Model collapse, also known by other names such as "AI inbreeding", "AI cannibalism", "Habsburg AI", and "model autophagy disorder" or "MAD" is a phenomenon noted in artificial intelligence studies, where machine learning models gradually degrade due to errors coming from uncurated synthetic data, or due to training on the outputs of another model such as prior versions of itself. It is unclear to what extent the phenomenon threatens the long-term development of such models, and some techniques have been proposed to mitigate the effect. == Characteristics == Shumailov et al. coined the term to describe two specific stages to the degradation of machine learning models: early model collapse and late model collapse: In early model collapse, the model begins losing information about the tails of the distribution – mostly affecting minority data. Later work highlighted that early model collapse is hard to notice, since overall performance may appear to improve, while the model loses performance on minority data. In late model collapse, the model loses a significant proportion of its performance, confusing concepts and losing most of its variance. == Mechanism == Using synthetic data as training data can lead to issues with the quality and reliability of the trained model. Model collapse occurs for three main reasons: functional approximation errors sampling errors learning errors Importantly, it happens in even the simplest of models, where not all of the error sources are present. In more complex models the errors often compound, leading to faster collapse. == Disagreement over real-world impact == Some researchers and commentators on model collapse warn that the phenomenon could fundamentally threaten future generative AI development: As AI-generated data is shared on the Internet, it will inevitably end up in future training datasets, which are often crawled from the Internet. If training on "slop" (large quantities of unlabeled synthetic data) inevitably leads to model collapse, this could therefore pose a difficult problem. However, recently, other researchers have disagreed with this argument, showing that if synthetic data accumulates alongside human-generated data, model collapse is avoided. The researchers argue that data accumulating over time is a more realistic description of reality than deleting all existing data every year, and that the real-world impact of model collapse may not be as catastrophic as feared. An alternative branch of the literature investigates the use of machine learning detectors and watermarking to identify model generated data and filter it out. == Mathematical models of the phenomenon == === 1D Gaussian model === In 2024, a first attempt has been made at illustrating collapse for the simplest possible model — a single dimensional normal distribution fit using unbiased estimators of mean and variance, computed on samples from the previous generation. To make this more precise, we say that original data follows a normal distribution X 0 ∼ N ( μ , σ 2 ) {\displaystyle X^{0}\sim {\mathcal {N}}(\mu ,\sigma ^{2})} , and we possess M 0 {\displaystyle M_{0}} samples X j 0 {\displaystyle X_{j}^{0}} for j ∈ { 1 , … , M 0 } {\displaystyle j\in {\{\,1,\dots ,M_{0}\,{}\}}} . Denoting a general sample X j i {\displaystyle X_{j}^{i}} as sample j ∈ { 1 , … , M i } {\displaystyle j\in {\{\,1,\dots ,M_{i}\,{}\}}} at generation i {\displaystyle i} , then the next generation model is estimated using the sample mean and variance: μ i + 1 = 1 M i ∑ j X j i ; σ i + 1 2 = 1 M i − 1 ∑ j ( X j i − μ i + 1 ) 2 . {\displaystyle \mu _{i+1}={\frac {1}{M_{i}}}\sum _{j}X_{j}^{i};\quad \sigma _{i+1}^{2}={\frac {1}{M_{i}-1}}\sum _{j}(X_{j}^{i}-\mu _{i+1})^{2}.} Leading to a conditionally normal next generation model X j i + 1 | μ i + 1 , σ i + 1 ∼ N ( μ i + 1 , σ i + 1 2 ) {\displaystyle X_{j}^{i+1}|\mu _{i+1},\;\sigma _{i+1}\sim {\mathcal {N}}(\mu _{i+1},\sigma _{i+1}^{2})} . In theory, this is enough to calculate the full distribution of X j i {\displaystyle X_{j}^{i}} . However, even after the first generation, the full distribution is no longer normal: It follows a variance-gamma distribution. To continue the analysis, instead of writing the probability density function at each generation, it is possible to explicitly construct them in terms of independent random variables using Cochran's theorem. To be precise, μ 1 {\displaystyle \mu _{1}} and σ 1 {\displaystyle \sigma _{1}} are independent, with μ 1 ∼ N ( μ , σ 2 M 0 ) {\displaystyle \mu _{1}\sim {\mathcal {N}}\left(\mu ,{\frac {\sigma ^{2}}{M_{0}}}\right)} and ( M 0 − 1 ) σ 1 2 ∼ σ 2 Γ ( M 0 − 1 2 , 1 2 ) {\displaystyle (M_{0}-1)\,\sigma _{1}^{2}\sim \sigma ^{2}\,\Gamma \left({\frac {M_{0}-1}{2}},{\frac {1}{2}}\right)} , following a Gamma distribution. Denoting with Z {\displaystyle Z} Gaussian random variables distributed according to N ( 0 , 1 ) {\displaystyle {\mathcal {N}}(0,1)} and with S i {\displaystyle S^{i}} random variables distributed with 1 M i − 1 − 1 Γ ( M i − 1 − 1 2 , 1 2 ) {\displaystyle {\frac {1}{M_{i-1}-1}}\Gamma \left({\frac {M_{i-1}-1}{2}},{\frac {1}{2}}\right)} , it turns out to be possible to write samples at each generation as X j 0 = μ + σ Z j 0 , {\textstyle X_{j}^{0}=\mu +\sigma Z_{j}^{0},} X j 1 = μ + σ M 0 Z 1 + σ S 1 Z j 1 , {\textstyle X_{j}^{1}=\mu +{\frac {\sigma }{\sqrt {M_{0}}}}Z^{1}+\sigma {\sqrt {S^{1}}}Z_{j}^{1},} and more generally X j n = μ + σ M 0 Z 1 + σ M 1 S 1 Z 2 + ⋯ + σ M n − 1 S 1 × ⋯ × S n − 1 Z n + σ S 1 × ⋯ × S n Z j n . {\displaystyle X_{j}^{n}=\mu +{\frac {\sigma }{\sqrt {M_{0}}}}Z^{1}+{\frac {\sigma }{\sqrt {M_{1}}}}{\sqrt {S^{1}}}Z^{2}+\dots +{\frac {\sigma }{\sqrt {M_{n-1}}}}{\sqrt {S^{1}\times \dots \times S^{n-1}}}Z^{n}+\sigma {\sqrt {S^{1}\times \dots \times S^{n}}}Z_{j}^{n}.