Dyme is a Dutch fintech start-up and subscription management app that allows users to cancel and renegotiate their recurring costs. In 2019, Dyme was the first independent Dutch company to receive a PSD2 licence from the Netherlands' central bank (DNB). == History == Dyme was founded in 2018 by Joran Iedema, David Knap, David Schogt and Wouter Florijn. The four had previously founded Cycleswap, a bicycle rental platform launched in 2015 and sold to the American platform Spinlister in 2016. The company gained notability in the Netherlands in 2020 when it appeared on Dutch television in Dragons Den, where Pieter Schoen made a €750,000 bid in an attempt to acquire 51.01% of the company. Dyme's Joran Iedema rejected the deal. == Recognition == Wired described Dyme as one of the "hottest start-ups in Europe" in 2021. As of 2021, the company reportedly had 350,000 registered users in the Netherlands and Great Britain.
Representation collapse
Representation collapse is a phenomenon in machine learning and representation learning where a model maps different inputs to the same or very similar embeddings, which means it loses important information about how the data is spread out. It is frequently encountered in self-supervised learning, especially within contrastive and non-contrastive frameworks, when training objectives or model architectures do not maintain variance across representations. Collapse results in degenerate solutions characterized by uninformative learned features, significantly impairing downstream task performance. Various techniques have been proposed to mitigate representation collapse, including the use of negative samples, architectural asymmetry, stop-gradient operations, variance regularization, and redundancy reduction objectives, as seen in methods such as SimCLR, BYOL, and VICReg. Comprehending and averting representation collapse is regarded as a fundamental challenge in the advancement of stable and efficient self-supervised learning systems.
Chelsea Finn
Chelsea Finn (born October 8, 1992) is an American computer scientist and assistant professor at Stanford University. Her research investigates intelligence through the interactions of robots, with the hope to create robotic systems that can learn how to learn. She previously worked for Google and currently is a co-founder of the startup Physical Intelligence. == Early life and education == Finn was an undergraduate student in electrical engineering and computer science at Massachusetts Institute of Technology. She then moved to the University of California, Berkeley, where she earned her Ph.D. in 2018 under Pieter Abbeel and Sergey Levine. Her work in the Berkeley Artificial Intelligence Lab (BAIR) focused on gradient based algorithms . Such algorithms allow machines to 'learn to learn', more akin to human learning than traditional machine learning systems. These “meta-learning” techniques train machines to quickly adapt, such that when they encounter new scenarios they can learn quickly. As a doctoral student she worked as an intern at Google Brain, where she worked on robot learning algorithms from deep predictive models. She delivered a massive open online course on deep reinforcement learning. She was the first woman to win the C.V. & Daulat Ramamoorthy Distinguished Research Award. == Research and career == Finn investigates the capabilities of robots to develop intelligence through learning and interaction. She has made use of deep learning algorithms to simultaneously learn visual perception and control robotic skills. She developed meta-learning approaches to train neural networks to take in student code and output useful feedback. She showed that the system could quickly adapt without too much input from the instructor. She trialled the programme on Code in Place, a 12,000 student course delivered by Stanford University every year. She found that 97.9% of the time the students agreed with the feedback being given. == Awards and honors == 2016 C.V. & Daulat Ramamoorthy Distinguished Research Award 2017 Electrical engineering and computer science rising star 2018 MIT Technology Review 35 Under 35 2018 ACM Doctoral Dissertation Award 2020 Samsung Advanced Institute of Technology AI Researcher of the Year 2020 Intel Rising Star Faculty Award 2021 Office of Naval Research Young Investigator Award 2022 IEEE Robotics and Automation Society Early Academic Career Award == Select publications == Finn, Chelsea; Abbeel, Pieter; Levine, Sergey (2017-07-17). "Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks". International Conference on Machine Learning. PMLR: 1126–1135. arXiv:1703.03400. Sergey Levine; Chelsea Finn; Trevor Darrell; Pieter Abbeel (2016). "End-to-End Training of Deep Visuomotor Policies". Journal of Machine Learning Research. 17 (39): 1–40. arXiv:1504.00702. ISSN 1533-7928. Wikidata Q90313375. Chelsea Finn; Ian Goodfellow; Sergey Levine (2016). "Unsupervised Learning for Physical Interaction through Video Prediction" (PDF). Advances in Neural Information Processing Systems 29. Advances in Neural Information Processing Systems. Wikidata Q46993574.
