There are lots of reasons why you might want to implement your own machine learning algorithms on Spark: you might want to experiment with a new idea, try and reproduce results from a recent research paper, or simply to use an existing technique that isn’t implemented in MLlib. In this talk, we’ll walk through the process of developing a new machine learning algorithm for Spark. We’ll start with the basics, by considering how we’d design a scale-out parallel implementation of our unsupervised learning technique. The bulk of the talk will focus on the details you need to know to turn an algorithm design into an efficient parallel implementation on Spark. We’ll start by reviewing a simple RDD-based implementation, show some improvements, point out some pitfalls to avoid, and iteratively extend our implementation to support contemporary Spark features like ML Pipelines and structured query processing. We’ll conclude by briefly examining some useful techniques to complement scale-out performance by scaling our code up, taking advantage of specialized hardware to accelerate single-worker performance. You’ll leave this talk with everything you need to build a new machine learning technique that runs on Spark.

1. Building parallel machine
learning algorithms:
scaling out and up
William Benton
willb@redhat.com • @willb

2. Motivation

3. Motivation

4. Motivation

5. Motivation

6. Forecast
Introducing our case study: self-organizing maps
Parallel implementations for partitioned collections (in particular, RDDs)
Beyond the RDD: data frames and ML pipelines
Practical considerations and key takeaways

7. Introducing our case study

10. Training self-organizing maps

11. Training self-organizing maps

12. Training self-organizing maps

13. Training self-organizing maps

14. Training self-organizing maps
while t < maxupdates:
random.shuffle(examples)
for ex in examples:
t = t + 1
if t == maxupdates:
break
bestMatch = closest(somt, ex)
for (unit, wt) in neighborhood(bestMatch, sigma(t)):
somt+1[unit] = somt[unit] + (ex - somt[unit]) * alpha(t) * wt

15. Training self-organizing maps
while t < maxupdates:
random.shuffle(examples)
for ex in examples:
t = t + 1
if t == maxupdates:
break
bestMatch = closest(somt, ex)
for (unit, wt) in neighborhood(bestMatch, sigma(t)):
somt+1[unit] = somt[unit] + (ex - somt[unit]) * alpha(t) * wt
process the training
set in random order

16. Training self-organizing maps
while t < maxupdates:
random.shuffle(examples)
for ex in examples:
t = t + 1
if t == maxupdates:
break
bestMatch = closest(somt, ex)
for (unit, wt) in neighborhood(bestMatch, sigma(t)):
somt+1[unit] = somt[unit] + (ex - somt[unit]) * alpha(t) * wt
process the training
set in random order
the neighborhood size controls
how much of the map around
the BMU is affected

17. Training self-organizing maps
while t < maxupdates:
random.shuffle(examples)
for ex in examples:
t = t + 1
if t == maxupdates:
break
bestMatch = closest(somt, ex)
for (unit, wt) in neighborhood(bestMatch, sigma(t)):
somt+1[unit] = somt[unit] + (ex - somt[unit]) * alpha(t) * wt
process the training
set in random order
the neighborhood size controls
how much of the map around
the BMU is affected
the learning rate controls
how much closer to the
example each unit gets

