text: 3 90 1.0 Mn Co Ge 80 2.5 0.9 0.1 Mn Co Ge Mn0.8Co0.2Ge 70 0.5 0.7 0.3 2.0 Mn Co Ge 0.6 0.4 60 Mn Co Ge 0.55 0.45 50 1.5 0.0 40 Mn0.5Co0.5Ge 30 1.0 -0.5 Mn Co Ge 0.4 0.6 Mn Co Ge 20 0.3 0.7 0.5 Mn Co Ge Mn0.2Co0.8Ge 10 -1.0 0.1 0.9 0 0.0 -4 -2 0 2 4 0.0 0.2 0.4 0.6 0.8 1.0 (a) (b) Magnetic Field (T) Co Concentration x · FIG. 2: (color online) (a) Magnetization curves of Mn − Co Ge at T = 0.2 T normalized to the magnetization at B = 5 T. 1 x x C (b) Magnetization energy of Mn − Co Ge derived from the data in (a) in absolute units (red squares) and taken from the 1 x x normalized magnetization (blue circles). The absolute energy values are directly calculated from III. SANS EXPERIMENT the individual magnetization curve of each mixed com- pound. The normalized magnetization energy denotes In order to identify the magnetic structure of the com- the energy from the normalized magnetization M/M 5T pounds, SANS measurements were carried out using the as shown in Fig. 2a. From this curve three diﬀerent ≤ SANS-1 instrument [31] at the FRM-II reactor in Garch- regimes can be distinguished: (i) For x 0.5 the mag- ing, Germany). Neutrons with a mean wavelength of netization energy is relatively high and decreases with ≤ ≤ λ = 0.6 nm and 1.2 nm were used. The sample–detector increasing Co concentration. (ii) For 0.5 x 0.8 the distance of 2, 7, and 20 meters was set to cover the range magnetization energy is low, which is correlated with a of momentum transfer Q from 0.02 nm−1 to 2.7 nm−1 high magnetic anisotropy, and is nearly independent of with the resolution equal to 20 %. The scattering in- the Co concentration. (iii) For x > 0.8 the normalized tensity was measured upon zero-ﬁeld cooling from the magnetization energy starts to increase again, whereas paramagnetic phase at T = 300 K to the ordered phase the absolute values become smaller due to the reduction at T = 5 K. of the magnetic moment at high Co concentration. This Figure 4(a-h) shows examples of the small-angle neu- result already suggests that the exchange mechanism in tron scattering maps for Mn − Co Ge with x from 0.0 the Mn − Co Ge system changes upon Co substitution 1 x x ∼ 1 x x ∼ to 0.8 at T = 5 K. The typical powder-like images were at x 0.5 and x 0.8 as indicated by the two dashed detected for the samples with x = 0.0 and 0.1 (Fig. 4a, lines in Fig. 2b. b). From high resolution X-ray data we conclude that From isothermal magnetization curves Arrott plots all samples have the same size of powder grains in the have been obtained in order to determine the ordering order of 10 microns [28, 29]. With further increase of temperature T . Only in the regime between x = 0.5 x up to 0.4, the intensity of the ring smears over the C and x = 0.7 a linear behavior of M1/β vs. (H/M) large Q-area (Fig. 4c, d). This implies that the cor- with β = 0.31 can be observed which allows for the relation length of the structure decreases dramatically. identiﬁcation of T [Fig. 3a for Mn Co Ge]. In the One should note that the evolution of the magnetic struc- C 0.3 0.7 range x < 0.5 the ﬁeld dependence of the magnetiza- ture of Mn1−xCoxGe with x shows a surprising similar- tion changes in a way that the Arrott plots cannot be ity to the evolution of the magnetic structure of pure extrapolated to the origin of the diagram [Fig. 3b for MnGe with the temperature [12]. For Co concentrations Mn Co Ge]. The reason for the deviation from linear- x > 0.4 the k-value decreases drastically (Fig. 4e-g). 0.7 0.3 ity of the Arrott plots is most likely related to ﬂuctua- For the compound with x = 0.9 the value of k is not tions close to the magnetic order transition which might detected within the resolution of the SANS instrument also be of ﬁrst order as known from MnSi [30]. Also (Fig. 4g). Therefore this compound exhibits ferromag- ≥ for x 0.8 the Arrott plots do not yield the ordering netic order rather than a helical spin structure. temperature [Fig. 3c for Mn Co Ge]. That brings The scattering intensity I(Q) was azimuthally aver- 0.1 0.9 to the conclusion that the small-angle neutron scatter- aged and plotted for compounds with 0.0 < x < 0.5 ing experiments are needed to investigate completely the in Fig. 5a and for compounds with 0.5 < x < 0.9 in microscopic nature of the magnetic states as function of Fig. 5b. The position of the Bragg reﬂection decreases the temperature for the diﬀerent mixed compounds. to one-tenth of Q from x = 0.0 towards x = 0.5. In M / M T 5 )gk/J( ygrenE noitazitengaM )stinu .bra( ygrenE noitazitengaM .mroN ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: Mn

text: Co

text: Ge

text: Mn

text: Co

text: Ge

text: Mn

text: Co

text: Ge

text: Mn

text: Co

text: Ge

text: Mn

text: Co

text: Ge

text: Mn

text: Co

text: Ge

text: Mn

text: Co

text: Ge

text: (a)

text: (b)

text: Magnetic

text: Field

text: (T)

text: Co

text: Concentration

text: x

text: FIG.

text: (color

text: online)

text: (a)

text: Magnetization

text: curves

text: of

text: Mn

text: Co

text: Ge

text: at

text: T

text: T

text: normalized

text: to

text: the

text: magnetization

text: at

text: B

text: T.

text: x

text: x

text: C

text: (b)

text: Magnetization

text: energy

text: of

text: Mn

text: Co

text: Ge

text: derived

text: from

text: the

text: data

text: in

text: (a)

text: in

text: absolute

text: units

text: (red

text: squares)

text: and

text: taken

text: from

text: the

text: x

text: x

text: normalized

text: magnetization

text: (blue

text: circles).

text: The

text: absolute

text: energy

text: values

text: are

text: directly

text: calculated

text: from

text: III.

text: SANS

text: EXPERIMENT

text: the

text: individual

text: magnetization

text: curve

text: of

text: each

text: mixed

text: com-

text: pound.

text: The

text: normalized

text: magnetization

text: energy

text: denotes

text: In

text: order

text: to

text: identify

text: the

text: magnetic

text: structure

text: of

text: the

text: com-

text: the

text: energy

text: from

text: the

text: normalized

text: magnetization

text: M/M

text: pounds,

text: SANS

text: measurements

text: were

text: carried

text: out

text: using

text: the

text: as

text: shown

text: in

text: Fig.

text: From

text: this

text: curve

text: three

text: diﬀerent

text: instrument

text: at

text: the

text: FRM-II

text: reactor

text: in

text: Garch-

text: regimes

text: can

text: be

text: distinguished:

text: (i)

text: For

text: x

text: the

text: mag-

text: ing,

text: Germany).

text: Neutrons

text: with

text: a

text: mean

text: wavelength

text: of

text: netization

text: energy

text: is

text: relatively

text: high

text: and

text: decreases

text: with

text: λ

text: nm

text: and

text: nm

text: were

text: used.

text: The

text: sample–detector

text: increasing

text: Co

text: concentration.

text: (ii)

text: For

text: x

text: the

text: distance

text: of

text: and

text: meters

text: was

text: set

text: to

text: cover

text: the

text: range

text: magnetization

text: energy

text: is

text: low,

text: which

text: is

text: correlated

text: with

text: a

text: of

text: momentum

text: transfer

text: Q

text: from

text: to

text: high

text: magnetic

text: anisotropy,

text: and

text: is

text: nearly

text: independent

text: of

text: with

text: the

text: resolution

text: equal

text: to

text: The

text: scattering

text: in-

text: the

text: Co

text: concentration.

text: (iii)

text: For

text: x

text: the

text: normalized

text: tensity

text: was

text: measured

text: upon

text: zero-ﬁeld

text: cooling

text: from

text: the

text: magnetization

text: energy

text: starts

text: to

text: increase

text: again,

text: whereas

text: paramagnetic

text: phase

text: at

text: T

text: K

text: to

text: the

text: ordered

text: phase

text: the

text: absolute

text: values

text: become

text: smaller

text: due

text: to

text: the

text: reduction

text: at

text: T

text: K.

text: of

text: the

text: magnetic

text: moment

text: at

text: high

text: Co

text: concentration.

text: This

text: Figure

text: shows

text: examples

text: of

text: the

text: small-angle

text: neu-

text: result

text: already

text: suggests

text: that

text: the

text: exchange

text: mechanism

text: in

text: tron

text: scattering

text: maps

text: for

text: Mn

text: Co

text: Ge

text: with

text: x

text: from

text: the

text: Mn

text: Co

text: Ge

text: system

text: changes

text: upon

text: Co

text: substitution

text: x

text: x

text: x

text: x

text: to

text: at

text: T

text: K.

text: The

text: typical

text: powder-like

text: images

text: were

text: at

text: x

text: and

text: x

text: as

text: indicated

text: by

text: the

text: two

text: dashed

text: detected

text: for

text: the

text: samples

text: with

text: x

text: and

text: (Fig.

text: lines

text: in

text: Fig.

text: b).

text: From

text: high

text: resolution

text: X-ray

text: data

text: we

text: conclude

text: that

text: From

text: isothermal

text: magnetization

text: curves

text: Arrott

text: plots

text: all

text: samples

text: have

text: the

text: same

text: size

text: of

text: powder

text: grains

text: in

text: the

text: have

text: been

text: obtained

text: in

text: order

text: to

text: determine

text: the

text: ordering

text: order

text: of

text: microns

text: With

text: further

text: increase

text: of

text: temperature

text: T

text: Only

text: in

text: the

text: regime

text: between

text: x

text: x

text: up

text: to

text: the

text: intensity

text: of

text: the

text: ring

text: smears

text: over

text: the

text: C

text: and

text: x

text: a

text: linear

text: behavior

text: of

text: vs.

text: (H/M)

text: large

text: Q-area

text: (Fig.

text: d).

text: This

text: implies

text: that

text: the

text: cor-

text: with

text: β

text: can

text: be

text: observed

text: which

text: allows

text: for

text: the

text: relation

text: length

text: of

text: the

text: structure

text: decreases

text: dramatically.

text: identiﬁcation

text: of

text: T

text: [Fig.

text: for

text: Mn

text: Co

text: Ge].

text: In

text: the

text: One

text: should

text: note

text: that

text: the

text: evolution

text: of

text: the

text: magnetic

text: struc-

text: C

text: range

text: x

text: the

text: ﬁeld

text: dependence

text: of

text: the

text: magnetiza-

text: ture

text: of

text: with

text: x

text: shows

text: a

text: surprising

text: similar-

text: tion

text: changes

text: in

text: a

text: way

text: that

text: the

text: Arrott

text: plots

text: cannot

text: be

text: ity

text: to

text: the

text: evolution

text: of

text: the

text: magnetic

text: structure

text: of

text: pure

text: extrapolated

text: to

text: the

text: origin

text: of

text: the

text: diagram

text: [Fig.

text: for

text: MnGe

text: with

text: the

text: temperature

text: For

text: Co

text: concentrations

text: Mn

text: Co

text: Ge].

text: The

text: reason

text: for

text: the

text: deviation

text: from

text: linear-

text: x

text: the

text: k-value

text: decreases

text: drastically

text: (Fig.