Sequential minimal optimization
Sequential minimal optimization (SMO) is an algorithm for solving the quadratic programming (QP) problem that arises during the training of support-vector machines (SVM). It was invented by John Platt in 1998 at Microsoft Research. SMO is widely used for training support vector machines and is implemented by the popular LIBSVM tool. The publication of the SMO algorithm in 1998 has generated a lot of excitement in the SVM community, as previously available methods for SVM training were much more complex and required expensive third-party QP solvers. == Optimization problem == Consider a binary classification problem with a dataset (x1, y1), ..., (xn, yn), where xi is an input vector and yi ∈ {-1, +1} is a binary label corresponding to it. A soft-margin support vector machine is trained by solving a quadratic programming problem, which is expressed in the dual form as follows: max α ∑ i = 1 n α i − 1 2 ∑ i = 1 n ∑ j = 1 n y i y j K ( x i , x j ) α i α j , {\displaystyle \max _{\alpha }\sum _{i=1}^{n}\alpha _{i}-{\frac {1}{2}}\sum _{i=1}^{n}\sum _{j=1}^{n}y_{i}y_{j}K(x_{i},x_{j})\alpha _{i}\alpha _{j},} subject to: 0 ≤ α i ≤ C , for i = 1 , 2 , … , n , {\displaystyle 0\leq \alpha _{i}\leq C,\quad {\mbox{ for }}i=1,2,\ldots ,n,} ∑ i = 1 n y i α i = 0 {\displaystyle \sum _{i=1}^{n}y_{i}\alpha _{i}=0} where C is an SVM hyperparameter and K(xi, xj) is the kernel function, both supplied by the user; and the variables α i {\displaystyle \alpha _{i}} are Lagrange multipliers. == Algorithm == SMO is an iterative algorithm for solving the optimization problem described above. SMO breaks this problem into a series of smallest possible sub-problems, which are then solved analytically. Because of the linear equality constraint involving the Lagrange multipliers α i {\displaystyle \alpha _{i}} , the smallest possible problem involves two such multipliers. Then, for any two multipliers α 1 {\displaystyle \alpha _{1}} and α 2 {\displaystyle \alpha _{2}} , the constraints are reduced to: 0 ≤ α 1 , α 2 ≤ C , {\displaystyle 0\leq \alpha _{1},\alpha _{2}\leq C,} y 1 α 1 + y 2 α 2 = k , {\displaystyle y_{1}\alpha _{1}+y_{2}\alpha _{2}=k,} and this reduced problem can be solved analytically: one needs to find a minimum of a one-dimensional quadratic function. k {\displaystyle k} is the negative of the sum over the rest of terms in the equality constraint, which is fixed in each iteration. The algorithm proceeds as follows: Find a Lagrange multiplier α 1 {\displaystyle \alpha _{1}} that violates the Karush–Kuhn–Tucker (KKT) conditions for the optimization problem. Pick a second multiplier α 2 {\displaystyle \alpha _{2}} and optimize the pair ( α 1 , α 2 ) {\displaystyle (\alpha _{1},\alpha _{2})} . Repeat steps 1 and 2 until convergence. When all the Lagrange multipliers satisfy the KKT conditions (within a user-defined tolerance), the problem has been solved. Although this algorithm is guaranteed to converge, heuristics are used to choose the pair of multipliers so as to accelerate the rate of convergence. This is critical for large data sets since there are n ( n − 1 ) / 2 {\displaystyle n(n-1)/2} possible choices for α i {\displaystyle \alpha _{i}} and α j {\displaystyle \alpha _{j}} . == Related work == The first approach to splitting large SVM learning problems into a series of smaller optimization tasks was proposed by Bernhard Boser, Isabelle Guyon, and Vladimir Vapnik. It is known as the "chunking algorithm". The algorithm starts with a random subset of the data, solves this problem, and iteratively adds examples which violate the optimality conditions. One disadvantage of this algorithm is that it is necessary to solve QP-problems scaling with the number of SVs. On real world sparse data sets, SMO can be more than 1000 times faster than the chunking algorithm. In 1997, E. Osuna, R. Freund, and F. Girosi proved a theorem which suggests a whole new set of QP algorithms for SVMs. By the virtue of this theorem a large QP problem can be broken down into a series of smaller QP sub-problems. A sequence of QP sub-problems that always add at least one violator of the Karush–Kuhn–Tucker (KKT) conditions is guaranteed to converge. The chunking algorithm obeys the conditions of the theorem, and hence will converge. The SMO algorithm can be considered a special case of the Osuna algorithm, where the size of the optimization is two and both Lagrange multipliers are replaced at every step with new multipliers that are chosen via good heuristics. The SMO algorithm is closely related to a family of optimization algorithms called Bregman methods or row-action methods. These methods solve convex programming problems with linear constraints. They are iterative methods where each step projects the current primal point onto each constraint.