} Note, that these are not joint distributions, as Z n {\displaystyle Z^{n}} and S n {\displaystyle S^{n}} depend directly on Z j n − 1 {\displaystyle Z_{j}^{n-1}} , but when considering X j n {\displaystyle X_{j}^{n}} on its own the formula above provides all the information about the full distribution. To analyse the model collapse, we can first calculate variance and mean of samples at generation n {\displaystyle n} . This would tell us what kind of distributions we expect to arrive at after n {\displaystyle n} generations. It is possible to find its exact value in closed form, but the mean and variance of the square root of gamma distribution are expressed in terms of gamma functions, making the result quite clunky. Following, it is possible to expand all results to second order in each of 1 / M i {\displaystyle 1/M_{i}} , assuming each sample size to be large. It is then possible to show that 1 σ 2 Var ( X j n ) = 1 M 0 + 1 M 1 + ⋯ + 1 M n − 1 + 1 + O ( M i − 2 ) . {\displaystyle {\frac {1}{\sigma ^{2}}}\operatorname {Var} (X_{j}^{n})={\frac {1}{M_{0}}}+{\frac {1}{M_{1}}}+\dots +{\frac {1}{M_{n-1}}}+1+{\mathcal {O}}\left(M_{i}^{-2}\right).} And if all sample sizes M i = M {\displaystyle M_{i}=M} are constant, this diverges linearly as n → ∞ {\displaystyle n\to \infty } : Var ( X j n ) = σ 2 ( 1 + n M ) ; E ( X j n ) = μ . {\displaystyle \operatorname {Var} (X_{j}^{n})=\sigma ^{2}\left(1+{\frac {n}{M}}\right);\quad \mathbb {E} (X_{j}^{n})=\mu .} This is the same scaling as for a single dimensional Gaussian random walk. However, divergence of the variance of X j n {\displaystyle X_{j}^{n}} does not directly provide any information about the corresponding estimates of μ n + 1 {\displaystyle \mu _{n+1}} and σ n + 1 {\displaystyle \sigma _{n+1}} , particularly how different they are from the original μ {\displaystyle \mu } and σ {\displaystyle \sigma } . It turns out to be possible to calculate the distance between the true distribution and the approximated distribution at step n + 1 {\displaystyle n+1} , using the Wasserstein-2 distance (which is also sometimes referred to as risk): E [ W 2 2 ( N ( μ , σ 2 ) , N ( μ n + 1 , σ n + 1 2 ) ) ] = 3 2 σ 2 ( 1 M 0 + 1 M 1 + ⋯ + 1 M n ) + O ( M i − 2 ) , {\displaystyle \mathbb {E} \left[\mathbb {W} _{2}^{2}\left({\mathcal {N}}(\mu ,\sigma ^{2}),{\mathcal {N}}(\mu _{n+1},\sigma _{n+1}^{2})\right)\right]={\frac {3}{2}}\sigma ^{2}\left({\frac {1}{M_{0}}}+{\frac {1}{M_{1}}}+\dots +{\frac {1}{M_{n}}}\right)+{\mathcal {O}}\left(M_{i}^{-2}\right),} Var [ W 2 2 ( N ( μ , σ 2 ) , N ( μ n + 1 , σ n + 1 2 ) ) ] = 1 2 σ 4 ( 3 M 0 2 + 3 M 1 2 + ⋯ + 3 M n 2 + ∑ i ≠ j 4 M i M j ) + O ( M i − 3 ) . {\displaystyle \operatorname {Var} \left[\mathbb {W} _{2}^{2}\left({\mathcal {N}}(\mu ,\sigma ^{2}),{\mathcal {N}}(\mu _{n+1},\sigma _{n+1}^{2})\right)\right]={\frac {1}{2}}\sigma ^{4}\left({\frac {3}{M_{0}^{2}}}+{\frac {3}{M_{1}^{2}}}+\dots +{\frac {3}{M_{n}^{2}}}+\sum _{i\neq j}{\frac {4}{M_{i}M_{j}}}\right)+{\mathcal {O}}\left(M_{i}^{-3}\right).} This directly shows why model collapse occurs in this simple model. Due to errors from re-sampling the approximated distribution, each generation ends up corresponding to a
Oculus Medium
Oculus Medium is a digital sculpting software that works with virtual reality headsets and 6DoF motion controllers. It is used to create and paint digital sculptures. Medium works only on Oculus Rift. It was released on December 5, 2016, following with a major update in 2018 introducing new features and a revamped UI. On December 9, 2019, Oculus Medium was acquired by Adobe and re-named to "Medium by Adobe".
Bitmap index
