prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What are the three teams that used conflict optimization in the challenge?

Read the following text and answer briefly.

Context 1: Paper Info

Title: Conflict Optimization for Binary CSP Applied to Minimum Partition into Plane Subgraphs and Graph Coloring
Publish Date: 25 Mar 2023
Author List: Loïc Crombez (from LIMOS, Université Clermont Auvergne), Guilherme Da Fonseca (from LIS, Aix-Marseille Université), Florian Fontan (from Independent Researcher), Yan Gerard (from LIMOS, Université Clermont Auvergne), Aldo Gonzalez-Lorenzo (from LIS, Aix-Marseille Université), Pascal Lafourcade (from LIMOS, Université Clermont Auvergne), Luc Libralesso (from LIMOS, Université Clermont Auvergne), Benjamin Momège (from Independent Researcher), Jack Spalding-Jamieson (from David R  Cheriton School of Computer Science, University of Waterloo), Brandon Zhang (from Independent Researcher), Da Zheng (from Department of Computer Science, University of Illinois at Urbana-Champaign)

Figure

Figure 1: A partition of the input graph of the CG:SHOP2022 instance vispecn2518 into 57 plane graphs It is the smallest instance of the challenge with 2518 segments On top left, you see all 57 colors together On top right, you see a clique of size 57, hence the solution is optimal Each of the 57 colors is then presented in small figures 
Figure 2: Number of colors over time for the instance vispecn13806 using different values p The algorithm uses σ = 0 15, easy vertices, q max = 59022, but does not use the BDFS nor any clique 
Figure 3: Number of colors over time with different values of q max obtained on the instance vispecn13806 Parameters are σ = 0 15, p = 1 2, no clique knowledge, and no BDFS 
Figure 4: Number of colors over time with and without clique knowledge and BDFS obtained on the instance vispecn13806 Parameters are σ = 0 15, p = 1 2, and q max = 1500000 
Figure 5: Number of colors over time for the instance vispecn13806 for different values of σ In both figures the algorithm uses p = 1 2, easy vertices, q max = 59022, but does not use the BDFS nor any clique For σ ≥ 0 25, no solution better than 248 colors is found 
Figure 6: Number of colors over time (in hours) for the instance vispecn13806 
Several CG:SHOP 2022 results We compare the size of the largest known clique to the smallest coloring found by each team on a selection of 14 CG:SHOP 2022 instances 
[20][21][22][23][24][25] with state-of-the-art graph coloring algorithms The conflict optimizer underperforms except on the geometric graphs r* and dsjr* CE39-0007), SEVERITAS (ANR-20-CE39-0005) and by the French government IDEX-ISITE initiative 16-IDEX-0001 (CAP[20][21][22][23][24][25] The work of Luc Libralesso is supported by the French ANR PRC grant DECRYPT (ANR-18-CE39-0007) 

abstract

CG:SHOP is an annual geometric optimization challenge and the 2022 edition proposed the problem of coloring a certain geometric graph defined by line segments  Surprisingly, the top three teams used the same technique, called conflict optimization  This technique has been introduced in the 2021 edition of the challenge, to solve a coordinated motion planning problem 
In this paper, we present the technique in the more general framework of binary constraint satisfaction problems (binary CSP)  Then, the top three teams describe their different implementations of the same underlying strategy  We evaluate the performance of those implementations to vertex color not only geometric graphs, but also other types of graphs 

Introduction

The CG:SHOP challenge (Computational Geometry: Solving Hard Optimization Problems) is an annual geometric optimization competition, whose first edition took place in 2019  The 2022 edition proposed a problem called minimum partition into plane subgraphs  The input is a graph G embedded in the plane with edges drawn as straight line segments, and the goal is to partition the set of edges into a small number of plane graphs (Fig  )  
This goal can be formulated as a vertex coloring problem on a graph G defined as follows  The vertices of G are the segments defining the edges of G, and the edges of G correspond to pairs of crossing segments (segments that intersect only at a common endpoint are not considered crossing)  The three top-ranking teams (Lasa, Gitastrophe, and Shadoks) on the CG:SHOP 2022 challenge all used a common approach called conflict optimization while the fourth team used a SAT-Boosted Tabu Search  
Conflict optimization is a technique used by Shadoks to obtain the first place in the CG:SHOP 2021 challenge for low-makespan coordinated motion planning , and the main ideas of the technique lent themselves well to the 2022 challenge  Next, we describe the conflict optimizer as a metaheuristic to solve constraint satisfaction problems (CSP)  
We start by describing a CSP  A CSP is a triple of • variables X = (x 1 ,       , x n ), Each of the 57 colors is then presented in small figures  • domains D = (D 1 ,       , D n ), and • constraints R  Each variable x i must be assigned a value in the corresponding domain D i such that all constraints are satisfied 
In general, the constraints may forbid arbitrary subsets of values  We restrict our attention to a particular type of constraints (binary CSP ), which only involve pairs of assignments  A partial evaluation is an assignment of a subset of the variables, called evaluated, with the remaining variables called non-evaluated 
All constraints involving a non-evaluated variable are satisfied by default  We only consider assignments and partial assignments that satisfy all constraints  The conflict optimizer iteratively modifies a partial evaluation with the goal of emptying the set S of non-evaluated variables, at which point it stops 
At each step, a variable x i is removed from S  If there exists a value x ∈ D i that satisfies all constraints, then we assign the value x to the variable x i   Otherwise, we proceed as follows  For each possible value x ∈ D i , we consider the set K(i, x) of variables (other than x i ) that are part of constraints violated by the assignment x i = x 
We assign to x i the value x that minimizes where w(j) is a weight function to be described later  The variables x j ∈ K(i, x) become non-evaluated and added to S  The weight function should be such that w(j) increases each time x j is added to S, in order to avoid loops that keep moving the same variables back and forth from S  Let q(j) be the number of times x j became non-evaluated 
A possible weight function is w(j) = q(j)  More generally, we can have w(j) = q(j) p for some exponent p (typically between 1 and 2)  Of course, several details of the conflict optimizer are left open  For example, which element to choose from S, whether some random noise should be added to w, and the decision to restart the procedure from scratch after a certain time 
The CSP as is, does not apply to optimization problems  However, we can, impose a maximum value k of the objective function in order to obtain a CSP  The conflict optimizer was introduced in a low makespan coordinated motion planning setting  In that setting, the variables are the robots, the domains are their paths (of length at most k) and the constraints forbid collisions between two paths 
In the graph coloring setting, the domains are the k colors of the vertices and the constraints forbid adjacent vertices from having the same color  The conflict optimizer can be adapted to non-binary CSP, but in that case multiple variables may be unassigned for a single violated constraint  The strategy has some resemblance to the similarly named min-conflicts algorithm , but notable differences are that a partial evaluation is kept instead of an invalid evaluation and the weight function that changes over time 
While the conflict optimization strategy is simple, there are different ways to apply it to the graph coloring problem  The goal of the paper is to present how the top three teams applied it or complemented it with additional strategies  We compare the relative benefits of each variant on the instances given in the CG:SHOP 2022 challenge 
We also compare them to baselines on some instances issued from graph coloring benchmarks  The paper is organized as follows  Section 2 presents the details of the conflict optimization strategy applied to graph coloring  In the three sections that follow, the three teams Lasa, Gitastrophe, and Shadoks present the different parameters and modified strategies that they used to make the algorithm more efficient for the CG:SHOP 2022 challenge 
The last section is devoted to the experimental results 

Literature Review

The study of graph coloring goes back to the 4-color problem (1852) and it has been intensively studied since the 1970s (see for surveys)  Many heuristics have been proposed , as well as exact algorithms   We briefly present two classes of algorithms: greedy algorithms and exact algorithms  Greedy algorithms 
These algorithms are used to find good quality initial solutions in a short amount of time  The classic greedy heuristic considers the vertices in arbitrary order and colors each vertex with the smallest non-conflicting color  The two most famous modern greedy heuristics are DSATUR and Recursive Largest First (RLF )  
At each step (until all vertices are colored), DSATUR selects the vertex v that has the largest number of different colors in its neighbourhood  Ties are broken by selecting a vertex with maximum degree  The vertex v is colored with the smallest non-conflicting color  RLF searches for a large independent set I, assigns the vertices I the same color, removes I from G , and repeats until all vertices are colored 
Exact algorithms  Some exact methods use a branch-and-bound strategy, for example extending the DSATUR heuristic by allowing it to backtrack   Another type of exact method (branch-and-cut-and-price) decomposes the vertex coloring problem into an iterative resolution of two sub-problems   The "master problem" maintains a small set of valid colors using a set-covering formulation 
The "pricing problem" finds a new valid coloring that is promising by solving a maximum weight independent set problem  Exact algorithms are usually able to find the optimal coloring for graphs with a few hundred vertices  However, even the smallest CG:SHOP 2022 competition instances involve at least a few thousands vertices 

Conflict Optimization for Graph Coloring

Henceforth, we will only refer to the intersection conflict graph G induced by the instance  Vertices will refer to the vertices V (G ), and edges will refer to the edges E(G )  Our goal is to partition the vertices using a minimum set of k color classes C = {C 1 ,       , C k }, where no two vertices in the same color class C i are incident to a common edge 

Conflict Optimization

TABUCOL inspired neighbourhood One classical approach for the vertex coloring involves allowing solutions with conflicting vertices (two adjacent vertices with the same color)  It was introduced in 1987 and called TABUCOL  It starts with an initial solution, removes a color (usually the one with the least number of vertices), and assigns uncolored vertices with a new color among the remaining ones 
This is likely to lead to some conflicts (i e  two adjacent vertices sharing a same color)  The local search scheme selects a conflicting vertex, and tries to swap its color, choosing the new coloring that minimises the number of conflicts  If it reaches a state with no conflict, it provides a solution with one color less than the initial solution 
The process is repeated until the stopping criterion is met  While the original TABUCOL algorithm includes a "tabu-list" mechanism to avoid cycling, it is not always sufficient, and requires some hyper-parameter tuning in order to obtain a good performance on a large variety of instances  To overcome this issue, we use a neighbourhood, but replace the "tabu-list" by the conflict optimizer scheme presented above 
PARTIALCOL inspired neighbourhood PARTIALCOL another local search algorithm solving the vertex coloring problem was introduced in 2008  This algorithm proposes a new local search scheme that allows partial coloring (thus allowing uncolored vertices)  The goal is to minimize the number of uncolored vertices 
Similarly to TABUCOL, PARTIALCOL starts with an initial solution, removes one color (unassigning its vertices), and performs local search iterations until no vertex is left uncolored  When coloring a vertex, the adjacent conflicting vertices are uncolored  Then, the algorithm repeats the process until all vertices are colored, or the stopping criterion is met 
This neighbourhood was also introduced alongside a tabu-search procedure  The tabu-search scheme is also replaced by a conflict-optimization scheme  Note that this neighbourhood was predominantly used by the other teams 

Finding Initial Solutions

Lasa team used two approaches to find initial solutions: 1  DSATUR is the classical graph coloring algorithm presented in Section 1  2  Orientation greedy is almost the only algorithm where the geometry of the segments is used  If segments are almost parallel, it is likely that they do not intersect (thus forming an independent set) 
This greedy algorithm first sorts the segments by orientation, ranging from − π 2 to π 2   For each segment in this order, the algorithm tries to color it using the first available color  If no color has been found, a new color is created for coloring the considered segment  This algorithm is efficient, produces interesting initial solutions and takes into account the specificities of the competition 

Solution Initialization

The gitastrophe team uses the traditional greedy algorithm of Welsh and Powell to obtain initial solutions: order the vertices in decreasing order of degree, and assign each vertex the minimum-label color not used by its neighbors  During the challenge Gitastrophe attempted to use different orderings for the greedy algorithm, such as sorting by the slope of the line segment associated with each vertex (as the orientation greedy initialization presented in Section 3), and also tried numerous other strategies 
Ultimately, after running the solution optimizer for approximately the same amount of time, all initializations resulted in an equal number of colors 