18. Parallel implementations for
partitioned collections

19. Historical aside: Amdahl’s Law
1
1 - p
lim So =sp —> ∞

20. What forces serial execution?

21. What forces serial execution?

22. What forces serial execution?
state[t+1] =
combine(state[t], x)

23. What forces serial execution?
state[t+1] =
combine(state[t], x)

24. What forces serial execution?
f1: (T, T) => T
f2: (T, U) => T

25. What forces serial execution?
f1: (T, T) => T
f2: (T, U) => T

26. What forces serial execution?
f1: (T, T) => T
f2: (T, U) => T

27. How can we fix these?
a ⊕ b = b ⊕ a
(a ⊕ b) ⊕ c = a ⊕ (b ⊕ c)

28. How can we fix these?
a ⊕ b = b ⊕ a
(a ⊕ b) ⊕ c = a ⊕ (b ⊕ c)

29. How can we fix these?
a ⊕ b = b ⊕ a
(a ⊕ b) ⊕ c = a ⊕ (b ⊕ c)

30. How can we fix these?
a ⊕ b = b ⊕ a
(a ⊕ b) ⊕ c = a ⊕ (b ⊕ c)

31. How can we fix these?
L-BGFSSGD
a ⊕ b = b ⊕ a
(a ⊕ b) ⊕ c = a ⊕ (b ⊕ c)

32. How can we fix these?
SGD L-BGFS
a ⊕ b = b ⊕ a
(a ⊕ b) ⊕ c = a ⊕ (b ⊕ c)
There will be examples of each
of these approaches for many
problems in the literature and
in open-source code!

33. Implementing atop RDDs
We’ll start with a batch implementation of our technique:
for t in (1 to iterations):
state = newState()
for ex in examples:
bestMatch = closest(somt-1, ex)
hood = neighborhood(bestMatch, sigma(t))
state.matches += ex * hood
state.hoods += hood
somt = newSOM(state.matches / state.hoods)

34. Implementing atop RDDs
for t in (1 to iterations):
state = newState()
for ex in examples:
bestMatch = closest(somt-1, ex)
hood = neighborhood(bestMatch, sigma(t))
state.matches += ex * hood
state.hoods += hood
somt = newSOM(state.matches / state.hoods)
Each batch produces a model that
can be averaged with other models

35. Implementing atop RDDs
Each batch produces a model that
can be averaged with other models
partition
for t in (1 to iterations):
state = newState()
for ex in examples:
bestMatch = closest(somt-1, ex)
hood = neighborhood(bestMatch, sigma(t))
state.matches += ex * hood
state.hoods += hood
somt = newSOM(state.matches / state.hoods)

36. Implementing atop RDDs
This won’t always work!
for t in (1 to iterations):
state = newState()
for ex in examples:
bestMatch = closest(somt-1, ex)
hood = neighborhood(bestMatch, sigma(t))
state.matches += ex * hood
state.hoods += hood
somt = newSOM(state.matches / state.hoods)

37. An implementation template
var nextModel = initialModel
for (int i = 0; i < iterations; i++) {
val current = sc.broadcast(nextModel)
val newState = examples.aggregate(ModelState.empty()) {
{ case (state: ModelState, example: Example) =>
state.update(current.value.lookup(example, i), example) }
{ case (s1: ModelState, s2: ModelState) => s1.combine(s2) }
}
nextModel = modelFromState(newState)
current.unpersist
}
var nextModel = initialModel
for (int i = 0; i < iterations; i++) {
val current = sc.broadcast(nextModel)
val newState = examples.aggregate(ModelState.empty()) {
{ case (state: ModelState, example: Example) =>
state.update(current.value.lookup(example, i), example) }
{ case (s1: ModelState, s2: ModelState) => s1.combine(s2) }
}
nextModel = modelFromState(newState)
current.unpersist
}

38. An implementation template
“fold”: update the state for
this partition with a single
new example
var nextModel = initialModel
for (int i = 0; i < iterations; i++) {
val current = sc.broadcast(nextModel)
val newState = examples.aggregate(ModelState.empty()) {
{ case (state: ModelState, example: Example) =>
state.update(current.value.lookup(example, i), example) }
{ case (s1: ModelState, s2: ModelState) => s1.combine(s2) }
}
nextModel = modelFromState(newState)
current.unpersist
}
var nextModel = initialModel
for (int i = 0; i < iterations; i++) {
val current = sc.broadcast(nextModel)
val newState = examples.aggregate(ModelState.empty()) {
{ case (state: ModelState, example: Example) =>
state.update(current.value.lookup(example, i), example) }
{ case (s1: ModelState, s2: ModelState) => s1.combine(s2) }
}
nextModel = modelFromState(newState)
current.unpersist
}