Top 10 AI Copywriting Tools Compared (2026)
In search of the best AI copywriting tool? An AI copywriting tool is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI copywriting tool slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
Sample complexity
The sample complexity of a machine learning algorithm represents the number of training-samples that it needs in order to successfully learn a target function. More precisely, the sample complexity is the number of training-samples that we need to supply to the algorithm, so that the function returned by the algorithm is within an arbitrarily small error of the best possible function, with probability arbitrarily close to 1. There are two variants of sample complexity: The weak variant fixes a particular input-output distribution; The strong variant takes the worst-case sample complexity over all input-output distributions. The No free lunch theorem, discussed below, proves that, in general, the strong sample complexity is infinite, i.e. that there is no algorithm that can learn the globally-optimal target function using a finite number of training samples. However, if we are only interested in a particular class of target functions (e.g., only linear functions) then the sample complexity is finite, and it depends linearly on the VC dimension on the class of target functions. == Definition == Let X {\displaystyle X} be a space which we call the input space, and Y {\displaystyle Y} be a space which we call the output space, and let Z {\displaystyle Z} denote the product X × Y {\displaystyle X\times Y} . For example, in the setting of binary classification, X {\displaystyle X} is typically a finite-dimensional vector space and Y {\displaystyle Y} is the set { − 1 , 1 } {\displaystyle \{-1,1\}} . Fix a hypothesis space H {\displaystyle {\mathcal {H}}} of functions h : X → Y {\displaystyle h\colon X\to Y} . A learning algorithm over H {\displaystyle {\mathcal {H}}} is a computable map from Z {\displaystyle Z} to H {\displaystyle {\mathcal {H}}} . In other words, it is an algorithm that takes as input a finite sequence of training samples and outputs a function from X {\displaystyle X} to Y {\displaystyle Y} . Typical learning algorithms include empirical risk minimization, without or with Tikhonov regularization. Fix a loss function L : Y × Y → R ≥ 0 {\displaystyle {\mathcal {L}}\colon Y\times Y\to \mathbb {R} _{\geq 0}} , for example, the square loss L ( y , y ′ ) = ( y − y ′ ) 2 {\displaystyle {\mathcal {L}}(y,y')=(y-y')^{2}} , where h ( x ) = y ′ {\displaystyle h(x)=y'} . For a given distribution ρ {\displaystyle \rho } on X × Y {\displaystyle X\times Y} , the expected risk of a hypothesis (a function) h ∈ H {\displaystyle h\in {\mathcal {H}}} is E ( h ) := E ρ [ L ( h ( x ) , y ) ] = ∫ X × Y L ( h ( x ) , y ) d ρ ( x , y ) {\displaystyle {\mathcal {E}}(h):=\mathbb {E} _{\rho }[{\mathcal {L}}(h(x),y)]=\int _{X\times Y}{\mathcal {L}}(h(x),y)\,d\rho (x,y)} In our setting, we have h = A ( S n ) {\displaystyle h={\mathcal {A}}(S_{n})} , where A {\displaystyle {\mathcal {A}}} is a learning algorithm and S n = ( ( x 1 , y 1 ) , … , ( x n , y n ) ) ∼ ρ n {\displaystyle S_{n}=((x_{1},y_{1}),\ldots ,(x_{n},y_{n}))\sim \rho ^{n}} is a sequence of vectors which are all drawn independently from ρ {\displaystyle \rho } . Define the optimal risk E H ∗ = inf h ∈ H E ( h ) . {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}={\underset {h\in {\mathcal {H}}}{\inf }}{\mathcal {E}}(h).