In image processing, computer vision and related fields, an image moment is a certain particular weighted average (moment) of the image pixels' intensities, or a function of such moments, usually chosen to have some attractive property or interpretation. Image moments are useful to describe objects after segmentation. Simple properties of the image which are found via image moments include area (or total intensity), its centroid, and information about its orientation. == Raw moments == For a 2D continuous function f(x,y) the moment (sometimes called "raw moment") of order (p + q) is defined as M p q = ∫ − ∞ ∞ ∫ − ∞ ∞ x p y q f ( x , y ) d x d y {\displaystyle M_{pq}=\int \limits _{-\infty }^{\infty }\int \limits _{-\infty }^{\infty }x^{p}y^{q}f(x,y)\,dx\,dy} for p,q = 0,1,2,... Adapting this to scalar (grayscale) image with pixel intensities I(x,y), raw image moments Mij are calculated by M i j = ∑ x ∑ y x i y j I ( x , y ) {\displaystyle M_{ij}=\sum _{x}\sum _{y}x^{i}y^{j}I(x,y)\,\!} In some cases, this may be calculated by considering the image as a probability density function, i.e., by dividing the above by ∑ x ∑ y I ( x , y ) {\displaystyle \sum _{x}\sum _{y}I(x,y)\,\!} A uniqueness theorem states that if f(x,y) is piecewise continuous and has nonzero values only in a finite part of the xy plane, moments of all orders exist, and the moment sequence (Mpq) is uniquely determined by f(x,y). Conversely, (Mpq) uniquely determines f(x,y). In practice, the image is summarized with functions of a few lower order moments. === Examples === Simple image properties derived via raw moments include: Area (for binary images) or sum of grey level (for greytone images): M 00 {\displaystyle M_{00}} Centroid: { x ¯ , y ¯ } = { M 10 M 00 , M 01 M 00 } {\displaystyle \{{\bar {x}},\ {\bar {y}}\}=\left\{{\frac {M_{10}}{M_{00}}},{\frac {M_{01}}{M_{00}}}\right\}} == Central moments == Central moments are defined as μ p q = ∫ − ∞ ∞ ∫ − ∞ ∞ ( x − x ¯ ) p ( y − y ¯ ) q f ( x , y ) d x d y {\displaystyle \mu _{pq}=\int \limits _{-\infty }^{\infty }\int \limits _{-\infty }^{\infty }(x-{\bar {x}})^{p}(y-{\bar {y}})^{q}f(x,y)\,dx\,dy} where x ¯ = M 10 M 00 {\displaystyle {\bar {x}}={\frac {M_{10}}{M_{00}}}} and y ¯ = M 01 M 00 {\displaystyle {\bar {y}}={\frac {M_{01}}{M_{00}}}} are the components of the centroid. If ƒ(x, y) is a digital image, then the previous equation becomes μ p q = ∑ x ∑ y ( x − x ¯ ) p ( y − y ¯ ) q f ( x , y ) {\displaystyle \mu _{pq}=\sum _{x}\sum _{y}(x-{\bar {x}})^{p}(y-{\bar {y}})^{q}f(x,y)} The central moments of order up to 3 are: μ 00 = M 00 , μ 01 = 0 , μ 10 = 0 , μ 11 = M 11 − x ¯ M 01 = M 11 − y ¯ M 10 , μ 20 = M 20 − x ¯ M 10 , μ 02 = M 02 − y ¯ M 01 , μ 21 = M 21 − 2 x ¯ M 11 − y ¯ M 20 + 2 x ¯ 2 M 01 , μ 12 = M 12 − 2 y ¯ M 11 − x ¯ M 02 + 2 y ¯ 2 M 10 , μ 30 = M 30 − 3 x ¯ M 20 + 2 x ¯ 2 M 10 , μ 03 = M 03 − 3 y ¯ M 02 + 2 y ¯ 2 M 01 . {\displaystyle {\begin{aligned}\mu _{00}&=M_{00},&\mu _{01}&=0,\\\mu _{10}&=0,&\mu _{11}&=M_{11}-{\bar {x}}M_{01}=M_{11}-{\bar {y}}M_{10},\\\mu _{20}&=M_{20}-{\bar {x}}M_{10},&\mu _{02}&=M_{02}-{\bar {y}}M_{01},\\\mu _{21}&=M_{21}-2{\bar {x}}M_{11}-{\bar {y}}M_{20}+2{\bar {x}}^{2}M_{01},&\mu _{12}&=M_{12}-2{\bar {y}}M_{11}-{\bar {x}}M_{02}+2{\bar {y}}^{2}M_{10},\\\mu _{30}&=M_{30}-3{\bar {x}}M_{20}+2{\bar {x}}^{2}M_{10},&\mu _{03}&=M_{03}-3{\bar {y}}M_{02}+2{\bar {y}}^{2}M_{01}.\end{aligned}}} It can be shown that: μ p q = ∑ m p ∑ n q ( p m ) ( q n ) ( − x ¯ ) ( p − m ) ( − y ¯ ) ( q − n ) M m n {\displaystyle \mu _{pq}=\sum _{m}^{p}\sum _{n}^{q}{p \choose m}{q \choose n}(-{\bar {x}})^{(p-m)}(-{\bar {y}})^{(q-n)}M_{mn}} Central moments are translational invariant. === Examples === Information about image orientation can be derived by first using the second order central moments to construct a covariance matrix. μ 20 ′ = μ 20 / μ 00 = M 20 / M 00 − x ¯ 2 μ 02 ′ = μ 02 / μ 00 = M 02 / M 00 − y ¯ 2 μ 11 ′ = μ 11 / μ 00 = M 11 / M 00 − x ¯ y ¯ {\displaystyle {\begin{aligned}\mu '_{20}&=\mu _{20}/\mu _{00}=M_{20}/M_{00}-{\bar {x}}^{2}\\\mu '_{02}&=\mu _{02}/\mu _{00}=M_{02}/M_{00}-{\bar {y}}^{2}\\\mu '_{11}&=\mu _{11}/\mu _{00}=M_{11}/M_{00}-{\bar {x}}{\bar {y}}\end{aligned}}} The covariance matrix of the image I ( x , y ) {\displaystyle I(x,y)} is now cov [ I ( x , y ) ] = [ μ 20 ′ μ 11 ′ μ 11 ′ μ 02 ′ ] . {\displaystyle \operatorname {cov} [I(x,y)]={\begin{bmatrix}\mu '_{20}&\mu '_{11}\\\mu '_{11}&\mu '_{02}\end{bmatrix}}.