text: ity

text: of

text: the

text: Arrott

text: plots

text: is

text: most

text: likely

text: related

text: to

text: ﬂuctua-

text: For

text: the

text: compound

text: with

text: x

text: the

text: value

text: of

text: k

text: is

text: not

text: tions

text: close

text: to

text: the

text: magnetic

text: order

text: transition

text: which

text: might

text: detected

text: within

text: the

text: resolution

text: of

text: the

text: SANS

text: instrument

text: also

text: be

text: of

text: ﬁrst

text: order

text: as

text: known

text: from

text: MnSi

text: Also

text: (Fig.

text: Therefore

text: this

text: compound

text: exhibits

text: ferromag-

text: for

text: x

text: the

text: Arrott

text: plots

text: do

text: not

text: yield

text: the

text: ordering

text: netic

text: order

text: rather

text: than

text: a

text: helical

text: spin

text: structure.

text: temperature

text: [Fig.

text: for

text: Mn

text: Co

text: Ge].

text: That

text: brings

text: The

text: scattering

text: intensity

text: I(Q)

text: was

text: azimuthally

text: aver-

text: to

text: the

text: conclusion

text: that

text: the

text: small-angle

text: neutron

text: scatter-

text: aged

text: and

text: plotted

text: for

text: compounds

text: with

text: x

text: ing

text: experiments

text: are

text: needed

text: to

text: investigate

text: completely

text: the

text: in

text: Fig.

text: and

text: for

text: compounds

text: with

text: x

text: in

text: microscopic

text: nature

text: of

text: the

text: magnetic

text: states

text: as

text: function

text: of

text: Fig.

text: The

text: position

text: of

text: the

text: Bragg

text: reﬂection

text: decreases

text: the

text: temperature

text: for

text: the

text: diﬀerent

text: mixed

text: compounds.

text: to

text: one-tenth

text: of

text: Q

text: from

text: x

text: towards

text: x

text: In

text: M

text: M

text: T

text: )gk/J(

text: ygrenE

text: noitazitengaM

text: )stinu

text: .bra(

text: ygrenE

text: noitazitengaM

text: .mroN

text: ##LTFigure##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##


text: 1997) with a bias of 1 added to the forget gate in Avg. # of Utterances Per Dialogue 14 Vocabulary Size 1,229 the style of (Pham et al., 2014). Training Dialogues 1,618 3 Experiments Validation Dialogues 500 Test Dialogues 1,117 3.1 Data # of Distinct Entities 452 # of Entity (or Slot) Types 8 For our experiments, we used dialogues ex- Table 1: Statistics of DSTC2 tracted from the Dialogue State Tracking Chal- lenge 2 (DSTC2) (Henderson et al., 2014), a restaurant reservation system dataset. While the model, drawn from previous work: • goal of the original challenge was building a sys- Per-Response Accuracy: Bordes and We- tem for inferring dialogue state, for our study, we ston (2016) report a per-turn response accu- use the version of the data from Bordes and We- racy, which tests their model’s ability to se- ston (2016), which ignores the dialogue state an- lect the system response at a certain timestep. notations, using only the raw text of the dialogues. Their system does a multiclass classiﬁcation The raw text includes user and system utterances over a predeﬁned candidate set of responses, as well as the API calls the system would make which was created by aggregating all system to the underlying KB in response to the user’s responses seen in the training, validation, and queries. Our model then aims to predict both these test sets. Our model actually generates each system utterances and API calls, each of which is individual token of the response, and we con- regarded as a turn of the dialogue. We use the sider a prediction to be correct only if every train/validation/test splits from this modiﬁed ver- token of the model output matches the corre- sion of the dataset. The dataset is appealing for a sponding token in the gold response. Evalu- number of reasons: 1) It is derived from a real- ating using this metric on our model is there- world system so it presents the kind of linguis- fore signiﬁcantly more stringent a test than tic diversity and conversational abilities we would for the model of Bordes and Weston (2016). hope for in an effective dialogue agent. 2) It is • Per-Dialogue Accuracy: Bordes and Weston grounded via an underlying knowledge base of (2016) also report a per-dialogue accuracy, restaurant entities and their attributes. 3) Previ- which assesses their model’s ability to pro- ous results have been reported on it so we can di- duce every system response of the dialogue rectly compare our model performance. We in- correctly. We calculate a similar value of dia- clude statistics of the dataset in Table 1. logue accuracy, though again our model gen- 3.2 Training erates every token of every response. We trained using a cross-entropy loss and the • BLEU: We use the BLEU metric, commonly Adam optimizer (Kingma and Ba, 2015), apply- employed in evaluating machine translation ing dropout (Hinton et al., 2012) as a regularizer systems (Papineni et al., 2002), which has to the input and output of the LSTM. We identiﬁed also been used in past literature for evaluating hyperparameters by random search, evaluating on dialogue systems (Ritter et al., 2011; Li et a held-out validation subset of the data. Dropout al., 2016). We calculate average BLEU score keep rates ranged from 0.75 to 0.95. We used word over all responses generated by the system, embeddings with size 300, and hidden layer and and primarily report these scores to gauge our cell sizes were set to 353, identiﬁed through our model’s ability to accurately generate the lan- search. We applied gradient clipping with a clip- guage patterns seen in DSTC2. value of 10 to avoid gradient explosions during training. The attention, output parameters, word • Entity F : Each system response in the test embeddings, and LSTM weights were randomly 1 data deﬁnes a gold set of entities. To compute initialized from a uniform unit-scaled distribution an entity F , we micro-average over the entire in the style of (Sussillo and Abbott, 2015). 1 set of system dialogue responses. This met- 3.3 Metrics ric evaluates the model’s ability to generate Evaluation of dialogue systems is known to be relevant entities from the underlying knowl- difﬁcult (Liu et al., 2016). We employ sev- edge base and to capture the semantics of the eral metrics for assessing speciﬁc aspects of our user-initiated dialogue ﬂow. ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

label: paragraph

text: with

text: a

text: bias

text: of

text: added

text: to

text: the

text: forget

text: gate

text: in

text: Avg.

label: table

text: of

text: Utterances

text: Per

text: Dialogue

text: Vocabulary

text: Size

text: the

text: style

text: of

text: (Pham

text: et

text: al.,

text: Training

text: Dialogues

label: section

text: Experiments

text: Validation

text: Dialogues

text: Test

text: Dialogues

text: Data

text: of

text: Distinct

text: Entities

text: of

text: Entity

text: (or

text: Slot)

text: Types

text: For

text: our

text: experiments,

text: we

text: used

text: dialogues

text: ex-

text: Table

text: Statistics

label: caption

text: of

text: tracted

text: from

text: the

text: Dialogue

text: State

text: Tracking

text: Chal-

text: lenge

text: (Henderson

text: et

text: al.,

text: a

text: restaurant

text: reservation

text: system

text: dataset.

text: While

text: the

text: model,

text: drawn

text: from

text: previous

text: work:

label: list

text: goal

text: of

text: the

text: original

text: challenge

text: was

text: building

text: a

text: sys-

text: Per-Response

text: Accuracy:

text: Bordes

text: and

text: We-

text: tem

text: for

text: inferring

text: dialogue

text: state,

text: for

text: our

text: study,

text: we

text: ston

text: report

text: a

text: per-turn

text: response

text: accu-

text: use

text: the

text: version

text: of

text: the

text: data

text: from

text: Bordes

text: and

text: We-

text: racy,

text: which

text: tests

text: their

text: model’s

text: ability

text: to

text: se-

text: ston

text: which

text: ignores

text: the

text: dialogue

text: state

text: an-

text: lect

text: the

text: system

text: response

text: at

text: a

text: certain

text: timestep.

text: notations,

text: using

text: only

text: the

text: raw

text: text

text: of

text: the

text: dialogues.

text: Their

text: system

text: does

text: a

text: multiclass

text: classiﬁcation

text: The

text: raw

text: text

text: includes

text: user

text: and

text: system

text: utterances

text: over

text: a

text: predeﬁned

text: candidate

text: set

text: of

text: responses,

text: as

text: well

text: as

text: the

text: API

text: calls

text: the

text: system

text: would

text: make

text: which

text: was

text: created

text: by

text: aggregating

text: all

text: system

text: to

text: the

text: underlying

text: KB

text: in

text: response

text: to

text: the

text: user’s

text: responses

text: seen

text: in

text: the

text: training,

text: validation,

text: and

text: queries.

text: Our

text: model

text: then

text: aims

text: to

text: predict

text: both

text: these

text: test

text: sets.

text: Our

text: model

text: actually

text: generates

text: each

text: system

text: utterances

text: and

text: API

text: calls,

text: each

text: of

text: which

text: is

text: individual

text: token

text: of

text: the

text: response,

text: and

text: we

text: con-

text: regarded

text: as

text: a

text: turn

text: of

text: the

text: dialogue.

text: We

text: use

text: the

text: sider

text: a

text: prediction

text: to

text: be

text: correct

text: only

text: if

text: every

text: train/validation/test

text: splits

text: from

text: this

text: modiﬁed

text: ver-

text: token

text: of

text: the

text: model

text: output

text: matches

text: the

text: corre-

text: sion

text: of

text: the

text: dataset.

text: The

text: dataset

text: is

text: appealing

text: for

text: a

text: sponding

text: token

text: in

text: the

text: gold

text: response.

text: Evalu-

text: number

text: of

text: reasons:

text: It

text: is

text: derived

text: from

text: a

text: real-

text: ating

text: using

text: this

text: metric

text: on

text: our

text: model

text: is

text: there-

text: world

text: system

text: so

text: it

text: presents

text: the

text: kind

text: of

text: linguis-

text: fore

text: signiﬁcantly

text: more

text: stringent

text: a

text: test

text: than

text: tic

text: diversity

text: and

text: conversational

text: abilities

text: we

text: would

text: for

text: the

text: model

text: of

text: Bordes

text: and

text: Weston

text: hope

text: for

text: in

text: an

text: effective

text: dialogue

text: agent.

text: It

text: is

text: Per-Dialogue

text: Accuracy:

text: Bordes

text: and

text: Weston

text: grounded

text: via

text: an

text: underlying

text: knowledge

text: base

text: of

text: also

text: report

text: a

text: per-dialogue

text: accuracy,

text: restaurant

text: entities

text: and

text: their

text: attributes.

text: Previ-

text: which

text: assesses

text: their

text: model’s

text: ability

text: to

text: pro-

text: ous

text: results

text: have

text: been

text: reported

text: on

text: it

text: so

text: we

text: can

text: di-

text: duce

text: every

text: system

text: response

text: of

text: the

text: dialogue

text: rectly

text: compare

text: our

text: model

text: performance.

text: We

text: in-

text: correctly.

text: We

text: calculate

text: a

text: similar

text: value

text: of

text: dia-

text: clude

text: statistics

text: of

text: the

text: dataset

text: in

text: Table

text: logue

text: accuracy,

text: though

text: again

text: our

text: model

text: gen-

text: Training

text: erates

text: every

text: token

text: of

text: every

text: response.

text: We

text: trained

text: using

text: a

text: cross-entropy

text: loss

text: and

text: the

text: BLEU:

text: We

text: use

text: the

text: BLEU

text: metric,

text: commonly

text: Adam

text: optimizer

text: (Kingma

text: and

text: Ba,

text: apply-

text: employed

text: in

text: evaluating

text: machine

text: translation

text: ing

text: dropout

text: (Hinton

text: et

text: al.,

text: as

text: a

text: regularizer

text: systems

text: (Papineni

text: et

text: al.,

text: which

text: has

text: to

text: the

text: input

text: and

text: output

text: of

text: the

text: LSTM.