Modifications to the Conflict Optimizer

Taking inspiration from memetic algorithms, which alternate between an intensification and a diversification stage, the algorithm continually switched between a phase using the above conflict score, and one minimizing only the number of conflicts  Thus during the conflict-minimization phase, the random variables f (C j ) and w(u) are both fixed equal to 1 leading to a conflict score
Each phase lasted for 10 5 iterations  Adding the conflict-minimization phase gave minor improvements to some of the challenge instances 

Shadoks

In this section, we describe the choices used by the Shadoks team for the options described in Section 2 1  The Shadoks generally chose to eliminate the color with the smallest number of elements  However, if the multistart option is toggled on, then a random color is used each time  The conflict set S is stored in a queue 
The Shadoks tried other strategies, but found that the queue gives the best results  The weight function used is w(u) = 1 + q(u) p , mostly with p = 1 2  The effect of the parameter p is shown in Fig    Notice that in all figures, the number of colors shown is the average of ten executions of the code using different random seeds 
The algorithm uses σ = 0 15, easy vertices, q max = 59022, but does not use the BDFS nor any clique  If q(u) is larger than a threshold q max , the Shadoks set w(u) = ∞ so that the vertex u never reenters S  If at some point an uncolored vertex v is adjacent to some vertex u of infinite weight in every color class, then the conflict optimizer is restarted 
When restarting, the initial coloring is shuffled by moving some vertices from their initial color class to a new one  Looking at Fig  , the value of q max does not seem to have much influence as long as it is not too small  Throughout the challenge the Shadoks almost exclusively used q max = 2000 • (75000/m) 2 , where m is the number of vertices 
This value roughly ensures a restart every few hours  q max =0 5k q max =5k q max =50k q max =100k q max =250k The Shadoks use the function f as a Gaussian random variable of mean 1 and variance σ  A good default value is σ = 0 15  The effect of the variance is shown in Fig    Notice that setting σ = 0 gives much worse results 
Option (e) The goal of BDFS is to further optimize very good solutions that the conflict optimizer is not able to improve otherwise  Fig  shows the influence of BDFS  While on this figure, the advantages of BDFS cannot be noticed, its use near the end of the challenge improved about 30 solutions  The bounded depth-first search (BDFS) algorithm tries to improve the dequeuing process 
The goal is to prevent a vertex in conflict with some adjacent colored vertices from entering in the conflict set  At the first level, the algorithm searches for a recoloring of some adjacent vertices which allows us to directly recolor the conflict vertex  If no solution is found, the algorithm  In both figures the algorithm uses p = 1 2, easy vertices, q max = 59022, but does not use the BDFS nor any clique 
For σ ≥ 0 25, no solution better than 248 colors is found  could recolor some vertices at larger distances from the conflict vertex  To do so, a local search is performed by trying to recolor vertices at a bounded distance from the conflict vertex in the current partial solution  The BDFS algorithm has two parameters: adjacency bound a max and depth d 
In order to recolor a vertex v, BDFS gets the set C of color classes with at most a max neighbors of v  If a class in C has no neighbor of v, v is assigned to C  Otherwise, for each class C ∈ C, BDFS tries to recolor the vertices in C which are adjacent to v by recursively calling itself with depth d − 1 
At depth d = 0 the algorithm stops trying to color the vertices  During the challenge the Shadoks used BDFS with parameters a max = 3 and d = 3  The depth was increased to 5 (resp  7) when the number of vertices in the queue was 2 (resp  1)  Degeneracy order Given a target number of colors k, we call easy vertices a set of vertices Y such that, if the remainder of the vertices of G are colored using k colors, then we are guaranteed to be able to color all vertices of G with k colors 
This is obtained using the degeneracy order Y   To obtain Y we iteratively remove from the graph a vertex v that has at most k − 1 neighbors, appending v to the end of Y   We repeat until no other vertex can be added to Y   Notice that, once we color the remainder of the graph with at least k colors, we can use a greedy coloring for Y in order from last to first without increasing the number of colors used 
Removing the easy vertices reduces the total number of vertices, making the conflict optimizer more effective  The Shadoks always toggle this option on (the challenge instances contain from 0 to 23% easy vertices) 

Results

We provide the results of the experiments performed with the code from the three teams on two classes of instances  First, we present the results on some selected CG:SHOP 2022 instances  These instances are intersection graphs of line segments  Second, we execute the code on graphs that are not intersection graphs, namely the classic DIMACS graphs , comparing the results of our conflict optimizer implementations to previous solutions 
The source code for the three teams is available at: • Lasa: https://github com/librallu/dogs-color • Gitastrophe: https://github com/jacketsj/cgshop2022-gitastrophe • Shadoks: https://github com/gfonsecabr/shadoks-CGSHOP2022

CG:SHOP 2022 Instances

We selected 14 instances (out of 225) covering the different types of instances given in the CG:SHOP 2022 challenge  The results are presented in Table   For comparison, we executed the HEAD code on some instances using the default parameters  The table shows the smallest number of colors for which HEAD found a solution 
We ran HEAD for 1 hour of repetitions for each target number of colors on a single CPU core (the HEAD solver takes the target number of colors as a parameter and we increased this parameter one by one)  At the end of the challenge, 8 colorings computed by Lasa, 11 colorings computed by Gitastrophe, and 23 colorings computed by Shadoks over 225 instances have been proved optimal (their number of colors is equal to the size of a clique) 
In order to compare the efficiency of the algorithms, we executed the different implementations on the CG:SHOP instance vispecn13806  The edge density of this graph is 19%, the largest clique that we found has 177 vertices and the best coloring found during the challenge uses 218 colors  Notice that vispecn13806 is the same instance used in other Shadoks experiments in Section 5  Notice also that HEAD algorithm provides 283 colors after one hour compared to less than 240 colors for the conflict optimizers 
We ran the three implementations on three different servers and compared the results shown in Figure   For each implementation, the x coordinate is the running time in hours, while the y coordinate is the smallest number of colors found at that time 

Results on DIMACS Graphs

We tested the implementation of each team on the DIMACS instances to gauge the performance of the conflict optimizer on other classes of graphs  We compared our results to the best known bounds and to the state of the art coloring algorithms HEAD and QACOL   The time limit for Lasa's algorithms is 1 hour 
CWLS is Lasa's conflict optimizer with the neighbourhood presented in TABUCOL , while PWLS is the optimizer with the neighbourhood presented in PARTIALCOL   Gitastrophe algorithm ran 10 minutes after which the number of colors no longer decreases  Shadoks algorithm ran for 1 hour without the BDFS option (results with BDFS are worse) 
Results are presented in Table   We only kept the difficult DIMACS instances  For the other instances, all the results match the best known bounds  The DIMACS instances had comparatively few edges (on the order of thousands or millions); the largest intersection graphs considered in the CG:SHOP challenge had over 1 5 billion edges 
We notice that the conflict optimizer works extremely poorly on random graphs, but it is fast and appears to perform well on geometric graphs (r250 5, r1000 1c, r1000 5, dsjr500 1c and dsjr500 5), matching the best-known results   Interestingly, these geometric graphs are not intersection graphs as in the CG:SHOP challenge, but are generated based on a distance threshold 
On the DIMACS graphs, Lasa implementation shows better performance than the other implementations 
Context 2: Sir Simon William English  (born 30 December 1961) is a New Zealand former National Party politician who served as the 39th prime minister of New Zealand from 2016 to 2017  He had previously served as the 17th deputy prime minister of New Zealand and minister of finance from 2008 to 2016 under John Key and the Fifth National Government 

A farmer and public servant before entering politics, English was elected to the New Zealand Parliament in  as the National Party's candidate in the Wallace electorate  He was elevated to Cabinet in 1996 and in 1999 was made minister of finance, although he served for less than a year due to his party's loss at the 1999 general election  In October 2001, English replaced Jenny Shipley as the leader of the National Party (and consequently as Leader of the Opposition)  He led the party to its worst defeat at the 2002 general election, and as a consequence, in October 2003 he was replaced as leader by Don Brash 

In November 2006, after Brash's resignation, English became deputy leader under John Key  After National's victory at the 2008 general election, he became deputy prime minister and was also made minister of finance for the second time  Under English's direction New Zealand's economy maintained steady growth during National's three terms of government  He became a list-only MP after stepping down as an electorate MP at the 2014 general election 

John Key resigned as leader of the National Party and prime minister in December 2016  English won the resulting leadership election unopposed and was sworn in as prime minister on 12 December 2016  His tenure was only ten months, and included a three-month election campaign  In the 2017 general election, National won the largest number of seats but fell short of a majority  The parties holding the balance of power declined to support the existing government, and English was subsequently replaced as prime minister by Jacinda Ardern, leader of the Labour Party  English initially continued on as Leader of the Opposition, but resigned as leader of the National Party on 27 February 2018 and left parliament two weeks later 

Early life
English was born on 30 December 1961 at Lumsden Maternity Centre in Lumsden  He is the eleventh of twelve children of Mervyn English and Norah (née O'Brien) English  His parents purchased Rosedale, a mixed sheep and cropping farm in Dipton, Southland from Mervyn's uncle, Vincent English, a bachelor, in 1944  English was born in the maternity unit at Lumsden 

English attended St Thomas's School in Winton, then boarded at St  Patrick's College in Upper Hutt, where he became head boy  He played in the first XV of the school's rugby team  English went on to study commerce at the University of Otago, where he was a resident at Selwyn College, and then completed an honours degree in English literature at Victoria University of Wellington 

After finishing his studies, English returned to Dipton and farmed for a few years  From 1987 to 1989, he worked in Wellington as a policy analyst for the New Zealand Treasury, at a time when the free market policies favoured by Labour's finance minister Roger Douglas (known collectively as "Rogernomics") were being implemented 

English joined the National Party in 1980, while at Victoria University  He served for a period as chairman of the Southland branch of the Young Nationals, and became a member of the Wallace electorate committee  After moving to Wellington, he served for periods on the Island Bay and Miramar electorate committees, respectively 

Fourth National Government (1990–1999)

At the 1990 general election, English stood as the National candidate in Wallace, replacing the retiring Derek Angus, and was elected with a large majority  He would hold this seat, renamed Clutha-Southland in 1996, until 2014  He and three other newly elected National MPs (Tony Ryall, Nick Smith, and Roger Sowry) were soon identified as rising stars in New Zealand politics, and at various points were dubbed the "brat pack", the "gang of four", and the "young Turks"  In his first term in parliament, English chaired a select committee into social services  He was made a parliamentary under-secretary in 1993, serving under the Minister of Health 

First period in cabinet (1996–1999)
In early 1996, English was elevated to cabinet by Prime Minister Jim Bolger, becoming the Minister for Crown Health Enterprises and Associate Minister of Education (to Wyatt Creech)  He was 34 at the time, becoming the cabinet's youngest member  After the 1996 general election, the National Party was forced into a coalition with New Zealand First to retain government  In the resulting cabinet reshuffle, English emerged as Minister of Health  However, as a condition of the coalition agreement, NZ First's Neil Kirton (a first-term MP) was made Associate Minister of Health, effectively becoming English's deputy  This arrangement was described in the press as a "shotgun marriage", and there were frequent differences of opinion between the two ministers  After their relationship became unworkable, Kirton was sacked from the role in August 1997, with the agreement of NZ First leader Winston Peters 

As Minister of Health, English was responsible for continuing the reforms to the public health system that National had begun after the 1990 general election  The reforms were unpopular, and health was perceived as one of the government's weaknesses, with the health portfolio consequently being viewed as a challenge  English believed that the unpopularity of the reforms was in part due to a failure in messaging, and encouraged his National colleagues to avoid bureaucratic and money-focused language (such as references to "balance sheets" and "user charges") and instead talk about the improvements to services the government's reforms would bring  He also rejected the idea that public hospitals could be run as commercial enterprises, a view which some of his colleagues had previously promoted 