A bitmap index is a special kind of database index that uses bitmaps. Bitmap indexes have traditionally been considered to work well for low-cardinality columns, which have a modest number of distinct values, either absolutely, or relative to the number of records that contain the data. The extreme case of low cardinality is Boolean data (e.g., does a resident in a city have internet access?), which has two values, True and False. Bitmap indexes use bit arrays (commonly called bitmaps) and answer queries by performing bitwise logical operations on these bitmaps. Bitmap indexes have a significant space and performance advantage over other structures for query of such data. Their drawback is they are less efficient than the traditional B-tree indexes for columns whose data is frequently updated: consequently, they are more often employed in read-only systems that are specialized for fast query - e.g., data warehouses, and generally unsuitable for online transaction processing applications. Some researchers argue that bitmap indexes are also useful for moderate or even high-cardinality data (e.g., unique-valued data) which is accessed in a read-only manner, and queries access multiple bitmap-indexed columns using the AND, OR or XOR operators extensively. Bitmap indexes are also useful in data warehousing applications for joining a large fact table to smaller dimension tables such as those arranged in a star schema. == Example == Continuing the internet access example, a bitmap index may be logically viewed as follows: On the left, Identifier refers to the unique number assigned to each resident, HasInternet is the data to be indexed, the content of the bitmap index is shown as two columns under the heading bitmaps. Each column in the left illustration under the Bitmaps header is a bitmap in the bitmap index. In this case, there are two such bitmaps, one for "has internet" Yes and one for "has internet" No. It is easy to see that each bit in bitmap Y shows whether a particular row refers to a person who has internet access. This is the simplest form of bitmap index. Most columns will have more distinct values. For example, the sales amount is likely to have a much larger number of distinct values. Variations on the bitmap index can effectively index this data as well. We briefly review three such variations. Note: Many of the references cited here are reviewed at (John Wu (2007)). For those who might be interested in experimenting with some of the ideas mentioned here, many of them are implemented in open source software such as FastBit, the Lemur Bitmap Index C++ Library, the Roaring Bitmap Java library and the Apache Hive Data Warehouse system. == Compression == For historical reasons, bitmap compression and inverted list compression were developed as separate lines of research, and only later were recognized as solving essentially the same problem. Software can compress each bitmap in a bitmap index to save space. There has been considerable amount of work on this subject. Though there are exceptions such as Roaring bitmaps, Bitmap compression algorithms typically employ run-length encoding, such as the Byte-aligned Bitmap Code, the Word-Aligned Hybrid code, the Partitioned Word-Aligned Hybrid (PWAH) compression, the Position List Word Aligned Hybrid, the Compressed Adaptive Index (COMPAX), Enhanced Word-Aligned Hybrid (EWAH) and the COmpressed 'N' Composable Integer SEt (CONCISE). These compression methods require very little effort to compress and decompress. More importantly, bitmaps compressed with BBC, WAH, COMPAX, PLWAH, EWAH and CONCISE can directly participate in bitwise operations without decompression. This gives them considerable advantages over generic compression techniques such as LZ77. BBC compression and its derivatives are used in a commercial database management system. BBC is effective in both reducing index sizes and maintaining query performance. BBC encodes the bitmaps in bytes, while WAH encodes in words, better matching current CPUs. "On both synthetic data and real application data, the new word aligned schemes use only 50% more space, but perform logical operations on compressed data 12 times faster than BBC." PLWAH bitmaps were reported to take 50% of the storage space consumed by WAH bitmaps and offer up to 20% faster performance on logical operations. Similar considerations can be done for CONCISE and Enhanced Word-Aligned Hybrid. The performance of schemes such as BBC, WAH, PLWAH, EWAH, COMPAX and CONCISE is dependent on the order of the rows. A simple lexicographical sort can divide the index size by 9 and make indexes several times faster. The larger the table, the more important it is to sort the rows. Reshuffling techniques have also been proposed to achieve the same results of sorting when indexing streaming data. == Encoding == Basic bitmap indexes use one bitmap for each distinct value. It is possible to reduce the number of bitmaps used by using a different encoding method. For example, it is possible to encode C distinct values using log(C) bitmaps with binary encoding. This reduces the number of bitmaps, further saving space, but to answer any query, most of the bitmaps have to be accessed. This makes it potentially not as effective as scanning a vertical projection of the base data, also known as a materialized view or projection index. Finding the optimal encoding method that balances (arbitrary) query performance, index size and index maintenance remains a challenge. Without considering compression, Chan and Ioannidis analyzed a class of multi-component encoding methods and came to the conclusion that two-component encoding sits at the kink of the performance vs. index size curve and therefore represents the best trade-off between index size and query performance. == Binning == For high-cardinality