text: We

text: identiﬁed

text: also

text: been

text: used

text: in

text: past

text: literature

text: for

text: evaluating

text: hyperparameters

text: by

text: random

text: search,

text: evaluating

text: on

text: dialogue

text: systems

text: (Ritter

text: et

text: al.,

text: Li

text: et

text: a

text: held-out

text: validation

text: subset

text: of

text: the

text: data.

text: Dropout

text: al.,

text: We

text: calculate

text: average

text: BLEU

text: score

text: keep

text: rates

text: ranged

text: from

text: to

text: We

text: used

text: word

text: over

text: all

text: responses

text: generated

text: by

text: the

text: system,

text: embeddings

text: with

text: size

text: and

text: hidden

text: layer

text: and

text: and

text: primarily

text: report

text: these

text: scores

text: to

text: gauge

text: our

text: cell

text: sizes

text: were

text: set

text: to

text: identiﬁed

text: through

text: our

text: model’s

text: ability

text: to

text: accurately

text: generate

text: the

text: lan-

text: search.

text: We

text: applied

text: gradient

text: clipping

text: with

text: a

text: clip-

text: guage

text: patterns

text: seen

text: in

text: value

text: of

text: to

text: avoid

text: gradient

text: explosions

text: during

text: training.

text: The

text: attention,

text: output

text: parameters,

text: word

text: Entity

text: F

text: Each

text: system

text: response

text: in

text: the

text: test

text: embeddings,

text: and

text: LSTM

text: weights

text: were

text: randomly

text: data

text: deﬁnes

text: a

text: gold

text: set

text: of

text: entities.

text: To

text: compute

text: initialized

text: from

text: a

text: uniform

text: unit-scaled

text: distribution

text: an

text: entity

text: F

text: we

text: micro-average

text: over

text: the

text: entire

text: in

text: the

text: style

text: of

text: (Sussillo

text: and

text: Abbott,

text: set

text: of

text: system

text: dialogue

text: responses.

text: This

text: met-

text: Metrics

text: ric

text: evaluates

text: the

text: model’s

text: ability

text: to

text: generate

text: Evaluation

text: of

text: dialogue

text: systems

text: is

text: known

text: to

text: be

text: relevant

text: entities

text: from

text: the

text: underlying

text: knowl-

text: difﬁcult

text: (Liu

text: et

text: al.,

text: We

text: employ

text: sev-

text: edge

text: base

text: and

text: to

text: capture

text: the

text: semantics

text: of

text: the

text: eral

text: metrics

text: for

text: assessing

text: speciﬁc

text: aspects

text: of

text: our

text: user-initiated

text: dialogue

text: ﬂow.

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##


text: 6 (cid:101) VILMOS PROKAJ AND JOHANNES RUF | || ∞ With ε replaced by ε and with G = F − , H = F , and W = ∆S , hence E [ W G ] < and | n 1 n n Q E [W G ] = 0 by Proposition 4, let z denote the corresponding random variable of Lemma 7. Q (cid:48) n (cid:81) (cid:48) If n = 0, we deﬁne Q by dQ /dQ = z, and the l∈em{ma· ·i·s pr−ove}n. If n > 0, we proceed iteratively. Consider t 0, , n 1 and assume that we have random · · · (cid:81) | (cid:101)∞ variables z , , z such that, in particular, E [Y n z F ] < . We now obtain a t+1 n Q i=t+1 (cid:81)i t random variable z by again applying Lemma 7, with ε replaced by ε and with G = F − , t t 1 H = F , W = ∆S , and Y replaced by Y n z . t t · · · i=t+1 i (cid:48) With the family (z0,(cid:48) , zn) now given, let us deﬁne Z(n) = ni=0 zi and Q by dQ(cid:48)/dQ = Z(n). To argue that S is a Q –local martingale, we may consider any sequence of stopping times that (cid:101) localizes S. Since all other assertions follow directly from the construction of Z(n) and the (cid:3) choice of ε, the lemma is proven. Proof of Theorem 1. We inductively construct a sequence (Q(n)) ∈N of probability measures, (cid:81) n 0 (cid:81) − equivalent to P, and a sequence (ε(n)) ∈N of positive reals using Lemma 8. To start, set Q( 1) = ∈ N n 0 − P. Now, ﬁx n for the moment and suppose that we have Q(n 1) and (ε(m)) ≤ such that − 0 0 m<n n 1 (1 + ε(m)) < 1 + ε. Choose ε(n) to be suﬃciently small such that n (1 + ε(m)) < 1 + ε, m=0 ∈ − ≤ (cid:81) − m=0 and for any A F with Q(n 1)[A] ε(n) we have P[A] < 2 n. Then apply Lemma 8 with ε − | | replaced by ε(n), and with Q = Q(n 1) and Y = e Sn to obtain a probability measure Q(n) with − density Z(n), tha(cid:104)t is dQ(n) = Z(n)(cid:105)dQ(n 1) = ( n Z(m(cid:104) ))dP. (cid:105) m=0 Due to the fact | − | (cid:80)≤ − − | − | ≤ P 1 Z(n) > ε(n) 2 n as Q(n 1) 1 Z(n) > ε(n) ε(n), (cid:81) | − | ∞ the Borel-Cantelli lemma yields ∈N 1 Z(n) < ; hence the inﬁnite product Z∞ = ∞ n 0 (cid:81) ≤ Z(n) converges and is positive P–almost surely. It is clear that Z∞ 1 + ε. n=0 We deﬁne the probab|il(cid:104)ity mea(cid:105)sure Q(cid:104)∈byNd(cid:105)Q/dP = Z∞ and(cid:104)deno(cid:105)te the correspon≤ding density process by Z = E [Z∞ F ], for each t . As Z(m) < 1 + ε we have Q (1 + ε)Q(t) t P t 0 m>t and as a result | | | | ≤ | | ∞ E Z e St = E e St (1 + ε)E e St < P t Q Q(t) | | ∞ ∈ N by the choice of Q(t); hence E [Z S p] < for all t, p . P t t 0 It remains to argue that ZS is a P–martingale or, equivalently, that S is a Q–martingale. | | ∞ ∈ N ∈ N Since we already have established E [ S ] < for all t , it suﬃces to ﬁx t and to prove | Q t 0 ∈ N that E [S F − ] = S − . To this end, recall that S(cid:34)is a Q(n)–loc(cid:12)al mar(cid:35)tingale for each n Q t t 1 t 1 (cid:89) (cid:12) 0 by Lemma 8(iii) and note that dominated convergence, Bayes for(cid:12)mula, and Proposition 4 yield (cid:12) (cid:12) n | | (cid:12) (cid:34) (cid:12) (cid:35) EQ[St Ft−1]Zt−1 = EP[StZ∞ Ft−1] = li↑m∞ EP(cid:12)(cid:12) St Z(m) Ft−1 (cid:89) (cid:12)(cid:12) n (cid:12) m=0 (cid:12) (cid:12) (cid:12) | dQ(n) n = lim E [S F − ] = S − lim E Z(m) F − n↑∞ Q(n) t t 1 dP t 1 n↑∞ P t 1 F − m=0 t 1 = S − Z − . t 1 t 1 (cid:3) This completes the proof. Appendix A In this appendix, we provide some measurability results necessary for the proof of Lemma 6. ⊂ Lemma 9. Let G be a sigma algebra with G F and let ξ be a random element in C(K), where | | ∞ | (K, m) is a compact metric space. Suppose that E [sup ∈ ξ(u) ] < and let η(u) = E [ξ(u) G ] ∈ P u K P for all u K. Then (η(u)) ∈ has a continuous modiﬁcation. u K ##LTLine##

text: VILMOS

text: PROKAJ

text: AND

text: JOHANNES

text: RUF

text: With

text: ε

text: replaced

text: by

text: ε

text: and

text: with

text: G

text: F

text: H

text: F

text: and

text: W

text: ∆S

text: hence

text: E

text: W

text: G

text: and

text: n

text: n

text: n

text: Q

text: E

text: [W

text: G

text: by

text: Proposition

text: let

text: z

text: denote

text: the

text: corresponding

text: random

text: variable

text: of

text: Lemma

text: Q

text: n

text: If

text: n

text: we

text: deﬁne

text: Q

text: by

text: dQ

text: /dQ

text: z,

text: and

text: the

text: l∈em{ma·

text: ·i·s

text: pr−ove}n.

text: If

text: n

text: we

text: proceed

text: iteratively.

text: Consider

text: t

text: n

text: and

text: assume

text: that

text: we

text: have

text: random

text: variables

text: z

text: z

text: such

text: that,

text: in

text: particular,

text: E

text: [Y

text: n

text: z

text: F

text: We

text: now

text: obtain

text: a

text: n

text: Q

text: t

text: random

text: variable

text: z

text: by

text: again

text: applying

text: Lemma

text: with

text: ε

text: replaced

text: by

text: ε

text: and

text: with

text: G

text: F

text: t

text: t

text: H

text: F

text: W

text: ∆S

text: and

text: Y

text: replaced

text: by

text: Y

text: n

text: z

text: t

text: t

text: i

text: With

text: the

text: family

text: zn)

text: now

text: given,

text: let

text: us

text: deﬁne

text: Z(n)

text: zi

text: and

text: Q

text: by

text: Z(n).

text: To

text: argue

text: that

text: S

text: is

text: a

text: Q

text: –local

text: martingale,

text: we

text: may

text: consider

text: any

text: sequence

text: of

text: stopping

text: times

text: that

text: localizes

text: S.

text: Since

text: all

text: other

text: assertions

text: follow

text: directly

text: from

text: the

text: construction

text: of

text: Z(n)

text: and

text: the

text: choice

text: of

text: ε,

text: the

text: lemma

text: is

text: proven.

text: Proof

text: of

text: Theorem

text: We

text: inductively

text: construct

text: a

text: sequence

text: (Q(n))

text: ∈N

text: of

text: probability

text: measures,

text: n

text: equivalent

text: to

text: P,

text: and

text: a

text: sequence

text: (ε(n))

text: ∈N

text: of

text: positive

text: reals

text: using

text: Lemma

text: To

text: start,

text: set

text: Q(

text: N

text: n

text: P.

text: Now,

text: ﬁx

text: n

text: for

text: the

text: moment

text: and

text: suppose

text: that

text: we

text: have

text: Q(n

text: and

text: (ε(m))

text: such

text: that

text: m<n

text: n

text: ε(m))

text: ε.

text: Choose

text: ε(n)

text: to

text: be

text: suﬃciently

text: small

text: such

text: that

text: n

text: ε(m))

text: ε,

text: and

text: for

text: any

text: A

text: F

text: with

text: Q(n

text: ε(n)

text: we

text: have

text: P[A]

text: n.

text: Then

text: apply

text: Lemma

text: with

text: ε

text: replaced

text: by

text: ε(n),

text: and

text: with

text: Q

text: Q(n

text: and

text: Y

text: e

text: Sn

text: to

text: obtain

text: a

text: probability

text: measure

text: Q(n)

text: with

text: density

text: Z(n),

text: is

text: dQ(n)

text: n

text: ))dP.

text: Due

text: to

text: the

text: fact

text: P

text: Z(n)

text: ε(n)

text: n

text: as

text: Q(n

text: Z(n)

text: ε(n)

text: ε(n),

text: the

text: Borel-Cantelli

text: lemma

text: yields

text: ∈N

text: Z(n)

text: hence

text: the

text: inﬁnite

text: product

text: Z∞

text: n

text: Z(n)

text: converges

text: and

text: is

text: positive

text: P–almost

text: surely.

text: It

text: is

text: clear

text: that

text: Z∞

text: ε.