} The eigenvectors of this matrix correspond to the major and minor axes of the image intensity, so the orientation can thus be extracted from the angle of the eigenvector associated with the largest eigenvalue towards the axis closest to this eigenvector. It can be shown that this angle Θ is given by the following formula: Θ = 1 2 arctan ( 2 μ 11 ′ μ 20 ′ − μ 02 ′ ) {\displaystyle \Theta ={\frac {1}{2}}\arctan \left({\frac {2\mu '_{11}}{\mu '_{20}-\mu '_{02}}}\right)} The above formula holds as long as: μ 20 ′ − μ 02 ′ ≠ 0 {\displaystyle \mu '_{20}-\mu '_{02}\neq 0} The eigenvalues of the covariance matrix can easily be shown to be λ i = μ 20 ′ + μ 02 ′ 2 ± 4 μ ′ 11 2 + ( μ ′ 20 − μ ′ 02 ) 2 2 , {\displaystyle \lambda _{i}={\frac {\mu '_{20}+\mu '_{02}}{2}}\pm {\frac {\sqrt {4{\mu '}_{11}^{2}+({\mu '}_{20}-{\mu '}_{02})^{2}}}{2}},} and are proportional to the squared length of the eigenvector axes. The relative difference in magnitude of the eigenvalues are thus an indication of the eccentricity of the image, or how elongated it is. The eccentricity is 1 − λ 2 λ 1 . {\displaystyle {\sqrt {1-{\frac {\lambda _{2}}{\lambda _{1}}}}}.} == Moment invariants == Moments are well-known for their application in image analysis, since they can be used to derive invariants with respect to specific transformation classes. The term invariant moments is often abused in this context. However, while moment invariants are invariants that are formed from moments, the only moments that are invariants themselves are the central moments. Note that the invariants detailed below are exactly invariant only in the continuous domain. In a discrete domain, neither scaling nor rotation are well defined: a discrete image transformed in such a way is generally an approximation, and the transformation is not reversible. These invariants therefore are only approximately invariant when describing a shape in a discrete image. === Translation invariants === The central moments μi j of any order are, by construction, invariant with respect to translations. === Scale invariants === Invariants ηi j with respect to both translation and scale can be constructed from central moments by dividing through a properly scaled zero-th central moment: η i j = μ i j μ 00 ( 1 + i + j 2 ) {\displaystyle \eta _{ij}={\frac {\mu _{ij}}{\mu _{00}^{\left(1+{\frac {i+j}{2}}\right)}}}\,\!} where i + j ≥ 2. Note that translational invariance directly follows by only using central moments. === Rotation invariants === As shown in the work of Hu, invariants with respect to translation, scale, and rotation can be constructed: I 1 = η 20 + η 02 {\displaystyle I_{1}=\eta _{20}+\eta _{02}} I 2 = ( η 20 − η 02 ) 2 + 4 η 11 2 {\displaystyle I_{2}=(\eta _{20}-\eta _{02})^{2}+4\eta _{11}^{2}} I 3 = ( η 30 − 3 η 12 ) 2 + ( 3 η 21 − η 03 ) 2 {\displaystyle I_{3}=(\eta _{30}-3\eta _{12})^{2}+(3\eta _{21}-\eta _{03})^{2}} I 4 = ( η 30 + η 12 ) 2 + ( η 21 + η 03 ) 2 {\displaystyle I_{4}=(\eta _{30}+\eta _{12})^{2}+(\eta _{21}+\eta _{03})^{2}} I 5 = ( η 30 − 3 η 12 ) ( η 30 + η 12 ) [ ( η 30 + η 12 ) 2 − 3 ( η 21 + η 03 ) 2 ] + ( 3 η 21 − η 03 ) ( η 21 + η 03 ) [ 3 ( η 30 + η 12 ) 2 − ( η 21 + η 03 ) 2 ] {\displaystyle I_{5}=(\eta _{30}-3\eta _{12})(\eta _{30}+\eta _{12})[(\eta _{30}+\eta _{12})^{2}-3(\eta _{21}+\eta _{03})^{2}]+(3\eta _{21}-\eta _{03})(\eta _{21}+\eta _{03})[3(\eta _{30}+\eta _{12})^{2}-(\eta _{21}+\eta _{03})^{2}]} I 6 = ( η 20 − η 02 ) [ ( η 30 + η 12 ) 2 − ( η 21 + η 03 ) 2 ] + 4 η 11 ( η 30 + η 12 ) ( η 21 + η 03 ) {\displaystyle I_{6}=(\eta _{20}-\eta _{02})[(\eta _{30}+\eta _{12})^{2}-(\eta _{21}+\eta _{03})^{2}]+4\eta _{11}(\eta _{30}+\eta _{12})(\eta _{21}+\eta _{03})} I 7 = ( 3 η 21 − η 03 ) ( η 30 + η 12 ) [ ( η 30 + η 12 ) 2 − 3 ( η 21 + η 03 ) 2 ] − ( η 30 − 3 η 12 ) ( η 21 + η 03 ) [ 3 ( η 30 + η 12 ) 2 − ( η 21 + η 03 ) 2 ] . {\displaystyle I_{7}=(3\eta _{21}-\eta _{03})(\eta _{30}+\eta _{12})[(\eta _{30}+\eta _{12})^{2}-3(\eta _{21}+\eta _{03})^{2}]-(\eta _{30}-3\eta _{12})(\eta _{21}+\eta _{03})[3(\eta _{30}+\eta _{12})^{2}-(\eta _{21}+\eta _{03})^{2}].} These are well-known as Hu moment invariants. The first one, I1, is analogous to the moment of inertia around the image's centroid, where the pixels' intensities are analogous to physical density. The first six, I1 ... I6, are reflection symmetric, i.e. they are unchanged if the image is changed to a mirror image. The last one, I7, is reflection antisymmetric (changes sign under reflection), which enables it to distinguish mirror images of otherwise identical im