By early 1997, as dissatisfaction with Bolger's leadership began to grow, English was being touted as a potential successor, along with Jenny Shipley and Doug Graham  His age (35) was viewed as the main impediment to a successful leadership run  National's leadership troubles were resolved in December 1997, when Bolger resigned and Shipley was elected to the leadership unopposed  English had been a supporter of Bolger as leader, but Shipley reappointed him Minister of Health in her new cabinet 

English was promoted to Minister of Finance in a reshuffle in January 1999, a position which was at the time subordinate to the Treasurer, Bill Birch  After a few months, the pair switched positions as part of Birch's transition to retirement, with English assuming the senior portfolio  In early interviews, he emphasised his wish to be seen as a pragmatist rather than an ideologue, and said that the initiatives of some of his predecessors (Roger Douglas's "Rogernomics" and Ruth Richardson's "Ruthanasia") had focused on "fruitless, theoretical debates" when "people just want to see problems solved" 

Opposition (1999–2008)

After the National Party lost the 1999 election to Helen Clark's Labour Party, English continued on in the shadow cabinet as National's spokesperson for finance  He was elected deputy leader of the party in February 2001, following the resignation of Wyatt Creech, with Gerry Brownlee being his unsuccessful opponent 

Leader of the Opposition
In October 2001, after months of speculation, Jenny Shipley resigned as leader of the National Party after being told she no longer had the support of the party caucus  English was elected as her replacement unopposed (with Roger Sowry as his deputy), and consequently became Leader of the Opposition  However, he did not openly organise against Shipley, and according to The Southland Times "there was almost an element of 'aw, shucks, I'll do it then' about Mr English's ascension" 

Aged 39 when he was elected, English became the second-youngest leader in the National Party's history, after Jim McLay (who was 38 when elected in 1984)  He also became only the third Southlander to lead a major New Zealand political party, after Joseph Ward and Adam Hamilton  However, English failed to improve the party's performance  In the 2002 election, National suffered its worst electoral defeat ever, gaining barely more than twenty percent of the vote  English described it as "the worst day of my political life"  Both party insiders and the general public were split as to how much to blame him for the loss, but most of the party believed that English would be able to rebuild National's support 

By late 2003, however, National's performance in opinion polls remained poor  The party had briefly increased its popularity in the year following the election, but by October its support had fallen to levels only slightly better than what it achieved in the last ballot  English also appeared in a boxing match for a charity against entertainer Ted Clarke  This did not boost his polling or that of the National party either, with suggestions that it devalued his image as a serious politician  Don Brash, former governor of the Reserve Bank and a relative newcomer to politics, began to build up support to replace English  On 28 October, Brash gained sufficient backing in Caucus to defeat English in a leadership contest 

Shadow cabinet roles and deputy leader
On 2 November 2003, when Brash changed responsibilities for certain MPs, English became National's spokesman for education, ranked at fifth place in the party's parliamentary hierarchy  He remained in parliament after the 2005 election  In his new shadow education portfolio, English performed strongly, and remained a party favourite despite his election defeat as leader in 2002, eventually being returned to the finance portfolio in August 2004 as deputy spokesman (while still retaining responsibility for education) 

In November 2006, Brash resigned as leader  English was considered as a potential replacement leader (running against John Key) or deputy leader (against incumbent Gerry Brownlee) in the ensuing leadership election  However, a contest was avoided when the MPs agreed a Key/English ticket would run unopposed in a display of party unity  English took over the deputy leadership and the finance portfolio in the Key shadow cabinet 

Fifth National Government (2008–2017)

Deputy Prime Minister and Minister of Finance (2008–2016)

At the 2008 election, English was re-elected by his electorate, winning by a margin of about 15,500 votes  He became Deputy Prime Minister of New Zealand and Minister of Finance in the fifth National Government, being sworn into office on 19 November 2008 and continued to serve in those roles until becoming Prime Minister on 12 December 2014  He was also made Minister of Infrastructure in National's first term of government and Minister responsible for Housing New Zealand Corporation and minister responsible for the New Zealand flag consideration process in its third 

He was comfortably re-elected in Clutha-Southland in the 2011 election but opted to run as a party-list candidate in 2014  

The pairing of John Key as leader of the National Party and English as his deputy has been compared to that of Bob Hawke and Paul Keating (in Australia) and Tony Blair and Gordon Brown (in the UK) 

English acceded to the role of Finance Minister in the continuing wake of the financial crisis  In response to New Zealand's rising debt, English made budget deficit-reduction his main priority  His first budget outlined three focuses in New Zealand's financial recovery: "improving the business environment and removing roadblocks to growth; investment in productive infrastructure; and improving the way government works"  One of his first acts was creating the National Infrastructure Unit, charged with formulating a plan for infrastructure projects and investments  He commissioned a government-wide spending review, with an aim to reducing government expenditure—with the exceptions of a two-year stimulus package and long-term increases on infrastructure spending 

In April 2011, the Opposition criticised English for suggesting that New Zealand businesses could use New Zealand's low wages to help it compete with Australia  The National Government campaigned for re-election in 2011 on its economic record  The Government boasted growth for five consecutive quarters up to mid-2010, totalling 1 6% of real GDP 

Strong growth resulted in a surplus of $473 million for the 2015/16 financial year, projected to rise to $8 5 billion by 2020/21  In his 2016 Economic and Fiscal Update address, English stated that reducing debt and tackling the costs of the 2016 Kaikōura earthquake were higher priorities than reducing rates of tax 

Allowances issue
In 2009, the media, including TVNZ and TV3 revealed that English was receiving about NZ$900 a week as part of a living allowance for ministers, to live in his own NZ$1 2 million Wellington home  At the time, English also received $276,200 in his annual salary as Deputy Prime Minister  It was also revealed other ministers with homes in the capital city were also claiming accommodation allowances  On 3 August 2009, Prime Minister John Key started a review of the housing allowances claimed by cabinet ministers  English subsequently paid back $12,000 and only claimed about $24,000 a year in living allowances  The Auditor-General's office said in September 2009 that they were making "preliminary enquiries" into parliamentary housing expenses in response to a letter of complaint from Progressive party leader Jim Anderton  Two days later English stated that he would no longer take up any housing allowance and had paid back all the allowance he had received since the November 2008 election 

Prime Minister (2016–2017)

John Key resigned on 12 December, and endorsed English as his successor in the resulting leadership election  Following the drop-out of both Judith Collins and Jonathan Coleman from the leadership election, English was sworn in as the 39th Prime Minister of New Zealand on 12 December 2016 

English appointed his first cabinet on 18 December  In a reshuffle, he appointed Steven Joyce to succeed him as Finance Minister, while most ministerial portfolios remained the same 

In February 2017, English did not attend Waitangi Day commemorations at the historic treaty grounds, reportedly in response to the Ngāpuhi iwi's decision to stop the Prime Minister from speaking at the marae  Ngāpuhi have protested the Government's negotiation of the Trans Pacific Partnership Agreement (TPPA), which the iwi believe infringes upon Māori sovereignty, and thus does not adhere to the Treaty of Waitangi  English had been invited to attend in an official capacity; his non-attendance was criticised by a Ngāpuhi elder and Opposition leader Andrew Little 

In his first overseas trip as Prime Minister, English travelled to Europe to discuss trade ties, including a prospective New Zealand–European Union free trade agreement  He first travelled to London on 13 January 2017 to meet British Prime Minister Theresa May  Discussing trade relations, English said the two nations were "natural partners" and would "continue to forge ties" after the UK's withdrawal from the EU  He also arranged to meet with London Mayor Sadiq Khan, Belgian Prime Minister Charles Michel and German Chancellor Angela Merkel   In a meeting with Merkel, English received crucial backing from Germany for a trade deal with the EU  On 16 January, English stated that his government would continue to promote TPPA, despite the United States' decision to withdraw from the agreement  He explained that Southeast Asian countries would now be treated as a priority in negotiations—he also asserted that the United States was ceding influence to China by its rejection of the trade pact 

At a press conference at the Beehive on 1 February 2017, English announced that the 2017 general election would be held on 23 September  The Prime Minister later confirmed that his party would approach ACT, United Future and the Māori Party if confidence and supply agreements were required to form a government following the election  In his second cabinet reshuffle on 24 April, English appointed Gerry Brownlee as his new Foreign Affairs Minister; he also promoted Nikki Kaye to the portfolio of Education Minister, and moved Mark Mitchell into the cabinet to become Defence Minister  The reshuffle was perceived as an election preparation 

On 13 February 2017, English welcomed Australian Prime Minister Malcolm Turnbull to Wellington  The two leaders reaffirmed their shared trade agenda, and discussed changes to the Australian citizenship pathway which will affect permanent residents originating from New Zealand 

On 19 June, it was reported that Todd Barclay, who succeeded English as MP for Clutha-Southland, had clandestinely recorded one of his employee's conversations the previous year, and that John Key's leaders' budget was used to pay a confidential settlement after the employee resigned  English admitted that he had been aware of the illegal recording and the settlement, and thus implicated in the scandal 

During the 2017 National campaign launch, English introduced a $379 million social investment package including digital learning academies for high school students, more resources for mathematics, and boosting support for teaching second languages in schools, and maintaining National Standards in the school curriculum  Prime Minister English also sought to defend National's financial management and economic track record and claimed that the opposition Labour Party would raise taxes  Early opinion polling had forecast a poor showing in the election for the Labour Party, but in early August 37-year-old Jacinda Ardern took over as Labour leader and seemingly energised younger voters 

At the 2017 general election, National won the largest share of the party vote (44 4%) and the largest number of seats (56) in the House Representatives  However, National lacked enough seats to govern alone due to two of the party's support partners, the Māori Party and United Future, losing their parliamentary seats  In response, English stated that the party would be entering into talks to form a coalition with New Zealand First  Following talks with the two largest parties, New Zealand First entered a coalition arrangement with the Labour Party  English was succeeded as prime minister by Jacinda Ardern on 26 October 

Opposition (2017–2018)

Leader of the Opposition
English was re-elected as National Party leader on 24 October 2017  At the time of his re-election, English announced his intention to stay on as leader until the next general election  On 13 February 2018, however, he stood down as National Party leader due to personal reasons, and instructed the party to put into motion the processes to elect a new leader  He also retired from Parliament  English's resignation followed weeks of speculation that he would step aside for a new leader  On 27 February, he was succeeded as party leader by Simon Bridges as the result of the leadership election held that day 

Post-premiership 
In 2018, English joined the board of Australian conglomerate, Wesfarmers  English serves in Chairmanships of Mount Cook Alpine Salmon, Impact Lab Ltd and Manawanui Support Ltd  He is also a director of The Instillery, Centre for Independent Studies and The Todd Corporation Limited, and is a member of the Impact Advisory Group of Macquarie Infrastructure and Real Assets 

Political and social views

English is regarded as more socially conservative than his predecessor, John Key  He has stated his opposition to voluntary euthanasia and physician-assisted suicide, same-sex civil unions, and the decriminalisation of prostitution  As Prime Minister he opposed any "liberalisation" of abortion law 

In 2004, English voted against a bill to establish civil unions for both same-sex and opposite-sex couples  In 2005, he voted for the Marriage (Gender Clarification) Amendment Bill, which would have amended the Marriage Act to define marriage as only between a man and a woman  English voted against the Marriage (Definition of Marriage) Amendment Bill, a bill that legalised same-sex marriage in New Zealand  However, in December 2016 he stated, "I'd probably vote differently now on the gay marriage issue  I don't think that gay marriage is a threat to anyone else's marriage" 