text: We

text: deﬁne

text: the

text: Z∞

text: the

text: correspon≤ding

text: density

text: process

text: by

text: Z

text: E

text: [Z∞

text: F

text: for

text: each

text: t

text: As

text: Z(m)

text: ε

text: we

text: have

text: Q

text: ε)Q(t)

text: t

text: P

text: t

text: m>t

text: and

text: as

text: a

text: result

text: E

text: Z

text: e

text: St

text: E

text: e

text: St

text: ε)E

text: e

text: St

text: P

text: t

text: Q

text: Q(t)

text: N

text: by

text: the

text: choice

text: of

text: Q(t);

text: hence

text: E

text: [Z

text: S

text: p]

text: for

text: all

text: t,

text: p

text: P

text: t

text: t

text: It

text: remains

text: to

text: argue

text: that

text: ZS

text: is

text: a

text: P–martingale

text: or,

text: equivalently,

text: that

text: S

text: is

text: a

text: Q–martingale.

text: N

text: N

text: Since

text: we

text: already

text: have

text: established

text: E

text: S

text: for

text: all

text: t

text: it

text: suﬃces

text: to

text: ﬁx

text: t

text: and

text: to

text: prove

text: Q

text: t

text: N

text: that

text: E

text: [S

text: F

text: S

text: To

text: this

text: end,

text: recall

text: that

text: a

text: for

text: each

text: n

text: Q

text: t

text: t

text: t

text: by

text: Lemma

text: and

text: note

text: that

text: dominated

text: convergence,

text: Bayes

text: and

text: Proposition

text: yield

text: n

text: EQ[St

text: EP[StZ∞

text: li↑m∞

text: St

text: Z(m)

text: n

text: dQ(n)

text: n

text: lim

text: E

text: [S

text: F

text: S

text: lim

text: E

text: Z(m)

text: F

text: n↑∞

text: Q(n)

text: t

text: t

text: dP

text: t

text: n↑∞

text: P

text: t

text: F

text: t

text: S

text: Z

text: t

text: t

text: This

text: completes

text: the

text: proof.

text: Appendix

text: A

text: In

text: this

text: appendix,

text: we

text: provide

text: some

text: measurability

text: results

text: necessary

text: for

text: the

text: proof

text: of

text: Lemma

text: Lemma

text: Let

text: G

text: be

text: a

text: sigma

text: algebra

text: with

text: G

text: F

text: and

text: let

text: ξ

text: be

text: a

text: random

text: element

text: in

text: C(K),

text: where

text: (K,

text: m)

text: is

text: a

text: compact

text: metric

text: space.

text: Suppose

text: that

text: E

text: [sup

text: ξ(u)

text: and

text: let

text: η(u)

text: E

text: [ξ(u)

text: G

text: P

text: u

text: K

text: P

text: for

text: all

text: u

text: K.

text: Then

text: (η(u))

text: has

text: a

text: continuous

text: modiﬁcation.

text: u

text: K

text: ##LTLine##


text: Neural Models for Sequence Chunking Feifei Zhai, Saloni Potdar, Bing Xiang, Bowen Zhou IBM Watson 1101 Kitchawan Road, Yorktown Heights, NY 10598 { } fzhai,potdars,bingxia,zhou @us.ibm.com Abstract O B-NP B-VP I-VP B-ADJP I-ADJP Many natural language understanding (NLU) tasks, such as shallow parsing (i.e., text chunking) and semantic slot ﬁll- But it could be much worse ing, require the assignment of representative labels to the meaningful chunks in a sentence. Most of the current deep neural network (DNN) based methods consider these tasks Figure 1: An example of text chunking where each word is as a sequence labeling problem, in which a word, rather labeled using the IOB scheme. The chunk “could be” is a than a chunk, is treated as the basic unit for labeling. These verb phrase (VP) and “it” is a single-word chunk with NP chunks are then inferred by the standard IOB (Inside-Outside- label. Beginning) labels. In this paper, we propose an alternative ap- proach by investigating the use of DNN for sequence chunk- ing, and propose three neural models so that each chunk can be treated as a complete unit for labeling. Experimental re- Most of the current DNN based approaches use the IOB sults show that the proposed neural sequence chunking mod- scheme to label chunks. However, this approach of these els can achieve start-of-the-art performance on both the text labels has a few drawbacks. First, we don’t have an ex- chunking and slot ﬁlling tasks. plicit model to learn and identify the scope of chunks in a sentence, instead we infer them implicitly (by IOB labels). Hence the learned model might not be able to fully utilize Introduction the training data which could result in poor performance. Semantic slot ﬁlling and shallow parsing which are stan- Second, some neural networks like RNN or LSTM have the dard NLU tasks fall under the umbrella of natural language ability to encode context information but don’t treat each understanding (NLU), which are usually solved by label- chunk as a complete unit. If we can eliminate this draw- ing meaningful chunks in a sentence. This kind of task is back, it could result in more accurate labeling, especially usually treated as a sequence labeling problem, where ev- for multi-word chunks. ery word in a sentence is assigned an IOB-based (Inside- Sequence chunking is a natural solution to overcome the Outside-Beginning) label. For example, in Figure 1, in the two drawbacks mentioned before. In sequence chunking, the sentence “But it could be much worse” we label “could” as original sequence labeling task is divided into two sub-tasks: B-VP, “be” as I-VP, and “it” as B-NP, while “But” belongs (1) Segmentation, to identify scope of the chunks explicitly; to an artiﬁcial class O. This labeling indicates that a chunk (2) Labeling, to label each chunk as a single unit based on “could be” is a verb phrase (VP) where the label preﬁx B the segmentation results. means the beginning word of the chunk, while I refers to the Lample et al. (2016) used a stack-LSTM (Dyer et al. other words within the same semantic chunk; and “it” is a 2015) and a transition-based algorithm for sequence chunk- single-word chunk with NP label. ing. In their paper, the segmentation step is based on shift- Such sequence labeling forms the basis for many recent reduce parser based actions. In this paper, we propose an deep network based approaches, e.g., convolutional neural alternative approach by relying only on the neural architec- networks (CNN), recurrent neural networks (RNN) or its tures for NLU. We investigate two different ways for seg- variation, long short-term memory networks (LSTM). RNN mentation: (1) using IOB labels; and (2) using pointer net- and LSTM are good at capturing sequential information works (Vinyals, Fortunato, and Jaitly 2015) and propose (Yao et al. 2013; Huang, Xu, and Yu 2015; Mesnil et al. three neural sequence chunking models. Pointer network 2015; Peng and Yao 2015; Yang, Salakhutdinov, and Co- performs better than the model using IOB. In addition, it also hen 2016; Kurata et al. 2016; Zhu and Yu 2016), whereas achieves state-of-the-art performance on both text chunking CNN can extract effective features for classiﬁcation (Xu and and slot ﬁlling tasks. Sarikaya 2013; Vu 2016). Basic Neural Networks (cid:13) Copyright c 2017, Association for the Advancement of Artiﬁcial Recurrent Neural Network Intelligence (www.aaai.org). All rights reserved. ##LTFigure## ##LTLine##

text: Neural

label: title

text: Models

text: for

text: Sequence

text: Chunking

text: Feifei

label: author

text: Zhai,

text: Saloni

text: Potdar,

text: Bing

text: Xiang,

text: Bowen

text: Zhou

text: IBM

text: Watson

text: Kitchawan

text: Road,

text: Yorktown

text: Heights,

text: NY

text: fzhai,potdars,bingxia,zhou

text: @us.ibm.com

text: Abstract

text: O

font: default

text: B-NP

text: B-VP

text: I-VP

text: B-ADJP

text: I-ADJP

text: Many

label: abstract

text: natural

text: language

text: understanding

text: (NLU)

text: tasks,

text: such

text: as

text: shallow

text: parsing

text: (i.e.,

text: text

text: chunking)

text: and

text: semantic

text: slot

text: ﬁll-

text: But

text: it

text: could

text: be

text: much

text: worse

text: ing,

text: require

text: the

text: assignment

text: of

text: representative

text: labels

text: to

text: the

text: meaningful

text: chunks

text: in

text: a

text: sentence.

text: Most

text: of

text: the

text: current

text: deep

text: neural

text: network

text: (DNN)

text: based

text: methods

text: consider

text: these

text: tasks

text: Figure

text: An

text: example

text: of

text: text

text: chunking

text: where

text: each

text: word

text: is

text: as

text: a

text: sequence

text: labeling

text: problem,

text: in

text: which

text: a

text: word,

text: rather

text: labeled

text: using

text: the

text: IOB

text: scheme.

text: The

text: chunk

text: “could

text: be”

text: is

text: a

text: than

text: a

text: chunk,

text: is

text: treated

text: as

text: the

text: basic

text: unit

text: for

text: labeling.

text: These

text: verb

text: phrase

text: (VP)

text: and

text: “it”

text: is

text: a

text: single-word

text: chunk

text: with

text: NP

text: chunks

text: are

text: then

text: inferred

text: by

text: the

text: standard

text: IOB

text: (Inside-Outside-

text: label.

text: Beginning)

text: labels.

text: In

text: this

text: paper,

text: we

text: propose

text: an

text: alternative

text: ap-

text: proach

text: by

text: investigating

text: the

text: use

text: of

text: DNN

text: for

text: sequence

text: chunk-

text: ing,

text: and

text: propose

text: three

text: neural

text: models

text: so

text: that

text: each

text: chunk

text: can

text: be

text: treated

text: as

text: a

text: complete

text: unit

text: for

text: labeling.

text: Experimental

text: re-

text: Most

text: of

text: the

text: current

text: DNN

text: based

text: approaches

text: use

text: the

text: IOB

text: sults

text: show

text: that

text: the

text: proposed

text: neural

text: sequence

text: chunking

text: mod-

text: scheme

text: to

text: label

text: chunks.

text: However,

text: this

text: approach

text: of

text: these

text: els

text: can

text: achieve

text: start-of-the-art

text: performance

text: on

text: both

text: the

text: text

text: labels

text: has

text: a

text: few

text: drawbacks.

text: First,

text: we

text: don’t

text: have

text: an

text: ex-

text: chunking

text: and

text: slot

text: ﬁlling

text: tasks.

text: plicit

text: model

text: to

text: learn

text: and

text: identify

text: the

text: scope

text: of

text: chunks

text: in

text: a

text: sentence,

text: instead

text: we

text: infer

text: them

text: implicitly

text: (by

text: IOB

text: labels).

text: Hence

text: the

text: learned

text: model

text: might

text: not

text: be

text: able

text: to

text: fully

text: utilize

text: Introduction

text: the

text: training

text: data

text: which

text: could

text: result

text: in

text: poor

text: performance.

text: Semantic

text: slot

text: ﬁlling

text: and

text: shallow

text: parsing

text: which

text: are

text: stan-

text: Second,

text: some

text: neural

text: networks

text: like

text: RNN

text: or

text: LSTM

text: have

text: the

text: dard

text: NLU

text: tasks

text: fall

text: under

text: the

text: umbrella

text: of

text: natural

text: language

text: ability

text: to

text: encode

text: context

text: information

text: but

text: don’t

text: treat

text: each

text: understanding

text: (NLU),

text: which

text: are

text: usually

text: solved

text: by

text: label-

text: chunk

text: as

text: a

text: complete

text: unit.

text: If

text: we

text: can

text: eliminate

text: this

text: draw-

text: ing

text: meaningful

text: chunks

text: in

text: a

text: sentence.

text: This

text: kind

text: of

text: task

text: is

text: back,

text: it

text: could

text: result

text: in

text: more

text: accurate

text: labeling,

text: especially

text: usually

text: treated

text: as

text: a

text: sequence

text: labeling

text: problem,

text: where

text: ev-

text: for

text: multi-word

text: chunks.