columns, it is useful to bin the values, where each bin covers multiple values and build the bitmaps to represent the values in each bin. This approach reduces the number of bitmaps used regardless of encoding method. However, binned indexes can only answer some queries without examining the base data. For example, if a bin covers the range from 0.1 to 0.2, then when the user asks for all values less than 0.15, all rows that fall in the bin are possible hits and have to be checked to verify whether they are actually less than 0.15. The process of checking the base data is known as the candidate check. In most cases, the time used by the candidate check is significantly longer than the time needed to work with the bitmap index. Therefore, binned indexes exhibit irregular performance. They can be very fast for some queries, but much slower if the query does not exactly match a bin. == History == The concept of bitmap index was first introduced by Professor Israel Spiegler and Rafi Maayan in their research "Storage and Retrieval Considerations of Binary Data Bases", published in 1985. The first commercial database product to implement a bitmap index was Computer Corporation of America's Model 204. Patrick O'Neil published a paper about this implementation in 1987. This implementation is a hybrid between the basic bitmap index (without compression) and the list of Row Identifiers (RID-list). Overall, the index is organized as a B+tree. When the column cardinality is low, each leaf node of the B-tree would contain long list of RIDs. In this case, it requires less space to represent the RID-lists as bitmaps. Since each bitmap represents one distinct value, this is the basic bitmap index. As the column cardinality increases, each bitmap becomes sparse and it may take more disk space to store the bitmaps than to store the same content as RID-lists. In this case, it switches to use the RID-lists, which makes it a B+tree index. == In-memory bitmaps == One of the strongest reasons for using bitmap indexes is that the intermediate results produced from them are also bitmaps and can be efficiently reused in further operations to answer more complex queries. Many programming languages support this as a bit array data structure. For example, Java has the BitSet class and .NET have the BitArray class. Some database systems that do not offer persistent bitmap indexes use bitmaps internally to speed up query processing. For example, PostgreSQL versions 8.1 and later implement a "bitmap index scan" optimization to speed up arbitrarily complex logical operations between available indexes on a single table. For tables with many columns, the total number of distinct indexes to satisfy all possible queries (with equality filtering conditions on either of the fields) grows very fast, being defined by this formula: C n [ n 2 ] ≡ n ! ( n − [ n 2 ] ) ! [ n 2 ] ! {\displaystyle \mathbf {C} _{n}^{\left[{\frac {n}{2}}\right]}\equiv {\frac {n!}{\left(n-\left[{\frac {n}{2}}\right]\right)!\left[{\frac {n}{2}}\right]!}}} . A bitmap index scan combines expressions on different indexes, thus requiring only one index per column t
Social influence bias
The social influence bias is an asymmetric herding effect on online social media platforms which makes users overcompensate for negative ratings but amplify positive ones. Driven by the desire to be accepted within a specific group, it surrounds the idea that people alter certain behaviors to be like those of the people within a group. Therefore, it is a subgroup term for various types of cognitive biases. Some social influence bias types include the bandwagon effect, authority bias, groupthinking effect, social comparison bias, social media bias and more. Understanding these biases helps us understand the term overall. However, the composition of the term "social influence bias" requires critical examination to understand the way that it affects individuals' and groups' lives. The term "influence" has 2 different types of stigma. For one, it surrounds the idea that people show their true inner selves when "under the influence". On the other end, it also proposes the idea that people are not their own selves when "under the influence". These tend to be constructions made by people, which also tend to fit the situation based on their own perspectives. So, even in social terms, it requires both sides to be examined to understand whether we truly are affected by context, or we remain to be and behave in terms of our own selves. The term "influence" doesn't necessarily say that there lies greater strength in our inner self's desires and decisions, nor does it say that external factors have the greater power. In a similar manner, both social and non-social judgments are to be associated with anxiety, but the same can't necessarily be said in the case of social conformity. So, the gray areas within this topic beg the question, "What does social influence bias say about us, and does it affect us all in the same way?" == Social media bias == Media bias is reflected in search systems in social