Secure coding
Secure coding is the practice of developing computer software in such a way that guards against the accidental introduction of security vulnerabilities. Defects, bugs and logic flaws are consistently the primary cause of commonly exploited software vulnerabilities. Through the analysis of thousands of reported vulnerabilities, security professionals have discovered that most vulnerabilities stem from a relatively small number of common software programming errors. By identifying the insecure coding practices that lead to these errors and educating developers on secure alternatives, organizations can take proactive steps to help significantly reduce or eliminate vulnerabilities in software before deployment. Some scholars have suggested that in order to effectively confront threats related to cybersecurity, proper security should be coded or "baked in" to the systems. With security being designed into the software, this ensures that there will be protection against insider attacks and reduces the threat to application security. Implementing secure coding practices is part of the secure by design approach to security engineering. == Buffer-overflow prevention == Buffer overflows, a common software security vulnerability, happen when a process tries to store data beyond a fixed-length buffer. For example, if there are 8 slots to store items in, there will be a problem if there is an attempt to store 9 items. In computer memory the overflowed data may overwrite data in the next location which can result in a security vulnerability (stack smashing) or program termination (segmentation fault). An example of a C program prone to a buffer overflow is If the user input is larger than the destination buffer, a buffer overflow will occur. To fix this unsafe program, use strncpy to prevent a possible buffer overflow. Another secure alternative is to dynamically allocate memory on the heap using malloc. In the above code snippet, the program attempts to copy the contents of src into dst, while also checking the return value of malloc() to ensure that enough memory was able to be allocated for the destination buffer. == Format-string attack prevention == A Format String Attack is when a malicious user supplies specific inputs that will eventually be entered as an argument to a function that performs formatting, such as printf(). The attack involves the adversary reading from or writing to the stack. The C printf function writes output to stdout. If the parameter of the printf function is not properly formatted, several security bugs can be introduced. Below is a program that is vulnerable to a format string attack. A malicious argument passed to the program could be "%s%s%s%s%s%s%s", which can crash the program from improper memory reads. == Integer-overflow prevention == Integer overflow occurs when an arithmetic operation results in an integer too large to be represented within the available space. A program which does not properly check for integer overflow introduces potential software bugs and exploits. Below is a function in C++ which attempts to confirm that the sum of x and y is less than or equal to a defined value MAX: The problem with the code is it does not check for integer overflow on the addition operation. If the sum of x and y is greater than the maximum possible value of an unsigned int, the addition operation will overflow and perhaps result in a value less than or equal to MAX, even though the sum of x and y is greater than MAX. Below is a function which checks for overflow by confirming the sum is greater than or equal to both x and y. If the sum did overflow, the sum would be less than x or less than y. == Path traversal prevention == Path traversal is a vulnerability whereby paths provided from an untrusted source are interpreted in such a way that unauthorised file