} Set h n = A ( S n ) {\displaystyle h_{n}={\mathcal {A}}(S_{n})} , for each sample size n {\displaystyle n} . h n {\displaystyle h_{n}} is a random variable and depends on the random variable S n {\displaystyle S_{n}} , which is drawn from the distribution ρ n {\displaystyle \rho ^{n}} . The algorithm A {\displaystyle {\mathcal {A}}} is called consistent if E ( h n ) {\displaystyle {\mathcal {E}}(h_{n})} probabilistically converges to E H ∗ {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}} . In other words, for all ϵ , δ > 0 {\displaystyle \epsilon ,\delta >0} , there exists a positive integer N {\displaystyle N} , such that, for all sample sizes n ≥ N {\displaystyle n\geq N} , we have Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] < δ . {\displaystyle \Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]<\delta .} The sample complexity of A {\displaystyle {\mathcal {A}}} is then the minimum N {\displaystyle N} for which this holds, as a function of ρ , ϵ {\displaystyle \rho ,\epsilon } , and δ {\displaystyle \delta } . We write the sample complexity as N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} to emphasize that this value of N {\displaystyle N} depends on ρ , ϵ {\displaystyle \rho ,\epsilon } , and δ {\displaystyle \delta } . If A {\displaystyle {\mathcal {A}}} is not consistent, then we set N ( ρ , ϵ , δ ) = ∞ {\displaystyle N(\rho ,\epsilon ,\delta )=\infty } . If there exists an algorithm for which N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is finite, then we say that the hypothesis space H {\displaystyle {\mathcal {H}}} is learnable. In others words, the sample complexity N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} defines the rate of consistency of the algorithm: given a desired accuracy ϵ {\displaystyle \epsilon } and confidence δ {\displaystyle \delta } , one needs to sample N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} data points to guarantee that the risk of the output function is within ϵ {\displaystyle \epsilon } of the best possible, with probability at least 1 − δ {\displaystyle 1-\delta } . In probably approximately correct (PAC) learning, one is concerned with whether the sample complexity is polynomial, that is, whether N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is bounded by a polynomial in 1 / ϵ {\displaystyle 1/\epsilon } and 1 / δ {\displaystyle 1/\delta } . If N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is polynomial for some learning algorithm, then one says that the hypothesis space H {\displaystyle {\mathcal {H}}} is PAC-learnable. This is a stronger notion than being learnable. == Unrestricted hypothesis space: infinite sample complexity == One can ask whether there exists a learning algorithm so that the sample complexity is finite in the strong sense, that is, there is a bound on the number of samples needed so that the algorithm can learn any distribution over the input-output space with a specified target error. More formally, one asks whether there exists a learning algorithm A {\displaystyle {\mathcal {A}}} , such that, for all ϵ , δ > 0 {\displaystyle \epsilon ,\delta >0} , there exists a positive integer N {\displaystyle N} such that for all n ≥ N {\displaystyle n\geq N} , we have sup ρ ( Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] ) < δ , {\displaystyle \sup _{\rho }\left(\Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]\right)<\delta ,} where h n = A ( S n ) {\displaystyle h_{n}={\mathcal {A}}(S_{n})} , with S n = ( ( x 1 , y 1 ) , … , ( x n , y n ) ) ∼ ρ n {\displaystyle S_{n}=((x_{1},y_{1}),\ldots ,(x_{n},y_{n}))\sim \rho ^{n}} as above. The No Free Lunch Theorem says that without restrictions on the hypothesis space H {\displaystyle {\mathcal {H}}} , this is not the case, i.e., there always exist "bad" distributions for which the sample complexity is arbitrarily large. Thus, in order to make statements about the rate of convergence of the quantity sup ρ ( Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] ) , {\displaystyle \sup _{\rho }\left(\Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]\right),} one must either constrain the space of probability distributions ρ {\displaystyle \rho } , e.g. via a parametric approach, or constrain the space of