text: ery

text: word

text: in

text: a

text: sentence

text: is

text: assigned

text: an

text: IOB-based

text: (Inside-

text: Sequence

text: chunking

text: is

text: a

text: natural

text: solution

text: to

text: overcome

text: the

text: Outside-Beginning)

text: label.

text: For

text: example,

text: in

text: Figure

text: in

text: the

text: two

text: drawbacks

text: mentioned

text: before.

text: In

text: sequence

text: chunking,

text: the

text: sentence

text: “But

text: it

text: could

text: be

text: much

text: worse”

text: we

text: label

text: “could”

text: as

text: original

text: sequence

text: labeling

text: task

text: is

text: divided

text: into

text: two

text: sub-tasks:

text: B-VP,

text: “be”

text: as

text: I-VP,

text: and

text: “it”

text: as

text: B-NP,

text: while

text: “But”

text: belongs

text: Segmentation,

text: to

text: identify

text: scope

text: of

text: the

text: chunks

text: explicitly;

text: to

text: an

text: artiﬁcial

text: class

text: O.

text: This

text: labeling

text: indicates

text: that

text: a

text: chunk

text: Labeling,

text: to

text: label

text: each

text: chunk

text: as

text: a

text: single

text: unit

text: based

text: on

text: “could

text: be”

text: is

text: a

text: verb

text: phrase

text: (VP)

text: where

text: the

text: label

text: preﬁx

text: B

text: the

text: segmentation

text: results.

text: means

text: the

text: beginning

text: word

text: of

text: the

text: chunk,

text: while

text: I

text: refers

text: to

text: the

text: Lample

text: et

text: al.

text: used

text: a

text: stack-LSTM

text: (Dyer

text: et

text: al.

text: other

text: words

text: within

text: the

text: same

text: semantic

text: chunk;

text: and

text: “it”

text: is

text: a

text: and

text: a

text: transition-based

text: algorithm

text: for

text: sequence

text: chunk-

text: single-word

text: chunk

text: with

text: NP

text: label.

text: ing.

text: In

text: their

text: paper,

text: the

text: segmentation

text: step

text: is

text: based

text: on

text: shift-

text: Such

text: sequence

text: labeling

text: forms

text: the

text: basis

text: for

text: many

text: recent

text: reduce

text: parser

text: based

text: actions.

text: In

text: this

text: paper,

text: we

text: propose

text: an

text: deep

text: network

text: based

text: approaches,

text: e.g.,

text: convolutional

text: neural

text: alternative

text: approach

text: by

text: relying

text: only

text: on

text: the

text: neural

text: architec-

text: networks

text: (CNN),

text: recurrent

text: neural

text: networks

text: (RNN)

text: or

text: its

text: tures

text: for

text: NLU.

text: We

text: investigate

text: two

text: different

text: ways

text: for

text: seg-

text: variation,

text: long

text: short-term

text: memory

text: networks

text: (LSTM).

text: RNN

text: mentation:

text: using

text: IOB

text: labels;

text: and

text: using

text: pointer

text: net-

text: and

text: LSTM

text: are

text: good

text: at

text: capturing

text: sequential

text: information

text: works

text: (Vinyals,

text: Fortunato,

text: and

text: Jaitly

text: and

text: propose

text: (Yao

text: et

text: al.

text: Huang,

text: Xu,

text: and

text: Yu

text: Mesnil

text: et

text: al.

text: three

text: neural

text: sequence

text: chunking

text: models.

text: Pointer

text: network

text: Peng

text: and

text: Yao

text: Yang,

text: Salakhutdinov,

text: and

text: Co-

text: performs

text: better

text: than

text: the

text: model

text: using

text: IOB.

text: In

text: addition,

text: it

text: also

text: hen

text: Kurata

text: et

text: al.

text: Zhu

text: and

text: Yu

text: whereas

text: achieves

text: state-of-the-art

text: performance

text: on

text: both

text: text

text: chunking

text: CNN

text: can

text: extract

text: effective

text: features

text: for

text: classiﬁcation

text: (Xu

text: and

text: and

text: slot

text: ﬁlling

text: tasks.

text: Sarikaya

text: Vu

text: Basic

text: Neural

text: Networks

text: Copyright

text: c

text: Association

text: for

text: the

text: Advancement

text: of

text: Artiﬁcial

text: Recurrent

text: Neural

text: Network

text: Intelligence

text: (www.aaai.org).

text: All

text: rights

text: reserved.

text: ##LTFigure##

text: ##LTLine##


text: Recurrent neural network (RNN) is a neural network NP VP ADJP that is suitable for modeling sequential information. Al- though theoretically it is able to capture long-distance de- O B B I B I pendencies, in practice it suffers from the gradient van- But it could be much worse ishing/exploding problems (Bengio, Simard, and Frasconi 1994). Long short-term memory networks (LSTM) were introduced to cope with these gradient problems and Figure 2: Model I: Single Bi-LSTM model for both segmen- model long-range dependencies (Hochreiter and Schmidhu- tation and labeling subtasks. ber 1997) by using a memory cell. Given an input sentence x = (x , x , ..., x ) where T is the sentence length, LSTM 1 2 T hidden state at timestep t is computed by: Model I For segmentation, the most straightforward and intuitive i = σ(Wix + Uih − + bi) t t t 1 way is to transform it into a sequence labeling problem with f = σ(Wfx + Ufh − + bf) 3 classes : I - inside, O - outside, B - beginning; and then un- t t t 1 o = σ(Wox + Uoh − + bo) derstand the scope of the chunks from these labels. Building t t t 1 (1) on this, we propose Model I, which is a Bi-LSTM as shown g = tanh(Wgx + Ugh − + bg) t (cid:12) t (cid:12) t 1 in Figure 2. In the model, we take the bi-LSTM hidden states ct = ft (cid:12) ct−1 + it gt generated by Formula (2) as features for both segmentation h = o tanh(c ) and labeling. t t t · · For example, we ﬁrst classify each word into an IOB label where σ( ) and tanh( ) are t(cid:12)he element-wise sigmoid and as shown in (Figure 2). Suppose a chunk begins at word i hyperbolic tangent functions, is the element-wise multi- − with length l (with one B label and followed by (l 1) I plication operator, and it,ft,ot are the input, forget and out- labels), then we can compute a feature vector for a chunk as put gates. ht−1 and ct−1 are the hidden state and memory follows: cell of previous timestep respectively. To simplify the nota- ←→ ←−→ ←−−→ tion, we use xt to denote both the word and its embedding. Ch = Average( h , h , ..., h − ) (3) The bi-directional LSTM (Bi-LSTM), a modiﬁcation of j i i+1 i+l 1 the LSTM, consists of a forward and a backward LSTM. The forward LSTM reads the input sentence as it−→is (−→from x−→to where ·j is the chunk index of the sentence, and 1 Average( ) computes the average of the input vectors. With x ) and computes the forward hidden states (h , h , ..., h ), T 1 2 T Ch , we apply a softmax layer over all chunk labels for la- while the backward LSTM reads the sentence in the reverse j beling. For example in Figure 2, “much worse” is identiﬁed o←r−der←−(from←−x to x ), and creates backward hidden states T 1 as a chunk with length 2; and we apply Formula (3) on its (h , h , ..., h ). Then for each timestep t, the →−hidden←−state hidden states, to ﬁnally get the “ADJP” label. 1 1 T of the Bi-LSTM is generated by concatenating h and h , Model II t t ←→ →− ←− A drawback of Model I is that a single Bi-LSTM may not ht = [ht; ht] (2) perform well on both segmentation and labeling subtasks. To overcome this we propose Model II, which follows the Convolutional Neural Network encoder-decoder framework ( Figure 3) (Sutskever, Vinyals, Convolutional Neural Networks (CNN) have been used to and Le 2014; Bahdanau, Cho, and Bengio 2014). Similar to extract features for sentence classiﬁcation (Kim 2014; Ma Model I, we employ a Bi-LSTM for segmentation with IOB et al. 2015; dos Santos, Xiang, and Zhou 2015). Given a labels1. This Bi-LSTM will also−→serv←−e as an encoder and sentence, a CNN with m ﬁlters and a ﬁlter size of n extracts create a sentence representation [h ; h ] (by concatenating T 1 a m-dimension feature vector from every n-gram phrase of the ﬁnal hidden state of the forward and backward LSTM) the sentence. A max-over-time pooling (max-pooling) layer which is used to initialize the decoder LSTM. is applied over all extracted feature vectors to create the ﬁnal We modify the general encoder-decoder framework and indicative feature vector (m-dimension) for the sentence. use chunks as the inputs instead of words. For example, Following this approach, we use CNN and max-pooling much worse is a chunk in Figure 3, and we take it as a sin- layer to extract features from chunks. For each identiﬁed gle input to the decoder. The input chunk representation C j chunk, we ﬁrst apply CNN to the embedding of its words consists of several parts. We ﬁrst use the CNNMax layer to (irrespective of it being a single-word chunk or chunk), and extract important information from words inside the chunk: then use the max-pooling layer on top to get the chunk fea- ture vector for labeling. We use CNNMax to denote the two Cx = g(x , x , ..., x − ) (4) j i i+1 i+l 1 layers hereafter. Proposed Models 1Note that in Model I and II, we cannot guarantee that label “O” In this section, we introduce the different neural models is not followed by “I” during segmentation. If so, we just take the for sequence chunking and discuss the ﬁnal learning objec- ﬁrst “I” as “B”. In future work it is advisable to add that as a hard tive. constraint.  : < 8 : < 8 ##LTFigure## ##LTLine##

text: Recurrent

text: neural

text: network

text: (RNN)

text: is

text: a

text: neural

text: network

text: NP

text: VP

text: ADJP

text: that

text: is

text: suitable

text: for

text: modeling

text: sequential

text: information.

text: Al-

text: though

text: theoretically

text: it

text: is

text: able

text: to

text: capture

text: long-distance

text: de-

text: O

text: B

text: B

text: I

text: B

text: I

text: pendencies,

text: in

text: practice

text: it

text: suffers

text: from

text: the

text: gradient

text: van-

text: But

text: it

text: could

text: be

text: much

text: worse

text: ishing/exploding

text: problems

text: (Bengio,

text: Simard,

text: and

text: Frasconi

text: Long

text: short-term

text: memory

text: networks

text: (LSTM)

text: were

text: introduced

text: to

text: cope

text: with

text: these

text: gradient

text: problems

text: and

text: Figure

text: Model

text: I:

text: Single

text: Bi-LSTM

text: model

text: for

text: both

text: segmen-

text: model

text: long-range

text: dependencies

text: (Hochreiter

text: and

text: Schmidhu-

text: tation

text: and

text: labeling

text: subtasks.

text: ber

text: by

text: using

text: a

text: memory

text: cell.

text: Given

text: an

text: input

text: sentence

text: x

text: (x

text: x

text: x

text: where

text: T

text: is

text: the

text: sentence

text: length,

text: LSTM

text: T

text: hidden

text: state

text: at

text: timestep

text: t

text: is

text: computed

text: by:

text: Model

text: I

text: For

text: segmentation,

text: the

text: most

text: straightforward

text: and

text: intuitive

text: i

text: σ(Wix

text: Uih

text: bi)

text: t

text: t

text: t

text: way

text: is

text: to

text: transform

text: it

text: into

text: a

text: sequence

text: labeling

text: problem

text: with

text: f

text: σ(Wfx

text: Ufh

text: bf)

text: classes

text: I

text: inside,

text: O

text: outside,

text: B

text: beginning;

text: and

text: then

text: un-

text: t

text: t

text: t

text: o

text: σ(Wox

text: Uoh

text: bo)

text: derstand

text: the

text: scope

text: of

text: the

text: chunks

text: from

text: these

text: labels.