access is possible. For example, consider a script that fetches an article by taking a filename, which is then read by the script and parsed. Such a script might use the following hypothetical URL to retrieve an article about dog food: https://www.example.net/cgi-bin/article.sh?name=dogfood.html If the script has no input checking, instead trusting that the filename is always valid, a malicious user could forge a URL to retrieve configuration files from the web server: https://www.example.net/cgi-bin/article.sh?name=../../../../../etc/passwd Depending on the script, this may expose the /etc/passwd file, which on Unix-like systems contains (among others) user IDs, their login names, home directory paths and shells. (See SQL injection for a similar attack.) == Regulatory drivers == Secure coding practices are increasingly mandated by regulatory frameworks governing the development and maintenance of software systems that process sensitive data. The Health Insurance Portability and Accountability Act (HIPAA) Security Rule requires covered entities to protect the integrity of protected health information through technical safeguards under 45 CFR 164.312(c)(1) and to implement mechanisms to authenticate electronic protected health information under 45 CFR 164.312(c)(2). The Payment Card Industry Data Security Standard (PCI DSS) version 4.0 Requirement 6.2 mandates that custom software is developed securely, including training developers in secure coding techniques (6.2.2), reviewing custom code for vulnerabilities before release (6.2.3), and addressing common software attacks in development practices (6.2.4).
Principle of rationality
The principle of rationality (or rationality principle) was coined by Karl R. Popper in his Harvard Lecture of 1963, and published in his book Myth of Framework. It is related to what he called the 'logic of the situation' in an Economica article of 1944/1945, published later in his book The Poverty of Historicism. According to Popper's rationality principle, agents act in the most adequate way according to the objective situation. It is an idealized conception of human behavior which he used to drive his model of situational analysis. Cognitive scientist Allen Newell elaborated on the principle in his account of knowledge level modeling. == Popper == Popper called for social science to be grounded in what he called situational analysis or situational logic. This requires building models of social situations which include individual actors and their relationship to social institutions, e.g. markets, legal codes, bureaucracies, etc. These models attribute certain aims and information to the actors. This forms the 'logic of the situation', the result of reconstructing meticulously all circumstances of an historical event. The 'principle of rationality' is the assumption that people are instrumental in trying to reach their goals, and this is what drives the model. Popper believed that this model could be continuously refined to approach the objective truth. Popper called his principle of rationality nearly empty (a technical term meaning without empirical content) and strictly speaking false, but nonetheless tremendously useful. These remarks earned him a lot of criticism because seemingly he had swerved from his famous Logic of Scientific Discovery. Among the many philosophers having discussed Popper's principle of rationality from the 1960s up to now are Noretta Koertge, R. Nadeau, Viktor J. Vanberg, Hans Albert, E. Matzner, Ian C. Jarvie, Mark A. Notturno, John Wettersten, Ian C. Böhm. == Newell == In the context of knowledge-based systems, Newell (in 1982) proposed the following principle of rationality: "If an agent has knowledge that one of its actions will lead to one of its goals, then the agent will select that action." This principle is employed by agents at the knowledge level to move closer to a desired goal. An important philosophical difference between Newell and Popper is that Newell argued that the knowledge level is real in the sense that it exists in nature and is not made up. This allowed Newell to treat the rationality principle as a way of understanding nature and avoid the problems Popper ran into by treating knowledge as non physical and therefore non empirical.