media. Kulshrestha and her team found through research in 2018 that the top-ranked results returned by these search engines can influence users' perceptions when they conduct searches for events or people, which is particularly reflected in political bias and polarizing topics. Fueled by confirmation bias, online echo chambers allow users to be steeped within their own ideology. Because social media is tailored to your interests and your selected friends, it is an easy outlet for political echo chambers. Social media bias is also reflected in hostile media effect. Social media has a place in disseminating news in modern society, where viewers are exposed to other people's comments while reading news articles. In their 2020 study, Gearhart and her team showed that viewers' perceptions of bias increased and perceptions of credibility decreased after seeing comments with which they held different opinions. == In research context == In observational data, how social influence affects collected judgment is challenging to fully understand. Positive social influence can accumulate and result in a rating bubble, while negative social influence is neutralized by crowd correction. This phenomenon was first described in a paper written by Lev Muchnik, Sinan Aral and Sean J. Taylor in 2014, then the question was revisited by Cicognani et al., whose experiment reinforced Munchnik's and his co-authors' results. == Relevance == Online customer reviews are trusted sources of information in various contexts such as online marketplaces, dining, accommodation, movies, or digital products. However, these online ratings are not immune to herd behavior, which means that subsequent reviews are not independent from each other. As on many such sites, preceding opinions are visible to a new reviewer, he or she can be heavily influenced by the antecedent evaluations in his or her decision about the certain product, service or online content. This form of herding behavior inspired Muchnik, Aral and Taylor to conduct their experiment on influence in social contexts. == Experimental design == Muchnik, Aral, and Taylor designed a large-scale randomized experiment to measure social influence on user reviews. The experiment was conducted on social news aggregation website like Reddit. The study lasted for 5 months, the authors randomly assigned 101 281 comments to one of the following treatment groups: up-treated (4049), down-treated (1942), or control (the proportions reflect the observed ratio of up-and down-votes. Comments which fell to the first group were given an up-vote upon the creation of the comment, the second group got a down-vote upon creation, the comments in the control group remained untouched. A vote is equivalent to a single rating (+1 or -1). As other users are unable to trace a user’s votes, they were unaware of the experiment. Due to randomization, comments in the control and the treatment group were not different in terms of expected rating. The treated comments were viewed more than 10 million times and rated 308 515 times by successive users. == Results == The up-vote treatment increased the probability of up-voting by the first viewer by 32% over the control group, while the probability of down-voting did not change compared to the control group, which means that users did not correct the random positive rating. The upward bias remained inplace for the observed 5-month period. The accumulating herding effect increased the comment’s mean rating by 25% compared to the control group comments. Positively manipulated comments did receive higher ratings at all parts of the distribution, which means that they were also more likely to collect extremely high scores. The negative manipulation created an asymmetric herd effect: although the probability of subsequent down-votes was increased by the negative treatment, the probability of up-voting also grew for these comments. The community performed a correction which neutralized the negative treatment and resulted non-different final mean ratings from the control group. The authors also compared the final mean scores of comments across the most active topic categories on the website. The observed positive herding effect was present in the "politics," "culture and society," and "business" subreddits, but was not applicable for "economics," "IT," "fun," and "general news".- == Implications == The skewed nature of online ratings makes review outcomes different to what it would be without the social influence bias. In a 2009 experiment by Hu, Zhang and Pavlou showed that the distribution of reviews of a certain product made by unconnected individuals is approximately normal, however, the rating of the same product on Amazon followed a J-Shaped distribution with twice as much five-star ratings than others. Cicognani, Figini and Magnani came to similar conclusions after their experiment conducted on a tourism services website: positive preceding ratings influenced raters' behavior more than mediocre ones. Positive crowd correction makes community-based opinions upward-biased.