text: Building

text: t

text: t

text: t

text: on

text: this,

text: we

text: propose

text: Model

text: I,

text: which

text: is

text: a

text: Bi-LSTM

text: as

text: shown

text: g

text: tanh(Wgx

text: Ugh

text: bg)

text: t

text: t

text: t

text: in

text: Figure

text: In

text: the

text: model,

text: we

text: take

text: the

text: bi-LSTM

text: hidden

text: states

text: ct

text: ft

text: it

text: gt

text: generated

text: by

text: Formula

text: as

text: features

text: for

text: both

text: segmentation

text: h

text: o

text: tanh(c

text: and

text: labeling.

text: t

text: t

text: t

text: For

text: example,

text: we

text: ﬁrst

text: classify

text: each

text: word

text: into

text: an

text: IOB

text: label

text: where

text: σ(

text: and

text: tanh(

text: are

text: element-wise

text: sigmoid

text: and

text: as

text: shown

text: in

text: (Figure

text: Suppose

text: a

text: chunk

text: begins

text: at

text: word

text: i

text: hyperbolic

text: tangent

text: functions,

text: is

text: the

text: element-wise

text: multi-

text: with

text: length

text: l

text: (with

text: one

text: B

text: label

text: and

text: followed

text: by

text: (l

text: I

text: plication

text: operator,

text: and

text: it,ft,ot

text: are

text: the

text: input,

text: forget

text: and

text: out-

text: labels),

text: then

text: we

text: can

text: compute

text: a

text: feature

text: vector

text: for

text: a

text: chunk

text: as

text: put

text: gates.

text: and

text: are

text: the

text: hidden

text: state

text: and

text: memory

text: follows:

text: cell

text: of

text: previous

text: timestep

text: respectively.

text: To

text: simplify

text: the

text: nota-

text: tion,

text: we

text: use

text: xt

text: to

text: denote

text: both

text: the

text: word

text: and

text: its

text: embedding.

text: Ch

text: Average(

text: h

text: h

text: h

text: The

text: bi-directional

text: LSTM

text: (Bi-LSTM),

text: a

text: modiﬁcation

text: of

text: j

text: i

text: i+l

text: the

text: LSTM,

text: consists

text: of

text: a

text: forward

text: and

text: a

text: backward

text: LSTM.

text: The

text: forward

text: LSTM

text: reads

text: the

text: input

text: sentence

text: as

text: it−→is

text: (−→from

text: x−→to

text: where

text: ·j

text: is

text: the

text: chunk

text: index

text: of

text: the

text: sentence,

text: and

text: Average(

text: computes

text: the

text: average

text: of

text: the

text: input

text: vectors.

text: With

text: x

text: and

text: computes

text: the

text: forward

text: hidden

text: states

text: (h

text: h

text: h

text: T

text: T

text: Ch

text: we

text: apply

text: a

text: softmax

text: layer

text: over

text: all

text: chunk

text: labels

text: for

text: la-

text: while

text: the

text: backward

text: LSTM

text: reads

text: the

text: sentence

text: in

text: the

text: reverse

text: j

text: beling.

text: For

text: example

text: in

text: Figure

text: “much

text: worse”

text: is

text: identiﬁed

text: o←r−der←−(from←−x

text: to

text: x

text: and

text: creates

text: backward

text: hidden

text: states

text: T

text: as

text: a

text: chunk

text: with

text: length

text: and

text: we

text: apply

text: Formula

text: on

text: its

text: (h

text: h

text: h

text: Then

text: for

text: each

text: timestep

text: t,

text: the

text: →−hidden←−state

text: hidden

text: states,

text: to

text: ﬁnally

text: get

text: the

text: “ADJP”

text: label.

text: T

text: of

text: the

text: Bi-LSTM

text: is

text: generated

text: by

text: concatenating

text: h

text: and

text: h

text: Model

text: II

text: t

text: t

text: A

text: drawback

text: of

text: Model

text: I

text: is

text: that

text: a

text: single

text: Bi-LSTM

text: may

text: not

text: ht

text: [ht;

text: ht]

text: perform

text: well

text: on

text: both

text: segmentation

text: and

text: labeling

text: subtasks.

text: To

text: overcome

text: this

text: we

text: propose

text: Model

text: II,

text: which

text: follows

text: the

text: Convolutional

text: Neural

text: Network

text: encoder-decoder

text: framework

text: Figure

text: (Sutskever,

text: Vinyals,

text: Convolutional

text: Neural

text: Networks

text: (CNN)

text: have

text: been

text: used

text: to

text: and

text: Le

text: Bahdanau,

text: Cho,

text: and

text: Bengio

text: Similar

text: to

text: extract

text: features

text: for

text: sentence

text: classiﬁcation

text: (Kim

text: Ma

text: Model

text: I,

text: we

text: employ

text: a

text: Bi-LSTM

text: for

text: segmentation

text: with

text: IOB

text: et

text: al.

text: dos

text: Santos,

text: Xiang,

text: and

text: Zhou

text: Given

text: a

text: This

text: Bi-LSTM

text: will

text: also−→serv←−e

text: as

text: an

text: encoder

text: and

text: sentence,

text: a

text: CNN

text: with

text: m

text: ﬁlters

text: and

text: a

text: ﬁlter

text: size

text: of

text: n

text: extracts

text: create

text: a

text: sentence

text: representation

text: [h

text: h

text: (by

text: concatenating

text: T

text: a

text: m-dimension

text: feature

text: vector

text: from

text: every

text: n-gram

text: phrase

text: of

text: the

text: ﬁnal

text: hidden

text: state

text: of

text: the

text: forward

text: and

text: backward

text: LSTM)

text: the

text: sentence.

text: A

text: max-over-time

text: pooling

text: (max-pooling)

text: layer

text: which

text: is

text: used

text: to

text: initialize

text: the

text: decoder

text: LSTM.

text: is

text: applied

text: over

text: all

text: extracted

text: feature

text: vectors

text: to

text: create

text: the

text: ﬁnal

text: We

text: modify

text: the

text: general

text: encoder-decoder

text: framework

text: and

text: indicative

text: feature

text: vector

text: (m-dimension)

text: for

text: the

text: sentence.

text: use

text: chunks

text: as

text: the

text: inputs

text: instead

text: of

text: words.

text: For

text: example,

text: Following

text: this

text: approach,

text: we

text: use

text: CNN

text: and

text: max-pooling

text: much

text: worse

text: is

text: a

text: chunk

text: in

text: Figure

text: and

text: we

text: take

text: it

text: as

text: a

text: sin-

text: layer

text: to

text: extract

text: features

text: from

text: chunks.

text: For

text: each

text: identiﬁed

text: gle

text: input

text: to

text: the

text: decoder.

text: The

text: input

text: chunk

text: representation

text: C

text: j

text: chunk,

text: we

text: ﬁrst

text: apply

text: CNN

text: to

text: the

text: embedding

text: of

text: its

text: words

text: consists

text: of

text: several

text: parts.

text: We

text: ﬁrst

text: use

text: the

text: CNNMax

text: layer

text: to

text: (irrespective

text: of

text: it

text: being

text: a

text: single-word

text: chunk

text: or

text: chunk),

text: and

text: extract

text: important

text: information

text: from

text: words

text: inside

text: the

text: chunk:

text: then

text: use

text: the

text: max-pooling

text: layer

text: on

text: top

text: to

text: get

text: the

text: chunk

text: fea-

text: ture

text: vector

text: for

text: labeling.

text: We

text: use

text: CNNMax

text: to

text: denote

text: the

text: two

text: Cx

text: g(x

text: x

text: x

text: j

text: i

text: i+l

text: layers

text: hereafter.

text: Proposed

text: Models

text: that

text: in

text: Model

text: I

text: and

text: II,

text: we

text: cannot

text: guarantee

text: that

text: label

text: “O”

text: In

text: this

text: section,

text: we

text: introduce

text: the

text: different

text: neural

text: models

text: is

text: not

text: followed

text: by

text: “I”

text: during

text: segmentation.

text: If

text: so,

text: we

text: just

text: take

text: the

text: for

text: sequence

text: chunking

text: and

text: discuss

text: the

text: ﬁnal

text: learning

text: objec-

text: ﬁrst

text: “I”

text: as

text: “B”.

text: In

text: future

text: work

text: it

text: is

text: advisable

text: to

text: add

text: that

text: as

text: a

text: hard

text: tive.

text: constraint.

