn}P_{m}(x)P_{n}(y)}
Department of Defense Directive 3000.09
Department of Defense Directive 3000.09 (DODD 3000.09), titled Autonomy in Weapon Systems, is the current U.S. military policy on autonomous weapons. It states: "Autonomous and semi-autonomous weapon systems will be designed to allow commanders and operators to exercise appropriate levels of human judgment over the use of force." == History == Then-Deputy Secretary of Defense Ashton Carter issued DOD's policy on autonomy in weapons systems, Department of Defense Directive (DODD) 3000.09, in November 2012. DOD updated the directive in January 2023. In February 2023, the US issued a related foreign policy proposal, Political Declaration on Responsible Military Use of Artificial Intelligence and Autonomy. == Definitions == There is no agreed definition of lethal autonomous weapon systems that is used in international fora. However, DODD 3000.09 provides definitions for different categories of autonomous weapon systems for the purposes of the U.S. military. These definitions are principally grounded in the role of the human operator with regard to target selection and engagement decisions, rather than in the technological sophistication of the weapon system. DODD 3000.09 defines LAWS as "weapon system[s] that, once activated, can select and engage targets without further intervention by a human operator." This concept of autonomy is also known as "human out of the loop" or "full autonomy." The directive contrasts LAWS with human-supervised, or "human on the loop," autonomous weapon systems, in which operators have the ability to monitor and halt a weapon's target engagement. Another category is semi-autonomous, or "human in the loop," weapon systems that "only engage individual targets or specific target groups that have been selected by a human operator." Semi-autonomous weapons include so-called "fire and forget" weapons, such as certain types of guided missiles, that deliver effects to human-identified targets using autonomous functions. The directive does not apply to autonomous or semi-autonomous cyberspace capabilities; unarmed platforms; unguided munitions; munitions manually guided by the operator (e.g., laser- or wire-guided munitions); mines; unexploded explosive ordnance; or autonomous or semi-autonomous systems that are not weapon systems, nor subject them to its guidelines. == Role of human operator == DODD 3000.09 requires that all systems, including LAWS, be designed to "allow commanders and operators to exercise appropriate levels of human judgment over the use of force." As noted in an August 2018 U.S. government white paper, "'appropriate' is a flexible term that reflects the fact that there is not a fixed, one-size-fits-all level of human judgment that should be applied to every context. What is 'appropriate' can differ across weapon systems, domains of warfare, types of warfare, operational contexts, and even across different functions in a weapon system." Furthermore, "human judgment over the use of force" does not require manual human "control" of the weapon system, as is often reported, but rather broader human involvement in decisions about how, when, where, and why the weapon will be employed. This includes a human determination that the weapon will be used "with appropriate care and in accordance with the law of war, applicable treaties, weapon system safety rules, and applicable rules of engagement." To aid this determination, DODD 3000.09 requires that "[a]dequate training, [tactics, techniques, and procedures], and doctrine are available, periodically reviewed, and used by system operators and commanders to understand the functioning, capabilities, and limitations of the system's autonomy in realistic operational conditions." The directive also requires that the weapon's human-machine interface be "readily understandable to trained operators" so they can make informed decisions regarding the weapon's use. == Weapons review process == DODD 3000.09 requires that the software and hardware of covered semi-autonomous and autonomous weapon systems, be tested and evaluated to ensure they:Function as anticipated in realistic operational environments against adaptive adversaries taking realistic and practicable countermeasures, [and] complete engagements within a timeframe and geographic area, as well as other relevant environmental and operational constraints, consistent with commander and operator intentions. If unable to do so, the systems will terminate the engagement or obtain additional operator input before continuing the engagement.Systems must also be "sufficiently robust to minimize the probability and consequences of failures." Any changes to the system's operating state—for example, due to machine learning—would require the system to go through testing and evaluation again to ensure that it has retained its safety features and ability to operate as intended. The directive also notes that "the use of AI capabilities in autonomous or semi-autonomous systems will be consistent with the DOD AI Ethical Principles." In addition to the standard weapons review process, a secondary senior-level review is required for covered autonomous and semi-autonomous systems. This review requires the Under Secretary of Defense for Policy (USD[P]), the vice chairman of the Joint Chiefs of Staff (VCJCS), and the Under Secretary of Defense for Research and Engineering (USD[R&E]) to approve the system before formal development. USD(P), VCJCS, and the Under Secretary of Defense for Acquisition and Sustainment (USD[A&S]) must then approve the system before fielding. In the event of "urgent military need," this senior-level review may be waived by the Deputy Secretary of Defense. DODD 3000.09 additionally establishes the Autonomous Weapon System Working Group—composed of representatives of USD(P); USD(R&E); USD(A&S); DOD General Counsel; the Chief Digital and AI Officer; the Director, Operational Test and Evaluation; and the chairman of the Joint Chiefs of Staff—to support and advise the senior-level review process. == Congressional notification == Per Section 251 of the FY2024 National Defense Authorization Act (NDAA; Pub. L. 118–31 (text) (PDF)), the Secretary of Defense is to notify the defense committees of any changes to DODD 3000.09 within 30 days. The Secretary is directed to provide a description of the modification and an explanation of the reasons for the modification. Section 1066 of the FY2025 NDAA (Pub. L. 118–159 (text) (PDF)) additionally requires the Secretary to "submit to the congressional defense committees a comprehensive report on the approval and deployment of lethal autonomous weapon systems by the United States," annually through December 31, 2029. Section 1061 of the FY2026 NDAA (P.L. Pub. L. 119–60 (menu; GPO has not yet published law)) amends the U.S. Code to require congressional notification of any waiver issued under DODD 3000.09. == AI safety == The second revision of DoDD 3000.09, effective January 25, 2023, requires that "The DoD will design and engineer AI capabilities to fulfill their intended functions while possessing the ability to detect and avoid unintended consequences, and the ability to disengage or deactivate deployed systems that demonstrate unintended behavior." == Criticism == As noted in the Bulletin of the Atomic Scientists, the policy requires that autonomous weapon systems that kill people or use kinetic force, selecting and engaging targets without further human intervention, be certified as compliant with "appropriate levels" and other standards, not that such weapon systems cannot meet these standards and are therefore forbidden. "Semi-autonomous" hunter-killers that autonomously identify and attack targets do not require certification.