Pivot to video
"Pivot to video" is a phrase referring to the trend, starting in 2015, of media publishing companies cutting staff resources for written content (generally published on their own web sites) in favor of short-form video content (often published on third-party platforms such as Facebook, Instagram, Twitter, YouTube, Snapchat, and TikTok). These moves were generally presented by publishers as a response to changes in social media traffic or to changes in the media consumption habits of younger audiences. However, many media commentators have argued that this shift was primarily motivated by advertising revenue, and that only advertisers, not consumers, prefer video over text. The pivot's contribution to job loss in the media industry has given the phrase "pivot to video" an association with decline, especially in a business context. Commentators have also noted a lack of transparency and accuracy in the viewership metrics reported by platforms such as Facebook, pointing out that abrupt shifts in platforms' proprietary algorithms can have devastating effects on publishers' viewership, traffic, and revenue. Following a scandal in which Facebook revealed it had artificially inflated numbers to its advertisers about how long viewers watched ads, many journalists and industry analysts concluded that the shift to video was based on such misleading or inaccurate metrics, which created a false impression that there was customer demand for additional video content. == History == Streaming media technology has been available since the early 1990s, though it was relatively low-fidelity and not widely available until the mid-2000s. In 2007, traditional media publishers including the New York Times, Washington Post and Time Inc. created new divisions to develop web videos, and Facebook launched its video platform. Twitter purchased micro-video service Vine in October 2012, began adding native video streaming in late 2014, and acquired video-streaming service Periscope in January 2015. An August 2014 profile on BuzzFeed noted the publisher's large investment into video production, and observed that "the future of BuzzFeed may not even be on BuzzFeed.com. One of the company’s nascent ideas, BuzzFeed Distributed, will be a team of 20 people producing content that lives entirely on other popular platforms, like Tumblr, Instagram or Snapchat." On 7 January 2015, Facebook issued a statement about "the shift to video," reporting that "since June 2014, Facebook has averaged more than 1 billion video views every day." Media critic John Herrman argued that "What the shift to Facebook video means is that Facebook is more interested in hosting the things media companies make than just spreading them, that it views links to outside pages as a problem to be solved, and that it sees Facebook-hosted video as an example of the solution." In February 2015, the digital video-journalism publisher NowThis announced that it would operate without a home page, producing content to be published directly on social media platforms. In April 2016, Mashable fired much of its editorial staff, attempting to pivot away from hard news coverage while "growing Mashable across every platform" and doubling down on branded content and video. By December 2017, following a sale to Ziff Davis, Mashable retreated from this focus on video; Bernard Gershon, president of GershonMedia, said that the announcement of many such "pivots" were actually aimed primarily at investors. By 2017, "advertiser interest in video [was] insatiable... Any CFO is going to say 'How can we get more video?'" according to an executive of the publishers' trade association Digital Content Next. Publishers such as Vanity Fair, the Washington Post, and Sports Illustrated began adapting their own articles into cheap video content, either dictated by a newsreader or animated as a slideshow with captions, which could be shared on social platforms or even played alongside the articles themselves. June 2017 saw numerous high-profile pivots to video. Vocativ laid off at least 20 staff, including its entire newsroom, explaining that "as the industry evolves, we are undertaking a strategic shift to focus exclusively on video content that will be distributed via social media and other platforms." Fox Sports eliminated its entire writing staff to focus on creating "premium video across all platforms." And MTV News announced a restructuring that would cut its writing team. Less than two years earlier, MTV News had hired Grantland co-founder Dan Fierman to lead a significant investment in "longform" political and cultural reporting, but Fierman left in April 2017, and in June MTV announced it was "shifting resources into short-form video content more in line with young people's media consumption habits." In July, Vice Media laid off at least 60 employees, including the