39. An implementation template
“reduce”: combine the
states from two partitions
var nextModel = initialModel
for (int i = 0; i < iterations; i++) {
val current = sc.broadcast(nextModel)
val newState = examples.aggregate(ModelState.empty()) {
{ case (state: ModelState, example: Example) =>
state.update(current.value.lookup(example, i), example) }
{ case (s1: ModelState, s2: ModelState) => s1.combine(s2) }
}
nextModel = modelFromState(newState)
current.unpersist
}
var nextModel = initialModel
for (int i = 0; i < iterations; i++) {
val current = sc.broadcast(nextModel)
val newState = examples.aggregate(ModelState.empty()) {
{ case (state: ModelState, example: Example) =>
state.update(current.value.lookup(example, i), example) }
{ case (s1: ModelState, s2: ModelState) => s1.combine(s2) }
}
nextModel = modelFromState(newState)
current.unpersist
}

40. An implementation template
var nextModel = initialModel
for (int i = 0; i < iterations; i++) {
val current = sc.broadcast(nextModel)
val newState = examples.aggregate(ModelState.empty()) {
{ case (state: ModelState, example: Example) =>
state.update(current.value.lookup(example, i), example) }
{ case (s1: ModelState, s2: ModelState) => s1.combine(s2) }
}
nextModel = modelFromState(newState)
current.unpersist
}
var nextModel = initialModel
for (int i = 0; i < iterations; i++) {
val current = sc.broadcast(nextModel)
val newState = examples.aggregate(ModelState.empty()) {
{ case (state: ModelState, example: Example) =>
state.update(current.value.lookup(example, i), example) }
{ case (s1: ModelState, s2: ModelState) => s1.combine(s2) }
}
nextModel = modelFromState(newState)
current.unpersist
} remove the stale
broadcasted model
broadcast the current working
model for this iteration

41. workersdriver (aggregate)
Implementing on RDDs
⊕ ⊕ ⊕ ⊕ ⊕ ⊕
⊕ ⊕ ⊕ ⊕ ⊕
⊕ ⊕ ⊕ ⊕

42. workersdriver (aggregate)
Implementing on RDDs
⊕ ⊕ ⊕ ⊕ ⊕ ⊕
⊕ ⊕ ⊕ ⊕ ⊕
⊕ ⊕ ⊕ ⊕

43. workersdriver (aggregate)
Implementing on RDDs

44. workersdriver (treeAggregate)
Implementing on RDDs
⊕
⊕
⊕
⊕
⊕ ⊕
⊕ ⊕

45. workersdriver (treeAggregate)
Implementing on RDDs
⊕
⊕
⊕
⊕
⊕ ⊕
⊕ ⊕

46. workersdriver (treeAggregate)
Implementing on RDDs
⊕
⊕
⊕
⊕
⊕ ⊕
⊕ ⊕
⊕
⊕
⊕
⊕

47. workersdriver (treeAggregate)
Implementing on RDDs
⊕
⊕
⊕
⊕
⊕
⊕
⊕ ⊕
driver (treeAggregate)
⊕
⊕
⊕
⊕

48. workersdriver (treeAggregate)
Implementing on RDDs
⊕
⊕
⊕
⊕
⊕ ⊕
⊕ ⊕
⊕ ⊕

49. workersdriver (treeAggregate)
Implementing on RDDs
⊕ ⊕

50. driver (treeAggregate) workers
Implementing on RDDs
⊕ ⊕

51. driver (treeAggregate) workers
Implementing on RDDs
⊕ ⊕⊕

52. Beyond the RDD: Data
frames and ML Pipelines

53. RDDs: some good parts
val rdd: RDD[String] = /* ... */
rdd.map(_ * 3.0).collect()
val df: DataFrame = /* data frame with one String-valued column */
df.select($"_1" * 3.0).show()

54. RDDs: some good parts
val rdd: RDD[String] = /* ... */
rdd.map(_ * 3.0).collect()
val df: DataFrame = /* data frame with one String-valued column */
df.select($"_1" * 3.0).show()
doesn’t compile

55. RDDs: some good parts
val rdd: RDD[String] = /* ... */
rdd.map(_ * 3.0).collect()
val df: DataFrame = /* data frame with one String-valued column */
df.select($"_1" * 3.0).show()
doesn’t compile