In 2009, English voted against the Misuse of Drugs (Medicinal Cannabis) Amendment Bill, a bill aimed at amending the Misuse of Drugs Act so that cannabis could be used for medical purposes 

Personal life 
English met his future wife, Mary Scanlon, at university  She was studying medicine at the time, and became a general practitioner  Both her parents were immigrants, her father being Samoan and her mother Italian, born on the island of Stromboli  They have six children: a daughter and five sons 

English is a practising Roman Catholic, but has stated that he considers his religious beliefs personal and thus separate from politics 

In June 2002, English took part in TV3's Fight For Life, a celebrity boxing fundraiser to raise money for the Yellow Ribbon anti-youth-suicide campaign, influenced by the death of a teenage nephew in 1997  He lost a split decision to former university colleague Ted Clarke 

Honours
In the 2018 Queen's Birthday Honours, English was appointed a Knight Companion of the New Zealand Order of Merit, for services of over 27 years to the State 
Context 3: The future of mobile CPUs, part 1: Today’s fork in the road | Ars Technica
2013 may be a big year for the evolution of smartphones and tablets 
Mobile computing's rise from niche market to the mainstream is among the most significant technological trends in our lifetimes  And to a large extent, it's been driven by the bounty of Moore’s Law—the rule that transistor density doubles every 24 months  Initially, most mobile devices relied on highly specialized hardware to meet stringent power and size budgets  But with so many transistors available, devices inevitably grew general-purpose capabilities  Most likely, that wasn't even the real motivation  The initial desire was probably to reduce costs by creating a more flexible software ecosystem with better re-use and faster time to market  As such, the first smartphones were very much a novelty, and it took many years before the world realized the potential of such devices  Apple played a major role by creating innovative smartphones that consumers craved and quickly adopted 
To some extent, this is where we still stand today  Smartphones are still (relatively) expensive and primarily interesting to the developed world  But over the next 10 years, this too will change  As Moore’s Law rolls on, the cost of a low-end smartphone will decline  At some point, the incremental cost will be quite minimal and many feature phones of today will be supplanted by smartphones  A $650 unsubsidized phone is well beyond the reach of most of the world compared to a $20 feature phone, but a $30 to $40 smartphone would naturally be very popular 
In this grand progression, 2013 will certainly be a significant milestone for mobile devices, smartphones and beyond  It's likely to be the first year in which tablets out-ship notebooks in the US  And in the coming years, this will lead to a confluence of high-end tablets and ultra-mobile notebooks as the world figures out how these devices co-exist, blend, hybridize, and/or merge 
Against this backdrop, in this two-part series, we'll explore the major trends and evolution for mobile SoCs  More importantly, we'll look to where the major vendors are likely going in the next several years 
Tablet and phone divergence
While phones and tablets are mobile devices that often share a great deal of software, it's becoming increasingly clear the two are very different products  These two markets have started to diverge and will continue doing so over time 
From a technical perspective, smartphones are far more compact and power constrained  Smartphone SoCs are limited to around 1W, both by batteries and by thermal dissipation  The raison d’etre of a smartphone is connectivity, so a cellular modem is an absolute necessity  For the cost sensitive-models that make up the vast majority of the market, the modem is integrated into the SoC itself  High-end designs favor discrete modems with a greater power budget instead  The main smartphone OSes today are iOS and Android, though Windows is beginning to make an appearance (perhaps with Linux or BlackBerry on the horizon)  Just as importantly, phone vendors like HTC must pass government certification and win the approval of carriers  There is very much a walled-garden aspect, where carriers control which devices can be attached to their networks, and in some cases devices can only be sold through a certain carrier  The business model places consumers quite far removed from the actual hardware 
In contrast, tablets are far more akin to the PC both technically and economically  The power budget for tablet SoCs is much greater, up to 4W for a passively cooled device and as high as 7-8W for systems with fans  This alone means there is a much wider range of tablet designs than smartphones  Moreover, the default connectivity for tablets is Wi-Fi rather than a cellular modem  The vast majority of tablets do not have cellular modems, and even fewer customers actually purchase a wireless data plan  As a result, cellular modems are almost always optional discrete components of the platform  The software ecosystem is relatively similar, with Microsoft, Apple, and Google OSes available  Because tablets eschew cellular modems, the time to market is faster, and they are much more commonly sold directly to consumers rather than through carriers  In terms of usage models, tablets are much more PC-like, with reasonable-sized screens that make games and media more attractive 
Looking forward, these distinctions will likely become more pronounced  Many tablets today use high-end smartphone SoCs, but the difference in power targets and expected performance is quite large  As the markets grow in volume, SoCs will inevitably bifurcate to focus on one market or the other  Even today, Apple is doing so, with the A6 for phones and the larger A6X for tablets  Other vendors may need to wait a few years to have the requisite volume, but eventually the two markets will be clearly separate 
Horizontal business model evolution
Another aspect of the mobile device market that is currently in flux and likely to change in the coming years is the business model for the chip and system vendors  Currently, Apple is the only company truly pursuing a vertically integrated model, where all phones and tablets are based on Apple’s own SoC designs and iOS  The tight integration between hardware and software has been a huge boon for Apple, and it has yielded superb products 
Samsung is one of the few others companies that takes a vertically integrated approach to phones and tablets, although in truth its strategy seems to be ambivalent on that point  Unlike Apple, Samsung’s SoCs are readily available to third parties, and some Samsung devices, such as the S7562 Galaxy S Duos, use SoCs from competitors  More recently though, there has been a trend of Samsung devices using Samsung SoCs, at least for the premier products  For the moment, Samsung’s approach is best characterized as a hybrid, particularly as the company lacks a bespoke OS 
The rest of the major SoC vendors (e g , Intel, Qualcomm, Nvidia, TI, Mediatek, etc ) have stayed pretty far away from actual mobile devices  These companies tend to focus on horizontal business models that avoid competing with customers or suppliers 
In the long term, mobile devices are likely to evolve similarly to the PC and favor a horizontal business model  The real advantage is one of flexibility; as costs drop and the market expands, it will be increasingly necessary for vendors like HTC to offer a wide range of phones based on radically different SoCs  While a vertically integrated company like Apple can focus and maintain leadership in a specific (and highly lucrative) niche, it would be very difficult to expand in many growing areas of the market  The differences between an iPhone 6 and a $20 feature phone are tremendous and would be very difficult for a single company to bridge 
However, SoC vendors will attempt to reap the benefits of vertical integration by providing complete reference platforms to OEMs  Conceptually, this is a form of "optional" system integration, where the phone vendor or carrier can get the entire platform from the SoC supplier  This has the principal advantages of reducing time to market while also providing a baseline quality and experience for consumers  Currently, this approach has mostly been tested in emerging markets, but it's likely to become more common over time  There is a crucial distinction between reference platforms and vertical integration  Namely, OEMs can always choose to customize a platform to differentiate, and the SoC vendor avoids dealing with consumers directly  Typically, most of the customization is in terms of software on top of a base operating system 
Quote:Moreover, that will make the transition to a 10nm node even more difficult, as the foundries will have to move from 20nm interconnects to 10nm interconnects and skip a generation The advances in technology lately allowing components on such a small scale to even be envisioned, much less planned for, are truly amazing 
Off topic: show
I present the first generation 'non-technical' rock:
I don't think your horizontal market development theory is supported by facts  Samsung and Apple are more vertically oriented than their competition, for starters  I know this article is narrowly focused on the hardware, but MS and Intel getting into hardware, Amazon getting into hardware, Google buying Moto, this is all vertical integration  How can you support the idea that this trend will be reversed with no real justification? I'm sure mobile chips will continue to specialize, but I don't think this means what you think it means  Automobile companies started making their own engines and with rare exceptions, never went back to being more horizontal  Same with retail and their store brands  Same with cloud companies and their servers  Same with mobile companies and their OSs  The horizontal market of PCs created by long-lasting standards and loose hegemony is the exception, not the norm 
Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?
I'm not so sure about several things:1- Moore's law's relevance  Moore's Law is about ICs  ICs are not as big a part of mobile computers as they are of desktops, even of laptops: screens, batteries, radios are a huge part of tablets' and phones' costs, as opposed to the bare SoC + RAM 2- The tablet vs phone dichotomy  For some reason (probably price insensitivity due to subsidies), Phones have a tendency to be more powerful than Tablets, ie phone SoCs are more than good enough for tablets  Since the OS and peripherals are the same, it makes more sense to design and build just one type of SoC, and just disable the phone-modem part of it (even the other radios are still required: BT, Wifi, GPS   ), same as Intel disable cache and cores for their entry-level CPUs  Once you're fabbing a SoC, it makes more sense to make more of the same than to setup a separate run of a cut-down SoC on an older process, unless volumes are huge  We might still be getting previous-generation, well amortized SoCs in cheaper tablets, though 3- On the contrary, I see a tablet and phone convergence (the ugly phablet)  I'm patiently waiting for the new 6"+ phones to replace my Nook Color and Galaxy Note 1 with a single device 4- The advantage of diversity ? Software is becoming ever more important than hardware  Multiplying SoCs means multiplying product development costs, making support and updates more difficult    Again, unless volumes are huge, OEMs are probaly better off going the way of the car industry and using modular "platforms" housed in different chassis with various screen sizes, keyboards, radios, digitizers   I'm wondering why the "single device" trend does not figure in your analysis  Is it stillborn ? Does it have no impact nor dependency on/with SoCs ?
Samsung has its own bespoke OS: Bada and it is used on an extensive line of devices  I think there are numbers somewhere that it outsold Windows Phone 7 for a time 
gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?First mover advantage 
SoC? System on a Chip I guess?
You're way off on the Moore's Law/cost of smartphones point  The processors used in today's high-end smartphones are already cheap, around $25  And there are less expensive options if you want a lower end product  In fact, the hardware in the whole smartphone is relatively cheap  Analyst's estimate the Z10's materials cost around $160, the iPhone 5 around $140  They're using expensive glass and metals, then there's the battery, memory, etc  which means the processor is a small factor of the cost And then there's the jump from $140 in materials to the unsubsidized costs  The reason these phones cost $650 is because of the high margins these companies are able to get and the high cost of hardware design and/or software development  But the point is that making the processors 4 times better/cheaper isn't going to change the economics of the smartphone  What will change the economics is commoditized designs and software and cheaper materials all around  Then you'll have a $50 smartphone that's decent 
Last edited by ggeezz on Wed Feb 13, 2013 9:17 am
bigterp wrote:SoC? System on a Chip I guess?Yup 
gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?Money and momentum, the x86 market is a huge money maker for Intel so it is able to recoup its huge investments for advanced foundries 
Quote:Currently, the only products using 3D integration are FPGAs from Xilinx,Doesn't Sony use it in the PS Vita? I thought I read somewhere that they had the CPU, main memory (2 dies) and video memory, so 4 dies in total, sitting on top of each other all on the same chip 
renoX wrote:gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?Money and momentum, the x86 market is a huge money maker for Intel so it is able to recoup its huge investments for advanced foundries Exactly and I would clarify that it's all about margins, the difference between what it costs to make a chip and what it sells for  The margins for desktop and server processors is huge because a) the whole product is expensive so $200 to $1000 for the chip is acceptable, and b) Intel has huge advantages in that space and little competition So Intel can afford to do the R&D to stay ahead of the curve and keep their position  When your smartphone chip sells for $25 you can't do the R&D to leapfrog a company that sells Xeons for $1000 and Core i5's for $200 