text: ##LTFigure##

text: ##LTLine##


text: Collobert, R.; Weston, J.; Bottou, L.; Karlen, M.; Ma, M.; Huang, L.; Xiang, B.; and Zhou, B. 2015. Kavukcuoglu, K.; and Kuksa, P. 2011. Natural language pro- Dependency-based convolutional neural networks for sen- cessing (almost) from scratch. Journal of Machine Learning tence embedding. In ACL, volume 2, 174–179. Research 12(Aug):2493–2537. Mesnil, G.; Dauphin, Y.; Yao, K.; Bengio, Y.; Deng, L.; dos Santos, C. N., and Gatti, M. 2014. Deep convolutional Hakkani-Tur, D.; He, X.; Heck, L.; Tur, G.; Yu, D.; et al. neural networks for sentiment analysis of short texts. In 2015. Using recurrent neural networks for slot ﬁlling in spo- COLING, 69–78. ken language understanding. IEEE/ACM Transactions on Audio, Speech, and Language Processing 23(3):530–539. dos Santos, C.; Xiang, B.; and Zhou, B. 2015. Classifying relations by ranking with convolutional neural networks. In Nallapati, R.; Zhou, B.; dos Santos, C.; Gulcehre, C.; and ACL, 626–634. Beijing, China: Association for Computa- Xiang, B. 2016. Abstractive text summarization using tional Linguistics. sequence-to-sequence rnns and beyond. In Proceedings of CoNLL. Durrett, G., and Klein, D. 2015. Neural crf parsing. In Peng, B., and Yao, K. 2015. Recurrent neural networks with Proceedings of ACL 2015, 302–312. external memory for language understanding. arXiv preprint Dyer, C.; Ballesteros, M.; Ling, W.; Matthews, A.; and arXiv:1506.00195. Smith, N. A. 2015. Transition-based dependency parsing Rastogi, P.; Cotterell, R.; and Eisner, J. 2016. Weighting with stack long short-term memory. In Proceedings of ACL ﬁnite-state transductions with neural context. In Proceed- 2015, 334–343. ings of NAACL 2016, 623–633. Hochreiter, S., and Schmidhuber, J. 1997. Long short-term Sha, F., and Pereira, F. 2003. Shallow parsing with con- memory. Neural computation 9(8):1735–1780. ditional random ﬁelds. In Proceedings of the 2003 Confer- Huang, Z.; Xu, W.; and Yu, K. 2015. Bidirectional ence of the North American Chapter of the ACL on Human lstm-crf models for sequence tagging. arXiv preprint Language Technology-Volume 1, 134–141. Association for arXiv:1508.01991. Computational Linguistics. Jaech, A.; Heck, L.; and Ostendorf, M. 2016. Domain adap- Shen, H., and Sarkar, A. 2005. Voting between multiple tation of recurrent neural networks for natural language un- data representations for text chunking. In Conference of the derstanding. arXiv preprint arXiv:1604.00117. Canadian Society for Computational Studies of Intelligence, 389–400. Springer. Kim, Y. 2014. Convolutional neural networks for sentence classiﬁcation. arXiv preprint arXiv:1408.5882. Sutskever, I.; Vinyals, O.; and Le, Q. V. 2014. Sequence to sequence learning with neural networks. In NIPS, 3104– Kudo, T., and Matsumoto, Y. 2001. Chunking with sup- 3112. port vector machines. In Proceedings of NAACL 2001, 1–8. Association for Computational Linguistics. Tjong Kim Sang, E. F., and Buchholz, S. 2000. Introduction to the conll-2000 shared task: Chunking. In Proceedings of Kudoh, T., and Matsumoto, Y. 2000. Use of support vec- the 2nd workshop on Learning language in logic and the 4th tor learning for chunk identiﬁcation. In Proceedings of the conference on Computational natural language learning- 2nd Workshop on Learning Language in Logic and the 4th Volume 7, 127–132. Association for Computational Linguis- Conference on Computational Natural Language Learning tics. - Volume 7, ConLL ’00, 142–144. Vinyals, O.; Fortunato, M.; and Jaitly, N. 2015. Pointer Kurata, G.; Xiang, B.; Zhou, B.; and Yu, M. 2016. Leverag- networks. In NIPS, 2692–2700. ing sentence-level information with encoder lstm for seman- Vu, N. T.; Gupta, P.; Adel, H.; Sch, H.; et al. 2016. Bi- tic slot ﬁlling. arXiv preprint arXiv:1601.01530. directional recurrent neural network with ranking loss for Lample, G.; Ballesteros, M.; Kawakami, K.; Subramanian, spoken language understanding. In ICASSP, 6060–6064. S.; and Dyer, C. 2016. Neural architectures for named entity IEEE. recognition. In In proceedings of NAACL 2016. Vu, N. T. 2016. Sequential convolutional neural networks Liu, B., and Lane, I. 2015. Recurrent neural network struc- for slot ﬁlling in spoken language understanding. arXiv tured output prediction for spoken language understanding. preprint arXiv:1606.07783. In Proc. NIPS Workshop on Machine Learning for Spoken Xu, P., and Sarikaya, R. 2013. Convolutional neural network Language Understanding and Interactions. based triangular crf for joint intent detection and slot ﬁlling. Liu, J.; Pasupat, P.; Cyphers, S.; and Glass, J. 2013a. Asgard: In Proceedings of ASRU 2013, 78–83. IEEE. A portable architecture for multilingual dialogue systems. In Yang, Z.; Salakhutdinov, R.; and Cohen, W. 2016. Multi- ICASSP. IEEE. task cross-lingual sequence tagging from scratch. arXiv Liu, J.; Pasupat, P.; Wang, Y.; Cyphers, S.; and Glass, J. preprint arXiv:1603.06270. 2013b. Query understanding enhanced by hierarchical pars- Yao, K.; Zweig, G.; Hwang, M.-Y.; Shi, Y.; and Yu, D. 2013. ing structures. In ASRU, 72–77. IEEE. Recurrent neural networks for language understanding. In Ma, X., and Hovy, E. 2016. End-to-end sequence la- INTERSPEECH, 2524–2528. beling via bi-directional lstm-cnns-crf. arXiv preprint Yao, K.; Peng, B.; Zhang, Y.; Yu, D.; Zweig, G.; and Shi, Y. arXiv:1603.01354. 2014. Spoken language understanding using long short-term

text: Collobert,

label: reference

text: R.;

text: Weston,

text: J.;

text: Bottou,

text: L.;

text: Karlen,

text: M.;

text: Ma,

text: M.;

text: Huang,

text: L.;

text: Xiang,

text: B.;

text: and

text: Zhou,

text: B.

text: Kavukcuoglu,

text: K.;

text: and

text: Kuksa,

text: P.

text: Natural

text: language

text: pro-

text: Dependency-based

text: convolutional

text: neural

text: networks

text: for

text: sen-

text: cessing

text: (almost)

text: from

text: scratch.

text: Journal

text: of

text: Machine

text: Learning

text: tence

text: embedding.

text: In

text: ACL,

text: volume

text: Research

text: Mesnil,

text: G.;

text: Dauphin,

text: Y.;

text: Yao,

text: K.;

text: Bengio,

text: Y.;

text: Deng,

text: L.;

text: dos

text: Santos,

text: C.

text: N.,

text: and

text: Gatti,

text: M.

text: Deep

text: convolutional

text: Hakkani-Tur,

text: D.;

text: He,

text: X.;

text: Heck,

text: L.;

text: Tur,

text: G.;

text: Yu,

text: D.;

text: et

text: al.

text: neural

text: networks

text: for

text: sentiment

text: analysis

text: of

text: short

text: texts.

text: In

text: Using

text: recurrent

text: neural

text: networks

text: for

text: slot

text: ﬁlling

text: in

text: spo-

text: COLING,

text: ken

text: language

text: understanding.

text: IEEE/ACM

text: Transactions

text: on

text: Audio,

text: Speech,

text: and

text: Language

text: Processing

text: dos

text: Santos,

text: C.;

text: Xiang,

text: B.;

text: and

text: Zhou,

text: B.

text: Classifying

text: relations

text: by

text: ranking

text: with

text: convolutional

text: neural

text: networks.

text: In

text: Nallapati,

text: R.;

text: Zhou,

text: B.;

text: dos

text: Santos,

text: C.;

text: Gulcehre,

text: C.;

text: and

text: ACL,

text: Beijing,

text: China:

text: Association

text: for

text: Computa-

text: Xiang,

text: B.

text: Abstractive

text: text

text: summarization

text: using

text: tional

text: Linguistics.

text: sequence-to-sequence

text: rnns

text: and

text: beyond.

text: In

text: Proceedings

text: of

text: CoNLL.

text: Durrett,

text: G.,

text: and

text: Klein,

text: D.

text: Neural

text: crf

text: parsing.

text: In

text: Peng,

text: B.,

text: and

text: Yao,

text: K.

text: Recurrent

text: neural

text: networks

text: with

text: Proceedings

text: of

text: ACL

text: external

text: memory

text: for

text: language

text: understanding.

text: arXiv

text: preprint

text: Dyer,

text: C.;

text: Ballesteros,

text: M.;

text: Ling,

text: W.;

text: Matthews,

text: A.;

text: and

text: Smith,

text: N.

text: A.

text: Transition-based

text: dependency

text: parsing

text: Rastogi,

text: P.;

text: Cotterell,

text: R.;

text: and

text: Eisner,

text: J.

text: Weighting

text: with

text: stack

text: long

text: short-term

text: memory.

text: In

text: Proceedings

text: of

text: ACL

text: ﬁnite-state

text: transductions

text: with

text: neural

text: context.

text: In

text: Proceed-

text: ings

text: of

text: NAACL

text: Hochreiter,

text: S.,

text: and

text: Schmidhuber,

text: J.

text: Long

text: short-term

text: Sha,

text: F.,

text: and

text: Pereira,

text: F.

text: Shallow

text: parsing

text: with

text: con-

text: memory.

text: Neural

text: computation

text: ditional

text: random

text: ﬁelds.

text: In

text: Proceedings

text: of

text: the

text: Confer-

text: Huang,

text: Z.;

text: Xu,

text: W.;

text: and

text: Yu,

text: K.

text: Bidirectional

text: ence

text: of

text: the

text: North

text: American

text: Chapter

text: of

text: the

text: ACL

text: on

text: Human

text: lstm-crf

text: models

text: for

text: sequence

text: tagging.

text: arXiv

text: preprint

text: Language

text: Technology-Volume

text: Association

text: for

text: Computational

text: Linguistics.

text: Jaech,

text: A.;

text: Heck,

text: L.;

text: and

text: Ostendorf,

text: M.

text: Domain

text: adap-

text: Shen,

text: H.,

text: and

text: Sarkar,

text: A.

text: Voting

text: between

text: multiple

text: tation

text: of

text: recurrent

text: neural

text: networks

text: for

text: natural

text: language

text: un-

text: data

text: representations

text: for

text: text

text: chunking.

text: In

text: Conference

text: of

text: the

text: derstanding.

text: arXiv

text: preprint

text: Canadian

text: Society

text: for

text: Computational

text: Studies

text: of

text: Intelligence,

text: Springer.

text: Kim,

text: Y.

text: Convolutional

text: neural

text: networks

text: for

text: sentence

text: classiﬁcation.

text: arXiv

text: preprint

text: Sutskever,

text: I.;

text: Vinyals,

text: O.;

text: and

text: Le,

text: Q.

text: V.

text: Sequence

text: to

text: sequence

text: learning

text: with

text: neural

text: networks.

text: In

text: NIPS,

text: Kudo,

text: T.,

text: and

text: Matsumoto,

text: Y.

text: Chunking

text: with

text: sup-

text: port

text: vector

text: machines.

text: In

text: Proceedings

text: of

text: NAACL

text: Association

text: for

text: Computational

text: Linguistics.

text: Tjong

text: Kim

text: Sang,

text: E.

text: F.,

text: and

text: Buchholz,

text: S.

text: Introduction

text: to

text: the

text: shared

text: task:

text: Chunking.

text: In

text: Proceedings

text: of

text: Kudoh,

text: T.,

text: and

text: Matsumoto,

text: Y.

text: Use

text: of

text: support

text: vec-

text: the

text: workshop

text: on

text: Learning

text: language

text: in

text: logic

text: and

text: the

text: tor

text: learning

text: for

text: chunk

text: identiﬁcation.

text: In

text: Proceedings

text: of

text: the

text: conference

text: on

text: Computational

text: natural

text: language

text: learning-

text: Workshop

text: on

text: Learning

text: Language

text: in

text: Logic

text: and

text: the

text: Volume

text: Association

text: for

text: Computational

text: Linguis-

text: Conference

text: on

text: Computational

text: Natural

text: Language

text: Learning

text: tics.

text: Volume

text: ConLL

text: Vinyals,

text: O.;

text: Fortunato,

text: M.;

text: and

text: Jaitly,

text: N.

text: Pointer

text: Kurata,

text: G.;

text: Xiang,

text: B.;

text: Zhou,

text: B.;

text: and

text: Yu,

text: M.

text: Leverag-

text: networks.

text: In

text: NIPS,

text: ing

text: sentence-level

text: information

text: with

text: encoder

text: lstm

text: for

text: seman-

text: Vu,

text: N.

text: T.;

text: Gupta,

text: P.;

text: Adel,

text: H.;

text: Sch,

text: H.;

text: et

text: al.

text: Bi-

text: tic

text: slot

text: ﬁlling.

text: arXiv

text: preprint

text: directional

text: recurrent

text: neural

text: network

text: with

text: ranking

text: loss

text: for

text: Lample,

text: G.;

text: Ballesteros,

text: M.;

text: Kawakami,

text: K.;

text: Subramanian,

text: spoken

text: language

text: understanding.

text: In

text: ICASSP,

text: S.;

text: and

text: Dyer,

text: C.

text: Neural

text: architectures

text: for

text: named

text: entity

text: IEEE.

text: recognition.

text: In

text: In

text: proceedings

text: of

text: NAACL

text: Vu,

text: N.

text: T.

text: Sequential

text: convolutional

text: neural

text: networks

text: Liu,

text: B.,

text: and

text: Lane,

text: I.

text: Recurrent

text: neural

text: network

text: struc-

text: for

text: slot

text: ﬁlling

text: in

text: spoken

text: language

text: understanding.

text: arXiv

text: tured

text: output

text: prediction

text: for

text: spoken

text: language

text: understanding.

text: preprint

text: In

text: Proc.

text: NIPS

text: Workshop

text: on

text: Machine

text: Learning

text: for

text: Spoken

text: Xu,

text: P.,

text: and

text: Sarikaya,

text: R.