Energy-based model
An energy-based model (EBM), also called Canonical Ensemble Learning (CEL) or Learning via Canonical Ensemble (LCE), is an application of canonical ensemble formulation from statistical physics for learning from data. The approach prominently appears in generative artificial intelligence. EBMs provide a unified framework for many probabilistic and non-probabilistic approaches to such learning, particularly for training graphical and other structured models. An EBM learns the characteristics of a target dataset and generates a similar but larger dataset. EBMs detect the latent variables of a dataset and generate new datasets with a similar distribution. Energy-based generative neural networks is a class of generative models, which aim to learn explicit probability distributions of data in the form of energy-based models, the energy functions of which are parameterized by modern deep neural networks. Boltzmann machines are a special form of energy-based models with a specific parametrization of the energy. == Description == For a given input x {\displaystyle x} , the model describes an energy E θ ( x ) {\displaystyle E_{\theta }(x)} such that the Boltzmann distribution P θ ( x ) = e − β E θ ( x ) Z ( θ ) {\displaystyle P_{\theta }(x)={e^{-\beta E_{\theta }(x)} \over Z(\theta )}} is a probability (density), and typically β = 1 {\displaystyle \beta =1} . Since the normalization constant: Z ( θ ) := ∫ x ∈ X e − β E θ ( x ) d x {\displaystyle Z(\theta ):=\int _{x\in X}e^{-\beta E_{\theta }(x)}dx} (also known as the partition function) depends on all the Boltzmann factors of all possible inputs x {\displaystyle x} , it cannot be easily computed or reliably estimated during training simply using standard maximum likelihood estimation. However, for maximizing the likelihood during training, the gradient of the log-likelihood of a single training example x {\displaystyle x} is given by using the chain rule: ∂ θ log ( P θ ( x ) ) = E x ′ ∼ P θ [ ∂ θ E θ ( x ′ ) ] − ∂ θ E θ ( x ) ( ∗ ) {\displaystyle \partial _{\theta }\log \left(P_{\theta }(x)\right)=\mathbb {E} _{x'\sim P_{\theta }}[\partial _{\theta }E_{\theta }(x')]-\partial _{\theta }E_{\theta }(x)\,()} The expectation in the above formula for the gradient can be approximately estimated by drawing samples x ′ {\displaystyle x'} from the distribution P θ {\displaystyle P_{\theta }} using Markov chain Monte Carlo (MCMC). Early energy-based models, such as the 2003 Boltzmann machine by Hinton, estimated this expectation via blocked Gibbs sampling. Newer approaches make use of more efficient Stochastic Gradient Langevin Dynamics (LD), drawing samples using: x 0 ′ ∼ P 0 , x i + 1 ′ = x i ′ − α 2 ∂ E θ ( x i ′ ) ∂ x i ′ + ϵ {\displaystyle x_{0}'\sim P_{0},x_{i+1}'=x_{i}'-{\frac {\alpha }{2}}{\frac {\partial E_{\theta }(x_{i}')}{\partial x_{i}'}}+\epsilon } , where ϵ ∼ N ( 0 , α ) {\displaystyle \epsilon \sim {\mathcal {N}}(0,\alpha )} . A replay buffer of past values x i ′ {\displaystyle x_{i}'} is used with LD to initialize the optimization module. The parameters θ {\displaystyle \theta } of the neural network are therefore trained in a generative manner via MCMC-based maximum likelihood estimation: the learning process follows an "analysis by synthesis" scheme, where within each learning iteration, the algorithm samples the synthesized examples from the current model by a gradient-based MCMC method (e.g., Langevin dynamics or Hybrid Monte Carlo), and then updates the parameters θ {\displaystyle \theta } based on the difference between the training examples and the synthesized ones – see equation ( ∗ ) {\displaystyle ()} . This process can be interpreted as an alternating mode seeking and mode shifting process, and also has an adversarial interpretation. Essentially, the model learns a function E θ {\displaystyle E_{\theta }} that associates low energies to correct values, and higher energies to incorrect values. After training, given a converged energy model E θ {\displaystyle E_{\theta }} , the Metropolis–Hastings algorithm can be used to draw new samples. The acceptance probability is given by: P a c c ( x i → x ∗ ) = min ( 1 , P θ ( x ∗ ) P θ ( x i ) ) . {\displaystyle P_{acc}(x_{i}\to x^{})=\min \left(1,{\frac {P_{\theta }(x^{})}{P_{\theta }(x_{i})}}\right).} == History == The term "energy-based models" was first coined in a 2003 JMLR paper where the authors defined a generalisation of independent components analysis to the overcomplete setting using EBMs. Other early work on EBMs proposed models that represented energy as a composition of latent and observable variables. == Characteristics == EBMs demonstrate useful properties: Simplicity and stability. The EBM is the only object that needs to be designed and trained. Separate networks need not be trained to ensure balance. Adaptive computation time. An EBM can generate sharp, diverse samples or (more quickly) coarse, less diverse samples. Given infinite time, this procedure produces true samples. Flexibility. In Variational Autoencoders (VAE) and flow-based models, the generator learns a map from a continuous space to a (possibly) discontinuous space containing different data modes. EBMs can learn to assign low energies to disjoint regions (multiple modes). Adaptive generation. EBM generators are implicitly defined by the probability distribution, and automatically adapt as the distribution changes (without training), allowing EBMs to address domains where generator training is impractical, as well as minimizing mode collapse and avoiding spurious modes from out-of-distribution samples. Compositionality. Individual models are unnormalized probability distributions, allowing models to be combined through product of experts or other hierarchical techniques. == Experimental results == On image datasets such as CIFAR-10 and ImageNet 32x32, an EBM model generated high-quality images relatively quickly. It supported combining features learned from one type of image for generating other types of images. It was able to generalize using out-of-distribution datasets, outperforming flow-based and autoregressive models. EBM was relatively resistant to adversarial perturbations, behaving better than models explicitly trained against them with training for classification. == Applications == Target applications include natural language processing, robotics and computer vision. The first energy-based generative neural network is the generative ConvNet proposed in 2016 for image patterns, where the neural network is a convolutional neural network. The model has been generalized to various domains to learn distributions of videos, and 3D voxels. They are made more effective in