56. RDDs: some good parts
val rdd: RDD[String] = /* ... */
rdd.map(_ * 3.0).collect()
val df: DataFrame = /* data frame with one String-valued column */
df.select($"_1" * 3.0).show()
doesn’t compile
crashes at runtime

57. RDDs: some good parts
rdd.map {
vec => (vec, model.value.closestWithSimilarity(vec))
}
val predict = udf ((vec: SV) =>
model.value.closestWithSimilarity(vec))
df.withColumn($"predictions", predict($"features"))

58. RDDs: some good parts
rdd.map {
vec => (vec, model.value.closestWithSimilarity(vec))
}
val predict = udf ((vec: SV) =>
model.value.closestWithSimilarity(vec))
df.withColumn($"predictions", predict($"features"))

59. RDDs versus query planning
val numbers1 = sc.parallelize(1 to 100000000)
val numbers2 = sc.parallelize(1 to 1000000000)
numbers1.cartesian(numbers2)
.map((x, y) => (x, y, expensive(x, y)))
.filter((x, y, _) => isPrime(x), isPrime(y))

60. RDDs versus query planning
val numbers1 = sc.parallelize(1 to 100000000)
val numbers2 = sc.parallelize(1 to 1000000000)
numbers1.filter(isPrime(_))
.cartesian(numbers2.filter(isPrime(_)))
.map((x, y) => (x, y, expensive(x, y)))

61. RDDs and the Java heap
val mat = Array(Array(1.0, 2.0), Array(3.0, 4.0))

62. RDDs and the Java heap
val mat = Array(Array(1.0, 2.0), Array(3.0, 4.0))
class
pointer flags size locks element pointer element pointer
class
pointer flags size locks 1.0
class
pointer flags size locks 3.0 4.0
2.0

63. RDDs and the Java heap
val mat = Array(Array(1.0, 2.0), Array(3.0, 4.0))
class
pointer flags size locks element pointer element pointer
class
pointer flags size locks 1.0
class
pointer flags size locks 3.0 4.0
2.0 32 bytes of data…

64. RDDs and the Java heap
val mat = Array(Array(1.0, 2.0), Array(3.0, 4.0))
class
pointer flags size locks element pointer element pointer
class
pointer flags size locks 1.0
class
pointer flags size locks 3.0 4.0
2.0
…and 64 bytes
of overhead!
32 bytes of data…

65. ML pipelines: a quick example
from pyspark.ml.clustering import KMeans
K, SEED = 100, 0xdea110c8
randomDF = make_random_df()
kmeans = KMeans().setK(K).setSeed(SEED).setFeaturesCol("features")
model = kmeans.fit(randomDF)
withPredictions = model.transform(randomDF).select("x", "y", "prediction")

66. Working with ML pipelines
estimator.fit(df)

67. Working with ML pipelines
estimator.fit(df) model.transform(df)

68. Working with ML pipelines
model.transform(df)

69. Working with ML pipelines
model.transform(df)

70. Working with ML pipelines
estimator.fit(df) model.transform(df)

71. Working with ML pipelines
estimator.fit(df) model.transform(df)
inputCol
epochs
seed
outputCol

72. private[som] trait SOMParams extends Params
with DefaultParamsWritable {
final val x: IntParam =
new IntParam(this, "x", "width of self-organizing map (>= 1)",
ParamValidators.gtEq(1))
final def getX: Int = $(x)
final def setX(value: Int): this.type = set(x, value)
// ...
Defining parameters
private[som] trait SOMParams extends Params
with DefaultParamsWritable {
final val x: IntParam =
new IntParam(this, "x", "width of self-organizing map (>= 1)",
ParamValidators.gtEq(1))
final def getX: Int = $(x)
final def setX(value: Int): this.type = set(x, value)
// ...