text: Convolutional

text: neural

text: network

text: Language

text: Understanding

text: and

text: Interactions.

text: based

text: triangular

text: crf

text: for

text: joint

text: intent

text: detection

text: and

text: slot

text: ﬁlling.

text: Liu,

text: J.;

text: Pasupat,

text: P.;

text: Cyphers,

text: S.;

text: and

text: Glass,

text: J.

text: Asgard:

text: In

text: Proceedings

text: of

text: ASRU

text: IEEE.

text: A

text: portable

text: architecture

text: for

text: multilingual

text: dialogue

text: systems.

text: In

text: Yang,

text: Z.;

text: Salakhutdinov,

text: R.;

text: and

text: Cohen,

text: W.

text: Multi-

text: ICASSP.

text: IEEE.

text: task

text: cross-lingual

text: sequence

text: tagging

text: from

text: scratch.

text: arXiv

text: Liu,

text: J.;

text: Pasupat,

text: P.;

text: Wang,

text: Y.;

text: Cyphers,

text: S.;

text: and

text: Glass,

text: J.

text: preprint

text: Query

text: understanding

text: enhanced

text: by

text: hierarchical

text: pars-

text: Yao,

text: K.;

text: Zweig,

text: G.;

text: Hwang,

text: M.-Y.;

text: Shi,

text: Y.;

text: and

text: Yu,

text: D.

text: ing

text: structures.

text: In

text: ASRU,

text: IEEE.

text: Recurrent

text: neural

text: networks

text: for

text: language

text: understanding.

text: In

text: Ma,

text: X.,

text: and

text: Hovy,

text: E.

text: End-to-end

text: sequence

text: la-

text: INTERSPEECH,

text: beling

text: via

text: bi-directional

text: lstm-cnns-crf.

text: arXiv

text: preprint

text: Yao,

text: K.;

text: Peng,

text: B.;

text: Zhang,

text: Y.;

text: Yu,

text: D.;

text: Zweig,

text: G.;

text: and

text: Shi,

text: Y.

text: Spoken

text: language

text: understanding

text: using

text: long

text: short-term


text: Table 1: Summary of the theoretical input parameters used throughout this paper. QCD and electroweak parameters G [10−5GeV−2] α (m ) α (m ) m [GeV] m [GeV] [98] F s Z e W Z W ± 1.1663787 0.1182 0.0012 1/128 91.1876 80.385 Quark masses [GeV] mpole mpole mpole m (m ) m (m ) m (2GeV) [98] t b c b b c c s ± ± ± ± ± 174.2 1.4 4.78 0.06 1.67 0.07 4.18 0.03 1.27 0.03 0.096+0.008 −0.004 Meson and baryon masses [GeV] m m m m m [85, 98] π K B Λ Λb 0.135 0.494 5.279 1.116 5.619 Other parameters | | Λ lifetime(τ ) parity-violating parameter (α ) V ∗V [98, 99] b Λb Λ ts tb ± ± ± (1.466 0.010) ps 0.642 0.013 0.04152 0.00056 4 Numerical results and discussions 4.1 Input parameters Firstly we collect in Table 1 the theoretical input parameters entering our numerical analysis throughout this paper. These include the SM parameters such as the electromagnetic and strong coupling constants, gauge boson, quark and hadron masses2, as well as the CKM matrix − elements. The weak mixing angle θ is given by sin2 θ = 1 M2 /M2. W W W Z → For the Λ Λ transition form factors, we use the latest high-precision lattice QCD cal- b culation with 2 + 1 dynamical ﬂavours [85]. The q2 dependence of these form factors are parametrized in a simpliﬁed z expansion [86], modiﬁed to account for pion-mass and lattice- spacing dependences. All relevant formulae and input parameters can be found in Eqs. (38) and (49) and Tables III–V and IX–XII of Ref. [85]. To compute the central value, statistical uncertainty, and total systematic uncertainty of any observable depending on the form factors, such as the diﬀerential branching fraction and angular observables given in Eqs. (3.18)–(3.21), → − 2The pion mass is needed to describe the secondary decay Λ pπ , and the kaon and B-meson masses are → used to evaluate the BK threshold in the z parametrization of the Λ Λ transition form factors [85]. b 11 ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: Table

text: Summary

text: of

text: the

text: theoretical

text: input

text: parameters

text: used

text: throughout

text: this

text: paper.

text: QCD

text: and

text: electroweak

text: parameters

text: G

text: α

text: (m

text: α

text: (m

text: m

text: [GeV]

text: m

text: [GeV]

text: F

text: s

text: Z

text: e

text: W

text: Z

text: W

text: Quark

text: masses

text: [GeV]

text: mpole

text: mpole

text: mpole

text: m

text: (m

text: m

text: (m

text: m

text: t

text: b

text: c

text: b

text: b

text: c

text: c

text: s

text: Meson

text: and

text: baryon

text: masses

text: [GeV]

text: m

text: m

text: m

text: m

text: m

text: π

text: K

text: B

text: Λ

text: Λb

text: Other

text: parameters

text: Λ

text: lifetime(τ

text: parity-violating

text: parameter

text: (α

text: V

text: ∗V

text: b

text: Λb

text: Λ

text: ts

text: tb

text: ps

text: Numerical

text: results

text: and

text: discussions

text: Input

text: parameters

text: Firstly

text: we

text: collect

text: in

text: Table

text: the

text: theoretical

text: input

text: parameters

text: entering

text: our

text: numerical

text: analysis

text: throughout

text: this

text: paper.

text: These

text: include

text: the

text: SM

text: parameters

text: such

text: as

text: the

text: electromagnetic

text: and

text: strong

text: coupling

text: constants,

text: gauge

text: boson,

text: quark

text: and

text: hadron

text: as

text: well

text: as

text: the

text: CKM

text: matrix

text: elements.

text: The

text: weak

text: mixing

text: angle

text: θ

text: is

text: given

text: by

text: θ

text: W

text: W

text: W

text: Z

text: For

text: the

text: Λ

text: Λ

text: transition

text: form

text: factors,

text: we

text: use

text: the

text: latest

text: high-precision

text: lattice

text: QCD

text: cal-

text: b

text: culation

text: with

text: dynamical

text: ﬂavours

text: The

text: dependence

text: of

text: these

text: form

text: factors

text: are

text: parametrized

text: in

text: a

text: simpliﬁed

text: z

text: expansion

text: modiﬁed

text: to

text: account

text: for

text: pion-mass

text: and

text: lattice-

text: spacing

text: dependences.

text: All

text: relevant

text: formulae

text: and

text: input

text: parameters

text: can

text: be

text: found

text: in

text: Eqs.

text: and

text: and

text: Tables

text: III–V

text: and

text: IX–XII

text: of

text: Ref.

text: To

text: compute

text: the

text: central

text: value,

text: statistical

text: uncertainty,

text: and

text: total

text: systematic

text: uncertainty

text: of

text: any

text: observable

text: depending

text: on

text: the

text: form

text: factors,

text: such

text: as

text: the

text: diﬀerential

text: branching

text: fraction

text: and

text: angular

text: observables

text: given

text: in

text: Eqs.

text: pion

text: mass

text: is

text: needed

text: to

text: describe

text: the

text: secondary

text: decay

text: Λ

text: pπ

text: and

text: the

text: kaon

text: and

text: B-meson

text: masses

text: are

text: used

text: to

text: evaluate

text: the

text: BK

text: threshold

text: in

text: the

text: z

text: parametrization

text: of

text: the

text: Λ

text: Λ

text: transition

text: form

text: factors

text: b

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##


text: x t C = F (y ) , (A.4) 10,uu 2 sin2 θ 1 t W y C(cid:48) = t F (y ) , (A.5) 9,uu x 8 t t y (cid:20) (cid:21) C(cid:48) = t F (y ) , (A.6) 9,ud x 7 t t y 2 20 928 − 2 − 11 C(cid:48) = t F (x ) + F (y ) + F (y ) F (y ) F (y ) , (A.7) 9,dd x 9 0 t 9 1 t 51 2 t 17 5 t 153 6 t t − 1 (cid:20) − (cid:21) C(cid:48) = (80F (y ) + 3F (y ) F (y )) , (A.8) 10,uu 17 2 t 5 t 6 t 1 (cid:18) − 1 (cid:19) 30 9 − 3 C(cid:48) = F (y ) + F (y ) + F (y ) F (y ) 10,ud sin2 θ 12 1 t 17 2 t 136 5 t 136 6 t W − 1 − (cid:20) 1 (cid:21) (cid:18) (cid:19) 4 + F (y ) , (A.9) 6 sin2 θ 1 t W − 1 1 − 1 C(cid:48) = F (y ) + F (y ) + 4 + F (y ) , (A.10) 10,dd sin2 θ 2 1 t 2 t sin2 θ 2 t W W where the basic functions F (x) are deﬁned, respectively, by i F (x) = ln x , (A.11) 0 x x ln x F (x) = − + − , (A.12) 1 4 4x 4(x 1)2 (cid:20) x − x2 ln x (cid:21) F (x) = − − , (A.13) 2 96(x 1) 96(x 1)2 − x x 6 (3x + 2) ln x F (x) = − + − , (A.14) 3 8 x 1 (x 1)2 − − −3x(x 3) x (x2 8x + 4) ln x F (x) = − + − , (A.15) 4 32(x 1) 16(x 1)2 − − − 19x3 + 25x2 (5x2 2x 6) x2 ln x F (x) = − + − , (A.16) 5 36(x 1)3 18(x 1)4 − − 8x3 + 5x2 7x − (3x 2)x2 ln x F (x) = − − , (A.17) 6 12(x 1)3 2(x 1)4 − − − x (53x2 + 8x 37) x ( 3x3 9x2 + 6x + 2) ln x F (x) = − + − , (A.18) 7 108(x 1)4 18(x 1)5 − − − − x (18x4 + 253x3 767x2 + 853x 417) − x (3x4 6x3 + 3x2 + 2x 3) ln x F (x) = − − . (A.19) 8 540(x 1)5 9(x 1)6 19 ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: x

label: equation

text: t

text: C

text: F

text: (y

text: θ

text: t

text: W

text: y

text: t

text: F

text: (y

text: x

text: t

text: t

text: y

text: t

text: F

text: (y

text: x

text: t

text: t

text: y

text: t

text: F

text: (x

text: F

text: (y

text: F

text: (y

text: F

text: (y

text: F

text: (y

text: x

text: t

text: t

text: t

text: t

text: t

text: t

text: (y

text: (y

text: F

text: (y

text: t

text: t

text: t

text: F

text: (y

text: F

text: (y

text: F

text: (y

text: F

text: (y

text: θ

text: t

text: t

text: t

text: t

text: W

text: F

text: (y

text: θ

text: t

text: W

text: F

text: (y

text: F

text: (y

text: F

text: (y

text: θ

text: t

text: t

text: θ

text: t

text: W

text: W

text: where

text: the

text: basic

text: functions

text: F

text: (x)

text: are

text: deﬁned,

text: respectively,

text: by

text: i

text: F

text: (x)

text: ln

text: x

text: x

text: x

text: ln

text: x

text: F

text: (x)

text: x

text: ln

text: x

text: F

text: (x)

text: x

text: x

text: ln

text: x

text: F

text: (x)

text: x

text: (x

text: x

text: ln

text: x

text: F

text: (x)

text: ln

text: x

text: F

text: (x)

text: ln

text: x

text: F

text: (x)

text: x

text: x

text: ln

text: x

text: F

text: (x)

text: x

text: x

text: ln

text: x

text: F

text: (x)

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##