their variants. They have proven useful for data generation (e.g., image synthesis, video synthesis, 3D shape synthesis, etc.), data recovery (e.g., recovering videos with missing pixels or image frames, 3D super-resolution, etc), data reconstruction (e.g., image reconstruction and linear interpolation ). == Alternatives == EBMs compete with techniques such as variational autoencoders (VAEs), generative adversarial networks (GANs) or normalizing flows. == Extensions == === Joint energy-based models === Joint energy-based models (JEM), proposed in 2020 by Grathwohl et al., allow any classifier with softmax output to be interpreted as energy-based model. The key observation is that such a classifier is trained to predict the conditional probability p θ ( y | x ) = e f → θ ( x ) [ y ] ∑ j = 1 K e f → θ ( x ) [ j ] for y = 1 , … , K and f → θ = ( f 1 , … , f K ) ∈ R K , {\displaystyle p_{\theta }(y|x)={\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{\sum _{j=1}^{K}e^{{\vec {f}}_{\theta }(x)[j]}}}\ \ {\text{ for }}y=1,\dotsc ,K{\text{ and }}{\vec {f}}_{\theta }=(f_{1},\dotsc ,f_{K})\in \mathbb {R} ^{K},} where f → θ ( x ) [ y ] {\displaystyle {\vec {f}}_{\theta }(x)[y]} is the y-th index of the logits f → {\displaystyle {\vec {f}}} corresponding to class y. Without any change to the logits it was proposed to reinterpret the logits to describe a joint probability density: p θ ( y , x ) = e f → θ ( x ) [ y ] Z ( θ ) , {\displaystyle p_{\theta }(y,x)={\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{Z(\theta )}},} with unknown partition function Z ( θ ) {\displaystyle Z(\theta )} and energy E θ ( x , y ) = − f θ ( x ) [ y ] {\displaystyle E_{\theta }(x,y)=-f_{\theta }(x)[y]} . By marginalization, we obtain the unnormalized density p θ ( x ) = ∑ y p θ ( y , x ) = ∑ y e f → θ ( x ) [ y ] Z ( θ ) =: e − E θ ( x ) , {\displaystyle p_{\theta }(x)=\sum _{y}p_{\theta }(y,x)=\sum _{y}{\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{Z(\theta )}}=:e^{-E_{\theta }(x)},} therefore, E θ ( x ) = − log ( ∑ y e f → θ ( x ) [ y ] Z ( θ ) ) , {\displaystyle E_{\theta }(x)=-\log \left(\sum _{y}{\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{Z(\theta )}}\right),} so that any classifier can be used to define an energy function E θ ( x ) {\displaystyle E_{\theta }(x)} .
Artificial consciousness
Artificial consciousness, also known as machine consciousness, synthetic consciousness, or digital consciousness, is consciousness hypothesized to be possible for artificial intelligence. It is also the corresponding field of study, which draws insights from philosophy of mind, philosophy of artificial intelligence, cognitive science and neuroscience. The term "sentience" can be used when specifically designating ethical considerations stemming from a form of phenomenal consciousness (P-consciousness, or the ability to feel qualia). Since sentience involves the ability to experience ethically positive or negative (i.e., valenced) mental states, it may justify welfare concerns and legal protection, as with non-human animals. Some scholars believe that consciousness is generated by the interoperation of various parts of the brain; these mechanisms are labeled the neural correlates of consciousness (NCC). Some further believe that constructing a system (e.g., a computer system) that can emulate this NCC interoperation would result in a system that is conscious. Some scholars reject the possibility of non-biological conscious beings. == Philosophical views == As there are many hypothesized types of consciousness, there are many potential implementations of artificial consciousness. In the philosophical literature, perhaps the most common taxonomy of consciousness is into "access" and "phenomenal" variants. Access consciousness concerns those aspects of experience that can be apprehended, while phenomenal consciousness concerns those aspects of experience that seemingly cannot be apprehended, instead being characterized qualitatively in terms of "raw feels", "what it is like" or qualia. === Plausibility debate === Type-identity theorists and other skeptics hold the view that consciousness can be realized only in particular physical systems because consciousness has properties that necessarily depend on physical constitution. In his 2001 article "Artificial Consciousness: Utopia or Real Possibility," Giorgio Buttazzo says that a common objection to artificial consciousness is that, "Working in a fully automated mode, they [the computers] cannot exhibit creativity, unreprogrammation (which means can 'no longer be reprogrammed', from rethinking), emotions, or free will. A computer, like a washing machine, is a slave operated by its components." For other theorists (e.g., functionalists), who define mental states in terms of causal roles, any system that can instantiate the same pattern of causal roles, regardless of physical constitution, will instantiate the same mental states, including consciousness. ==== Thought experiments ==== David Chalmers proposed two thought experiments intending to demonstrate that "functionally isomorphic" systems (those with the same "fine-grained functional organization", i.e., the same information processing) will have qualitatively identical conscious experiences, regardless of whether they are based on biological neurons or digital hardware. The "fading qualia" is a reductio ad absurdum thought experiment. It involves replacing, one by one, the neurons of a brain with a functionally identical component, for example based on a silicon chip. Chalmers makes the hypothesis, knowing it in advance to be absurd, that "the qualia fade or disappear" when neurons are replaced one-by-one with identical silicon equivalents. Since the original neurons and their silicon counterparts are functionally identical, the brain's information processing should remain unchanged, and the subject's behaviour and introspective reports would stay exactly the same. Chalmers argues that this leads to an absurd conclusion: the subject would continue to report normal conscious experiences even as their actual qualia fade away. He concludes that the subject's qualia actually don't fade, and that the resulting robotic brain, once every neuron is replaced, would remain just as sentient as the original biological brain. Similarly, the "dancing qualia" thought experiment is another reductio ad absurdum argument. It supposes that two functionally isomorphic systems could have different perceptions (for instance, seeing the same object in different colors, like red and blue). It involves a switch that alternates between a chunk of brain that causes the perception of red, and a functionally isomorphic