editor-in-chief of Vice Sports, while expanding video production. August 2017 saw Mic cut ten writers and directed the remainder of the newsroom to generate videos for social platforms. CEO Chris Altchek said "When you think about how many hours people spend watching video versus reading, the audience has already spoken." The move was ultimately unsuccessful, and Mic laid off the majority of its staff a year later before being sold to Bustle Media Group for a fraction of its former value. In September 2017, the for-profit wiki-hosting company Fandom began adding commercially produced videos to its otherwise user-generated wiki subdomains, explicitly citing the need to "keep up with user and advertiser expectations" by "diversifying our content," claiming without substantiation that "consumer patterns are changing," necessitating the addition of "complementary video" to accommodate that supposed need. Objection to the content in these videos and its sharp contrast against the content of the wiki sites to which they were applied led to vocal user backlash, leading Fandom CCO Dorth Raphaely to offer the following non-committal response: "I agree that with these videos in particular we did not deliver the right type of content experience." Movie Pilot CEO Tobi Bauckhage explained his company's fall 2017 layoffs as part of moving "from a text-based publishing model to video... a reaction to the fact that Facebook has changed their algorithms in favor of video instead of referral traffic over the last 12 months and we were losing money in the publishing bit of our business." As part of the company's change in direction, the majority of its staff was laid off and its parent company was sold to Webedia. In November 2017, magazine publisher Condé Nast cut jobs, reduced the frequency of several magazines, and shut down the print edition of Teen Vogue, then invested significant new resources in video production, with a senior executive saying "In the next 24 months, I hope that video is half our business... It’s critical. It’s the macro trend of content consumption." In February 2018, Vox Media cut approximately 50 employees, primarily those assigned to "social video," as Vox CEO Jim Bankoff admitted that those efforts were not "viable audience or revenue growth drivers." In August 2020, Facebook Inc. (now Meta Platforms) pivoted Instagram to video in an effort to replicate the success of TikTok and appeal to a younger audience, introducing "reels" as a form of video and promoting them aggressively. Reels accounted more than half the 20 most-viewed posts on Facebook; however, most of these reels were anonymous aggregations of content from TikTok. Elon Musk declared in early 2024 that X (formerly Twitter) was now a "video-first platform", which has been described by critics as a "pivot to video". == As euphemism == In 2017, Journalist Brian Feldman said that "'Pivoting to video' has become a business strategy for digital publishers common enough in recent months to be a kind of cliché — a slick way to describe something else: layoffs." In response, writers use the phrase as gallows humor shorthand for death or cancellation, as in "how do i tell my bf i want our relationship to pivot to video" (SkyNews' Mollie Goodfellow) or "Horse broke its leg, so we had to take it out back and help it 'pivot to video'" (blogger Anil Dash). == Facebook metrics controversy == In September 2016, Facebook admitted that it had reported artificially inflated numbers to its advertisers about how long viewers watched ads leading to an overestimation of 60-80%. Plaintiffs in a later court case allege the discrepancy was as high as 150-900%. Facebook apologized in an official statement and in multiple staff appearances at New York Advertising Week. Two months later, Facebook disclosed additional discrepancies in audience metrics. In October 2018, a California federal court unsealed the text of a class action lawsuit filed by advertisers against Facebook, alleging that Facebook had known since 2015 that its viewership numbers were highly inflated, that internal records showed it "was far from an hon
Superquadrics