I am happy to see Kanter here at Ars, I like his writing and he maintains Real World Tech, where Linus Torvalds often shows up to comment on CPU arch and other interesting topics 
ggeezz wrote:renoX wrote:gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?Money and momentum, the x86 market is a huge money maker for Intel so it is able to recoup its huge investments for advanced foundries Exactly and I would clarify that it's all about margins, the difference between what it costs to make a chip and what it sells for  The margins for desktop and server processors is huge because a) the whole product is expensive so $200 to $1000 for the chip is acceptable, and b) Intel has huge advantages in that space and little competition So Intel can afford to do the R&D to stay ahead of the curve and keep their position  When your smartphone chip sells for $25 you can't do the R&D to leapfrog a company that sells Xeons for $1000 and Core i5's for $200 Spot on Intel are able to piggyback other development efforts off the highly lucrative mainstream x86 market which generates the huge sums of money to fund their amazing fab technology The question for the future is how the economics will stack up when overall device costs fall significantly and there is a big downward pressure on SoC prices  In that situation, can Intel still justify bringing their A-game to a market where products are essentially commoditised and you have processors selling for a only a few dollars each?The lesson from their previous involvement in the DRAM market is that they probably won't want to be involved because there isn't enough money to be made to justify manufacturing phone SoCs on a cutting edge, or near cutting edge process  In that scenario, Intel may not totally abandon the market but they might just stick to manufacturing SoCs on nodes that are a step or two behind the state of the art 
solomonrex wrote:I don't think your horizontal market development theory is supported by facts  Samsung and Apple are more vertically oriented than their competition, for starters  I know this article is narrowly focused on the hardware, but MS and Intel getting into hardware, Amazon getting into hardware, Google buying Moto, this is all vertical integration  How can you support the idea that this trend will be reversed with no real justification? I'm sure mobile chips will continue to specialize, but I don't think this means what you think it means  Automobile companies started making their own engines and with rare exceptions, never went back to being more horizontal  Same with retail and their store brands  Same with cloud companies and their servers  Same with mobile companies and their OSs  The horizontal market of PCs created by long-lasting standards and loose hegemony is the exception, not the norm Yea, each year Amazon, MS, Apple and Google look more and more the same 
Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that 
gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?Intel's called Chipzilla for a reason up
Lagrange wrote:The question for the future is how the economics will stack up when overall device costs fall significantly and there is a big downward pressure on SoC prices  In that situation, can Intel still justify bringing their A-game to a market where products are essentially commoditised and you have processors selling for a only a few dollars each?The lesson from their previous involvement in the DRAM market is that they probably won't want to be involved because there isn't enough money to be made to justify manufacturing phone SoCs on a cutting edge, or near cutting edge process  In that scenario, Intel may not totally abandon the market but they might just stick to manufacturing SoCs on nodes that are a step or two behind the state of the art I think the processing is a bigger advantage than many realize  If Intel can stay ahead in process design - which this article seems to indicate - they should have a major advantage  All else being equal a 14nm chip should be significantly faster and more efficient than the same chip at 22nm  Add in the fact that yields increase geometrically - you can fit a lot more 14nm chips on a given wafer size vs 22nm (or 32nm for the other manufacturers ) and you have a very appealing proposition  And then add in the fact that Intel actually has a pretty good graphics stack and IP  It's not a sure thing by any means, but I suspect ARM may have just prodded a sleeping giant edit: Also worth noting, Intel, TSMC, and Samsung are the only manufacturers who are building out 450nm wafers  This will increase yields dramatically  Of course Samsung and TSMC will build ARM out, but it definitely puts quite a bit of pressure on all other manufacturers  As the article mentions Intel and Samsung are the only ones who control production top to bottom, and Samsung must share some of the benefits with ARM 
As someone who has worked in the semiconductor industry for longer than contemporary fanboys have existed, I'm getting a bit fed-up seeing many of these articles which rewrite history with analyses distorted by the lens of the contemporary Apple or Samsung fanboy The mobile industry moved to horizontal integration a long time ago  Better indicators than these odd contemporary obsessions with the relatively non-innovative Samsung and Apple where when Motorola spun out its semiconductor division as Freescale, Nokia stopped making it's own custom designs with TI and ST, and Ericsson spun out it's Ericsson Mobile Platforms division and formed ST-Ericsson with ST The true innovation in the mobile market was done a decade or more ago mainly by Moto/Nokia/Ericsson/TI/Qualcomm, and Samsung and Apple had little to do with it  Under the hood most stuff has been on a simple linear evolutionary path by the SoC providers since then  The phone manufacturers have then mainly been simply sticking these off-the-shelf SoCs (and their included low-level software stacks) in a box, a job made all the easier with the SoC manufacturer collaboration providing the bulk of the work for the AOSP 
Last edited by paul5ra on Wed Feb 13, 2013 11:06 am
introiboad wrote:I am happy to see Kanter here at Ars, I like his writing and he maintains Real World Tech, where Linus Torvalds often shows up to comment on CPU arch and other interesting topics Indeed  Most tech writing in this area is atrocious  This piece is one of the few well informed articles I've read in a long time 
ggeezz wrote:Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that The word you're looking for is Haswell, as far as I know 
Mabsark
ggeezz wrote:Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that Actually, that trend will not simply keep increasing going forward  The reason desktop/laptop sales are stagnating/decreasing is due to the fact that most people already have one and therefore don't need to buy another one  The exact same thing will happen with tablets as well  Sales are increasing now because people without tablets are buying them  When most people already own a tablet, they won't be buying a new one every year and therefore sales will stagnate/decrease The PC market is saturated and in a couple of years, the tablet market will be saturated too  Basically, in order to increase sales in a saturated market, you need to increase the population growth or decrease the longevity of the product 
gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?Probably a mix of a lot of things  One big thing was during this recession, Intel was the ONLY fab company that didn't scale back their R&D  That alone gave Intel a large advantage Intel has almost always been ahead  One of the reasons could be that Intel works with much higher margins than many of the commodity companies like Samsung and TSMC Outside of the P4 flop and some of the monopolistic abuses, Intel has typically been selling to high end customers that are willing to pay a premium for "the best" Intel has a large benefit of having a relatively "good name" when it comes to CPUs, so they can effectively charge a brand-name premium I'm sure there are other reasons, and probably better reasons, but these are the main ones that I think of 
Mabsark wrote:Actually, that trend will not simply keep increasing going forward  The reason desktop/laptop sales are stagnating/decreasing is due to the fact that most people already have one and therefore don't need to buy another one  The exact same thing will happen with tablets as well  Sales are increasing now because people without tablets are buying them  When most people already own a tablet, they won't be buying a new one every year and therefore sales will stagnate/decrease The PC market is saturated and in a couple of years, the tablet market will be saturated too  Basically, in order to increase sales in a saturated market, you need to increase the population growth or decrease the longevity of the product That's true as long as most people are still buying both a tablet and a laptop when each needs to be replaced  I think the assumption is that, as you say, the tablet market will saturate, with people just replacing existing ones, but the desktop/laptop market could decrease much farther than that, if most people stop replacing them at all  I'm not sure of the likelihood of that, but I think that's where this idea comes from 
ggeezz wrote:Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that The upcoming Haswell chip is showing to consume 1/3 the power of IvyBridge at peak, consumes 1/20th the power at idle, all the while maintaining Identical or better performance This chip should actually compete with ARM CPUs on both power/performance and idle I am expecting a large war 
Apple once again is dictating the performance in the mobile industry  Nice to see others being able to keep the pace, as well 
paul5ra wrote:As someone who has worked in the semiconductor industry for longer than contemporary fanboys have existed, I'm getting a bit fed-up seeing many of these articles which rewrite history with analyses distorted by the lens of the contemporary Apple or Samsung fanboy The mobile industry moved to horizontal integration a long time ago  Better indicators than these odd contemporary obsessions with the relatively non-innovative Samsung and Apple where when Motorola spun out its semiconductor division as Freescale, Nokia stopped making it's own custom designs with TI and ST, and Ericsson spun out it's Ericsson Mobile Platforms division and formed ST-Ericsson with ST The true innovation in the mobile market was done a decade or more ago mainly by Moto/Nokia/Ericsson/TI/Qualcomm, and Samsung and Apple had little to do with it  Under the hood most stuff has been on a simple evolutionary path by the SoC providers since then Yeah, and most of the innovation in the automobile industry came about before Henry Ford came into the business  Doesn't change the fact that cars would probably have been an asterisk in the history books under "toys for rich people" if it weren't for him The same applies to to mobile computing for Apple, Samsung, et al 
SheldonRoss wrote:Lagrange wrote:The question for the future is how the economics will stack up when overall device costs fall significantly and there is a big downward pressure on SoC prices  In that situation, can Intel still justify bringing their A-game to a market where products are essentially commoditised and you have processors selling for a only a few dollars each?The lesson from their previous involvement in the DRAM market is that they probably won't want to be involved because there isn't enough money to be made to justify manufacturing phone SoCs on a cutting edge, or near cutting edge process  In that scenario, Intel may not totally abandon the market but they might just stick to manufacturing SoCs on nodes that are a step or two behind the state of the art I think the processing is a bigger advantage than many realize  If Intel can stay ahead in process design - which this article seems to indicate - they should have a major advantage  All else being equal a 14nm chip should be significantly faster and more efficient than the same chip at 22nm  Add in the fact that yields increase geometrically - you can fit a lot more 14nm chips on a given wafer size vs 22nm (or 32nm for the other manufacturers ) and you have a very appealing proposition  And then add in the fact that Intel actually has a pretty good graphics stack and IP  My point was that Intel might have a one or two process advantage over the rest of the industry at the cutting edge but that doesn't mean that they can afford to manufacture on those processes for very low margin parts  If the SoC market becomes increasingly commoditised, there isn't going to be the money to justify making them in a state of the art fab Remember that one of the big selling points of Itanium was that it would make use of process advantages that were effectively paid for by the mainstream x86 market  That didn't quite work out in practice and Itanium processors were often well behind Xeons in process technology 
paul5ra wrote:As someone who has worked in the semiconductor industry for longer than contemporary fanboys have existed, I'm getting a bit fed-up seeing many of these articles which rewrite history with analyses distorted by the lens of the contemporary Apple or Samsung fanboy The mobile industry moved to horizontal integration a long time ago  Better indicators than these odd contemporary obsessions with the relatively non-innovative Samsung and Apple where when Motorola spun out its semiconductor division as Freescale, Nokia stopped making it's own custom designs with TI and ST, and Ericsson spun out it's Ericsson Mobile Platforms division and formed ST-Ericsson with ST The true innovation in the mobile market was done a decade or more ago mainly by Moto/Nokia/Ericsson/TI/Qualcomm, and Samsung and Apple had little to do with it  Under the hood most stuff has been on a simple linear evolutionary path by the SoC providers since then  The phone manufacturers have then mainly been simply sticking these off-the-shelf SoCs (and their included low-level software stacks) in a box, a job made all the easier with the SoC manufacturer collaboration providing the bulk of the work for the AOSP Just goes to show that people who have worked in an industry for a long time don't always understand what that industry is doing You haven't been working in it long enough to seem to know that it was Acorn and Apple that invented the mobile ARM CPU in the first place  All those companies you've mentioned have just been working off Acorn and Apple's pioneering work  Now, Apple is back at it again, very successfully, and all the companies you mentioned that produce chips with ARM IP in them are licensing them from the company Acorn and Apple formed—ARM 