73. private[som] trait SOMParams extends Params
with DefaultParamsWritable {
final val x: IntParam =
new IntParam(this, "x", "width of self-organizing map (>= 1)",
ParamValidators.gtEq(1))
final def getX: Int = $(x)
final def setX(value: Int): this.type = set(x, value)
// ...
Defining parameters
private[som] trait SOMParams extends Params
with DefaultParamsWritable {
final val x: IntParam =
new IntParam(this, "x", "width of self-organizing map (>= 1)",
ParamValidators.gtEq(1))
final def getX: Int = $(x)
final def setX(value: Int): this.type = set(x, value)
// ...

74. Defining parameters
private[som] trait SOMParams extends Params
with DefaultParamsWritable {
final val x: IntParam =
new IntParam(this, "x", "width of self-organizing map (>= 1)",
ParamValidators.gtEq(1))
final def getX: Int = $(x)
final def setX(value: Int): this.type = set(x, value)
// ...
private[som] trait SOMParams extends Params
with DefaultParamsWritable {
final val x: IntParam =
new IntParam(this, "x", "width of self-organizing map (>= 1)",
ParamValidators.gtEq(1))
final def getX: Int = $(x)
final def setX(value: Int): this.type = set(x, value)
// ...

75. Defining parameters
private[som] trait SOMParams extends Params
with DefaultParamsWritable {
final val x: IntParam =
new IntParam(this, "x", "width of self-organizing map (>= 1)",
ParamValidators.gtEq(1))
final def getX: Int = $(x)
final def setX(value: Int): this.type = set(x, value)
// ...
private[som] trait SOMParams extends Params
with DefaultParamsWritable {
final val x: IntParam =
new IntParam(this, "x", "width of self-organizing map (>= 1)",
ParamValidators.gtEq(1))
final def getX: Int = $(x)
final def setX(value: Int): this.type = set(x, value)
// ...

76. Defining parameters
private[som] trait SOMParams extends Params
with DefaultParamsWritable {
final val x: IntParam =
new IntParam(this, "x", "width of self-organizing map (>= 1)",
ParamValidators.gtEq(1))
final def getX: Int = $(x)
final def setX(value: Int): this.type = set(x, value)
// ...
private[som] trait SOMParams extends Params
with DefaultParamsWritable {
final val x: IntParam =
new IntParam(this, "x", "width of self-organizing map (>= 1)",
ParamValidators.gtEq(1))
final def getX: Int = $(x)
final def setX(value: Int): this.type = set(x, value)
// ...

77. Don’t repeat yourself
/**
* Common params for KMeans and KMeansModel
*/
private[clustering] trait KMeansParams extends Params
with HasMaxIter with HasFeaturesCol
with HasSeed with HasPredictionCol with HasTol { /* ... */ }

78. Estimators and transformers
estimator.fit(df)

79. Estimators and transformers
estimator.fit(df)

80. Estimators and transformers
estimator.fit(df) model.transform(df)

81. Estimators and transformers
estimator.fit(df) model.transform(df)

82. Estimators and transformers
estimator.fit(df) model.transform(df)

83. Validate and transform at once
def transformSchema(schema: StructType):
StructType = {
// check that the input columns exist...
// ...and are the proper type
// ...and that the output columns don’t exist
// ...and then make a new schema
}

84. Validate and transform at once
def transformSchema(schema: StructType):
StructType = {
// check that the input columns exist…
require(schema.fieldNames.contains($(featuresCol)))
// ...and are the proper type
// ...and that the output columns don’t exist
// ...and then make a new schema
}

85. Validate and transform at once
def transformSchema(schema: StructType):
StructType = {
// check that the input columns exist...
// ...and are the proper type
schema($(featuresCol)) match {
case sf: StructField => require(sf.dataType.equals(VectorType))
}
// ...and that the output columns don’t exist
// ...and then make a new schema
}

86. Validate and transform at once
def transformSchema(schema: StructType):
StructType = {
// check that the input columns exist…
// ...and are the proper type
// ...and that the output columns don’t exist
require(!schema.fieldNames.contains($(predictionCol)))
require(!schema.fieldNames.contains($(similarityCol)))
// ...and then make a new schema
}

87. Validate and transform at once
def transformSchema(schema: StructType):
StructType = {
// check that the input columns exist…
// ...and are the proper type
// ...and that the output columns don’t exist
// ...and then make a new schema
schema.add($(predictionCol), "int")
.add($(similarityCol), "double")
}