silicon chip, that causes the perception of blue. Since both perform the same function within the brain, the subject would not notice any change during the switch. Chalmers argues that this would be highly implausible if the qualia were truly switching between red and blue, hence the contradiction. Therefore, he concludes that the equivalent digital system would not only experience qualia, but it would perceive the same qualia as the biological system (e.g., seeing the same color). Greg Egan's short story Learning To Be Me (mentioned in §In fiction), illustrates how undetectable duplication of the brain and its functionality could be from a first-person perspective. Critics object that Chalmers' proposal begs the question in assuming that all mental properties and external connections are already sufficiently captured by abstract causal organization. Van Heuveln et al. argue that the dancing qualia argument contains an equivocation fallacy, conflating a "change in experience" between two systems with an "experience of change" within a single system. Mogensen argues that the fading qualia argument can be resisted by appealing to vagueness at the boundaries of consciousness and the holistic structure of conscious neural activity, which suggests consciousness may require specific biological substrates rather than being substrate-independent. Anil Seth argues that the complexity of brain neurons intrinsically matters in addition to their function and that it is not possible to replace any part of the brain with a perfect silicon equivalent. He points out that some of biological neurons exhibit activity aimed at cleaning up metabolic waste products, and writes that a perfect silicon replacement would require a silicon-based metabolism, but silicon is not suitable for creating such artificial metabolism. ==== In large language models ==== In 2022, Google engineer Blake Lemoine made a viral claim that Google's LaMDA chatbot was sentient. Lemoine supplied as evidence the chatbot's humanlike answers to many of his questions; however, the chatbot's behavior was judged by the scientific community as likely a consequence of mimicry, rather than machine sentience. Lemoine's claim was widely derided for being ridiculous. Moreover, attributing consciousness based solely on the basis of LLM outputs or the immersive experience created by an algorithm is considered a fallacy. However, while philosopher Nick Bostrom states that LaMDA is unlikely to be conscious, he additionally poses the question of "what grounds would a person have for being sure about it?" One would have to have access to unpublished information about LaMDA's architecture, and also would have to understand how consciousness works, and then figure out how to map the philosophy onto the machine: "(In the absence of these steps), it seems like one should be maybe a little bit uncertain. [...] there could well be other systems now, or in the relatively near future, that would start to satisfy the criteria." David Chalmers argued in 2023 that LLMs today display impressive conversational and general intelligence abilities, but are likely not conscious yet, as they lack some features that may be necessary, such as recurrent processing, a global workspace, and unified agency. Nonetheless, he considers that non-biological systems can be conscious, and suggested that future, extended models (LLM+s) incorporating these elements might eventually meet the criteria for consciousness, raising both profound scientific questions and significant ethical challenges. However, the view that consciousness can exist without biological phenomena is controversial and some reject it. Kristina Šekrst cautions that anthropomorphic terms such as "hallucination" can obscure important ontological differences between artificial and human cognition. While LLMs may produce human-like outputs, she argues that it does not justify ascribing mental states or consciousness to them. Instead, she advocates for an epistemological framework (such as reliabilism) that recognizes the distinct nature of AI knowledge production. She suggests that apparent understanding in LLMs may be a sophisticated form of AI hallucination. She also questions what would happen if an LLM were trained without any mention of consciousness. === Testing === Sentience is an inherently first-person phenomenon. Because of that, and due to the lack of an empirical definition of sentience, directly measuring it may be impossible. Although systems may display numerous behaviors correlated with sentience, determining whether a system is sentient is known as the hard pr
Double descent
Double descent in statistics and machine learning is the phenomenon where a model's error rate on the test set initially decreases with the number of parameters, then peaks, then decreases again. This phenomenon has been considered surprising, as it contradicts assumptions about overfitting in classical machine learning. The increase usually occurs near the interpolation threshold, where the number of parameters is the same as the number of training data points (the model is just large enough to fit the training data). Or, more precisely, it is the maximum number of samples on which the model/training procedure achieves approximately on average 0 training error. == History == Early observations of what would later be called double descent in specific models date back to 1989. The term "double descent" was coined by Belkin et. al. in 2019, when the phenomenon gained popularity as a broader concept exhibited by many models. The latter development was prompted by a perceived contradiction between the conventional wisdom that too many parameters in the model result in a significant overfitting error (an extrapolation of the bias–variance tradeoff), and the empirical observations in the 2010s that some modern machine learning techniques tend to perform better with larger models. == Theoretical models == Double descent occurs in linear regression with isotropic Gaussian covariates and isotropic Gaussian noise. A model of double descent at the thermodynamic limit has been analyzed using the replica trick, and the result has been confirmed numerically. A number of works have suggested that double descent can be explained using the concept of effective dimension: While a network may have a large number of parameters, in practice only a subset of those parameters are relevant for generalization performance, as measured by the local Hessian curvature. This explanation is formalized through PAC-Bayes compression-based generalization bounds, which show that less complex models are expected to generalize better under a Solomonoff prior.