Last edited by melgross on Wed Feb 13, 2013 11:13 am
Mark Havel wrote:ggeezz wrote:Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that The word you're looking for is Haswell, as far as I know If tablets move into the $100-200 range, is there going to be room for Haswell?So long as there is a higher-end tablet market, then Haswell will be able to shine, but it's going to be a much more powerful and costly part than the sort of ARM based hardware that often runs tablets  If we see a race to the bottom where price is the dominant motivator behind purchases, then a high performance SoC will struggle to make its mark 
melgross wrote:paul5ra wrote:As someone who has worked in the semiconductor industry for longer than contemporary fanboys have existed, I'm getting a bit fed-up seeing many of these articles which rewrite history with analyses distorted by the lens of the contemporary Apple or Samsung fanboy The mobile industry moved to horizontal integration a long time ago  Better indicators than these odd contemporary obsessions with the relatively non-innovative Samsung and Apple where when Motorola spun out its semiconductor division as Freescale, Nokia stopped making it's own custom designs with TI and ST, and Ericsson spun out it's Ericsson Mobile Platforms division and formed ST-Ericsson with ST The true innovation in the mobile market was done a decade or more ago mainly by Moto/Nokia/Ericsson/TI/Qualcomm, and Samsung and Apple had little to do with it  Under the hood most stuff has been on a simple linear evolutionary path by the SoC providers since then  The phone manufacturers have then mainly been simply sticking these off-the-shelf SoCs (and their included low-level software stacks) in a box, a job made all the easier with the SoC manufacturer collaboration providing the bulk of the work for the AOSP Just goes to show that people who have worked in an industry for a long time don't always understand what that industry is doing You haven't been working in it long enough to seem to know that it was Acorn and Apple that invented the mobile ARM CPU in the first place  All those companies you've mentioned have just been working off Acorn and Apple's pioneering work  Now, Apple is back at it again, very successfully, and all the companies you mentioned that produce chips with ARM IP in them are licensing them from the company Acorn and Apple formed—ARM Of course I realise ARM IP has indeed been a major driving factor too (though only one if several architectures before ARM became dominant), though I see ARM's influence on the mobile industry as having nothing to do with modern day Apple and only one small piece of the puzzle  My point is that the hard electrical engineering, mathematics, DSP, semiconductor physics/chemistry, RF engineering, analogue design, CAD etc  that make modern telecommunications possible has very little to do with the fashion companies who consumers (and unfortunately much of the tech media) associate with it and give the credit (though in this respect Samsung does deserve a bit more credit for their work on NAND flash and displays)  The industry simply would not exist TODAY without the overwhelming horizontal integration that already dominates 
Quote:In the long term, mobile devices are likely to evolve similarly to the PC and favor a horizontal business model  The real advantage is one of flexibility; as costs drop and the market expands, it will be increasingly necessary for vendors like HTC to offer a wide range of phones based on radically different SoCs  You don't mention in the article that each SoC necessarily requires a bit of parallel dev work unlike the PC  In the PC world there is a standard BIOS and HW architecture that allows for pluggable designs  On a highly integrated SoC this is untrue  HTC suffers because it has to support radically different SoCs, their drivers and boot loaders, etc  Quote:While a vertically integrated company like Apple can focus and maintain leadership in a specific (and highly lucrative) niche, it would be very difficult to expand in many growing areas of the market  The differences between an iPhone 6 and a $20 feature phone are tremendous and would be very difficult for a single company to bridge It's only difficult because Apple chooses to ignore that market, not because they can't  If they can release a $99 Apple TV, they can surely cobble together a $20 feature phone if they chose to eschew 8GB of NAND, BT, WiFi, a specialized dock connector, LTE, and their specialized processors  In other words, build the equivalent of an iPod shuffle with a horrible screen and no OS to speak of 
paul5ra wrote:melgross wrote:paul5ra wrote:As someone who has worked in the semiconductor industry for longer than contemporary fanboys have existed, I'm getting a bit fed-up seeing many of these articles which rewrite history with analyses distorted by the lens of the contemporary Apple or Samsung fanboy The mobile industry moved to horizontal integration a long time ago  Better indicators than these odd contemporary obsessions with the relatively non-innovative Samsung and Apple where when Motorola spun out its semiconductor division as Freescale, Nokia stopped making it's own custom designs with TI and ST, and Ericsson spun out it's Ericsson Mobile Platforms division and formed ST-Ericsson with ST The true innovation in the mobile market was done a decade or more ago mainly by Moto/Nokia/Ericsson/TI/Qualcomm, and Samsung and Apple had little to do with it  Under the hood most stuff has been on a simple linear evolutionary path by the SoC providers since then  The phone manufacturers have then mainly been simply sticking these off-the-shelf SoCs (and their included low-level software stacks) in a box, a job made all the easier with the SoC manufacturer collaboration providing the bulk of the work for the AOSP Just goes to show that people who have worked in an industry for a long time don't always understand what that industry is doing You haven't been working in it long enough to seem to know that it was Acorn and Apple that invented the mobile ARM CPU in the first place  All those companies you've mentioned have just been working off Acorn and Apple's pioneering work  Now, Apple is back at it again, very successfully, and all the companies you mentioned that produce chips with ARM IP in them are licensing them from the company Acorn and Apple formed—ARM Of course I realise ARM IP has indeed been a major driving factor too (though only one if several architectures before ARM became dominant), though I see ARM's influence on the mobile industry as having nothing to do with modern day Apple and only one piece of the puzzle  My point is that the hard electrical engineering, mathematics, DSP, semiconductor physics/chemistry, RF engineering, analogue design,etc  that make modern telecommunications possible has very little to do with the fashion companies who consumers (and unfortunately much of the tech media) associate with it and give the credit (though in this respect Samsung does deserve a bit more credit for their work on NAND flash and displays)  The industry simply would not exist TODAY without the overwhelming horizontal integration that already dominates Yes the efforts of these companies getting cellular communications standardized were immense  And the technology matured  And then they didn't do much with it  It took some youngin's to look at the problem fresh and add the UI that make today's smartphones work  As we have all seen, the moment your technology has matured is the moment you are screwed because someone else now has the opportunity to look at it as a black box and make something new  Each of those manufacturers knew that smartphones would eventually be awesome, but none of them had the UI and software design to make a truly breakout product  Imagine if Motorola would have been smart enough to buy the Android guys instead of Google  Instead, Google bought a bunch of patents on that cellular black box to try to defend it's platform And when you think about it, which consumes more man years of engineering effort per year at this point     iterating that cellular black box or developing the OS, services and apps that power today's smartphones?
Intel had better decide that they are competing in this space "for real", or they are screwed  They've already let the Atom languish for five years, during which ARM has completely caught up in performance Just like Tim Cook said, if you don't cannibalize your own markets someone else will do it for you Whether Intel will embrace that concept in time remains to be seen  Personally, I hope they don't; if Intel transforms into a chipless Fab company (like TSMC) everyone benefits 
I still think Samsung has the advantage long term because they have both the SOC and the memory products  As mentioned in the article, TSV's (Through Silicon Via's) are going to be quite a disruption  Today, people normally stack an LPDDR2 package on top of their SOC package (POP or Package On Package)  Within the LPDDR2 package, you could have a stack of DRAM die typically with wire bonding connecting the die within the package Once you more to TSV's, you can have a LOT more connections between the SOC and its DRAM's  While this is being standardized through JEDEC (http://www jedec org/category/technolog     a/3d-ics-0), Samsung has all the pieces in house to do whatever they want  You could see a 512 bit or higher bus from the SOC to the memory  The trick is that the memory and the SOC need to line up with each other when you stack them  This gives Samsung an inherent advantage This isn't just going to impact mobile either  Take a look at that JEDEC link  It also lists High Bandwidth Memory (HBM)  This is a 1024 bit bus that provides 128GBytes/s to 256GBytes/s of bandwidth to a stack of up to 8 DRAM's  Here is your processor that includes 8-16 cores and 4GBytes of really, really, fast DRAM    No DIMMs required  How many of them do you want in your server rack?If I was Intel or Apple, I would be thinking seriously about making some investments in Micron to guarantee they make some compelling DRAM's to integrate with their SOC's and processors    otherwise Samsung is going to blow them out of the water on bandwidth 
Great_Scott wrote:Intel had better decide that they are competing in this space "for real", or they are screwed  They've already let the Atom languish for five years, during which ARM has completely caught up in performance Just like Tim Cook said, if you don't cannibalize your own markets someone else will do it for you Whether Intel will embrace that concept in time remains to be seen  Personally, I hope they don't; if Intel transforms into a chipless Fab company (like TSMC) everyone benefits It's true that Atom has stood still for too long, but honestly it's pretty amazing how Atom is still competitive with current ARM chips  The Z2760 is even 32nm vs 28nm of the latest Krait and A15 chips But that's all changing with Atom moving to the tick tock schedule this year  It wouldn't even surprise me to see Apple move to Intel chips for IOS And I don't see how Intel moving to a chipless Fab company would help everyone  It certainly wouldn't help Intel 
Mabsark wrote:ggeezz wrote:Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that Actually, that trend will not simply keep increasing going forward  The reason desktop/laptop sales are stagnating/decreasing is due to the fact that most people already have one and therefore don't need to buy another one  The exact same thing will happen with tablets as well  Sales are increasing now because people without tablets are buying them  When most people already own a tablet, they won't be buying a new one every year and therefore sales will stagnate/decrease The PC market is saturated and in a couple of years, the tablet market will be saturated too  Basically, in order to increase sales in a saturated market, you need to increase the population growth or decrease the longevity of the product Yes and no  I'm not sure the tablet market will saturate in a "couple of years " It may be more like 5 years  But that's a quibble Here's the real issue  Right now Apple wants you to own an iPhone AND iPad AND Macbook AND iWatch AND Apple TV  Microsoft, OTOH, is making the Surface so that you could ditch your laptop and just use a Surface  Not everyone, but some people If 5 years from now, we're in a world where a significant number of people use a Surface-type device instead of a laptop, then the PC market is going to contract significantly  Maybe some of the tablet-like devices will use moderately expensive Intel chips, but some of them are going to use cheaper chips 
GravyGraphics wrote:I still think Samsung has the advantage long term because they have both the SOC and the memory products  As mentioned in the article, TSV's (Through Silicon Via's) are going to be quite a disruption  Today, people normally stack an LPDDR2 package on top of their SOC package (POP or Package On Package)  Within the LPDDR2 package, you could have a stack of DRAM die typically with wire bonding connecting the die within the package Once you more to TSV's, you can have a LOT more connections between the SOC and its DRAM's  While this is being standardized through JEDEC (http://www jedec org/category/technolog     a/3d-ics-0), Samsung has all the pieces in house to do whatever they want  You could see a 512 bit or higher bus from the SOC to the memory  The trick is that the memory and the SOC need to line up with each other when you stack them  This gives Samsung an inherent advantage This isn't just going to impact mobile either  Take a look at that JEDEC link  It also lists High Bandwidth Memory (HBM)  This is a 1024 bit bus that provides 128GBytes/s to 256GBytes/s of bandwidth to a stack of up to 8 DRAM's  Here is your processor that includes 8-16 cores and 4GBytes of really, really, fast DRAM    No DIMMs required  How many of them do you want in your server rack?If I was Intel or Apple, I would be thinking seriously about making some investments in Micron to guarantee they make some compelling DRAM's to integrate with their SOC's and processors    otherwise Samsung is going to blow them out of the water on bandwidth Why not AMD? Last I checked they still made memory   and processors/GPUs 