hypotheses H {\displaystyle {\mathcal {H}}} , as in distribution-free approaches. == Restricted hypothesis space: finite sample-complexity == The latter approach leads to concepts such as VC dimension and Rademacher complexity which control the complexity of the space H {\displaystyle {\mathcal {H}}} . A smaller hypothesis space introduces more bias into the inference process, meaning that E H ∗ {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}} may be greater than the best possible risk in a larger space. However, by restricting the complexity of the hypothesis space it becomes possible for an algorithm to produce more uniformly consistent functions. This trade-off leads to the concept of regularization. It is a theorem from VC theory that the following three statements are equivalent for a hypothesis space H {\displaystyle {\mathcal {H}}} : H {\displaystyle {\mathcal {H}}} is PAC-learnable. The VC dimension of H {\displaystyle {\mathcal {H}}} is finite. H {\displaystyle {\mathcal {H}}} is a uniform Glivenko-Cantelli class. This gives a way to prove that certain hypothesis spaces are PAC learnable, and by extension, learnable. === An example of a PAC-learnable hypothesis space === X = R d , Y = { − 1 , 1 } {\displaystyle X=\mathbb {R} ^{d},Y=\{-1,1\}} , and let H {\displaystyle {\mathcal {H}}} be the space of affine functions on X {\displaystyle X} , that is, functions of the form x ↦ ⟨ w , x ⟩ + b {\displaystyle x\mapsto \langl
Alberto Broggi
Alberto Broggi is General Manager at VisLab srl (spinoff of the University of Parma acquired by Silicon-Valley company Ambarella Inc. in June 2015) and a professor of Computer Engineering at the University of Parma in Italy. == Research in computer vision, hardware, and AV == Broggi's research activities started in 1991–1994. His group together with the Dipartimento di Elettronica, Politecnico di Torino, Italy, built their own hardware architecture (named PAPRICA, for PArallel PRocessor for Image Checking and Analysis, based on 256 single-bit processing elements working in SIMD fashion) and installed it on board of a mobile laboratory (Mob-Lab) to develop and test some initial concepts in the field of intelligent vehicles. In 1996, Broggi's group worked to develop a real vehicle prototype (named ARGO, a Lancia Thema passenger car which was equipped with vision sensors, processing systems, and vehicle actuators) and developed the necessary software and hardware that made it able to drive autonomously on standard roads. Broggi's research group (called VisLab from then on) gathered all their findings in a book, which was then also translated in Chinese. When Broggi was with the University of Pavia, his research was extended and applied to extreme conditions (automatic driving on snow and ice): in 2001, VisLab led the research effort of providing a vehicle (RAS, Robot Antartico di Superficie) with sensing capabilities so that it was able to automatically follow the vehicle in front. In 2010 Broggi's group embarked on driving 4 vehicles autonomously from Italy to China with no human intervention. This challenge is called VIAC, for VisLab Intercontinental Autonomous Challenge . Soon after this, Broggi was awarded a second ERC grant (Proof of concept) to industrialize some of the results obtained and successfully tested on the VIAC vehicles. On July 12, 2013, VisLab tested the BRAiVE vehicle in downtown Parma, negotiating two-way narrow rural roads, pedestrian crossings, traffic lights, artificial bumps, pedestrian areas, and tight roundabouts. The vehicle traveled from Parma University Campus up to Piazza della Pilotta (downtown Parma): a 20 minutes run in a real environment, together with real traffic at 11am on a working day, that required absolutely no human intervention. Part of this test was driven with nobody in the driver seat, for the first time ever on public roads.