88. Training on data frames
def fit(examples: DataFrame) = {
import examples.sparkSession.implicits._
import org.apache.spark.ml.linalg.{Vector=>SV}
val dfexamples = examples.select($(exampleCol)).rdd.map {
case Row(sv: SV) => sv
}
/* construct a model object with the result of training */
new SOMModel(train(dfexamples, $(x), $(y)))
}

89. Practical considerations

90. Improve serial execution times
2
6
6
4
0 0 1
0 1 0
0 0 1
1 0 0
3
7
7
5 •
2
4
0.1
0.7
0.2
3
5
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91. Improve serial execution times
2
6
6
4
0 0 1
0 1 0
0 0 1
1 0 0
3
7
7
5 •
2
4
0.1
0.7
0.2
3
5
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92. Improve serial execution times
2
6
6
4
0 0 1
0 1 0
0 0 1
1 0 0
3
7
7
5 •
2
4
0.1
0.7
0.2
3
5
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99. ⇥
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•
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0.1 0.7 0.2
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0.1 0.7 0.2
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100. ⇥
0 0 1
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•
⇥
0.1 0.7 0.2
⇤
⇥
0 1 0
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•
⇥
0.1 0.7 0.2
⇤
⇥
0 0 1
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•
⇥
0.1 0.7 0.2
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⇥
1 0 0
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⇥
0.1 0.7 0.2
⇤
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<latexit sha1_base64="yGPDKZdOXUPJZlyEHQdtfy2cnBM=">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</latexit>

101. ⇥
0 0 1
⇤
•
⇥
0.1 0.7 0.2
⇤
⇥
0 1 0
⇤
•
⇥
0.1 0.7 0.2
⇤
⇥
0 0 1
⇤
•
⇥
0.1 0.7 0.2
⇤
⇥
1 0 0
⇤
•
⇥
0.1 0.7 0.2
⇤
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libraryDependencies +=
"org.scalanlp" %% "breeze-natives" % "0.13.1"

102. val vec = Array[Double](/* ... */)

103. val vec = Array[Double](/* ... */)

104. def dot[S](a: Array[S], b: Array[S])
(implicit num: Numeric[S]): S = {
import num._
(0 until a.length).foldLeft(num.zero)({
(acc, i) => acc + a(i) * b(i)
})
}
val vec = Array[Double](/* ... */)

105. def dot[S](a: Array[S], b: Array[S])
(implicit num: Numeric[S]): S = {
import num._
(0 until a.length).foldLeft(num.zero)({
(acc, i) => acc + a(i) * b(i)
})
}
val vec = Array[Double](/* ... */)
dot(Array(0.1d, 0.2d, 0.3d), Array(1.0d, 0.0d, 0.0d))
dot(Array(0.1f, 0.2f, 0.3f), Array(1.0f, 0.0f, 0.0f))

106. val vec = Array[Double](/* ... */)
vdppd
vdppd
0.1d 0.2d 1.0d 0.0d
0.3d (unused) 0.0d (unused)
def dot[S](a: Array[S], b: Array[S])
(implicit num: Numeric[S]): S = {
import num._
(0 until a.length).foldLeft(num.zero)({
(acc, i) => acc + a(i) * b(i)
})
}

107. val vec = Array[Double](/* ... */)
vdppd
vdppd
0.1d 0.2d 1.0d 0.0d
0.3d (unused) 0.0d (unused)
vdpps
0.3f unused0.2f0.1f 0.0f unused0.0f1.0f
def dot[S](a: Array[S], b: Array[S])
(implicit num: Numeric[S]): S = {
import num._
(0 until a.length).foldLeft(num.zero)({
(acc, i) => acc + a(i) * b(i)
})
}

108. KEY TAKEAWAYS

113. THANKS!willb@redhat.com • @willb
https://chapeau.freevariable.com
https://radanalytics.io
also: “Spark for Library Developers”
Room 2014 at 5:40 PM today