In mathematics, the superquadrics or super-quadrics (also superquadratics) are a family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by arbitrary powers. They can be seen as the three-dimensional relatives of the superellipses. The term may refer to the solid object or to its surface, depending on the context. The equations below specify the surface; the solid is specified by replacing the equality signs by less-than-or-equal signs. The superquadrics include many shapes that resemble cubes, octahedra, cylinders, lozenges and spindles, with rounded or sharp corners. Because of their flexibility and relative simplicity, they are popular geometric modeling tools, especially in computer graphics. It becomes an important geometric primitive widely used in computer vision, robotics, and physical simulation. Some authors, such as Alan Barr, define "superquadrics" as including both the superellipsoids and the supertoroids. In modern computer vision literatures, superquadrics and superellipsoids are used interchangeably, since superellipsoids are the most representative and widely utilized shape among all the superquadrics. Comprehensive coverage of geometrical properties of superquadrics and methods of their recovery from range images and point clouds are covered in several computer vision literatures. == Formulas == === Implicit equation === The surface of the basic superquadric is given by | x | r + | y | s + | z | t = 1 {\displaystyle \left|x\right|^{r}+\left|y\right|^{s}+\left|z\right|^{t}=1} where r, s, and t are positive real numbers that determine the main features of the superquadric. Namely: less than 1: a pointy octahedron modified to have concave faces and sharp edges. exactly 1: a regular octahedron. between 1 and 2: an octahedron modified to have convex faces, blunt edges and blunt corners. exactly 2: a sphere greater than 2: a cube modified to have rounded edges and corners. infinite (in the limit): a cube Each exponent can be varied independently to obtain combined shapes. For example, if r=s=2, and t=4, one obtains a solid of revolution which resembles an ellipsoid with round cross-section but flattened ends. This formula is a special case of the superellipsoid's formula if (and only if) r = s. If any exponent is allowed to be negative, the shape extends to infinity. Such shapes are sometimes called super-hyperboloids. The basic shape above spans from -1 to +1 along each coordinate axis. The general superquadric is the result of scaling this basic shape by different amounts A, B, C along each axis. Its general equation is | x A | r + | y B | s + | z C | t = 1. {\displaystyle \left|{\frac {x}{A}}\right|^{r}+\left|{\frac {y}{B}}\right|^{s}+\left|{\frac {z}{C}}\right|^{t}=1.} === Parametric description === Parametric equations in terms of surface parameters u and v (equivalent to longitude and latitude if m equals 2) are x ( u , v ) = A g ( v , 2 r ) g ( u , 2 r ) y ( u , v ) = B g ( v , 2 s ) f ( u , 2 s ) z ( u , v ) = C f ( v , 2 t ) − π 2 ≤ v ≤ π 2 , − π ≤ u < π , {\displaystyle {\begin{aligned}x(u,v)&{}=Ag\left(v,{\frac {2}{r}}\right)g\left(u,{\frac {2}{r}}\right)\\y(u,v)&{}=Bg\left(v,{\frac {2}{s}}\right)f\left(u,{\frac {2}{s}}\right)\\z(u,v)&{}=Cf\left(v,{\frac {2}{t}}\right)\\&-{\frac {\pi }{2}}\leq v\leq {\frac {\pi }{2}},\quad -\pi \leq u<\pi ,\end{aligned}}} where the auxiliary functions are f ( ω , m ) = sgn ( sin ω ) | sin ω | m g ( ω , m ) = sgn ( cos ω ) | cos ω | m {\displaystyle {\begin{aligned}f(\omega ,m)&{}=\operatorname {sgn}(\sin \omega )\left|\sin \omega \right|^{m}\\g(\omega ,m)&{}=\operatorname {sgn}(\cos \omega )\left|\cos \omega \right|^{m}\end{aligned}}} and the sign function sgn(x) is sgn ( x ) = { − 1 , x < 0 0 , x = 0 + 1 , x > 0. {\displaystyle \operatorname {sgn}(x)={\begin{cases}-1,&x<0\\0,&x=0\\+1,&x>0.\end{cases}}} === Spherical product === Barr introduces the spherical product which given two plane curves produces a 3D surface. If f ( μ ) = ( f 1 ( μ ) f 2 ( μ ) ) , g ( ν ) = ( g 1 ( ν ) g 2 ( ν ) ) {\displaystyle f(\mu )={\begin{pmatrix}f_{1}(\mu )\\f_{2}(\mu )\end{pmatrix}},\quad g(\nu )={\begin{pmatrix}g_{1}(\nu )\\g_{2}(\nu )\end{pmatrix}}} are two plane curves then the spherical product is h ( μ , ν ) = f ( μ ) ⊗ g ( ν ) = ( f 1 ( μ ) g 1 ( ν ) f 1 ( μ ) g 2 ( ν ) f 2 ( μ ) ) {\displaystyle h(\mu ,\nu )=f(\mu )\otimes g(\nu )={\begin{pmatrix}f_{1}(\mu )\ g_{1}(\nu )\\f_{1}(\mu )\ g_{2}(\nu )\\f_{2}(\mu )\end{pmatrix}}} This is similar to the typical parametric equation of a sphere: x = x 0 + r sin θ cos φ y = y 0 + r sin θ sin φ ( 0 ≤ θ ≤ π , 0 ≤ φ < 2 π ) z = z 0 + r cos θ {\displaystyle {\begin{aligned}x&=x_{0}+r\sin \theta \;\cos \varphi \\y&=y_{0}+r\sin \theta \;\sin \varphi \qquad (0\leq \theta \leq \pi ,\;0\leq \varphi <2\pi )\\z&=z_{0}+r\cos \theta \end{aligned}}} which give rise to the name spherical product. Barr uses the spherical product to define quadric surfaces, like ellipsoids, and hyperboloids as well as the torus, superellipsoid, superquadric hyperboloids of one and two sheets, and supertoroids. == Plotting code == The following GNU Octave code generates a mesh approximation of a superquadric:
Batch cryptography
Batch cryptography is a field of cryptology focused on the design of cryptographic protocols that perform operations—such as encryption, decryption, key exchange, and authentication—on multiple inputs simultaneously, rather than processing each input individually. Batching cryptographic operations can significantly reduce the marginal cost of handling individual inputs—a principle that was first introduced by Amos Fiat in 1989.