ground_truth: Lasa, Gitastrophe, and Shadoks.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: When did the 2017 general election be held?

Read the following text and answer briefly.

Context 4: \section{Introduction}
\label{sec:introduction}

Probabilistic models have proven to be very useful in a lot of applications in signal processing where signal estimation is needed \cite{rabiner1989tutorial,arulampalam2002tutorial,ji2008bayesian}  Some of their advantages are that 1) they force the designer to specify all the assumptions of the model, 2) they provide a clear separation between the model and the algorithm used to solve it, and 3) they usually provide some measure of uncertainty about the estimation 

On the other hand, adaptive filtering is a standard approach in estimation problems when the input is received as a stream of data that is potentially non-stationary  This approach is widely understood and applied to several problems such as echo cancellation \cite{gilloire1992adaptive}, noise cancellation \cite{nelson1991active}, and channel equalization \cite{falconer2002frequency} 

Although these two approaches share some underlying relations, there are very few connections in the literature  The first important attempt in the signal processing community to relate these two fields was the connection between a linear Gaussian state-space model (i e  Kalman filter) and the RLS filter, by Sayed and Kailath \cite{sayed1994state} and then by Haykin \emph{et al } \cite{haykin1997adaptive}  The RLS adaptive filtering algorithm emerges naturally when one defines a particular state-space model (SSM) and then performs exact inference in that model  This approach was later exploited in \cite{van2012kernel} to design a kernel RLS algorithm based on Gaussian processes 

A first attempt to approximate the LMS filter from a probabilistic perspective was presented in \cite{park2014probabilistic}, focusing on a kernel-based implementation  The algorithm of \cite{park2014probabilistic} makes use of a Maximum a Posteriori (MAP) estimate as an approximation for the predictive step  However, this approximation does not preserve the estimate of the uncertainty in each step, therefore degrading the performance of the algorithm 

In this work, we provide a similar connection between state-space models and least-mean-squares (LMS)  Our approach is based on approximating the posterior distribution with an isotropic Gaussian distribution  We show how the computation of this approximated posterior leads to a linear-complexity algorithm, comparable to the standard LMS  Similar approaches have already been developed for a variety of problems such as channel equalization using recurrent RBF neural networks \cite{cid1994recurrent}, or Bayesian forecasting \cite{harrison1999bayesian}  Here, we show the usefulness of this probabilistic approach for adaptive filtering 

The probabilistic perspective we adopt throughout this work presents two main advantages  Firstly, a novel LMS algorithm with adaptable step size emerges naturally with this approach, making it suitable for both stationary and non-stationary environments  The proposed algorithm has less free parameters than previous LMS algorithms with variable step size \cite{kwong1992variable,aboulnasr1997robust,shin2004variable}, and its parameters are easier to be tuned w r t  these algorithms and standard LMS  Secondly, the use of a probabilistic model provides us with an estimate of the error variance, which is useful in many applications 

Experiments with simulated and real data show the advantages of the presented approach with respect to previous works  However, we remark that the main contribution of this paper is that it opens the door to introduce more Bayesian machine learning techniques, such as variational inference and Monte Carlo sampling methods \cite{barber2012bayesian}, to adaptive filtering \\


\section{Probabilistic Model}

Throughout this work, we assume the observation model to be linear-Gaussian with the following distribution,

\begin{equation}
p(y_k|{\bf w}_k) = \mathcal{N}(y_k;{\bf x}_k^T {\bf w}_k , \sigma_n^2),
\label{eq:mess_eq}
\end{equation}
where  $\sigma_n^2$ is the variance of the observation noise, ${\bf x}_k$ is the regression vector and ${\bf w}_k$ is the parameter vector to be sequentially estimated, both $M$-dimensional column vectors 


In a non-stationary scenario, ${\bf w}_k$ follows a dynamic process  In particular, we consider a diffusion process (random-walk model) with variance $\sigma_d^2$ for this parameter vector:


\begin{equation}
p({\bf w}_k|{\bf w}_{k-1})= \mathcal{N}({\bf w}_k;{\bf w}_{k-1}, \sigma_d^2 {\bf I}),
\label{eq:trans_eq}
\end{equation}
where $\bf I$ denotes the identity matrix  In order to initiate the recursion, we assume the following prior distribution on ${\bf w}_k$

\begin{equation}
p({\bf w}_0)= \mathcal{N}({\bf w}_0;0, \sigma_d^2{\bf I}) \nonumber
\end{equation}

\section{Exact inference in this model: Revisiting the RLS filter}

Given the described probabilistic SSM, we would like to infer the posterior probability distribution $p({\bf w}_k|y_{1:k})$ 
Since all involved distributions are Gaussian, one can perform exact inference, leveraging the probability rules in a straightforward manner  The resulting probability distribution is
\begin{equation}
p({\bf w}_k|y_{1:k}) =  \mathcal{N}({\bf w}_k;{\bf\boldsymbol\mu}_{k}, \boldsymbol\Sigma_{k}), \nonumber
\end{equation}
in which the mean vector ${\bf\boldsymbol\mu}_{k}$ is given by
\begin{equation}
{\bf\boldsymbol\mu}_k = {\bf\boldsymbol\mu}_{k-1} + {\bf K}_k (y_k - {\bf x}_k^T {\bf\boldsymbol\mu}_{k-1}){\bf x}_k, \nonumber
\end{equation}
where we have introduced the auxiliary variable
\begin{equation}
{\bf K}_k = \frac{ \left(\boldsymbol\Sigma_{k-1} + \sigma_d^2 {\bf I}\right)}{{\bf x}_k^T  \left(\boldsymbol\Sigma_{k-1} + \sigma_d^2 {\bf I}\right)  {\bf x}_k + \sigma_n^2}, \nonumber
\end{equation}
and the covariance matrix $\boldsymbol\Sigma_k$ is obtained as
\begin{equation}
\boldsymbol\Sigma_k = \left( {\bf I} -  {\bf K}_k{\bf x}_k {\bf x}_k^T \right) ( \boldsymbol\Sigma_{k-1} +\sigma_d^2), \nonumber
\end{equation}
Note that the mode of $p({\bf w}_k|y_{1:k})$, i e  the maximum-a-posteriori estimate (MAP), coincides with the RLS adaptive rule
\begin{equation}
{{\bf w}}_k^{(RLS)} = {{\bf w}}_{k-1}^{(RLS)} + {\bf K}_k (y_k - {\bf x}_k^T {{\bf w}}_{k-1}^{(RLS)}){\bf x}_k  
\label{eq:prob_rls}
\end{equation}
This rule is similar to the one introduced in \cite{haykin1997adaptive} 

Finally, note that the covariance matrix $\boldsymbol\Sigma_k$ is a measure of the uncertainty of the estimate ${\bf w}_k$ conditioned on the observed data $y_{1:k}$  Nevertheless, for many applications a single scalar summarizing the variance of the estimate could prove to be sufficiently useful  In the next section, we show how such a scalar is obtained naturally when $p({\bf w}_k|y_{1:k})$ is approximated with an isotropic Gaussian distribution  We also show that this approximation leads to an LMS-like estimation 
 


\section{Approximating the posterior distribution: LMS filter }

The proposed approach consists in approximating the posterior distribution $p({\bf w}_k|y_{1:k})$, in general a multivariate Gaussian distribution with a full covariance matrix, by an isotropic spherical Gaussian distribution 

\begin{equation}
\label{eq:aprox_post}
\hat{p}({\bf w}_{k}|y_{1:k})=\mathcal{N}({\bf w}_{k};{\bf \hat{\boldsymbol\mu}}_{k}, \hat{\sigma}_{k}^2 {\bf I} ) 
\end{equation}

In order to estimate the mean and covariance of the approximate distribution $\hat{p}({\bf w}_{k}|y_{1:k})$, we propose to select those that minimize the Kullback-Leibler divergence with respect to the original distribution, i e , 

\begin{equation}
\{\hat{\boldsymbol\mu}_k,\hat{\sigma}_k\}=\arg \displaystyle{  \min_{\hat{\boldsymbol\mu}_k,\hat{\sigma}_k}} \{ D_{KL}\left(p({\bf w}_{k}|y_{1:k}))\| \hat{p}({\bf w}_{k}|y_{1:k})\right) \}  \nonumber
\end{equation}

The derivation of the corresponding minimization problem can be found in Appendix A  In particular, the optimal mean and the covariance are found as
\begin{equation}
{\hat{\boldsymbol\mu}}_{k} = {\boldsymbol\mu}_{k};~~~~~~ \hat{\sigma}_{k}^2 = \frac{{\sf Tr}\{ \boldsymbol\Sigma_k\} }{M} 
\label{eq:sigma_hat}
\end{equation}


We now show that by using \eqref{eq:aprox_post} in the recursive predictive and filtering expressions we obtain an LMS-like adaptive rule  First, let us assume that we have an approximate posterior distribution at $k-1$, $\hat{p}({\bf w}_{k-1}|y_{1:k-1}) =  \mathcal{N}({\bf w}_{k-1};\hat{\bf\boldsymbol\mu}_{k-1}, \hat{\sigma}_{k-1}^2 {\bf I} )$  Since all involved distributions are Gaussian, the predictive distribution
is obtained as %
\begin{eqnarray}
\hat{p}({\bf w}_k|y_{1:k-1}) &=& \int p({\bf w}_k|{\bf w}_{k-1}) \hat{p}({\bf w}_{k-1}|y_{1:k-1}) d{\bf w}_{k-1} \nonumber\\
&=& \mathcal{N}({\bf w}_k;{\bf\boldsymbol\mu}_{k|k-1}, \boldsymbol\Sigma_{k|k-1}), 
\label{eq:approx_pred}
\end{eqnarray}
where the mean vector and covariance matrix are given by
\begin{eqnarray}
\hat{\bf\boldsymbol\mu}_{k|k-1} &=& \hat{\bf\boldsymbol\mu}_{k-1} \nonumber \\
\hat{\boldsymbol\Sigma}_{k|k-1} &=& (\hat{\sigma}_{k-1}^2 + \sigma_d^2 ){\bf I}\nonumber 
\end{eqnarray}

From \eqref{eq:approx_pred}, the posterior distribution at time $k$ can be computed using Bayes' Theorem and standard Gaussian manipulations (see for instance \cite[Ch  4]{murphy2012machine})  Then, we approximate the posterior $p({\bf w}_k|y_{1:k})$ with an isotropic Gaussian,
\begin{equation}
\hat{p}({\bf w}_k|y_{1:k}) =  \mathcal{N}({\bf w}_k ; {\hat{\boldsymbol\mu}}_{k}, \hat{\sigma}_k^2 {\bf I} ),\nonumber
\end{equation}
where 
\begin{eqnarray}
{\hat{\boldsymbol\mu}}_{k} &= & {\hat{\boldsymbol\mu}}_{k-1}+ \frac{ (\hat{\sigma}_{k-1}^2+ \sigma_d^2)  }{(\hat{\sigma}_{k-1}^2+ \sigma_d^2)  \|{\bf x}_k\|^2 + \sigma_n^2} (y_k - {\bf x}_k^T {\hat{\boldsymbol\mu}}_{k-1}){\bf x}_k  \nonumber  \\
&=& {\hat{\boldsymbol\mu}}_{k-1}+ \eta_k (y_k - {\bf x}_k^T {\hat{\boldsymbol\mu}}_{k-1}){\bf x}_k   
\label{eq:prob_lms}
\end{eqnarray}
Note that, instead of a gain matrix ${\bf K}_k$ as in Eq ~\eqref{eq:prob_rls}, we now have a scalar gain $\eta_k$ that operates as a variable step size 


Finally, to obtain the posterior variance, which is our measure of uncertainty, we apply \eqref{eq:sigma_hat} and the trick ${\sf Tr}\{{\bf x}_k{\bf x}_k^T\}= {\bf x}_k^T{\bf x}_k= \|{\bf x}_k \|^2$,

\begin{eqnarray}
\hat{\sigma}_k^2 &=& \frac{{\sf Tr}(\boldsymbol\Sigma_k)}{M} \\
&=& \frac{1}{M}{\sf Tr}\left\{ \left( {\bf I} -  \eta_k {\bf x}_k {\bf x}_k^T \right) (\hat{\sigma}_{k-1}^2 +\sigma_d^2)\right\} \\
&=& \left(1 - \frac{\eta_k \|{\bf x}_k\|^2}{M}\right)(\hat{\sigma}_{k-1}^2 +\sigma_d^2) 
\label{eq:sig_k}
\end{eqnarray}
If MAP estimation is performed, we obtain  an adaptable step-size LMS estimation

\begin{equation}
{\bf w}_{k}^{(LMS)} = {\bf w}_{k-1}^{(LMS)} + \eta_k (y_k - {\bf x}_k^T {\bf w}_{k-1}^{(LMS)}){\bf x}_k, 	
\label{eq:lms}
\end{equation}
with
\begin{equation}
\eta_k = \frac{ (\hat{\sigma}_{k-1}^2+ \sigma_d^2)  }{(\hat{\sigma}_{k-1}^2+ \sigma_d^2)  \|{\bf x}_k\|^2 + \sigma_n^2} \nonumber
\end{equation}
At this point, several interesting remarks can be made:

\begin{itemize}

\item The adaptive rule \eqref{eq:lms} has linear complexity since it does not require us to compute the full matrix $\boldsymbol\Sigma_k$ 