Action model learning
Action model learning (sometimes abbreviated action learning) is an area of machine learning concerned with the creation and modification of a software agent's knowledge about the effects and preconditions of the actions that can be executed within its environment. This knowledge is usually represented in a logic-based action description language and used as input for automated planners. Learning action models is important when goals change. When an agent acted for a while, it can use its accumulated knowledge about actions in the domain to make better decisions. Thus, learning action models differs from reinforcement learning. It enables reasoning about actions instead of expensive trials in the world. Action model learning is a form of inductive reasoning, where new knowledge is generated based on the agent's observations. The usual motivation for action model learning is the fact that manual specification of action models for planners is often a difficult, time-consuming, and error-prone task (especially in complex environments). == Action models == Given a training set E {\displaystyle E} consisting of examples e = ( s , a , s ′ ) {\displaystyle e=(s,a,s')} , where s , s ′ {\displaystyle s,s'} are observations of a world state from two consecutive time steps t , t ′ {\displaystyle t,t'} and a {\displaystyle a} is an action instance observed in time step t {\displaystyle t} , the goal of action model learning in general is to construct an action model ⟨ D , P ⟩ {\displaystyle \langle D,P\rangle } , where D {\displaystyle D} is a description of domain dynamics in action description formalism like STRIPS, ADL or PDDL and P {\displaystyle P} is a probability function defined over the elements of D {\displaystyle D} . However, many state of the art action learning methods assume determinism and do not induce P {\displaystyle P} . In addition to determinism, individual methods differ in how they deal with other attributes of domain (e.g. partial observability or sensoric noise). == Action learning methods == === State of the art === Recent action learning methods take various approaches and employ a wide variety of tools from different areas of artificial intelligence and computational logic. As an example of a method based on propositional logic, we can mention SLAF (Simultaneous Learning and Filtering) algorithm, which uses agent's observations to construct a long propositional formula over time and subsequently interprets it using a satisfiability (SAT) solver. Another technique, in which learning is converted into a satisfiability problem (weighted MAX-SAT in this case) and SAT solvers are used, is implemented in ARMS (Action-Relation Modeling System). Two mutually similar, fully declarative approaches to action learning were based on logic programming paradigm Answer Set Programming (ASP) and its extension, Reactive ASP. In another example, bottom-up inductive logic programming approach was employed. Several different solutions are not directly logic-based. For example, the action model learning using a perceptron algorithm or the multi level greedy search over the space of possible action models. In the older paper from 1992, the action model learning was studied as an extension of reinforcement learning. Nonetheless, further algorithms can be found that operate under different assumptions: FAMA can work even when some observations are missing, and it produces a general (lifted) planning model. It treats learning an action model like a planning problem, making sure the learned model matches the observations given. NOLAM can learn general action models even from noisy or imperfect data. LOCM focuses only on the order of actions in the data, ignoring any details about the states between those actions. The family of safe action model (SAM) learning methods create models that guarantee any plans made with them will actually work in the real world. There's also an extension called N-SAM that can learn action models with numeric conditions and effects. Additionally, numeric action models like N-SAM can be used to improve reinforcement learning (RL) performance through the RAMP algorithm. === Literature === Most action learning research papers are published in journals and conferences focused on artificial intelligence in general (e.g. Journal of Artificial Intelligence Research (JAIR), Artificial Intelligence, Applied Artificial Intelligence (AAI) or AAAI conferences). Despite mutual relevance of the topics, action model learning is usually not addressed in planning conferences like the International Conference on Automated Planning and Scheduling (ICAPS).