\item For a stationary model, we have $\sigma_d^2=0$ in \eqref{eq:prob_lms} and \eqref{eq:sig_k}  In this case, the algorithm remains valid and both the step size and the error variance, $\hat{\sigma}_{k}$, vanish over time $k$  

\item Finally, the proposed adaptable step-size LMS has only two parameters, $\sigma_d^2$ and $\sigma_n^2$, (and only one, $\sigma_n^2$, in stationary scenarios) in contrast to other variable step-size algorithms \cite{kwong1992variable,aboulnasr1997robust,shin2004variable}  More interestingly, both $\sigma_d^2$ and $\sigma_n^2$ have a clear underlying physical meaning, and they can be estimated in many cases  We will comment more about this in the next section  
\end{itemize}



\section{Experiments}
\label{sec:experiments}

We evaluate the performance of the proposed algorithm in both stationary and tracking experiments  In the first experiment, we estimate a fixed vector ${\bf w}^{o}$ of dimension $M=50$  The entries of the vector are independently and uniformly chosen in the range $[-1,1]$  Then, the vector is normalized so that $\|{\bf w}^o\|=1$  Regressors $\boldsymbol{x}_{k}$ are zero-mean Gaussian vectors with identity covariance matrix  The additive noise variance is such that the SNR is $20$ dB



ground_truth: 23 September.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How are smartphones and tablets different from a technical perspective?

Read the following text and answer briefly.

Context 4:  We compare our algorithm with standard RLS and three other LMS-based algorithms: LMS, NLMS \cite{sayed2008adaptive}, VSS-LMS \cite{shin2004variable} \footnote{The used parameters for each algorithm are: for RLS $\lambda=1$, $\epsilon^{-1}=0 01$; for LMS $\mu=0 01$; for NLMS $\mu=0 5$; and for VSS-LMS $\mu_{max}=1$, $\alpha=0 95$, $C=1e-4$ } The probabilistic LMS algorithm in \cite{park2014probabilistic} is not simulated because it is not suitable for stationary environments 

In stationary environments, the proposed algorithm has only one parameter, $\sigma^2_n$  We simulate both the scenario where we have perfectly knowledge of the amount of noise (probLMS1) and the case where the value $\sigma^2_n$ is $100$ times smaller than the actual value (probLMS2)  The Mean-Square Deviation (${\sf MSD} = {\mathbb E} \| {\bf w}_0 - {\bf w}_k \|^2$), averaged out over $50$ independent simulations, is presented in Fig  \ref{fig:msd_statationary} 



\begin{figure}[htb]
\centering
\begin{minipage}[b]{\linewidth}
  \centering
  \centerline{\includegraphics[width=\textwidth]{results_stationary_MSD}}
\end{minipage}
\caption{Performance in terms of MSD of probabilistic LMS with both optimal (probLMS1) and suboptimal (probLMS2) compared to LMS, NLMS, VS-LMS, and RLS }
\label{fig:msd_statationary}
\end{figure}

The performance of probabilistic LMS is close to RLS (obviously at a much lower computational cost) and largely outperforms previous variable step-size LMS algorithms proposed in the literature  Note that, when the model is stationary, i e  $\sigma^2_d=0$ in \eqref{eq:trans_eq},  both the uncertainty $\hat{\sigma}^2_k$, and the adaptive step size $\eta_k$, vanish over time  This implies that the error tends to zero when $k$ goes to infinity  Fig  \ref{fig:msd_statationary} also shows that the proposed approach is not very sensitive to a bad choice of its only parameter, as demonstrated by the good results of probLMS2, which uses a $\sigma^2_n$ that is $100$ times smaller than the optimal value  


\begin{figure}[htb]
\centering
\begin{minipage}[b]{\linewidth}
  \centering
  \centerline{\includegraphics[width=\textwidth]{fig2_final}}
\end{minipage}
\caption{Real part of one coefficient of the measured and estimated channel in experiment two  The shaded area represents two standard deviations from the prediction {(the mean of the posterior distribution)} }
\label{fig_2}
\end{figure}


\begin{table}[ht]
\begin{footnotesize}
\setlength{\tabcolsep}{2pt}
\def1 5mm{1 5mm}
\begin{center}
\begin{tabular}{|l@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|}
\hline
Method &  LMS &  NLMS & LMS-2013 & VSSNLMS & probLMS & RLS \\
\hline
\hline
MSD (dB) &-28 45 &-21 07 &-14 36 &-26 90 &-28 36 &-25 97\\
\hline                                                                     
\end{tabular}
\end{center}
\caption{Steady-state MSD of the different algorithms for the tracking of a real MISO channel }
\label{tab:table_MSD}
\end{footnotesize}

\end{table}
\newpage
In a second experiment, we test the tracking capabilities of the proposed algorithm with {real} data of a wireless MISO channel acquired in a realistic indoor scenario  More details on the setup can be found in \cite{gutierrez2011frequency}  Fig  \ref{fig_2} shows the real part of one of the channels, and the estimate of the proposed algorithm  The shaded area represents the estimated uncertainty for each prediction, i e  $\hat{\mu}_k\pm2\hat{\sigma}_k$  Since the experimental setup does not allow us to obtain the optimal values for the parameters, we fix these parameters to their values that optimize the steady-state mean square deviation (MSD)  \hbox{Table \ref{tab:table_MSD}} shows this steady-state MSD of the estimate of the MISO channel with different methods  As can be seen, the best tracking performance is obtained by standard LMS and the proposed method  





\section{Conclusions and Opened Extensions}
\label{sec:conclusions}

{We have presented a probabilistic interpretation of the least-mean-square filter  The resulting algorithm is an adaptable step-size LMS that performs well both in stationary and tracking scenarios  Moreover, it has fewer free parameters than previous approaches and these parameters have a clear physical meaning  Finally, as stated in the introduction, one of the advantages of having a probabilistic model is that it is easily extensible:}

\begin{itemize}
\item If, instead of using an isotropic Gaussian distribution in the approximation, we used a Gaussian with diagonal covariance matrix, we would obtain a similar algorithm with different step sizes and measures of uncertainty, for each component of ${\bf w}_k$  Although this model can be more descriptive, it needs more parameters to be tuned, and the parallelism with LMS vanishes 
\item Similarly, if we substitute the transition model of \eqref{eq:trans_eq} by an Ornstein-Uhlenbeck process, 

\begin{equation}
p({\bf w}_k|{\bf w}_{k-1})= \mathcal{N}({\bf w}_k;\lambda {\bf w}_{k-1}, \sigma_d^2), \nonumber
\label{eq:trans_eq_lambda}
\end{equation}
a similar algorithm is obtained but with a forgetting factor $\lambda$ multiplying ${\bf w}_{k-1}^{(LMS)}$ in \eqref{eq:lms}  This algorithm may have improved performance under such a kind of autoregresive dynamics of ${\bf w}_{k}$, though, again, the connection with standard LMS becomes dimmer 

\item As in \cite{park2014probabilistic}, the measurement model \eqref{eq:mess_eq} can be changed to obtain similar adaptive algorithms for classification, ordinal regression, and Dirichlet regression for compositional data  

\item A similar approximation technique could be applied to more complex dynamical models, i e  switching dynamical models \cite{barber2010graphical}  The derivation of efficient adaptive algorithms that explicitly take into account a switch in the dynamics of the parameters of interest is a non-trivial and open problem, though the proposed approach could be useful 

\item Finally, like standard LMS, this algorithm can be kernelized for its application in estimation under non-linear scenarios 

\end{itemize}


\begin{appendices}

\section{KL divergence between a general gaussian distribution and an isotropic gaussian}
\label{sec:kl}

 We want to approximate  $p_{{\bf x}_1}(x) = \mathcal{N}({\bf x}; \boldsymbol\mu_1,\boldsymbol\Sigma_1)$ by $p_{{\bf x}_2}({\bf x}) = \mathcal{N}({\bf x}; \boldsymbol\mu_2,\sigma_2^2 {\bf I})$  In order to do so, we have to compute the parameters of $p_{{\bf x}_2}({\bf x})$, $\boldsymbol\mu_2$ and $\sigma_2^2$, that minimize the following Kullback-Leibler divergence,

\begin{eqnarray}
D_{KL}(p_{{\bf x}_1}\| p_{{\bf x}_2}) &=&\int_{-\infty}^{\infty} p_{{\bf x}_1}({\bf x}) \ln{\frac{p_{{\bf x}_1}({\bf x})}{p_{{\bf x}_2}({\bf x})}}d{\bf x} \nonumber  \\
&= &  \frac{1}{2} \{ -M + {\sf Tr}(\sigma_2^{-2} {\bf I}\cdot \boldsymbol\Sigma_1^{-1})  \nonumber \\
  & &  + (\boldsymbol\mu_2 - \boldsymbol\mu_1 )^T \sigma^{-2}_2{\bf I} (\boldsymbol\mu_2 - \boldsymbol\mu_1 )  \nonumber \\
 & &   +  \ln \frac{{\sigma_2^2}^M}{\det\boldsymbol\Sigma_1} \}   
\label{eq:divergence}
\end{eqnarray}
Using symmetry arguments, we obtain 
\begin{equation}
\boldsymbol\mu_2^{*} =\arg \displaystyle{  \min_{\boldsymbol\mu_2}} \{ D_{KL}(p_{{\bf x}_1}\| p_{{\bf x}_2}) \} = \boldsymbol\mu_1 
\end{equation}
Then, \eqref{eq:divergence} gets simplified into 

\begin{eqnarray}
D_{KL}(p_{{\bf x}_1}\| p_{{\bf x}_2}) = \frac{1}{2}\lbrace { -M + {\sf Tr}(\frac{\boldsymbol\Sigma_1}{\sigma_2^{2}}) + \ln \frac{\sigma_2^{2M}}{\det\boldsymbol\Sigma_1}}\rbrace 
\end{eqnarray}
The variance $\sigma_2^2$ is computed in order to minimize this Kullback-Leibler divergence as

\begin{eqnarray}
\sigma_2^{2*} &=& \arg\min_{\sigma_2^2} D_{KL}(P_{x_1}\| P_{x_2}) \nonumber \\
 &=& \arg\min_{\sigma_2^2}\{ \sigma_2^{-2}{\sf Tr}\{\boldsymbol\Sigma_1\} + M\ln \sigma_2^{2} \}  
\end{eqnarray}
Deriving and making it equal zero leads to

\begin{equation}
\frac{\partial}{\partial \sigma_2^2} \left[ \frac{{\sf Tr}\{\boldsymbol\Sigma_1\}}{\sigma_2^{2}} + M \ln \sigma_2^{2} \right] = \left  {\frac{M}{\sigma_2^{2}}-\frac{{\sf Tr}\{\boldsymbol\Sigma_1\}}{(\sigma_2^{2})^2}}\right|_{\sigma_2^{2}=\sigma_2^{2*}}\left  =0 \right   
\nonumber
\end{equation}
Finally, since the divergence has a single extremum in $R_+$,
\begin{equation}
\sigma_2^{2*} = \frac{{\sf Tr}\{\boldsymbol\Sigma_1\}}{M} 
\end{equation}




\end{appendices}

\vfill
\clearpage

\bibliographystyle{IEEEbib}




ground_truth: Smartphones are more compact and power constrained.